Metrics for 2sin (example 3.3)

analyze103.0ms (0.7%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	50.6%	49.4%	0%	0%	0%	0
0%	0%	50.6%	49.4%	0%	0%	0%	1
0%	0%	50.6%	49.4%	0%	0%	0%	2
0%	0%	25.3%	74.7%	0%	0%	0%	3
0%	0%	25.3%	74.7%	0%	0%	0%	4
0%	0%	19%	81%	0%	0%	0%	5
0%	0%	15.8%	84.2%	0%	0%	0%	6
0%	0%	11.1%	88.9%	0%	0%	0%	7
0%	0%	8.7%	91.3%	0%	0%	0%	8
0%	0%	5.9%	94.1%	0%	0%	0%	9
0%	0%	4.5%	95.5%	0%	0%	0%	10
0%	0%	3.1%	96.9%	0%	0%	0%	11
0%	0%	2.7%	97.3%	0%	0%	0%	12

Compiler

Compiled 28 to 18 computations (35.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 40.0ms

ival-sin: 12.0ms (29.6% of total)

ival-<: 7.0ms (17.3% of total)

...c/correct-round.rkt:119:19: 6.0ms (14.8% of total)

ival-mult: 3.0ms (7.4% of total)

ival-fabs: 3.0ms (7.4% of total)

ival-<=: 3.0ms (7.4% of total)

ival-add: 2.0ms (4.9% of total)

ival-sub: 2.0ms (4.9% of total)

ival-and: 1.0ms (2.5% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample6.8s (48.1%)

Results

3.7s	26201×	0	precondition
1.2s	4436×	1	valid
458.0ms	3820×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 4.0s

ival-sin: 870.0ms (21.6% of total)

...c/correct-round.rkt:119:19: 804.0ms (19.9% of total)

ival-<: 433.0ms (10.7% of total)

ival-<=: 423.0ms (10.5% of total)

ival-mult: 409.0ms (10.1% of total)

ival-add: 296.0ms (7.3% of total)

ival-fabs: 282.0ms (7% of total)

ival-sub: 227.0ms (5.6% of total)

ival-and: 138.0ms (3.4% of total)

backward-pass: 105.0ms (2.6% of total)

const: 47.0ms (1.2% of total)

Bogosity

preprocess46.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

376×	`fnmadd-define`
344×	`fnmsub-define`
344×	`fmsub-define`
320×	`sum3-define`
308×	`fmm-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	46
1	43	42
2	94	42
3	198	42
4	507	42
5	917	42
6	1285	42
7	1548	42
8	1684	42
9	1711	42
0	6	7
1	9	7
2	14	7
3	21	7
4	31	7
5	63	7
6	122	7
7	210	7
8	295	7
9	401	7
10	479	7
11	485	7
0	485	7

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(- (sin (+ x eps)) (sin x))

Outputs
(- (sin (+ x eps)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Call 2

Inputs
(- (sin (+ x eps)) (sin x))
(- (sin (+ (neg x) eps)) (sin (neg x)))
(- (sin (+ x (neg eps))) (sin x))
(neg (- (sin (+ (neg x) eps)) (sin (neg x))))
(neg (- (sin (+ x (neg eps))) (sin x)))
(- (sin (+ eps x)) (sin eps))

Outputs
(- (sin (+ x eps)) (sin x))
(- (sin (+ (neg x) eps)) (sin (neg x)))
(+ (sin x) (sin (- eps x)))
(- (sin (+ x (neg eps))) (sin x))
(- (sin (- x eps)) (sin x))
(neg (- (sin (+ (neg x) eps)) (sin (neg x))))
(- (sin (- x eps)) (sin x))
(neg (- (sin (+ x (neg eps))) (sin x)))
(+ (sin x) (sin (- eps x)))
(- (sin (+ eps x)) (sin eps))
(- (sin (+ x eps)) (sin eps))

explain93.0ms (0.7%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
220	2	(-1.9527437492280147e-131 1.107869717900018e-133)	5	(7.906697221524028e-285 2.0647855124499167e-286)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
6	1	(-187.4627652821368 1.7615816217441026e-10)	2	(68.43922430872213 4.970146358281208e-7)	`(sin.f64 (+.f64 x eps))`
0	0	-	0	-	`x`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`eps`

Results

40.0ms	270×	1	valid
15.0ms	234×	0	valid
4.0ms	4×	3	valid
1.0ms	4×	2	valid

Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-sin: 16.0ms (51.1% of total)

ival-add: 7.0ms (22.4% of total)

backward-pass: 5.0ms (16% of total)

ival-sub: 4.0ms (12.8% of total)

const: 1.0ms (3.2% of total)

eval0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	64.4%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(sin.f64 x)
✓	cost-diff	(+.f64 x eps)
✓	cost-diff	(sin.f64 (+.f64 x eps))
✓	cost-diff	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Rules

124×	`fnmadd-define`
122×	`sum3-define`
80×	`fma-lowering-fma.f32`
80×	`fnmsub-define`
80×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	9	18
2	14	18
3	21	18
4	31	18
5	63	18
6	122	18
7	210	18
8	295	18
9	401	18
10	479	18
11	485	18
0	485	18

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(- (sin (+ x eps)) (sin x))
(sin (+ x eps))
(+ x eps)
x
eps
(sin x)

Outputs
(- (sin (+ x eps)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin (+ x eps))
(sin.f64 (+.f64 x eps))
(+ x eps)
(+.f64 x eps)
x
eps
(sin x)
(sin.f64 x)

localize39.0ms (0.3%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	99.7%	(sin.f64 (+.f64 x eps))
✓	accuracy	64.7%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Results

20.0ms	135×	1	valid
8.0ms	117×	0	valid
2.0ms	2×	3	valid
0.0ms	2×	2	valid

Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-sin: 9.0ms (52.3% of total)

ival-add: 4.0ms (23.2% of total)

ival-sub: 3.0ms (17.4% of total)

backward-pass: 2.0ms (11.6% of total)

const: 0.0ms (0% of total)

series4.0ms (0%)

Counts

4 → 84

Calls

Call 1

Inputs
#<alt (- (sin (+ x eps)) (sin x))>
#<alt (sin (+ x eps))>
#<alt (+ x eps)>
#<alt (sin x)>

Outputs
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (cos eps)))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin x)>
#<alt (+ (sin x) (* eps (cos x)))>
#<alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))>
#<alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>

Calls

21 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	inf	(- (sin (+ x eps)) (sin x))
0.0ms	eps	@	0	(- (sin (+ x eps)) (sin x))
0.0ms	x	@	0	(- (sin (+ x eps)) (sin x))
0.0ms	x	@	-inf	(- (sin (+ x eps)) (sin x))
0.0ms	x	@	inf	(+ x eps)

rewrite284.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

2788×	`-lowering-.f32`
2788×	`-lowering-.f64`
2132×	`/-lowering-/.f32`
2132×	`/-lowering-/.f64`
2068×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	49	16
2	402	16
3	5232	16
0	8309	16

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 177

Calls

Call 1

Inputs
(- (sin (+ x eps)) (sin x))
(sin (+ x eps))
(+ x eps)
(sin x)

Outputs
(+.f64 (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 #s(literal 0 binary64) (sin.f64 x))))
(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
(+.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 (+.f64 x eps)))
(+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (-.f64 (+.f64 (.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (+.f64 (.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))))))
(+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))
(+.f64 (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) (.f64 (sin.f64 x) (cos.f64 eps)))
(+.f64 (+.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (.f64 (sin.f64 x) (cos.f64 eps))) (.f64 (cos.f64 x) (sin.f64 eps)))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (-.f64 (+.f64 (.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (+.f64 (.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64)))))))
(-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
(-.f64 #s(literal 0 binary64) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))))
(-.f64 (+.f64 (sin.f64 (+.f64 x eps)) #s(literal 0 binary64)) (sin.f64 x))
(fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 (sin.f64 (+.f64 x eps)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))
(fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))) (-.f64 (+.f64 (.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (+.f64 (.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))))))
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (+.f64 (.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))))))
(fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))
(fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))) (/.f64 (sin.f64 (+.f64 x eps)) (-.f64 (+.f64 (.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (+.f64 (.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))))))
(fma.f64 (+.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps)))))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 #s(literal -1 binary64) (sin.f64 x) (sin.f64 (+.f64 x eps)))
(fma.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3/2 binary64)) (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3/2 binary64)) (-.f64 (+.f64 (.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (+.f64 (.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))))))
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(.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 4 binary64)) (pow.f64 (.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 2 binary64)))) (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))) (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))
(.f64 (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))) (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))) (.f64 (sin.f64 x) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))))))
(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))
(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (cos.f64 eps)))
(-.f64 (.f64 (sin.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))) (.f64 (cos.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))))
(-.f64 (/.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (sin.f64 (-.f64 x eps))) (/.f64 (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (sin.f64 (-.f64 x eps))))
(sin.f64 (+.f64 x eps))
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (cos.f64 eps)))
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps)))
(fma.f64 (sin.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps))) (neg.f64 (.f64 (cos.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))))
(/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps))))))
(/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (.f64 (sin.f64 x) (.f64 (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (cos.f64 eps))))) (+.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps)))))
(/.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (sin.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps)))))))
(/.f64 (neg.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps)))) (neg.f64 (sin.f64 (-.f64 x eps))))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (pow.f64 (.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64))) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (cos.f64 eps))))
(.f64 (+.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (cos.f64 eps)))))))
(.f64 (.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps))))
(+.f64 x eps)
(+.f64 eps x)
(+.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (neg.f64 (/.f64 (.f64 eps eps) (-.f64 x eps))))
(-.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x eps)))
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))
(fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))
(fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 (/.f64 (.f64 eps eps) (-.f64 x eps))))
(fma.f64 (/.f64 (.f64 x x) (-.f64 (.f64 x x) (.f64 eps eps))) (+.f64 x eps) (neg.f64 (/.f64 (.f64 eps eps) (-.f64 x eps))))
(fma.f64 (/.f64 (.f64 x x) (-.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps)))) (+.f64 (.f64 x x) (.f64 eps (+.f64 x eps))) (neg.f64 (/.f64 (.f64 eps eps) (-.f64 x eps))))
(neg.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))))
(neg.f64 (/.f64 (-.f64 (.f64 x x) (.f64 eps eps)) (-.f64 #s(literal 0 binary64) (-.f64 x eps))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps)))) (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x)))))
(neg.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 #s(literal 0 binary64) (-.f64 x eps))) (-.f64 x eps)))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))
(/.f64 (-.f64 (.f64 x x) (.f64 eps eps)) (-.f64 x eps))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps)))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x)))))
(/.f64 (*.f64 (+.f64 x eps) (-.f64 #s(literal 0 binary64) (-.f64 x eps))) (-.f64 #s(literal 0 binary64) (-.f64 x eps)))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))))) (.f64 (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 eps (.f64 eps eps)) (.f64 x (*.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (-.f64 (.f64 eps eps) (.f64 x x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)))) (.f64 (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x))) (-.f64 (.f64 x (.f64 x x)) (.f64 eps (*.f64 eps eps)))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)))) (.f64 (-.f64 x eps) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 eps eps) (+.f64 (.f64 x x) (.f64 eps eps))))))
(/.f64 (-.f64 (.f64 eps eps) (.f64 x x)) (-.f64 eps x))
(/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 eps eps) (.f64 eps eps))) (.f64 (-.f64 x eps) (+.f64 (.f64 x x) (*.f64 eps eps))))
(/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x eps)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps)))
(/.f64 (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x x))))) (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x)))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)))) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x)))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 eps eps) (+.f64 (.f64 x x) (*.f64 eps eps)))) (-.f64 x eps)))
(/.f64 (.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 eps eps) (.f64 eps eps))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x x) (.f64 eps eps)) (-.f64 x eps)))
(/.f64 (.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) #s(literal 1 binary64)) (+.f64 (.f64 x x) (*.f64 eps (-.f64 eps x))))
(/.f64 (.f64 (-.f64 (.f64 x x) (*.f64 eps eps)) #s(literal 1 binary64)) (-.f64 x eps))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))))
(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 #s(literal 0 binary64) (-.f64 x eps)))) (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 x eps))))
(/.f64 (neg.f64 (-.f64 (.f64 eps eps) (.f64 x x))) (neg.f64 (-.f64 eps x)))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x x) (-.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 x x) (-.f64 x eps))) (+.f64 (.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x eps))) (.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 x x) (-.f64 x eps))) (.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x eps)))) (+.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x eps))))
(/.f64 (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 eps (.f64 eps eps)) (.f64 x (*.f64 x x))))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))) (-.f64 (.f64 x (.f64 x x)) (.f64 eps (*.f64 eps eps))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 eps eps) (+.f64 (.f64 x x) (.f64 eps eps)))))
(/.f64 (.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 eps eps) (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (+.f64 (.f64 x x) (*.f64 eps eps)))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal -1 binary64))
(.f64 (+.f64 x eps) (.f64 (-.f64 x eps) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))
(*.f64 (+.f64 x eps) (/.f64 (-.f64 x eps) (-.f64 x eps)))
(.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (*.f64 eps (-.f64 eps x)))))
(.f64 (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x))) (.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))))
(.f64 (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x))) (/.f64 (+.f64 x eps) (+.f64 (.f64 x x) (*.f64 eps (-.f64 eps x)))))
(.f64 (-.f64 (.f64 x x) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (*.f64 eps (-.f64 eps x))))))
(.f64 (.f64 (+.f64 x eps) (-.f64 #s(literal 0 binary64) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 x eps))))
(*.f64 #s(literal 1 binary64) (+.f64 x eps))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x)))) (+.f64 (.f64 x (.f64 x x)) (.f64 eps (*.f64 eps eps))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (-.f64 (.f64 x x) (*.f64 eps eps)))
(.f64 (-.f64 (.f64 eps eps) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x)))
(.f64 (/.f64 (-.f64 (.f64 x x) (.f64 eps eps)) (-.f64 (.f64 x x) (*.f64 eps eps))) (+.f64 x eps))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 eps (-.f64 eps x)) (.f64 (.f64 eps (-.f64 eps x)) (.f64 eps (-.f64 eps x)))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 eps (-.f64 eps x)) (-.f64 (.f64 eps (-.f64 eps x)) (.f64 x x)))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 eps (-.f64 eps x)) (.f64 eps (-.f64 eps x))))) (-.f64 (.f64 x x) (*.f64 eps (-.f64 eps x))))
(.f64 (/.f64 (-.f64 (.f64 x x) (.f64 eps eps)) (-.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps)))) (+.f64 (.f64 x x) (*.f64 eps (+.f64 x eps))))
(sin.f64 x)

simplify239.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

3796×	`-lowering-.f32`
3796×	`-lowering-.f64`
2064×	`+-lowering-+.f64`
2064×	`+-lowering-+.f32`
1456×	`fnmadd-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	107	488
1	327	465
2	963	459
3	3572	459
0	8267	459

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

Inputs
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)

Outputs
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) #s(literal -1 binary64))))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)) (.f64 x (+.f64 (cos.f64 eps) #s(literal -1 binary64))))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(-.f64 (+.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)) (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))) (cos.f64 eps))))) x)
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))) (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 eps (+.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (cos eps)))
(+.f64 (sin.f64 eps) (*.f64 x (cos.f64 eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+.f64 (.f64 x (cos.f64 eps)) (.f64 (+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(+.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))) (cos.f64 eps)) x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin x)
(sin.f64 x)
(+ (sin x) (* eps (cos x)))
(+.f64 (sin.f64 x) (*.f64 eps (cos.f64 x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+.f64 (.f64 eps (cos.f64 x)) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 x)))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(+.f64 (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 x)) (.f64 (.f64 eps (cos.f64 x)) (+.f64 (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
eps
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
x
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
x
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
eps
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/120 binary64)))))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)

eval30.0ms (0.2%)

Compiler: Compiled 7060 to 730 computations (89.7% saved)

prune34.0ms (0.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	252	9	261
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	252	10	262

Accuracy

100.0%

Counts

262 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.8%	(-.f64 (sin.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 x (*.f64 x #s(literal -1/5040 binary64))))))))))
▶	62.7%	(-.f64 (sin.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/120 binary64))))))))
✓	64.4%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	99.5%	(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
▶	99.8%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
▶	99.5%	(.f64 eps (+.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
	99.4%	(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))) (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
▶	99.1%	(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
	98.5%	(*.f64 eps (cos.f64 x))
▶	96.9%	(sin.f64 eps)

Compiler

Compiled 321 to 216 computations (32.7% saved)

simplify144.0ms (1%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64))
✓	cost-diff	0	(.f64 (+.f64 (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))
✓	cost-diff	0	(+.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))
✓	cost-diff	0	(.f64 eps (+.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
✓	cost-diff	0	(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
✓	cost-diff	0	(cos.f64 x)
✓	cost-diff	0	(+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))))
✓	cost-diff	0	(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/120 binary64)))))))
✓	cost-diff	0	(+.f64 x eps)
✓	cost-diff	0	(sin.f64 (+.f64 x eps))
✓	cost-diff	0	(-.f64 (sin.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/120 binary64))))))))
✓	cost-diff	0	(sin.f64 eps)
✓	cost-diff	128	(/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))
✓	cost-diff	128	(sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)))
✓	cost-diff	128	(.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
✓	cost-diff	128	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))

Rules

2036×	`fnmadd-define`
1772×	`fma-define`
1730×	`fma-lowering-fma.f32`
1730×	`fma-lowering-fma.f64`
1412×	`-lowering-.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	44	293
1	120	278
2	433	274
3	1972	274
4	5557	274
5	7429	274
0	8595	274

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2)))
(sin (/ (+ eps 0) 2))
(/ (+ eps 0) 2)
(+ eps 0)
eps
0
2
(cos (/ (+ eps (* x 2)) 2))
(/ (+ eps (* x 2)) 2)
(+ eps (* x 2))
(* x 2)
x
(sin eps)
eps
(- (sin (+ x eps)) (* x (+ 1 (* (* x x) (+ -1/6 (* x (* x 1/120)))))))
(sin (+ x eps))
(+ x eps)
x
eps
(* x (+ 1 (* (* x x) (+ -1/6 (* x (* x 1/120))))))
(+ 1 (* (* x x) (+ -1/6 (* x (* x 1/120)))))
1
(* (* x x) (+ -1/6 (* x (* x 1/120))))
(* x x)
(+ -1/6 (* x (* x 1/120)))
-1/6
(* x (* x 1/120))
(* x 1/120)
1/120
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
eps
(+ (cos x) (* -1/2 (* eps (sin x))))
(cos x)
x
(* -1/2 (* eps (sin x)))
-1/2
(* eps (sin x))
(sin x)
(* eps (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* (* eps eps) 1/24) -1/2))))
eps
(+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* (* eps eps) 1/24) -1/2)))
(* (+ (* (* eps eps) -1/6) 1) (cos x))
(+ (* (* eps eps) -1/6) 1)
(* (* eps eps) -1/6)
(* eps eps)
-1/6
1
(cos x)
x
(* (* eps (sin x)) (+ (* (* eps eps) 1/24) -1/2))
(* eps (sin x))
(sin x)
(+ (* (* eps eps) 1/24) -1/2)
(* (* eps eps) 1/24)
1/24
-1/2

Outputs
(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
(.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))))
(* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2)))
(.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))))
(sin (/ (+ eps 0) 2))
(sin.f64 (/.f64 eps #s(literal 2 binary64)))
(/ (+ eps 0) 2)
(/.f64 eps #s(literal 2 binary64))
(+ eps 0)
eps
eps
0
#s(literal 0 binary64)
2
#s(literal 2 binary64)
(cos (/ (+ eps (* x 2)) 2))
(cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))
(/ (+ eps (* x 2)) 2)
(/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))
(+ eps (* x 2))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(* x 2)
(*.f64 #s(literal 2 binary64) x)
x
(sin eps)
(sin.f64 eps)
eps
(- (sin (+ x eps)) (* x (+ 1 (* (* x x) (+ -1/6 (* x (* x 1/120)))))))
(+.f64 (sin.f64 (+.f64 eps x)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (+.f64 (.f64 x (*.f64 x #s(literal -1/120 binary64))) #s(literal 1/6 binary64)))))))
(sin (+ x eps))
(sin.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(* x (+ 1 (* (* x x) (+ -1/6 (* x (* x 1/120))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))
(+ 1 (* (* x x) (+ -1/6 (* x (* x 1/120)))))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64))))))
1
#s(literal 1 binary64)
(* (* x x) (+ -1/6 (* x (* x 1/120))))
(.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64)))))
(* x x)
(*.f64 x x)
(+ -1/6 (* x (* x 1/120)))
(+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64)))
-1/6
#s(literal -1/6 binary64)
(* x (* x 1/120))
(.f64 (.f64 x x) #s(literal 1/120 binary64))
(* x 1/120)
(*.f64 x #s(literal 1/120 binary64))
1/120
#s(literal 1/120 binary64)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64)))))
eps
(+ (cos x) (* -1/2 (* eps (sin x))))
(+.f64 (cos.f64 x) (.f64 (sin.f64 x) (.f64 eps #s(literal -1/2 binary64))))
(cos x)
(cos.f64 x)
x
(* -1/2 (* eps (sin x)))
(.f64 (sin.f64 x) (.f64 eps #s(literal -1/2 binary64)))
-1/2
#s(literal -1/2 binary64)
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(sin x)
(sin.f64 x)
(* eps (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* (* eps eps) 1/24) -1/2))))
(.f64 eps (+.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64))))) (.f64 (.f64 eps (sin.f64 x)) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))))))
eps
(+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* (* eps eps) 1/24) -1/2)))
(+.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64))))) (.f64 (.f64 eps (sin.f64 x)) (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)))))
(* (+ (* (* eps eps) -1/6) 1) (cos x))
(.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(+ (* (* eps eps) -1/6) 1)
(+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64))))
(* (* eps eps) -1/6)
(.f64 eps (.f64 eps #s(literal -1/6 binary64)))
(* eps eps)
(*.f64 eps eps)
-1/6
#s(literal -1/6 binary64)
1
#s(literal 1 binary64)
(cos x)
(cos.f64 x)
x
(* (* eps (sin x)) (+ (* (* eps eps) 1/24) -1/2))
(.f64 (.f64 eps (sin.f64 x)) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(sin x)
(sin.f64 x)
(+ (* (* eps eps) 1/24) -1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)))
(* (* eps eps) 1/24)
(.f64 (.f64 eps eps) #s(literal 1/24 binary64))
1/24
#s(literal 1/24 binary64)
-1/2
#s(literal -1/2 binary64)

localize299.0ms (2.1%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 eps (+.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
✓	accuracy	100.0%	(*.f64 eps (sin.f64 x))
✓	accuracy	99.7%	(.f64 (.f64 eps eps) #s(literal 1/24 binary64))
✓	accuracy	99.7%	(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
✓	accuracy	100.0%	(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
✓	accuracy	100.0%	(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
✓	accuracy	100.0%	(+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))))
✓	accuracy	100.0%	(*.f64 eps (sin.f64 x))
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal 1/120 binary64)))
✓	accuracy	99.7%	(sin.f64 (+.f64 x eps))
✓	accuracy	99.6%	(.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64)))))
✓	accuracy	65.5%	(-.f64 (sin.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/120 binary64))))))))
✓	accuracy	100.0%	(sin.f64 eps)
✓	accuracy	100.0%	(*.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)))
✓	accuracy	100.0%	(.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
✓	accuracy	99.8%	(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))

Results

138.0ms	132×	1	valid
87.0ms	120×	0	valid
4.0ms	2×	3	valid
3.0ms	2×	2	valid

Compiler

Compiled 316 to 45 computations (85.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 125.0ms

ival-mult: 45.0ms (36.1% of total)

ival-add: 22.0ms (17.6% of total)

...c/correct-round.rkt:119:19: 16.0ms (12.8% of total)

backward-pass: 14.0ms (11.2% of total)

ival-sin: 12.0ms (9.6% of total)

ival-cos: 7.0ms (5.6% of total)

ival-div: 5.0ms (4% of total)

ival-sub: 2.0ms (1.6% of total)

const: 1.0ms (0.8% of total)

series37.0ms (0.3%)

Counts

24 → 444

Calls

Call 1

Inputs
#<alt (* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)>
#<alt (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2)))>
#<alt (sin (/ (+ eps 0) 2))>
#<alt (/ (+ eps 0) 2)>
#<alt (sin eps)>
#<alt (- (sin (+ x eps)) (* x (+ 1 (* (* x x) (+ -1/6 (* x (* x 1/120)))))))>
#<alt (sin (+ x eps))>
#<alt (+ x eps)>
#<alt (* x (+ 1 (* (* x x) (+ -1/6 (* x (* x 1/120))))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (cos x)>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* eps (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* (* eps eps) 1/24) -1/2))))>
#<alt (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* (* eps eps) 1/24) -1/2)))>
#<alt (* (+ (* (* eps eps) -1/6) 1) (cos x))>
#<alt (+ (* (* eps eps) -1/6) 1)>
#<alt (cos (/ (+ eps (* x 2)) 2))>
#<alt (* x 2)>
#<alt (* (* x x) (+ -1/6 (* x (* x 1/120))))>
#<alt (* x (* x 1/120))>
#<alt (* eps (sin x))>
#<alt (* (* eps eps) -1/6)>
#<alt (* (* eps eps) 1/24)>

Outputs
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))>
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (* -1/120 (pow x 5))>
#<alt (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120))>
#<alt (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4)))))>
#<alt (* (pow x 5) (- (+ (* 1/6 (/ 1 (pow x 2))) (/ (sin (+ eps x)) (pow x 5))) (+ 1/120 (/ 1 (pow x 4)))))>
#<alt (* -1/120 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 5) (- (+ 1/120 (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 5))) (/ 1 (pow x 4)))) (* 1/6 (/ 1 (pow x 2))))))>
#<alt (- (sin x) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (cos eps)))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin x)>
#<alt (+ (sin x) (* eps (cos x)))>
#<alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))>
#<alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* 1/120 (pow x 5))>
#<alt (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* 1/120 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))>
#<alt (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))>
#<alt (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt eps>
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))>
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (* eps x)))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps x))>
#<alt (* x (+ (* -1/2 eps) (* 1/12 (* eps (pow x 2)))))>
#<alt (* x (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/240 (* eps (pow x 2))) (* 1/12 eps)))))>
#<alt (* x (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/240 eps) (* 1/10080 (* eps (pow x 2)))))))))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (* 1/24 (* (pow eps 4) (sin x)))>
#<alt (* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))>
#<alt (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))>
#<alt (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))>
#<alt (* 1/24 (* (pow eps 4) (sin x)))>
#<alt (* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))>
#<alt (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))>
#<alt (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))>
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))>
#<alt (* 1/24 (* (pow eps 3) (sin x)))>
#<alt (* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))>
#<alt (* 1/24 (* (pow eps 3) (sin x)))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2))))) (* eps (- (* 1/24 (pow eps 2)) 1/2))))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* -1/6 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2))))))))))>
#<alt (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))>
#<alt (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))>
#<alt (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))>
#<alt (* -1/6 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* -1/6 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (+ (* -1/2 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (pow eps 2))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/24 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* 1/24 (+ 1 (* -1/6 (pow eps 2))))))))))>
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))>
#<alt 1>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* -1/6 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))>
#<alt (* 1/120 (pow x 4))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* 1/120 (pow x 4))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps x)>
#<alt (* x (+ eps (* -1/6 (* eps (pow x 2)))))>
#<alt (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))>
#<alt (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>

Calls

111 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
3.0ms	x	@	inf	(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
2.0ms	x	@	inf	(* eps (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* (* eps eps) 1/24) -1/2))))
2.0ms	x	@	-inf	(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
1.0ms	x	@	inf	(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)

rewrite385.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

5584×	`-lowering-.f32`
5584×	`-lowering-.f64`
2632×	`/-lowering-/.f32`
2632×	`/-lowering-/.f64`
2360×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	44	205
1	266	193
2	2819	191
0	10169	191

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 525

Calls

Call 1

Inputs
(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2)))
(sin (/ (+ eps 0) 2))
(/ (+ eps 0) 2)
(sin eps)
(- (sin (+ x eps)) (* x (+ 1 (* (* x x) (+ -1/6 (* x (* x 1/120)))))))
(sin (+ x eps))
(+ x eps)
(* x (+ 1 (* (* x x) (+ -1/6 (* x (* x 1/120))))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(cos x)
(* -1/2 (* eps (sin x)))
(* eps (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* (* eps eps) 1/24) -1/2))))
(+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* (* eps eps) 1/24) -1/2)))
(* (+ (* (* eps eps) -1/6) 1) (cos x))
(+ (* (* eps eps) -1/6) 1)
(cos (/ (+ eps (* x 2)) 2))
(* x 2)
(* (* x x) (+ -1/6 (* x (* x 1/120))))
(* x (* x 1/120))
(* eps (sin x))
(* (* eps eps) -1/6)
(* (* eps eps) 1/24)

Outputs
(/.f64 (.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))))))) #s(literal 2 binary64))
(/.f64 (.f64 (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))))) #s(literal 2 binary64)) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))))
(.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))))
(.f64 (cos.f64 (/.f64 (+.f64 eps (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)))
(.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) (sin.f64 (/.f64 eps #s(literal 2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (/.f64 eps #s(literal 2 binary64)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))))))))
(/.f64 (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))))) #s(literal 2 binary64))
(/.f64 (neg.f64 (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))))))) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))))))) #s(literal -1 binary64))
(.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))))
(.f64 (cos.f64 (/.f64 (+.f64 eps (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (sin.f64 (/.f64 eps #s(literal 2 binary64))))
(.f64 (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))))) #s(literal 1/2 binary64))
(sin.f64 (/.f64 eps #s(literal 2 binary64)))
(neg.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) eps)) #s(literal -1 binary64)))
(neg.f64 (/.f64 eps #s(literal -2 binary64)))
(/.f64 eps #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) eps))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) eps) #s(literal 1 binary64)))
(/.f64 (.f64 eps eps) (.f64 #s(literal 2 binary64) eps))
(/.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal -2 binary64))
(/.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 2 binary64) (.f64 eps eps)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) eps)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) eps)) #s(literal 2 binary64))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 eps eps))
(/.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(pow.f64 (/.f64 #s(literal 2 binary64) eps) #s(literal -1 binary64))
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(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/216 binary64))))) (neg.f64 (+.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 eps (.f64 eps eps)) eps)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps))))))
(/.f64 (neg.f64 (+.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 eps (.f64 eps eps)) eps)) #s(literal -1 binary64))) (neg.f64 (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) #s(literal -1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/36 binary64) (.f64 (.f64 eps (.f64 eps eps)) eps))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps))))
(pow.f64 (/.f64 (+.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 eps (.f64 eps eps)) eps)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/216 binary64))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) #s(literal -1 binary64)) (+.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 eps (.f64 eps eps)) eps)) #s(literal -1 binary64))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/216 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 eps (.f64 eps eps)) eps)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))
(.f64 (+.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 eps (.f64 eps eps)) eps)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) #s(literal -1 binary64))))
(cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))
(cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal -2 binary64)))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(+.f64 (.f64 x (.f64 x #s(literal -1/6 binary64))) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/120 binary64)))))
(+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/120 binary64)))) (.f64 x (.f64 x #s(literal -1/6 binary64))))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64)))) (.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/120 binary64))))))
(+.f64 (.f64 (.f64 x (.f64 x #s(literal -1/6 binary64))) #s(literal 1 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/120 binary64)))) #s(literal 1 binary64)))
(fma.f64 x (.f64 x #s(literal -1/6 binary64)) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 1/120 binary64)))))
(fma.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/120 binary64)))) (.f64 x (*.f64 x #s(literal -1/6 binary64))))
(fma.f64 x (.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x x)) (.f64 x (*.f64 x #s(literal -1/6 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))) (.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 1/120 binary64))))))
(fma.f64 (.f64 x x) #s(literal -1/6 binary64) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 1/120 binary64)))))
(fma.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/120 binary64))) (.f64 x (*.f64 x #s(literal -1/6 binary64))))
(fma.f64 #s(literal -1/6 binary64) (.f64 x x) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 1/120 binary64)))))
(fma.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x (.f64 x x)) (.f64 x (*.f64 x #s(literal -1/6 binary64))))
(fma.f64 (.f64 x (.f64 x #s(literal 1/120 binary64))) (.f64 x x) (.f64 x (*.f64 x #s(literal -1/6 binary64))))
(fma.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal 1/120 binary64)) (.f64 x (*.f64 x #s(literal -1/6 binary64))))
(fma.f64 (.f64 x (.f64 x #s(literal -1/6 binary64))) #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 1/120 binary64)))) #s(literal 1 binary64)))
(fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/120 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64))))
(fma.f64 (.f64 #s(literal -1/6 binary64) x) x (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 1/120 binary64)))))
(fma.f64 (.f64 (.f64 x (.f64 x #s(literal 1/120 binary64))) x) x (.f64 x (*.f64 x #s(literal -1/6 binary64))))
(fma.f64 (.f64 (.f64 x x) (.f64 x #s(literal 1/120 binary64))) x (.f64 x (*.f64 x #s(literal -1/6 binary64))))
(/.f64 (+.f64 (.f64 #s(literal -1/216 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (+.f64 (.f64 (.f64 x (.f64 x #s(literal -1/6 binary64))) (.f64 x (.f64 x #s(literal -1/6 binary64)))) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/120 binary64)))) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/120 binary64))))) (.f64 (.f64 x (.f64 x #s(literal -1/6 binary64))) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 1/120 binary64))))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x #s(literal -1/6 binary64))) (.f64 x (.f64 x #s(literal -1/6 binary64)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/120 binary64)))) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/120 binary64)))))) (-.f64 (.f64 x (.f64 x #s(literal -1/6 binary64))) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/120 binary64))))))
(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64))))) (+.f64 #s(literal 1/36 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/120 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal 1/120 binary64))) #s(literal -1/6 binary64)))))
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64)))) (-.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64)))))
(/.f64 (.f64 (+.f64 #s(literal -1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)))) (.f64 x x)) (+.f64 #s(literal 1/36 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/120 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal 1/120 binary64))) #s(literal -1/6 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64))) (.f64 x x)) (-.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64)))))
(.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64))))))
(.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/120 binary64))))))
(.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64)))))
(.f64 (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64)))) (.f64 x x))
(.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/120 binary64))))) #s(literal 1 binary64))
(.f64 (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64))))) x)
(.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64))))) (*.f64 x x))
(.f64 x (.f64 x #s(literal 1/120 binary64)))
(.f64 (.f64 x x) #s(literal 1/120 binary64))
(.f64 #s(literal 1/120 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 1/120 binary64)) x)
(+.f64 (.f64 eps (sin.f64 x)) (.f64 (sin.f64 x) #s(literal 0 binary64)))
(+.f64 (.f64 eps (sin.f64 x)) (.f64 #s(literal 0 binary64) (sin.f64 x)))
(+.f64 (.f64 (sin.f64 x) #s(literal 0 binary64)) (.f64 eps (sin.f64 x)))
(+.f64 (.f64 #s(literal 0 binary64) (sin.f64 x)) (.f64 eps (sin.f64 x)))
(fma.f64 eps (sin.f64 x) (*.f64 (sin.f64 x) #s(literal 0 binary64)))
(fma.f64 eps (sin.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 #s(literal 0 binary64) (sin.f64 x) (*.f64 eps (sin.f64 x)))
(fma.f64 (sin.f64 x) eps (*.f64 (sin.f64 x) #s(literal 0 binary64)))
(fma.f64 (sin.f64 x) eps (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 (sin.f64 x) #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(/.f64 (.f64 (sin.f64 x) (.f64 eps (.f64 eps eps))) (.f64 eps eps))
(/.f64 (.f64 (sin.f64 x) (.f64 eps eps)) eps)
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (sin.f64 x)) (.f64 eps eps))
(/.f64 (.f64 (.f64 eps eps) (sin.f64 x)) eps)
(*.f64 eps (sin.f64 x))
(*.f64 (sin.f64 x) eps)
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal -1/6 binary64))) (*.f64 eps eps))
(/.f64 (.f64 (.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64))) eps)
(.f64 eps (.f64 eps #s(literal -1/6 binary64)))
(.f64 eps (.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(.f64 #s(literal -1/6 binary64) (.f64 (*.f64 eps eps) #s(literal 1 binary64)))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(.f64 (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) #s(literal 1 binary64))
(.f64 (.f64 eps #s(literal -1/6 binary64)) eps)
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal 1/24 binary64))) (*.f64 eps eps))
(/.f64 (.f64 (.f64 eps eps) (*.f64 eps #s(literal 1/24 binary64))) eps)
(.f64 eps (.f64 eps #s(literal 1/24 binary64)))
(.f64 (.f64 eps eps) #s(literal 1/24 binary64))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(.f64 (.f64 eps #s(literal 1/24 binary64)) eps)

simplify249.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

4300×	`-lowering-.f32`
4300×	`-lowering-.f64`
2158×	`+-lowering-+.f64`
2158×	`+-lowering-+.f32`
1706×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	507	4569
1	1753	4212
2	6161	4211
0	8038	4211

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 444

Calls

Call 1

Inputs
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* -1/120 (pow x 5))
(* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
(* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4)))))
(* (pow x 5) (- (+ (* 1/6 (/ 1 (pow x 2))) (/ (sin (+ eps x)) (pow x 5))) (+ 1/120 (/ 1 (pow x 4)))))
(* -1/120 (pow x 5))
(* -1 (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/120 (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 5))) (/ 1 (pow x 4)))) (* 1/6 (/ 1 (pow x 2))))))
(- (sin x) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* 1/120 (pow x 5))
(* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* 1/120 (pow x 5))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps x))
(* x (+ (* -1/2 eps) (* 1/12 (* eps (pow x 2)))))
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/240 (* eps (pow x 2))) (* 1/12 eps)))))
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/240 eps) (* 1/10080 (* eps (pow x 2)))))))))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* 1/24 (* (pow eps 4) (sin x)))
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(* 1/24 (* (pow eps 4) (sin x)))
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))
(* 1/24 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(* 1/24 (* (pow eps 3) (sin x)))
(* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2))))) (* eps (- (* 1/24 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* -1/6 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2))))))))))
(+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(cos x)
(+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))
(+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))
(+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/24 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* 1/24 (+ 1 (* -1/6 (pow eps 2))))))))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
1
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (* -1/6 (pow eps 2)))
(* -1/6 (pow eps 2))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* -1/6 (pow eps 2))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* -1/6 (pow x 2))
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))
(* 1/120 (pow x 4))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* 1/120 (pow x 4))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps x)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))

Outputs
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/6 binary64))) (.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 x #s(literal -2 binary64))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 x (-.f64 (.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (.f64 x (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 x (+.f64 (.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (.f64 x (-.f64 (.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 x #s(literal 1/3 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 1/2 (* eps (cos x)))
(.f64 (.f64 eps (cos.f64 x)) #s(literal 1/2 binary64))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(.f64 eps (+.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (.f64 (.f64 eps (sin.f64 x)) #s(literal -1/4 binary64))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(.f64 eps (+.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (.f64 eps (+.f64 (.f64 (.f64 eps (cos.f64 x)) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(.f64 eps (+.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (.f64 eps (+.f64 (.f64 (sin.f64 x) #s(literal -1/4 binary64)) (.f64 eps (+.f64 (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 eps (.f64 (sin.f64 x) #s(literal 1/48 binary64)))))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(-.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 x (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 x (-.f64 (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal -1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 x (-.f64 (.f64 x (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 x #s(literal 1/6 binary64))))) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (*.f64 eps #s(literal -1/645120 binary64)))))))))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 eps eps) #s(literal 1/120 binary64)))))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/120 binary64) (.f64 eps (*.f64 eps #s(literal -1/5040 binary64)))))))))
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps))))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+.f64 (sin.f64 eps) (.f64 x (+.f64 (.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(+.f64 (sin.f64 eps) (.f64 x (+.f64 (.f64 x (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1/6 binary64) (cos.f64 eps)))))) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))))
(* -1/120 (pow x 5))
(*.f64 #s(literal -1/120 binary64) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))))
(* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (-.f64 (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))))
(* (pow x 5) (- (+ (* 1/6 (/ 1 (pow x 2))) (/ (sin (+ eps x)) (pow x 5))) (+ 1/120 (/ 1 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (/.f64 (sin.f64 (+.f64 eps x)) (pow.f64 x #s(literal 5 binary64))) (-.f64 (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))))
(* -1/120 (pow x 5))
(*.f64 #s(literal -1/120 binary64) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (neg.f64 (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 x x)))))
(* -1 (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2))))))
(.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 x x)))) (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 5 binary64))))
(* -1 (* (pow x 5) (- (+ 1/120 (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 5))) (/ 1 (pow x 4)))) (* 1/6 (/ 1 (pow x 2))))))
(.f64 (+.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (sin.f64 (+.f64 eps x)) (pow.f64 x #s(literal 5 binary64)))) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 x x)))) (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 5 binary64))))
(- (sin x) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(-.f64 (sin.f64 x) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal 1/120 binary64) (*.f64 x x))))))))
(- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(-.f64 (+.f64 (.f64 eps (cos.f64 x)) (sin.f64 x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal 1/120 binary64) (.f64 x x))))))))
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(+.f64 (sin.f64 x) (-.f64 (.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal 1/120 binary64) (.f64 x x)))))))))
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(+.f64 (sin.f64 x) (-.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal 1/120 binary64) (*.f64 x x)))))))))
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(-.f64 (sin.f64 (+.f64 eps x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal 1/120 binary64) (*.f64 x x))))))))
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(-.f64 (sin.f64 (+.f64 eps x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal 1/120 binary64) (*.f64 x x))))))))
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(-.f64 (sin.f64 (+.f64 eps x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal 1/120 binary64) (*.f64 x x))))))))
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(-.f64 (sin.f64 (+.f64 eps x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal 1/120 binary64) (*.f64 x x))))))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(-.f64 (sin.f64 (+.f64 eps x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal 1/120 binary64) (*.f64 x x))))))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(-.f64 (sin.f64 (+.f64 eps x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal 1/120 binary64) (*.f64 x x))))))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(-.f64 (sin.f64 (+.f64 eps x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal 1/120 binary64) (*.f64 x x))))))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(-.f64 (sin.f64 (+.f64 eps x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal 1/120 binary64) (*.f64 x x))))))))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (cos eps)))
(+.f64 (sin.f64 eps) (*.f64 x (cos.f64 eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+.f64 (sin.f64 eps) (.f64 x (+.f64 (cos.f64 eps) (.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(+.f64 (sin.f64 eps) (.f64 x (+.f64 (cos.f64 eps) (.f64 x (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (.f64 #s(literal -1/6 binary64) (*.f64 x (cos.f64 eps))))))))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
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(.f64 (.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (.f64 (cos.f64 x) #s(literal -1/8 binary64))))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/48 binary64))) (.f64 (cos.f64 x) #s(literal -1/8 binary64)))))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 eps))
(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(-.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (-.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal -1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(+.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (-.f64 (.f64 x (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal 1/6 binary64))))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))
(.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal 1/120 binary64) (.f64 x x)))))
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))
(.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal 1/120 binary64) (.f64 x x)))))
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))
(.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal 1/120 binary64) (.f64 x x)))))
(* 1/120 (pow x 4))
(*.f64 #s(literal 1/120 binary64) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 x x))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 x x))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 x x))))
(* 1/120 (pow x 4))
(*.f64 #s(literal 1/120 binary64) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 x x))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 x x))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 x x))))
(* 1/120 (pow x 2))
(.f64 #s(literal 1/120 binary64) (.f64 x x))
(* 1/120 (pow x 2))
(.f64 #s(literal 1/120 binary64) (.f64 x x))
(* 1/120 (pow x 2))
(.f64 #s(literal 1/120 binary64) (.f64 x x))
(* 1/120 (pow x 2))
(.f64 #s(literal 1/120 binary64) (.f64 x x))
(* 1/120 (pow x 2))
(.f64 #s(literal 1/120 binary64) (.f64 x x))
(* 1/120 (pow x 2))
(.f64 #s(literal 1/120 binary64) (.f64 x x))
(* 1/120 (pow x 2))
(.f64 #s(literal 1/120 binary64) (.f64 x x))
(* 1/120 (pow x 2))
(.f64 #s(literal 1/120 binary64) (.f64 x x))
(* 1/120 (pow x 2))
(.f64 #s(literal 1/120 binary64) (.f64 x x))
(* 1/120 (pow x 2))
(.f64 #s(literal 1/120 binary64) (.f64 x x))
(* 1/120 (pow x 2))
(.f64 #s(literal 1/120 binary64) (.f64 x x))
(* 1/120 (pow x 2))
(.f64 #s(literal 1/120 binary64) (.f64 x x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps x)
(*.f64 eps x)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(.f64 x (+.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps (.f64 x x)))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(.f64 x (+.f64 eps (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal -1/6 binary64)) (.f64 eps (.f64 #s(literal 1/120 binary64) (*.f64 x x)))))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
(.f64 x (+.f64 eps (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal -1/6 binary64)) (.f64 (.f64 x x) (+.f64 (.f64 eps (.f64 (.f64 x x) #s(literal -1/5040 binary64))) (.f64 eps #s(literal 1/120 binary64))))))))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))

eval134.0ms (0.9%)

Compiler: Compiled 31823 to 2528 computations (92.1% saved)

prune100.0ms (0.7%)

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	1005	17	1022
Fresh	1	3	4
Picked	3	2	5
Done	1	0	1
Total	1010	22	1032

Accuracy

100.0%

Counts

1032 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	57.4%	(/.f64 (.f64 (+.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 (sin.f64 x) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64))))))) (*.f64 eps eps)) eps)
	99.1%	(+.f64 (.f64 (.f64 eps (sin.f64 x)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (cos.f64 x)))
	99.5%	(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
	97.0%	(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (+.f64 (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))))
	97.0%	(+.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
▶	99.8%	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
▶	99.7%	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64)))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
	99.5%	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
	99.1%	(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/48 binary64))) (.f64 (cos.f64 x) #s(literal -1/8 binary64)))))))) #s(literal 2 binary64))
	96.8%	(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))
	97.0%	(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/6 binary64)))))))))
✓	99.5%	(.f64 eps (+.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
	51.5%	(.f64 eps (+.f64 (.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))) (cos.f64 x)) (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
	99.4%	(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))) (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
	98.2%	(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
✓	99.1%	(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
	96.9%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
▶	97.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps x) #s(literal 1/12 binary64))))))))
	96.8%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
▶	98.5%	(*.f64 eps (cos.f64 x))
▶	96.9%	eps

Compiler

Compiled 904 to 579 computations (36% saved)

simplify180.0ms (1.3%)

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Program
✓	cost-diff	(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64)))))
✓	cost-diff	(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))
✓	cost-diff	(.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64)))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
✓	cost-diff	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64)))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
✓	cost-diff	(cos.f64 x)
✓	cost-diff	(*.f64 eps (cos.f64 x))
✓	cost-diff	(+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps x) #s(literal 1/12 binary64)))))
✓	cost-diff	(.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 eps x) #s(literal 1/12 binary64))))))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 eps x) #s(literal 1/12 binary64)))))))
✓	cost-diff	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps x) #s(literal 1/12 binary64))))))))
✓	cost-diff	(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64))))))))
✓	cost-diff	(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (*.f64 eps #s(literal -1/645120 binary64)))))))))
✓	cost-diff	(.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
✓	cost-diff	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))

Rules

3228×	`sum3-define`
2344×	`-lowering-.f32`
2344×	`-lowering-.f64`
1990×	`+-lowering-+.f64`
1990×	`+-lowering-+.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	43	425
1	136	379
2	497	379
3	1651	379
4	4545	379
5	7084	379
6	7488	379
7	7608	379
8	7608	379
9	7820	379
0	8461	379

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2)))
(* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))))))
eps
(+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))
1/2
(* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))))
(* eps eps)
(+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))
-1/48
(* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))
(+ 1/3840 (* eps (* eps -1/645120)))
1/3840
(* eps (* eps -1/645120))
(* eps -1/645120)
-1/645120
(cos (/ (+ eps (* x 2)) 2))
(/ (+ eps (* x 2)) 2)
(+ eps (* x 2))
(* x 2)
x
2
eps
(* eps (+ 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* (* eps x) 1/12)))))))
eps
(+ 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* (* eps x) 1/12))))))
1
(* x (+ (* eps -1/2) (* x (+ -1/2 (* (* eps x) 1/12)))))
x
(+ (* eps -1/2) (* x (+ -1/2 (* (* eps x) 1/12))))
(* eps -1/2)
-1/2
(* x (+ -1/2 (* (* eps x) 1/12)))
(+ -1/2 (* (* eps x) 1/12))
(* (* eps x) 1/12)
(* eps x)
1/12
(* eps (cos x))
eps
(cos x)
x
(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))) (cos (/ (+ eps (* x 2)) 2)))
(* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))))
eps
(+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))
1/2
(* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))
(* eps eps)
(+ -1/48 (* (* eps eps) 1/3840))
-1/48
(* (* eps eps) 1/3840)
1/3840
(cos (/ (+ eps (* x 2)) 2))
(/ (+ eps (* x 2)) 2)
(+ eps (* x 2))
(* x 2)
x
2

Outputs
(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2))) 2)
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))))) (.f64 (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (.f64 eps #s(literal 2 binary64))))
(* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2)))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))))) (.f64 eps (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))
(* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))))))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))
eps
(+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))))))
1/2
#s(literal 1/2 binary64)
(* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))))
(* eps eps)
(*.f64 eps eps)
(+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))
(+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))))
-1/48
#s(literal -1/48 binary64)
(* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))
(+ 1/3840 (* eps (* eps -1/645120)))
(+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))
1/3840
#s(literal 1/3840 binary64)
(* eps (* eps -1/645120))
(.f64 (.f64 eps eps) #s(literal -1/645120 binary64))
(* eps -1/645120)
(*.f64 eps #s(literal -1/645120 binary64))
-1/645120
#s(literal -1/645120 binary64)
(cos (/ (+ eps (* x 2)) 2))
(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
(/ (+ eps (* x 2)) 2)
(/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
(+ eps (* x 2))
(+.f64 eps (*.f64 x #s(literal 2 binary64)))
(* x 2)
(*.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)
eps
(* eps (+ 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* (* eps x) 1/12)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 eps #s(literal 1/12 binary64)))))))))
eps
(+ 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* (* eps x) 1/12))))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 eps #s(literal 1/12 binary64))))))))
1
#s(literal 1 binary64)
(* x (+ (* eps -1/2) (* x (+ -1/2 (* (* eps x) 1/12)))))
(.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 eps #s(literal 1/12 binary64)))))))
x
(+ (* eps -1/2) (* x (+ -1/2 (* (* eps x) 1/12))))
(+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 eps #s(literal 1/12 binary64))))))
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(* x (+ -1/2 (* (* eps x) 1/12)))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 eps #s(literal 1/12 binary64)))))
(+ -1/2 (* (* eps x) 1/12))
(+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 eps #s(literal 1/12 binary64))))
(* (* eps x) 1/12)
(.f64 x (.f64 eps #s(literal 1/12 binary64)))
(* eps x)
(*.f64 eps x)
1/12
#s(literal 1/12 binary64)
(* eps (cos x))
(*.f64 eps (cos.f64 x))
eps
(cos x)
(cos.f64 x)
x
(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))) (cos (/ (+ eps (* x 2)) 2))) 2)
(.f64 (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps #s(literal 1/3840 binary64))))))))))
(* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))) (cos (/ (+ eps (* x 2)) 2)))
(.f64 (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))))))))
(* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))))))
eps
(+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))
(+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps #s(literal 1/3840 binary64)))))))
1/2
#s(literal 1/2 binary64)
(* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps #s(literal 1/3840 binary64))))))
(* eps eps)
(*.f64 eps eps)
(+ -1/48 (* (* eps eps) 1/3840))
(+.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps #s(literal 1/3840 binary64))))
-1/48
#s(literal -1/48 binary64)
(* (* eps eps) 1/3840)
(.f64 eps (.f64 eps #s(literal 1/3840 binary64)))
1/3840
#s(literal 1/3840 binary64)
(cos (/ (+ eps (* x 2)) 2))
(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
(/ (+ eps (* x 2)) 2)
(/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
(+ eps (* x 2))
(+.f64 eps (*.f64 x #s(literal 2 binary64)))
(* x 2)
(*.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)

localize322.0ms (2.3%)

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64)))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
✓	accuracy	99.8%	(.f64 (.f64 eps eps) #s(literal 1/3840 binary64))
✓	accuracy	99.8%	(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
✓	accuracy	99.7%	(.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64))))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(*.f64 eps (cos.f64 x))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 eps x) #s(literal 1/12 binary64))))
✓	accuracy	100.0%	(+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps x) #s(literal 1/12 binary64)))))
✓	accuracy	99.8%	(.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 eps x) #s(literal 1/12 binary64))))))
✓	accuracy	99.7%	(.f64 (.f64 eps x) #s(literal 1/12 binary64))
✓	accuracy	99.8%	(.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))
✓	accuracy	99.8%	(.f64 eps (.f64 eps #s(literal -1/645120 binary64)))
✓	accuracy	99.8%	(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
✓	accuracy	99.7%	(.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))))

Results

149.0ms	252×	0	valid
2.0ms	2×	1	valid
2.0ms	1×	3	valid
1.0ms	1×	2	valid

Compiler

Compiled 432 to 44 computations (89.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 72.0ms

ival-mult: 35.0ms (48.8% of total)

...c/correct-round.rkt:119:19: 17.0ms (23.7% of total)

ival-add: 11.0ms (15.3% of total)

ival-cos: 5.0ms (7% of total)

ival-div: 2.0ms (2.8% of total)

const: 1.0ms (1.4% of total)

backward-pass: 1.0ms (1.4% of total)

series45.0ms (0.3%)

Counts

22 → 408

Calls

Call 1

Inputs
#<alt (* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2))) 2)>
#<alt (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2)))>
#<alt (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))))))>
#<alt (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))>
#<alt (* eps (+ 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* (* eps x) 1/12)))))))>
#<alt (+ 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* (* eps x) 1/12))))))>
#<alt (* x (+ (* eps -1/2) (* x (+ -1/2 (* (* eps x) 1/12)))))>
#<alt (+ (* eps -1/2) (* x (+ -1/2 (* (* eps x) 1/12))))>
#<alt (* eps (cos x))>
#<alt (cos x)>
#<alt (* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))) (cos (/ (+ eps (* x 2)) 2))) 2)>
#<alt (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))) (cos (/ (+ eps (* x 2)) 2)))>
#<alt (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))))>
#<alt (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))>
#<alt (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))))>
#<alt (cos (/ (+ eps (* x 2)) 2))>
#<alt (* eps (* eps -1/645120))>
#<alt (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))>
#<alt (* (* eps x) 1/12)>
#<alt (* x (+ -1/2 (* (* eps x) 1/12)))>
#<alt (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))>
#<alt (* (* eps eps) 1/3840)>

Outputs
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* -1/322560 (* (pow eps 7) (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* (pow eps 7) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))>
#<alt (* (pow eps 7) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))))>
#<alt (* (pow eps 7) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 6))))))>
#<alt (* -1/322560 (* (pow eps 7) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -1 (* (pow eps 7) (+ (* -1/1920 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))>
#<alt (* -1 (* (pow eps 7) (+ (* -1/1920 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4)))))))>
#<alt (* -1 (* (pow eps 7) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 6))) (+ (* -1/1920 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))>
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))>
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* -1/645120 (* (pow eps 7) (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* (pow eps 7) (+ (* -1/645120 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/3840 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))>
#<alt (* (pow eps 7) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/645120 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/3840 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))))>
#<alt (* (pow eps 7) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/645120 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* 1/3840 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 6)))))))>
#<alt (* -1/645120 (* (pow eps 7) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -1 (* (pow eps 7) (+ (* -1/3840 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/645120 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))>
#<alt (* -1 (* (pow eps 7) (+ (* -1/3840 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/645120 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4)))))))>
#<alt (* -1 (* (pow eps 7) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 6))) (+ (* -1/3840 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/645120 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))))))))>
#<alt (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))>
#<alt (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (* -1/645120 (pow eps 7))>
#<alt (* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* (pow eps 7) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* -1/645120 (pow eps 7))>
#<alt (* -1 (* (pow eps 7) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/48 (pow eps 2)))>
#<alt (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))>
#<alt (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))>
#<alt (* -1/645120 (pow eps 6))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* (pow eps 6) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* -1/645120 (pow eps 6))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* (pow eps 6) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))))>
#<alt (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))))>
#<alt (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))))>
#<alt (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))>
#<alt (* -1 (* (pow eps 2) (* x (+ 1/2 (* -1/12 (pow x 2))))))>
#<alt (* (pow eps 2) (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt eps>
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))>
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))>
#<alt (* 1/12 (* (pow eps 2) (pow x 3)))>
#<alt (* (pow x 3) (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))))>
#<alt (* (pow x 3) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))))>
#<alt (* (pow x 3) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ eps (pow x 3))))))>
#<alt (* 1/12 (* (pow eps 2) (pow x 3)))>
#<alt (* -1 (* (pow x 3) (+ (* -1/12 (pow eps 2)) (* 1/2 (/ eps x)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))) x)) (* -1/12 (pow eps 2)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)) x)) (* -1/12 (pow eps 2)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (* eps x)))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))>
#<alt (* 1/12 (* eps (pow x 3)))>
#<alt (* (pow x 3) (- (* 1/12 eps) (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (/ 1 (pow x 3)))) (* 1/2 (/ 1 x))))>
#<alt (* 1/12 (* eps (pow x 3)))>
#<alt (* -1 (* (pow x 3) (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1/2) x)) (* -1/12 eps))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2) x)) (* -1/12 eps))))>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))>
#<alt (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))>
#<alt (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))>
#<alt (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))>
#<alt (* eps (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))>
#<alt (* eps (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))>
#<alt (* eps (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))>
#<alt (* -1 (* eps (* x (+ 1/2 (* -1/12 (pow x 2))))))>
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))>
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))>
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))>
#<alt (* -1/2 (* eps x))>
#<alt (* x (+ (* -1/2 eps) (* -1/2 x)))>
#<alt (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))>
#<alt (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))>
#<alt (* 1/12 (* eps (pow x 3)))>
#<alt (* (pow x 3) (- (* 1/12 eps) (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))>
#<alt (* 1/12 (* eps (pow x 3)))>
#<alt (* -1 (* (pow x 3) (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1/2) x)) (* -1/12 eps))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1/2) x)) (* -1/12 eps))))>
#<alt (* -1/2 (pow x 2))>
#<alt (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))>
#<alt (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))>
#<alt (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))>
#<alt (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))>
#<alt (* eps (+ (* -1/2 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))))>
#<alt (* eps (+ (* -1/2 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))))>
#<alt (* eps (+ (* -1/2 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))))>
#<alt (* -1 (* eps (* x (+ 1/2 (* -1/12 (pow x 2))))))>
#<alt (* -1 (* eps (+ (* 1/2 (/ (pow x 2) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))>
#<alt (* -1 (* eps (+ (* 1/2 (/ (pow x 2) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))>
#<alt (* -1 (* eps (+ (* 1/2 (/ (pow x 2) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))>
#<alt (* -1/2 x)>
#<alt (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))>
#<alt (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))>
#<alt (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))>
#<alt (* eps (- (* 1/12 (pow x 2)) 1/2))>
#<alt (* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))>
#<alt (* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))>
#<alt (* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))>
#<alt (* -1 (* eps (+ 1/2 (* -1/12 (pow x 2)))))>
#<alt (* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps))))))>
#<alt (* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps))))))>
#<alt (* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps))))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))>
#<alt (* 1/12 (* eps (pow x 2)))>
#<alt (* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))>
#<alt (* 1/12 (* eps (pow x 2)))>
#<alt (* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ eps x))) x)) (* 1/12 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ eps x))) x)) (* 1/12 eps)))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt eps>
#<alt (+ eps (* -1/2 (* eps (pow x 2))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 1/1920 (* (pow eps 5) (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x)))))))>
#<alt (* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4)))))>
#<alt (* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4)))))>
#<alt (* 1/1920 (* (pow eps 5) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))>
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))>
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* 1/3840 (* (pow eps 5) (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* (pow eps 5) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/3840 (cos (* 1/2 (+ eps (* 2 x)))))))>
#<alt (* (pow eps 5) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/3840 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))))))>
#<alt (* (pow eps 5) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/3840 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))))))>
#<alt (* 1/3840 (* (pow eps 5) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/3840 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/3840 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/3840 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))>
#<alt (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))>
#<alt (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* 1/3840 (pow eps 5))>
#<alt (* (pow eps 5) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* 1/3840 (pow eps 5))>
#<alt (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))>
#<alt (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))>
#<alt (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/48 (pow eps 2)))>
#<alt (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))>
#<alt (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))>
#<alt (* 1/3840 (pow eps 4))>
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* 1/3840 (pow eps 4))>
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))>
#<alt (* -1/645120 (pow eps 6))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* -1/645120 (pow eps 6))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))>
#<alt (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))>
#<alt (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))>
#<alt (* -1/645120 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* -1/645120 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* 1/12 (* eps x))>
#<alt (* 1/12 (* eps x))>
#<alt (* 1/12 (* eps x))>
#<alt (* 1/12 (* eps x))>
#<alt (* 1/12 (* eps x))>
#<alt (* 1/12 (* eps x))>
#<alt (* 1/12 (* eps x))>
#<alt (* 1/12 (* eps x))>
#<alt (* 1/12 (* eps x))>
#<alt (* 1/12 (* eps x))>
#<alt (* 1/12 (* eps x))>
#<alt (* 1/12 (* eps x))>
#<alt (* 1/12 (* eps x))>
#<alt (* 1/12 (* eps x))>
#<alt (* 1/12 (* eps x))>
#<alt (* 1/12 (* eps x))>
#<alt (* 1/12 (* eps x))>
#<alt (* 1/12 (* eps x))>
#<alt (* 1/12 (* eps x))>
#<alt (* 1/12 (* eps x))>
#<alt (* 1/12 (* eps x))>
#<alt (* 1/12 (* eps x))>
#<alt (* 1/12 (* eps x))>
#<alt (* 1/12 (* eps x))>
#<alt (* -1/2 x)>
#<alt (* x (- (* 1/12 (* eps x)) 1/2))>
#<alt (* x (- (* 1/12 (* eps x)) 1/2))>
#<alt (* x (- (* 1/12 (* eps x)) 1/2))>
#<alt (* 1/12 (* eps (pow x 2)))>
#<alt (* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))>
#<alt (* 1/12 (* eps (pow x 2)))>
#<alt (* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))>
#<alt (* -1/2 x)>
#<alt (+ (* -1/2 x) (* 1/12 (* eps (pow x 2))))>
#<alt (+ (* -1/2 x) (* 1/12 (* eps (pow x 2))))>
#<alt (+ (* -1/2 x) (* 1/12 (* eps (pow x 2))))>
#<alt (* 1/12 (* eps (pow x 2)))>
#<alt (* eps (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))))>
#<alt (* eps (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))))>
#<alt (* eps (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))))>
#<alt (* 1/12 (* eps (pow x 2)))>
#<alt (* -1 (* eps (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))))>
#<alt (* -1 (* eps (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))))>
#<alt (* -1 (* eps (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))>
#<alt (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))>
#<alt (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))>
#<alt (* 1/3840 (pow eps 4))>
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* 1/3840 (pow eps 4))>
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>

Calls

102 calls:

Time	Variable		Point	Expression
8.0ms	eps	@	inf	(* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2)))
2.0ms	x	@	inf	(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2))) 2)
1.0ms	x	@	inf	(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))) (cos (/ (+ eps (* x 2)) 2))) 2)
1.0ms	eps	@	inf	(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2))) 2)
1.0ms	eps	@	-inf	(* eps (+ 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* (* eps x) 1/12)))))))

rewrite347.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

3198×	`fma-lowering-fma.f32`
3198×	`fma-lowering-fma.f64`
2798×	`-lowering-.f32`
2798×	`-lowering-.f64`
1850×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	43	317
1	256	281
2	2393	281
0	8323	281

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 423

Calls

Call 1

Inputs
(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2)))
(* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))))))
(+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))
(* eps (+ 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* (* eps x) 1/12)))))))
(+ 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* (* eps x) 1/12))))))
(* x (+ (* eps -1/2) (* x (+ -1/2 (* (* eps x) 1/12)))))
(+ (* eps -1/2) (* x (+ -1/2 (* (* eps x) 1/12))))
(* eps (cos x))
(cos x)
(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))) (cos (/ (+ eps (* x 2)) 2)))
(* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))))
(+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))
(* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))))
(cos (/ (+ eps (* x 2)) 2))
(* eps (* eps -1/645120))
(* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))
(* (* eps x) 1/12)
(* x (+ -1/2 (* (* eps x) 1/12)))
(* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))
(* (* eps eps) 1/3840)

Outputs
(.f64 eps (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))))))) (.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))))
(.f64 eps (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))))))) (.f64 eps (.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))))
(.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))))))) (.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))))))) (.f64 eps (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))))
(.f64 (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))))))) #s(literal 2 binary64)))
(.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))))))) (.f64 eps (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))) #s(literal 2 binary64))
(.f64 (.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))))))))
(.f64 (.f64 #s(literal 2 binary64) eps) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))
(.f64 (.f64 #s(literal 2 binary64) (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))))))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
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(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1/2304 binary64) (.f64 #s(literal 1/14745600 binary64) (.f64 (.f64 eps eps) (.f64 eps eps)))) (.f64 eps eps))) (neg.f64 (+.f64 #s(literal -1/48 binary64) (.f64 #s(literal -1/3840 binary64) (.f64 eps eps)))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps #s(literal 1/3840 binary64))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps #s(literal 1/3840 binary64)))))
(.f64 (+.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps #s(literal 1/3840 binary64)))) (.f64 eps eps))
(.f64 (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps #s(literal 1/3840 binary64))))) eps)
(.f64 eps (.f64 eps #s(literal 1/3840 binary64)))
(.f64 (.f64 eps eps) #s(literal 1/3840 binary64))
(.f64 #s(literal 1/3840 binary64) (.f64 eps eps))
(.f64 (.f64 eps #s(literal 1/3840 binary64)) eps)

simplify376.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

6664×	`-lowering-.f32`
6664×	`-lowering-.f64`
3538×	`+-lowering-+.f64`
3538×	`+-lowering-+.f32`
1540×	`sum4-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	567	6377
1	2015	6004
2	7657	6001
0	8417	6001

Stop Event

1×	iter limit
1×	node limit

Counts

408 → 408

Calls

Call 1

Inputs
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* -1/322560 (* (pow eps 7) (cos (* 1/2 (+ eps (* 2 x))))))
(* (pow eps 7) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))
(* (pow eps 7) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))))
(* (pow eps 7) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 6))))))
(* -1/322560 (* (pow eps 7) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* (pow eps 7) (+ (* -1/1920 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))
(* -1 (* (pow eps 7) (+ (* -1/1920 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4)))))))
(* -1 (* (pow eps 7) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 6))) (+ (* -1/1920 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))))))))
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* -1/645120 (* (pow eps 7) (cos (* 1/2 (+ eps (* 2 x))))))
(* (pow eps 7) (+ (* -1/645120 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/3840 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))
(* (pow eps 7) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/645120 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/3840 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))))
(* (pow eps 7) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/645120 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* 1/3840 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 6)))))))
(* -1/645120 (* (pow eps 7) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* (pow eps 7) (+ (* -1/3840 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/645120 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))
(* -1 (* (pow eps 7) (+ (* -1/3840 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/645120 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4)))))))
(* -1 (* (pow eps 7) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 6))) (+ (* -1/3840 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/645120 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))))))))
(* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
(+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))))
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* -1/645120 (pow eps 7))
(* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 7) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* -1/645120 (pow eps 7))
(* -1 (* (pow eps 7) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))))))
1/2
(+ 1/2 (* -1/48 (pow eps 2)))
(+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))
(+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))
(* -1/645120 (pow eps 6))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 6) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* -1/645120 (pow eps 6))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 6) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))))
(* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2)))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))
(* -1 (* (pow eps 2) (* x (+ 1/2 (* -1/12 (pow x 2))))))
(* (pow eps 2) (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(* 1/12 (* (pow eps 2) (pow x 3)))
(* (pow x 3) (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))))
(* (pow x 3) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))))
(* (pow x 3) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ eps (pow x 3))))))
(* 1/12 (* (pow eps 2) (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/12 (pow eps 2)) (* 1/2 (/ eps x)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))) x)) (* -1/12 (pow eps 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)) x)) (* -1/12 (pow eps 2)))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* 1/12 (* eps (pow x 3)))
(* (pow x 3) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))
(* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (/ 1 (pow x 3)))) (* 1/2 (/ 1 x))))
(* 1/12 (* eps (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1/2) x)) (* -1/12 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2) x)) (* -1/12 eps))))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))
(* eps (* x (- (* 1/12 (pow x 2)) 1/2)))
(* eps (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))
(* eps (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))
(* eps (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))
(* -1 (* eps (* x (+ 1/2 (* -1/12 (pow x 2))))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))
(* -1/2 (* eps x))
(* x (+ (* -1/2 eps) (* -1/2 x)))
(* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))
(* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))
(* 1/12 (* eps (pow x 3)))
(* (pow x 3) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))
(* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))
(* 1/12 (* eps (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1/2) x)) (* -1/12 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1/2) x)) (* -1/12 eps))))
(* -1/2 (pow x 2))
(+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))
(+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))
(+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))
(* eps (* x (- (* 1/12 (pow x 2)) 1/2)))
(* eps (+ (* -1/2 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))))
(* eps (+ (* -1/2 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))))
(* eps (+ (* -1/2 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))))
(* -1 (* eps (* x (+ 1/2 (* -1/12 (pow x 2))))))
(* -1 (* eps (+ (* 1/2 (/ (pow x 2) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))
(* -1 (* eps (+ (* 1/2 (/ (pow x 2) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))
(* -1 (* eps (+ (* 1/2 (/ (pow x 2) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))
(* -1/2 x)
(+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))
(+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))
(+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))
(* eps (- (* 1/12 (pow x 2)) 1/2))
(* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))
(* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))
(* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))
(* -1 (* eps (+ 1/2 (* -1/12 (pow x 2)))))
(* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps))))))
(* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps))))))
(* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps))))))
(* -1/2 eps)
(+ (* -1/2 eps) (* -1/2 x))
(+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(* 1/12 (* eps (pow x 2)))
(* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))
(* 1/12 (* eps (pow x 2)))
(* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ eps x))) x)) (* 1/12 eps)))
(* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ eps x))) x)) (* 1/12 eps)))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 1/1920 (* (pow eps 5) (cos (* 1/2 (+ eps (* 2 x))))))
(* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x)))))))
(* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4)))))
(* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4)))))
(* 1/1920 (* (pow eps 5) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* (pow eps 5) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))))))
(* -1 (* (pow eps 5) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))
(* -1 (* (pow eps 5) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* 1/3840 (* (pow eps 5) (cos (* 1/2 (+ eps (* 2 x))))))
(* (pow eps 5) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/3840 (cos (* 1/2 (+ eps (* 2 x)))))))
(* (pow eps 5) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/3840 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))))))
(* (pow eps 5) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/3840 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))))))
(* 1/3840 (* (pow eps 5) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* (pow eps 5) (+ (* -1/3840 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))))))
(* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/3840 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))
(* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/3840 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))
(* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* 1/3840 (pow eps 5))
(* (pow eps 5) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))
(* 1/3840 (pow eps 5))
(* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))
(* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))
(* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))
1/2
(+ 1/2 (* -1/48 (pow eps 2)))
(+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))
(+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))
(* 1/3840 (pow eps 4))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))
(* 1/3840 (pow eps 4))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))
(* -1/48 (pow eps 2))
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))
(* -1/645120 (pow eps 6))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* -1/645120 (pow eps 6))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* 1/3840 (pow eps 2))
(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))
(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))
(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))
(* -1/645120 (pow eps 4))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* -1/645120 (pow eps 4))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* 1/12 (* eps x))
(* 1/12 (* eps x))
(* 1/12 (* eps x))
(* 1/12 (* eps x))
(* 1/12 (* eps x))
(* 1/12 (* eps x))
(* 1/12 (* eps x))
(* 1/12 (* eps x))
(* 1/12 (* eps x))
(* 1/12 (* eps x))
(* 1/12 (* eps x))
(* 1/12 (* eps x))
(* 1/12 (* eps x))
(* 1/12 (* eps x))
(* 1/12 (* eps x))
(* 1/12 (* eps x))
(* 1/12 (* eps x))
(* 1/12 (* eps x))
(* 1/12 (* eps x))
(* 1/12 (* eps x))
(* 1/12 (* eps x))
(* 1/12 (* eps x))
(* 1/12 (* eps x))
(* 1/12 (* eps x))
(* -1/2 x)
(* x (- (* 1/12 (* eps x)) 1/2))
(* x (- (* 1/12 (* eps x)) 1/2))
(* x (- (* 1/12 (* eps x)) 1/2))
(* 1/12 (* eps (pow x 2)))
(* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(* 1/12 (* eps (pow x 2)))
(* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(* -1/2 x)
(+ (* -1/2 x) (* 1/12 (* eps (pow x 2))))
(+ (* -1/2 x) (* 1/12 (* eps (pow x 2))))
(+ (* -1/2 x) (* 1/12 (* eps (pow x 2))))
(* 1/12 (* eps (pow x 2)))
(* eps (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))))
(* eps (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))))
(* eps (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))))
(* 1/12 (* eps (pow x 2)))
(* -1 (* eps (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))))
(* -1 (* eps (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))))
(* -1 (* eps (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))))
(* -1/48 (pow eps 2))
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))
(* 1/3840 (pow eps 4))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* 1/3840 (pow eps 4))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))

Outputs
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (+.f64 (.f64 (.f64 eps (sin.f64 x)) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))))))))
(* -1/322560 (* (pow eps 7) (cos (* 1/2 (+ eps (* 2 x))))))
(.f64 #s(literal -1/322560 binary64) (.f64 (pow.f64 eps #s(literal 7 binary64)) (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x)))))
(* (pow eps 7) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (.f64 #s(literal -1/322560 binary64) (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x)))) (.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1/1920 binary64) (.f64 eps eps)))))
(* (pow eps 7) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))))
(.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1/1920 binary64) (.f64 eps eps))) (+.f64 (.f64 #s(literal -1/322560 binary64) (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x)))) (/.f64 (.f64 #s(literal -1/24 binary64) (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) x)))) (pow.f64 eps #s(literal 4 binary64))))))
(* (pow eps 7) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 6))))))
(.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (.f64 #s(literal -1/322560 binary64) (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x)))) (+.f64 (+.f64 (.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1/1920 binary64) (.f64 eps eps))) (/.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (pow.f64 eps #s(literal 6 binary64)))) (/.f64 (.f64 #s(literal -1/24 binary64) (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) x)))) (pow.f64 eps #s(literal 4 binary64))))))
(* -1/322560 (* (pow eps 7) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 #s(literal -1/322560 binary64) (.f64 (pow.f64 eps #s(literal 7 binary64)) (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x)))))
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(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
(.f64 eps (.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))))))))))
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
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(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
(.f64 eps (.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))))))))))
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
(.f64 eps (.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))))))))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
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(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
(.f64 eps (.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))))))))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
(.f64 eps (.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))))))))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
(.f64 eps (.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))))))))))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/3840 binary64) (.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))))
(* -1/645120 (pow eps 7))
(*.f64 (pow.f64 eps #s(literal 7 binary64)) #s(literal -1/645120 binary64))
(* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps))))
(* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
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(* (pow eps 7) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 6 binary64))) (+.f64 #s(literal 1/645120 binary64) (/.f64 #s(literal 1/48 binary64) (pow.f64 eps #s(literal 4 binary64)))))))
(* -1/645120 (pow eps 7))
(*.f64 (pow.f64 eps #s(literal 7 binary64)) #s(literal -1/645120 binary64))
(* -1 (* (pow eps 7) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))
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(* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))
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(* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))))))
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1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/48 (pow eps 2)))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))
(+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))
(+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64))))))
(+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))
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(* -1/645120 (pow eps 6))
(*.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/645120 binary64))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps))))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
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(* (pow eps 6) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
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(* -1/645120 (pow eps 6))
(*.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/645120 binary64))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps))))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) (-.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/48 binary64) (pow.f64 eps #s(literal 4 binary64))))))
(* (pow eps 6) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
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(* eps (+ 1 (* -1/2 (pow x 2))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x x))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64))) (*.f64 eps x)))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64))) (*.f64 eps x)))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64))) (*.f64 eps x)))))
(* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2)))
(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64))) (.f64 x (*.f64 eps eps)))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))
(.f64 (.f64 eps eps) (+.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64)))) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps) (/.f64 #s(literal 1 binary64) eps))))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))
(.f64 (.f64 eps eps) (+.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64)))) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps) (/.f64 #s(literal 1 binary64) eps))))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))
(.f64 (.f64 eps eps) (+.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64)))) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps) (/.f64 #s(literal 1 binary64) eps))))
(* -1 (* (pow eps 2) (* x (+ 1/2 (* -1/12 (pow x 2))))))
(.f64 (.f64 eps eps) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal -1/12 binary64))) (neg.f64 x)))
(* (pow eps 2) (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
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(* (pow eps 2) (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(.f64 (.f64 eps eps) (-.f64 (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) eps) (/.f64 #s(literal 1 binary64) eps)) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal -1/12 binary64))))))
(* (pow eps 2) (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(.f64 (.f64 eps eps) (-.f64 (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) eps) (/.f64 #s(literal 1 binary64) eps)) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal -1/12 binary64))))))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 eps eps))))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(+.f64 eps (.f64 x (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 eps x))) (.f64 #s(literal 1/12 binary64) (.f64 (.f64 x (*.f64 eps eps)) x)))))
(* 1/12 (* (pow eps 2) (pow x 3)))
(.f64 (.f64 x (.f64 x x)) (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))
(* (pow x 3) (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))))
(.f64 (.f64 x (.f64 x x)) (+.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))))
(* (pow x 3) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))))
(.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 eps x) (/.f64 (/.f64 (*.f64 eps eps) x) x)))))
(* (pow x 3) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ eps (pow x 3))))))
(.f64 (.f64 x (.f64 x x)) (+.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 eps x) (/.f64 (/.f64 (.f64 eps eps) x) x)))) (/.f64 eps (.f64 x (*.f64 x x)))))
(* 1/12 (* (pow eps 2) (pow x 3)))
(.f64 (.f64 x (.f64 x x)) (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))
(* -1 (* (pow x 3) (+ (* -1/12 (pow eps 2)) (* 1/2 (/ eps x)))))
(.f64 (.f64 x (.f64 x x)) (neg.f64 (+.f64 (.f64 eps (.f64 eps #s(literal -1/12 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 eps x)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))) x)) (* -1/12 (pow eps 2)))))
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(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (+.f64 (.f64 (.f64 eps (sin.f64 x)) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))))))))
(* 1/1920 (* (pow eps 5) (cos (* 1/2 (+ eps (* 2 x))))))
(.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 1/1920 binary64) (pow.f64 eps #s(literal 5 binary64))))
(* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x)))))))
(.f64 (pow.f64 eps #s(literal 5 binary64)) (+.f64 (/.f64 (.f64 #s(literal -1/24 binary64) (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x)))) (.f64 eps eps)) (.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) #s(literal 1/1920 binary64))))
(* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4)))))
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(* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4)))))
(.f64 (pow.f64 eps #s(literal 5 binary64)) (+.f64 (/.f64 (.f64 #s(literal -1/24 binary64) (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x)))) (.f64 eps eps)) (+.f64 (/.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (pow.f64 eps #s(literal 4 binary64))) (.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) #s(literal 1/1920 binary64)))))
(* 1/1920 (* (pow eps 5) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 1/1920 binary64) (pow.f64 eps #s(literal 5 binary64))))
(* -1 (* (pow eps 5) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))))))
(.f64 (+.f64 (.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) #s(literal -1/1920 binary64)) (.f64 #s(literal 1/24 binary64) (/.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (.f64 eps eps)))) (*.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 5 binary64))))
(* -1 (* (pow eps 5) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))
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(* -1 (* (pow eps 5) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))
(.f64 (-.f64 (+.f64 (.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) #s(literal -1/1920 binary64)) (.f64 #s(literal 1/24 binary64) (/.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (.f64 eps eps)))) (/.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (pow.f64 eps #s(literal 4 binary64)))) (*.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 5 binary64))))
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(.f64 #s(literal 2 binary64) (.f64 eps (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64)))))))))
(+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))
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(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))
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(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))
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(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(.f64 (.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64))))))) (*.f64 eps #s(literal 2 binary64)))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(.f64 (.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64))))))) (*.f64 eps #s(literal 2 binary64)))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(.f64 (.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64))))))) (*.f64 eps #s(literal 2 binary64)))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(.f64 (.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64))))))) (*.f64 eps #s(literal 2 binary64)))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(.f64 (.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64))))))) (*.f64 eps #s(literal 2 binary64)))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(.f64 (.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64))))))) (*.f64 eps #s(literal 2 binary64)))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(.f64 (.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64))))))) (*.f64 eps #s(literal 2 binary64)))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(.f64 (.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64))))))) (*.f64 eps #s(literal 2 binary64)))
(* 1/2 (* eps (cos x)))
(.f64 eps (.f64 (cos.f64 x) #s(literal 1/2 binary64)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(.f64 eps (+.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (.f64 (.f64 eps (sin.f64 x)) #s(literal -1/4 binary64))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
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(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(.f64 eps (+.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (.f64 eps (+.f64 (.f64 (sin.f64 x) #s(literal -1/4 binary64)) (.f64 eps (+.f64 (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (.f64 eps (sin.f64 x)) #s(literal 1/48 binary64))))))))
(* 1/3840 (* (pow eps 5) (cos (* 1/2 (+ eps (* 2 x))))))
(.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 1/3840 binary64) (pow.f64 eps #s(literal 5 binary64))))
(* (pow eps 5) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/3840 (cos (* 1/2 (+ eps (* 2 x)))))))
(.f64 (pow.f64 eps #s(literal 5 binary64)) (+.f64 (.f64 #s(literal -1/48 binary64) (/.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (.f64 eps eps))) (.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) #s(literal 1/3840 binary64))))
(* (pow eps 5) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/3840 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))))))
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(* (pow eps 5) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/3840 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))))))
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(* 1/3840 (* (pow eps 5) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 1/3840 binary64) (pow.f64 eps #s(literal 5 binary64))))
(* -1 (* (pow eps 5) (+ (* -1/3840 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))))))
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(* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/3840 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))
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(* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/3840 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))
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(* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
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(+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(-.f64 (.f64 eps (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64)))))))) (.f64 (.f64 (.f64 eps x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))))
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(.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps))))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps))))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps))))
(* -1/645120 (pow eps 4))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/645120 binary64))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps))))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps))))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps))))
(* 1/12 (* eps x))
(.f64 eps (.f64 #s(literal 1/12 binary64) x))
(* 1/12 (* eps x))
(.f64 eps (.f64 #s(literal 1/12 binary64) x))
(* 1/12 (* eps x))
(.f64 eps (.f64 #s(literal 1/12 binary64) x))
(* 1/12 (* eps x))
(.f64 eps (.f64 #s(literal 1/12 binary64) x))
(* 1/12 (* eps x))
(.f64 eps (.f64 #s(literal 1/12 binary64) x))
(* 1/12 (* eps x))
(.f64 eps (.f64 #s(literal 1/12 binary64) x))
(* 1/12 (* eps x))
(.f64 eps (.f64 #s(literal 1/12 binary64) x))
(* 1/12 (* eps x))
(.f64 eps (.f64 #s(literal 1/12 binary64) x))
(* 1/12 (* eps x))
(.f64 eps (.f64 #s(literal 1/12 binary64) x))
(* 1/12 (* eps x))
(.f64 eps (.f64 #s(literal 1/12 binary64) x))
(* 1/12 (* eps x))
(.f64 eps (.f64 #s(literal 1/12 binary64) x))
(* 1/12 (* eps x))
(.f64 eps (.f64 #s(literal 1/12 binary64) x))
(* 1/12 (* eps x))
(.f64 eps (.f64 #s(literal 1/12 binary64) x))
(* 1/12 (* eps x))
(.f64 eps (.f64 #s(literal 1/12 binary64) x))
(* 1/12 (* eps x))
(.f64 eps (.f64 #s(literal 1/12 binary64) x))
(* 1/12 (* eps x))
(.f64 eps (.f64 #s(literal 1/12 binary64) x))
(* 1/12 (* eps x))
(.f64 eps (.f64 #s(literal 1/12 binary64) x))
(* 1/12 (* eps x))
(.f64 eps (.f64 #s(literal 1/12 binary64) x))
(* 1/12 (* eps x))
(.f64 eps (.f64 #s(literal 1/12 binary64) x))
(* 1/12 (* eps x))
(.f64 eps (.f64 #s(literal 1/12 binary64) x))
(* 1/12 (* eps x))
(.f64 eps (.f64 #s(literal 1/12 binary64) x))
(* 1/12 (* eps x))
(.f64 eps (.f64 #s(literal 1/12 binary64) x))
(* 1/12 (* eps x))
(.f64 eps (.f64 #s(literal 1/12 binary64) x))
(* 1/12 (* eps x))
(.f64 eps (.f64 #s(literal 1/12 binary64) x))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* x (- (* 1/12 (* eps x)) 1/2))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 #s(literal 1/12 binary64) x))))
(* x (- (* 1/12 (* eps x)) 1/2))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 #s(literal 1/12 binary64) x))))
(* x (- (* 1/12 (* eps x)) 1/2))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 #s(literal 1/12 binary64) x))))
(* 1/12 (* eps (pow x 2)))
(.f64 eps (.f64 (*.f64 x x) #s(literal 1/12 binary64)))
(* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x)))
(* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x)))
(* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x)))
(* 1/12 (* eps (pow x 2)))
(.f64 eps (.f64 (*.f64 x x) #s(literal 1/12 binary64)))
(* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x)))
(* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x)))
(* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x)))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(+ (* -1/2 x) (* 1/12 (* eps (pow x 2))))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 #s(literal 1/12 binary64) x))))
(+ (* -1/2 x) (* 1/12 (* eps (pow x 2))))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 #s(literal 1/12 binary64) x))))
(+ (* -1/2 x) (* 1/12 (* eps (pow x 2))))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 #s(literal 1/12 binary64) x))))
(* 1/12 (* eps (pow x 2)))
(.f64 eps (.f64 (*.f64 x x) #s(literal 1/12 binary64)))
(* eps (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))))
(.f64 eps (+.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) (.f64 x (/.f64 #s(literal -1/2 binary64) eps))))
(* eps (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))))
(.f64 eps (+.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) (.f64 x (/.f64 #s(literal -1/2 binary64) eps))))
(* eps (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))))
(.f64 eps (+.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) (.f64 x (/.f64 #s(literal -1/2 binary64) eps))))
(* 1/12 (* eps (pow x 2)))
(.f64 eps (.f64 (*.f64 x x) #s(literal 1/12 binary64)))
(* -1 (* eps (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))))
(.f64 (-.f64 #s(literal 0 binary64) eps) (+.f64 (.f64 (.f64 x x) #s(literal -1/12 binary64)) (/.f64 (.f64 x #s(literal 1/2 binary64)) eps)))
(* -1 (* eps (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))))
(.f64 (-.f64 #s(literal 0 binary64) eps) (+.f64 (.f64 (.f64 x x) #s(literal -1/12 binary64)) (/.f64 (.f64 x #s(literal 1/2 binary64)) eps)))
(* -1 (* eps (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))))
(.f64 (-.f64 #s(literal 0 binary64) eps) (+.f64 (.f64 (.f64 x x) #s(literal -1/12 binary64)) (/.f64 (.f64 x #s(literal 1/2 binary64)) eps)))
(* -1/48 (pow eps 2))
(.f64 #s(literal -1/48 binary64) (.f64 eps eps))
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64)))))
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64)))))
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64)))))
(* 1/3840 (pow eps 4))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/3840 binary64))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (.f64 eps eps))))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (.f64 eps eps))))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (.f64 eps eps))))
(* 1/3840 (pow eps 4))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/3840 binary64))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (.f64 eps eps))))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (.f64 eps eps))))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (.f64 eps eps))))
(* 1/3840 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3840 binary64))

eval134.0ms (0.9%)

Compiler: Compiled 30931 to 2744 computations (91.1% saved)

prune108.0ms (0.8%)

Pruning

27 alts after pruning (21 fresh and 6 done)

	Pruned	Kept	Total
New	847	10	857
Fresh	4	11	15
Picked	1	4	5
Done	0	2	2
Total	852	27	879

Accuracy

100.0%

Counts

879 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	57.4%	(/.f64 (.f64 (+.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 (sin.f64 x) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64))))))) (*.f64 eps eps)) eps)
	99.1%	(+.f64 (.f64 (.f64 eps (sin.f64 x)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (cos.f64 x)))
	99.5%	(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
	97.0%	(+.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
	99.7%	(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps #s(literal 1/3840 binary64))))))) (.f64 eps (.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))))
▶	99.8%	(.f64 (.f64 (/.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))))))))) eps) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))))) (-.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))))) #s(literal 1/2 binary64))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
✓	99.8%	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
	99.6%	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64)))))) (+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (+.f64 (.f64 (.f64 eps (sin.f64 x)) #s(literal 1/48 binary64)) (*.f64 (cos.f64 x) #s(literal -1/8 binary64)))))))) #s(literal 2 binary64))
✓	99.7%	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64)))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
	99.5%	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
	99.1%	(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
	96.8%	(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))
✓	99.5%	(.f64 eps (+.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
	51.5%	(.f64 eps (+.f64 (.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))) (cos.f64 x)) (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
▶	99.4%	(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))) (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
▶	98.2%	(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
✓	99.1%	(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
	97.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x)))))
	97.1%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64))))))))
	97.1%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))))
	96.7%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps (.f64 (*.f64 x x) #s(literal 1/12 binary64))) x)))
	96.9%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
	97.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
▶	96.8%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
▶	5.1%	(.f64 eps (.f64 (.f64 x (.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x))))
✓	98.5%	(*.f64 eps (cos.f64 x))
✓	96.9%	eps

Compiler

Compiled 1121 to 663 computations (40.9% saved)

simplify284.0ms (2%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 eps (sin.f64 x))
✓	cost-diff	0	(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
✓	cost-diff	0	(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))) (.f64 (+.f64 (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))
✓	cost-diff	0	(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))) (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
✓	cost-diff	0	(.f64 eps (.f64 x #s(literal -1/2 binary64)))
✓	cost-diff	0	(cos.f64 x)
✓	cost-diff	0	(+.f64 (cos.f64 x) (.f64 eps (.f64 x #s(literal -1/2 binary64))))
✓	cost-diff	0	(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 x (.f64 x x))
✓	cost-diff	128	(.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x)))
✓	cost-diff	128	(.f64 eps (.f64 (.f64 x (.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x))))
✓	cost-diff	0	(*.f64 eps #s(literal -1/2 binary64))
✓	cost-diff	0	(.f64 x (.f64 eps #s(literal -1/2 binary64)))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 x (.f64 eps #s(literal -1/2 binary64))))
✓	cost-diff	0	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
✓	cost-diff	0	(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))))) eps)
✓	cost-diff	0	(/.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))))))))) eps) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))))) (-.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))))) #s(literal 1/2 binary64)))))
✓	cost-diff	0	(.f64 (/.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))))))))) eps) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))))) (-.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))))) #s(literal 1/2 binary64))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
✓	cost-diff	0	(.f64 (.f64 (/.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))))))))) eps) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))))) (-.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))))) #s(literal 1/2 binary64))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))

Rules

4610×	`-lowering-.f32`
4610×	`-lowering-.f64`
3590×	`+-lowering-+.f64`
3590×	`+-lowering-+.f32`
1280×	`sum5-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	61	729
1	187	637
2	670	637
3	3385	637
4	5937	635
5	6744	635
0	8189	635

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (* (/ (* (+ 1/8 (* (* eps (* eps eps)) (* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))))) eps) (+ 1/4 (* (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) (- (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) 1/2)))) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (/ (* (+ 1/8 (* (* eps (* eps eps)) (* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))))) eps) (+ 1/4 (* (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) (- (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) 1/2)))) (cos (/ (+ eps (* x 2)) 2)))
(/ (* (+ 1/8 (* (* eps (* eps eps)) (* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))))) eps) (+ 1/4 (* (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) (- (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) 1/2))))
(* (+ 1/8 (* (* eps (* eps eps)) (* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))))) eps)
(+ 1/8 (* (* eps (* eps eps)) (* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))))))
1/8
(* (* eps (* eps eps)) (* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))))
(* eps (* eps eps))
eps
(* eps eps)
(* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))))
(* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))
(+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))
-1/48
(* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))
(+ 1/3840 (* (* eps eps) -1/645120))
1/3840
(* (* eps eps) -1/645120)
-1/645120
(* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))
(+ 1/4 (* (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) (- (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) 1/2)))
1/4
(* (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) (- (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) 1/2))
(* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))
(* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))
(- (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) 1/2)
1/2
(cos (/ (+ eps (* x 2)) 2))
(/ (+ eps (* x 2)) 2)
(+ eps (* x 2))
(* x 2)
x
2
(* eps (+ 1 (* x (* eps -1/2))))
eps
(+ 1 (* x (* eps -1/2)))
1
(* x (* eps -1/2))
x
(* eps -1/2)
-1/2
(* eps (* (* x (* x x)) (+ (* eps 1/12) (/ -1/2 x))))
eps
(* (* x (* x x)) (+ (* eps 1/12) (/ -1/2 x)))
(* x (* x x))
x
(* x x)
(+ (* eps 1/12) (/ -1/2 x))
(* eps 1/12)
1/12
(/ -1/2 x)
-1/2
(* eps (+ (cos x) (* eps (* x -1/2))))
eps
(+ (cos x) (* eps (* x -1/2)))
(cos x)
x
(* eps (* x -1/2))
(* x -1/2)
-1/2
(* eps (+ (* -1/2 (* eps (sin x))) (* (+ (* (* eps eps) -1/6) 1) (cos x))))
eps
(+ (* -1/2 (* eps (sin x))) (* (+ (* (* eps eps) -1/6) 1) (cos x)))
(* -1/2 (* eps (sin x)))
-1/2
(* eps (sin x))
(sin x)
x
(* (+ (* (* eps eps) -1/6) 1) (cos x))
(+ (* (* eps eps) -1/6) 1)
(* (* eps eps) -1/6)
(* eps eps)
-1/6
1
(cos x)

Outputs
(* (* (/ (* (+ 1/8 (* (* eps (* eps eps)) (* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))))) eps) (+ 1/4 (* (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) (- (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) 1/2)))) (cos (/ (+ eps (* x 2)) 2))) 2)
(/.f64 (.f64 #s(literal 2 binary64) (.f64 eps (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))))) (.f64 eps (.f64 eps (.f64 eps (.f64 eps (.f64 eps eps))))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))) (+.f64 #s(literal 1/4 binary64) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (.f64 (.f64 eps eps) (+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (*.f64 eps #s(literal -1/645120 binary64)))))))) #s(literal -1/2 binary64))))))
(* (/ (* (+ 1/8 (* (* eps (* eps eps)) (* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))))) eps) (+ 1/4 (* (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) (- (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) 1/2)))) (cos (/ (+ eps (* x 2)) 2)))
(/.f64 (.f64 eps (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))))) (.f64 eps (.f64 eps (.f64 eps (.f64 eps (.f64 eps eps))))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (.f64 (.f64 eps eps) (+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))))) #s(literal -1/2 binary64))))))
(/ (* (+ 1/8 (* (* eps (* eps eps)) (* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))))) eps) (+ 1/4 (* (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) (- (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) 1/2))))
(/.f64 (.f64 eps (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))))) (.f64 eps (.f64 eps (.f64 eps (.f64 eps (.f64 eps eps)))))))) (+.f64 #s(literal 1/4 binary64) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (.f64 (.f64 eps eps) (+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))))) #s(literal -1/2 binary64))))))
(* (+ 1/8 (* (* eps (* eps eps)) (* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))))) eps)
(.f64 eps (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))))) (.f64 eps (.f64 eps (.f64 eps (.f64 eps (*.f64 eps eps))))))))
(+ 1/8 (* (* eps (* eps eps)) (* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))))))
(+.f64 #s(literal 1/8 binary64) (.f64 (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))))) (.f64 eps (.f64 eps (.f64 eps (.f64 eps (.f64 eps eps)))))))
1/8
#s(literal 1/8 binary64)
(* (* eps (* eps eps)) (* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))))
(.f64 (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))))) (.f64 eps (.f64 eps (.f64 eps (.f64 eps (.f64 eps eps))))))
(* eps (* eps eps))
(.f64 eps (.f64 eps eps))
eps
(* eps eps)
(*.f64 eps eps)
(* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))))
(.f64 (.f64 eps (.f64 eps eps)) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (*.f64 eps #s(literal -1/645120 binary64)))))))))
(* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))
(.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64))))))))
(+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))
(+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64))))))
-1/48
#s(literal -1/48 binary64)
(* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))
(+ 1/3840 (* (* eps eps) -1/645120))
(+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64))))
1/3840
#s(literal 1/3840 binary64)
(* (* eps eps) -1/645120)
(.f64 eps (.f64 eps #s(literal -1/645120 binary64)))
-1/645120
#s(literal -1/645120 binary64)
(* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))
(.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (*.f64 eps #s(literal -1/645120 binary64)))))))
(+ 1/4 (* (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) (- (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) 1/2)))
(+.f64 #s(literal 1/4 binary64) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (.f64 (.f64 eps eps) (+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (*.f64 eps #s(literal -1/645120 binary64)))))))) #s(literal -1/2 binary64)))))
1/4
#s(literal 1/4 binary64)
(* (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) (- (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) 1/2))
(.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (.f64 (.f64 eps eps) (+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (*.f64 eps #s(literal -1/645120 binary64)))))))) #s(literal -1/2 binary64))))
(* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64))))))))
(* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))
(.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (*.f64 eps #s(literal -1/645120 binary64)))))))
(- (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) 1/2)
(+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))))) #s(literal -1/2 binary64))
1/2
#s(literal 1/2 binary64)
(cos (/ (+ eps (* x 2)) 2))
(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
(/ (+ eps (* x 2)) 2)
(/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
(+ eps (* x 2))
(+.f64 eps (*.f64 x #s(literal 2 binary64)))
(* x 2)
(*.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)
(* eps (+ 1 (* x (* eps -1/2))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
eps
(+ 1 (* x (* eps -1/2)))
(+.f64 #s(literal 1 binary64) (.f64 eps (.f64 x #s(literal -1/2 binary64))))
1
#s(literal 1 binary64)
(* x (* eps -1/2))
(.f64 eps (.f64 x #s(literal -1/2 binary64)))
x
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(* eps (* (* x (* x x)) (+ (* eps 1/12) (/ -1/2 x))))
(.f64 x (.f64 x (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/12 binary64) (*.f64 eps x))) eps)))
eps
(* (* x (* x x)) (+ (* eps 1/12) (/ -1/2 x)))
(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/12 binary64) (.f64 eps x))))
(* x (* x x))
(.f64 x (.f64 x x))
x
(* x x)
(*.f64 x x)
(+ (* eps 1/12) (/ -1/2 x))
(+.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x))
(* eps 1/12)
(*.f64 eps #s(literal 1/12 binary64))
1/12
#s(literal 1/12 binary64)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
-1/2
#s(literal -1/2 binary64)
(* eps (+ (cos x) (* eps (* x -1/2))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
eps
(+ (cos x) (* eps (* x -1/2)))
(+.f64 (cos.f64 x) (.f64 eps (.f64 x #s(literal -1/2 binary64))))
(cos x)
(cos.f64 x)
x
(* eps (* x -1/2))
(.f64 eps (.f64 x #s(literal -1/2 binary64)))
(* x -1/2)
(*.f64 x #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(* eps (+ (* -1/2 (* eps (sin x))) (* (+ (* (* eps eps) -1/6) 1) (cos x))))
(.f64 eps (+.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))))
eps
(+ (* -1/2 (* eps (sin x))) (* (+ (* (* eps eps) -1/6) 1) (cos x)))
(+.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))))
(* -1/2 (* eps (sin x)))
(.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x))
-1/2
#s(literal -1/2 binary64)
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(sin x)
(sin.f64 x)
x
(* (+ (* (* eps eps) -1/6) 1) (cos x))
(.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(+ (* (* eps eps) -1/6) 1)
(+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))
(* (* eps eps) -1/6)
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* eps eps)
(*.f64 eps eps)
-1/6
#s(literal -1/6 binary64)
1
#s(literal 1 binary64)
(cos x)
(cos.f64 x)

localize326.0ms (2.3%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (+.f64 (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))
✓	accuracy	100.0%	(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))) (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
✓	accuracy	100.0%	(*.f64 eps (sin.f64 x))
✓	accuracy	99.7%	(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
✓	accuracy	100.0%	(.f64 eps (.f64 x #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
✓	accuracy	100.0%	(+.f64 (cos.f64 x) (.f64 eps (.f64 x #s(literal -1/2 binary64))))
✓	accuracy	99.9%	(.f64 eps (.f64 (.f64 x (.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x))))
✓	accuracy	99.8%	(.f64 x (.f64 x x))
✓	accuracy	99.5%	(*.f64 eps #s(literal 1/12 binary64))
✓	accuracy	84.1%	(.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x)))
✓	accuracy	100.0%	(.f64 x (.f64 eps #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(*.f64 eps #s(literal -1/2 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (.f64 x (.f64 eps #s(literal -1/2 binary64))))
✓	accuracy	100.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
✓	accuracy	99.8%	(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
✓	accuracy	99.8%	(.f64 (.f64 eps (.f64 eps eps)) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))
✓	accuracy	99.8%	(.f64 (.f64 eps eps) #s(literal -1/645120 binary64))
✓	accuracy	99.5%	(.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))

Results

211.0ms	255×	0	valid
3.0ms	1×	5	exit

Compiler

Compiled 989 to 62 computations (93.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 141.0ms

ival-mult: 86.0ms (60.9% of total)

...c/correct-round.rkt:119:19: 20.0ms (14.2% of total)

ival-add: 20.0ms (14.2% of total)

ival-div: 5.0ms (3.5% of total)

ival-cos: 5.0ms (3.5% of total)

ival-sin: 2.0ms (1.4% of total)

backward-pass: 1.0ms (0.7% of total)

ival-sub: 1.0ms (0.7% of total)

const: 1.0ms (0.7% of total)

series58.0ms (0.4%)

Counts

27 → 516

Calls

Call 1

Inputs
#<alt (* (* (/ (* (+ 1/8 (* (* eps (* eps eps)) (* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))))) eps) (+ 1/4 (* (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) (- (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) 1/2)))) (cos (/ (+ eps (* x 2)) 2))) 2)>
#<alt (* (/ (* (+ 1/8 (* (* eps (* eps eps)) (* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))))) eps) (+ 1/4 (* (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) (- (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) 1/2)))) (cos (/ (+ eps (* x 2)) 2)))>
#<alt (/ (* (+ 1/8 (* (* eps (* eps eps)) (* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))))) eps) (+ 1/4 (* (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) (- (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) 1/2))))>
#<alt (* (+ 1/8 (* (* eps (* eps eps)) (* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))))) eps)>
#<alt (* eps (+ 1 (* x (* eps -1/2))))>
#<alt (+ 1 (* x (* eps -1/2)))>
#<alt (* x (* eps -1/2))>
#<alt (* eps -1/2)>
#<alt (* eps (* (* x (* x x)) (+ (* eps 1/12) (/ -1/2 x))))>
#<alt (* (* x (* x x)) (+ (* eps 1/12) (/ -1/2 x)))>
#<alt (* x (* x x))>
#<alt (* x x)>
#<alt (* eps (+ (cos x) (* eps (* x -1/2))))>
#<alt (+ (cos x) (* eps (* x -1/2)))>
#<alt (cos x)>
#<alt (* eps (* x -1/2))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (+ (* (* eps eps) -1/6) 1) (cos x))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (+ (* (* eps eps) -1/6) 1) (cos x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* eps (sin x))>
#<alt (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))>
#<alt (* (* eps eps) -1/645120)>
#<alt (* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))))>
#<alt (cos (/ (+ eps (* x 2)) 2))>
#<alt (* eps 1/12)>
#<alt (* (* eps eps) -1/6)>
#<alt (* (+ (* (* eps eps) -1/6) 1) (cos x))>

Outputs
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (- (* -1/16 (cos x)) (* 1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 2 (* eps (- (* 1/96 (sin x)) (* -1/96 (sin x))))) (* 2 (- (* -1/16 (cos x)) (* 1/48 (cos x))))))))))>
#<alt (* -1/322560 (* (pow eps 7) (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* (pow eps 7) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (* 2 (/ (- (* 1/1280 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x)))))) (pow eps 2)))))>
#<alt (* (pow eps 7) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* 2 (/ (- (* -31/160 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* -336 (- (* 1/1280 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))))) (* -41/480 (cos (* 1/2 (+ eps (* 2 x))))))) (pow eps 4))) (* 2 (/ (- (* 1/1280 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x)))))) (pow eps 2))))))>
#<alt (* (pow eps 7) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* 2 (/ (- (* -31/160 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* -336 (- (* 1/1280 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))))) (* -41/480 (cos (* 1/2 (+ eps (* 2 x))))))) (pow eps 4))) (+ (* 2 (/ (- (* 1/1280 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x)))))) (pow eps 2))) (* 2 (/ (- (* 567/20 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* -336 (- (* -31/160 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* -336 (- (* 1/1280 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))))) (* -41/480 (cos (* 1/2 (+ eps (* 2 x)))))))) (+ (* 13/2 (cos (* 1/2 (+ eps (* 2 x))))) (* 55104 (- (* 1/1280 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x)))))))))) (pow eps 6)))))))>
#<alt (* -1/322560 (* (pow eps 7) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -1 (* (pow eps 7) (+ (* -2 (/ (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) (pow eps 2))) (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))>
#<alt (* -1 (* (pow eps 7) (+ (* -2 (/ (- (* -31/160 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (+ (* -336 (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))) (* -41/480 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))) (pow eps 4))) (+ (* -2 (/ (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) (pow eps 2))) (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))))>
#<alt (* -1 (* (pow eps 7) (+ (* -2 (/ (- (* -31/160 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (+ (* -336 (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))) (* -41/480 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))) (pow eps 4))) (+ (* -2 (/ (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) (pow eps 2))) (+ (* -2 (/ (- (* 567/20 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (+ (* -336 (- (* -31/160 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (+ (* -336 (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))) (* -41/480 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))) (+ (* 13/2 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 55104 (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))))) (pow eps 6))) (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))))>
#<alt (* 2 (/ (* eps (* (cos (* 1/2 eps)) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2))))))>
#<alt (+ (* -2 (/ (* eps (* x (* (sin (* 1/2 eps)) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3)))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2)))))) (* 2 (/ (* eps (* (cos (* 1/2 eps)) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2)))))))>
#<alt (+ (* 2 (/ (* eps (* (cos (* 1/2 eps)) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2)))))) (* x (+ (* -2 (/ (* eps (* (sin (* 1/2 eps)) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2)))))) (* -1 (/ (* eps (* x (* (cos (* 1/2 eps)) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3)))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2)))))))))>
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#<alt (* 1/2 eps)>
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#<alt (* 1/8 eps)>
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#<alt eps>
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#<alt eps>
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#<alt (* (pow eps 3) (- (* 1/2949120 (pow eps 2)) 1/110592))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (+ 1/2949120 (* -31/4954521600 (pow eps 2)))) 1/110592))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (+ 1/2949120 (* (pow eps 2) (- (* 1/14680064000 (pow eps 2)) 31/4954521600)))) 1/110592))>
#<alt (* -1/268485921865728000 (pow eps 15))>
#<alt (* (pow eps 15) (- (* 1/532710162432000 (/ 1 (pow eps 2))) 1/268485921865728000))>
#<alt (* (pow eps 15) (- (* 1/532710162432000 (/ 1 (pow eps 2))) (+ 1/268485921865728000 (/ 31/66588770304000 (pow eps 4)))))>
#<alt (* (pow eps 15) (- (+ (* 1/532710162432000 (/ 1 (pow eps 2))) (* 1/14680064000 (/ 1 (pow eps 6)))) (+ 1/268485921865728000 (/ 31/66588770304000 (pow eps 4)))))>
#<alt (* -1/268485921865728000 (pow eps 15))>
#<alt (* -1 (* (pow eps 15) (- 1/268485921865728000 (* 1/532710162432000 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 15) (- (+ 1/268485921865728000 (/ 31/66588770304000 (pow eps 4))) (* 1/532710162432000 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 15) (- (+ 1/268485921865728000 (/ 31/66588770304000 (pow eps 4))) (+ (* 1/532710162432000 (/ 1 (pow eps 2))) (* 1/14680064000 (/ 1 (pow eps 6)))))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (* 1/12 eps)>
#<alt (* 1/12 eps)>
#<alt (* 1/12 eps)>
#<alt (* 1/12 eps)>
#<alt (* 1/12 eps)>
#<alt (* 1/12 eps)>
#<alt (* 1/12 eps)>
#<alt (* 1/12 eps)>
#<alt (* 1/12 eps)>
#<alt (* 1/12 eps)>
#<alt (* 1/12 eps)>
#<alt (* 1/12 eps)>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))>
#<alt (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))>
#<alt (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))>
#<alt (* -1/6 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* -1/6 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (+ (* -1/2 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (pow eps 2))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/24 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* 1/24 (+ 1 (* -1/6 (pow eps 2))))))))))>
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))>

Calls

129 calls:

Time	Variable		Point	Expression
12.0ms	eps	@	0	(* eps (* (* x (* x x)) (+ (* eps 1/12) (/ -1/2 x))))
4.0ms	x	@	inf	(* (* (/ (* (+ 1/8 (* (* eps (* eps eps)) (* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))))) eps) (+ 1/4 (* (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) (- (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) 1/2)))) (cos (/ (+ eps (* x 2)) 2))) 2)
4.0ms	x	@	0	(* (* (/ (* (+ 1/8 (* (* eps (* eps eps)) (* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))))) eps) (+ 1/4 (* (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) (- (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) 1/2)))) (cos (/ (+ eps (* x 2)) 2))) 2)
2.0ms	eps	@	inf	(* (* (/ (* (+ 1/8 (* (* eps (* eps eps)) (* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))))) eps) (+ 1/4 (* (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) (- (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) 1/2)))) (cos (/ (+ eps (* x 2)) 2))) 2)
2.0ms	eps	@	-inf	(* (* (/ (* (+ 1/8 (* (* eps (* eps eps)) (* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))))) eps) (+ 1/4 (* (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) (- (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) 1/2)))) (cos (/ (+ eps (* x 2)) 2))) 2)

rewrite390.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

4046×	`-lowering-.f32`
4046×	`-lowering-.f64`
2486×	`/-lowering-/.f32`
2486×	`/-lowering-/.f64`
1722×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	61	428
1	347	372
2	3173	372
0	8343	372

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 386

Calls

Call 1

Inputs
(* (* (/ (* (+ 1/8 (* (* eps (* eps eps)) (* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))))) eps) (+ 1/4 (* (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) (- (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) 1/2)))) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (/ (* (+ 1/8 (* (* eps (* eps eps)) (* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))))) eps) (+ 1/4 (* (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) (- (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) 1/2)))) (cos (/ (+ eps (* x 2)) 2)))
(/ (* (+ 1/8 (* (* eps (* eps eps)) (* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))))) eps) (+ 1/4 (* (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) (- (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) 1/2))))
(* (+ 1/8 (* (* eps (* eps eps)) (* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))))) eps)
(* eps (+ 1 (* x (* eps -1/2))))
(+ 1 (* x (* eps -1/2)))
(* x (* eps -1/2))
(* eps -1/2)
(* eps (* (* x (* x x)) (+ (* eps 1/12) (/ -1/2 x))))
(* (* x (* x x)) (+ (* eps 1/12) (/ -1/2 x)))
(* x (* x x))
(* x x)
(* eps (+ (cos x) (* eps (* x -1/2))))
(+ (cos x) (* eps (* x -1/2)))
(cos x)
(* eps (* x -1/2))
(* eps (+ (* -1/2 (* eps (sin x))) (* (+ (* (* eps eps) -1/6) 1) (cos x))))
(+ (* -1/2 (* eps (sin x))) (* (+ (* (* eps eps) -1/6) 1) (cos x)))
(* -1/2 (* eps (sin x)))
(* eps (sin x))
(* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))
(* (* eps eps) -1/645120)
(* (* eps (* eps eps)) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (* (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))))
(cos (/ (+ eps (* x 2)) 2))
(* eps 1/12)
(* (* eps eps) -1/6)
(* (+ (* (* eps eps) -1/6) 1) (cos x))

Outputs
(/.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 eps (.f64 eps (.f64 eps (.f64 (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64))))))) (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64))))))))))))) (.f64 eps (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps eps) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))) #s(literal -1/2 binary64))))))
(/.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/8 binary64) (.f64 eps (.f64 eps (.f64 eps (.f64 (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64))))))) (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))))))))))) (.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps eps) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))) #s(literal -1/2 binary64))))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))) (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps eps) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64))))))) #s(literal -1/2 binary64))))) (.f64 eps (+.f64 #s(literal 1/8 binary64) (.f64 eps (.f64 eps (.f64 eps (.f64 (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64))))))) (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))))))))))
(/.f64 (.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 eps (.f64 eps (.f64 eps (.f64 (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64))))))) (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64))))))))))))) (neg.f64 eps)) (.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))) (+.f64 (neg.f64 (.f64 (.f64 eps eps) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))) #s(literal -1/2 binary64))))) #s(literal -1/4 binary64)))
(/.f64 (.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 eps (.f64 eps (.f64 eps (.f64 (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64))))))) (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64))))))))))))) (.f64 eps (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))) #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps eps) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64)))))) (+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))) #s(literal -1/2 binary64))))))
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(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal -2 binary64)))
(*.f64 eps #s(literal 1/12 binary64))
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(.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) (cos.f64 x))

simplify371.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

6668×	`-lowering-.f32`
6668×	`-lowering-.f64`
3570×	`+-lowering-+.f64`
3570×	`+-lowering-+.f32`
1760×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	683	7865
1	2423	7086
0	8670	7086

Stop Event

1×	iter limit
1×	node limit

Counts

516 → 516

Calls

Call 1

Inputs
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (- (* -1/16 (cos x)) (* 1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 2 (* eps (- (* 1/96 (sin x)) (* -1/96 (sin x))))) (* 2 (- (* -1/16 (cos x)) (* 1/48 (cos x))))))))))
(* -1/322560 (* (pow eps 7) (cos (* 1/2 (+ eps (* 2 x))))))
(* (pow eps 7) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (* 2 (/ (- (* 1/1280 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x)))))) (pow eps 2)))))
(* (pow eps 7) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* 2 (/ (- (* -31/160 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* -336 (- (* 1/1280 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))))) (* -41/480 (cos (* 1/2 (+ eps (* 2 x))))))) (pow eps 4))) (* 2 (/ (- (* 1/1280 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x)))))) (pow eps 2))))))
(* (pow eps 7) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* 2 (/ (- (* -31/160 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* -336 (- (* 1/1280 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))))) (* -41/480 (cos (* 1/2 (+ eps (* 2 x))))))) (pow eps 4))) (+ (* 2 (/ (- (* 1/1280 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x)))))) (pow eps 2))) (* 2 (/ (- (* 567/20 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* -336 (- (* -31/160 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* -336 (- (* 1/1280 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))))) (* -41/480 (cos (* 1/2 (+ eps (* 2 x)))))))) (+ (* 13/2 (cos (* 1/2 (+ eps (* 2 x))))) (* 55104 (- (* 1/1280 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x)))))))))) (pow eps 6)))))))
(* -1/322560 (* (pow eps 7) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* (pow eps 7) (+ (* -2 (/ (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) (pow eps 2))) (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))
(* -1 (* (pow eps 7) (+ (* -2 (/ (- (* -31/160 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (+ (* -336 (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))) (* -41/480 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))) (pow eps 4))) (+ (* -2 (/ (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) (pow eps 2))) (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))))
(* -1 (* (pow eps 7) (+ (* -2 (/ (- (* -31/160 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (+ (* -336 (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))) (* -41/480 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))) (pow eps 4))) (+ (* -2 (/ (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) (pow eps 2))) (+ (* -2 (/ (- (* 567/20 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (+ (* -336 (- (* -31/160 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (+ (* -336 (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))) (* -41/480 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))) (+ (* 13/2 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 55104 (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))))) (pow eps 6))) (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))))
(* 2 (/ (* eps (* (cos (* 1/2 eps)) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2))))))
(+ (* -2 (/ (* eps (* x (* (sin (* 1/2 eps)) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3)))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2)))))) (* 2 (/ (* eps (* (cos (* 1/2 eps)) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2)))))))
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(* 2 (/ (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2))))))
(* 2 (/ (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2))))))
(* 2 (/ (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2))))))
(* 2 (/ (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2))))))
(* 2 (/ (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2))))))
(* 2 (/ (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2))))))
(* 2 (/ (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2))))))
(* 2 (/ (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2))))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (- (* -1/16 (cos x)) (* 1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (- (+ (* -1/16 (cos x)) (* eps (- (* 1/96 (sin x)) (* -1/96 (sin x))))) (* 1/48 (cos x))))))))
(* -1/645120 (* (pow eps 7) (cos (* 1/2 (+ eps (* 2 x))))))
(* (pow eps 7) (- (+ (* -1/645120 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1280 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))) (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))
(* (pow eps 7) (- (+ (* -31/160 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/645120 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1280 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))) (+ (* -336 (/ (- (* 1/1280 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x)))))) (pow eps 4))) (+ (* -41/480 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))))
(* (pow eps 7) (- (+ (* -31/160 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/645120 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* 1/1280 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 567/20 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 6)))))) (+ (* -336 (/ (- (* -31/160 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* -336 (- (* 1/1280 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))))) (* -41/480 (cos (* 1/2 (+ eps (* 2 x))))))) (pow eps 6))) (+ (* -336 (/ (- (* 1/1280 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x)))))) (pow eps 4))) (+ (* -41/480 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 13/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 6))) (* 55104 (/ (- (* 1/1280 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x)))))) (pow eps 6))))))))))
(* -1/645120 (* (pow eps 7) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* (pow eps 7) (+ (* -1 (/ (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) (pow eps 2))) (* 1/645120 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))
(* -1 (* (pow eps 7) (+ (* -1 (/ (- (* -31/160 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (+ (* -336 (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))) (* -41/480 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))) (pow eps 4))) (+ (* -1 (/ (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) (pow eps 2))) (* 1/645120 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))))
(* -1 (* (pow eps 7) (+ (* -1 (/ (- (* -31/160 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (+ (* -336 (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))) (* -41/480 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))) (pow eps 4))) (+ (* -1 (/ (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) (pow eps 2))) (+ (* -1 (/ (- (* 567/20 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (+ (* -336 (- (* -31/160 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (+ (* -336 (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))) (* -41/480 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))) (+ (* 13/2 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 55104 (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))))) (pow eps 6))) (* 1/645120 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))))
(/ (* eps (* (cos (* 1/2 eps)) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2)))))
(+ (* -1 (/ (* eps (* x (* (sin (* 1/2 eps)) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3)))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2)))))) (/ (* eps (* (cos (* 1/2 eps)) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2))))))
(+ (* x (+ (* -1 (/ (* eps (* (sin (* 1/2 eps)) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2)))))) (* -1/2 (/ (* eps (* x (* (cos (* 1/2 eps)) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3)))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2)))))))) (/ (* eps (* (cos (* 1/2 eps)) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2))))))
(+ (* x (+ (* -1 (/ (* eps (* (sin (* 1/2 eps)) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2)))))) (* x (+ (* -1/2 (/ (* eps (* (cos (* 1/2 eps)) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2)))))) (* 1/6 (/ (* eps (* x (* (sin (* 1/2 eps)) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3)))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2)))))))))) (/ (* eps (* (cos (* 1/2 eps)) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2))))))
(/ (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2)))))
(/ (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2)))))
(/ (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2)))))
(/ (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2)))))
(/ (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2)))))
(/ (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2)))))
(/ (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2)))))
(/ (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2)))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* -1/645120 (pow eps 7))
(* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 7) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* -1/645120 (pow eps 7))
(* -1 (* (pow eps 7) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))))))
(* 1/8 eps)
(* eps (+ 1/8 (* -1/110592 (pow eps 6))))
(* eps (+ 1/8 (* (pow eps 6) (- (* 1/2949120 (pow eps 2)) 1/110592))))
(* eps (+ 1/8 (* (pow eps 6) (- (* (pow eps 2) (+ 1/2949120 (* -31/4954521600 (pow eps 2)))) 1/110592))))
(* -1/268485921865728000 (pow eps 19))
(* (pow eps 19) (- (* 1/532710162432000 (/ 1 (pow eps 2))) 1/268485921865728000))
(* (pow eps 19) (- (* 1/532710162432000 (/ 1 (pow eps 2))) (+ 1/268485921865728000 (/ 31/66588770304000 (pow eps 4)))))
(* (pow eps 19) (- (+ (* 1/532710162432000 (/ 1 (pow eps 2))) (* 1/14680064000 (/ 1 (pow eps 6)))) (+ 1/268485921865728000 (/ 31/66588770304000 (pow eps 4)))))
(* -1/268485921865728000 (pow eps 19))
(* -1 (* (pow eps 19) (- 1/268485921865728000 (* 1/532710162432000 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 19) (- (+ 1/268485921865728000 (/ 31/66588770304000 (pow eps 4))) (* 1/532710162432000 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 19) (- (+ 1/268485921865728000 (/ 31/66588770304000 (pow eps 4))) (+ (* 1/532710162432000 (/ 1 (pow eps 2))) (* 1/14680064000 (/ 1 (pow eps 6)))))))
eps
(* eps (+ 1 (* -1/2 (* eps x))))
(* eps (+ 1 (* -1/2 (* eps x))))
(* eps (+ 1 (* -1/2 (* eps x))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* -1/2 (* (pow eps 2) x)))
(* -1/2 (* (pow eps 2) x))
(* x (+ (* -1/2 (pow eps 2)) (/ eps x)))
(* x (+ (* -1/2 (pow eps 2)) (/ eps x)))
(* x (+ (* -1/2 (pow eps 2)) (/ eps x)))
(* -1/2 (* (pow eps 2) x))
(* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2)))))
(* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2)))))
(* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2)))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* -1/2 (* eps x)))
(* -1/2 (* eps x))
(* x (+ (* -1/2 eps) (/ 1 x)))
(* x (+ (* -1/2 eps) (/ 1 x)))
(* x (+ (* -1/2 eps) (/ 1 x)))
(* -1/2 (* eps x))
(* -1 (* x (- (* 1/2 eps) (/ 1 x))))
(* -1 (* x (- (* 1/2 eps) (/ 1 x))))
(* -1 (* x (- (* 1/2 eps) (/ 1 x))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* -1/2 (* eps x)))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (/ 1 eps)))
(* eps (+ (* -1/2 x) (/ 1 eps)))
(* eps (+ (* -1/2 x) (/ 1 eps)))
(* -1/2 (* eps x))
(* -1 (* eps (- (* 1/2 x) (/ 1 eps))))
(* -1 (* eps (- (* 1/2 x) (/ 1 eps))))
(* -1 (* eps (- (* 1/2 x) (/ 1 eps))))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 (* eps (pow x 2)))
(* eps (+ (* -1/2 (pow x 2)) (* 1/12 (* eps (pow x 3)))))
(* eps (+ (* -1/2 (pow x 2)) (* 1/12 (* eps (pow x 3)))))
(* eps (+ (* -1/2 (pow x 2)) (* 1/12 (* eps (pow x 3)))))
(* 1/12 (* (pow eps 2) (pow x 3)))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (* 1/12 (pow x 3))))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (* 1/12 (pow x 3))))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (* 1/12 (pow x 3))))
(* 1/12 (* (pow eps 2) (pow x 3)))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (* 1/12 (pow x 3))))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (* 1/12 (pow x 3))))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (* 1/12 (pow x 3))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))
(* (pow x 2) (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))
(* (pow x 2) (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))
(* 1/12 (* (pow eps 2) (pow x 3)))
(* (pow x 3) (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))))
(* (pow x 3) (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))))
(* (pow x 3) (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))))
(* 1/12 (* (pow eps 2) (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/12 (pow eps 2)) (* 1/2 (/ eps x)))))
(* -1 (* (pow x 3) (+ (* -1/12 (pow eps 2)) (* 1/2 (/ eps x)))))
(* -1 (* (pow x 3) (+ (* -1/12 (pow eps 2)) (* 1/2 (/ eps x)))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/12 (* eps x)) 1/2))
(* (pow x 2) (- (* 1/12 (* eps x)) 1/2))
(* (pow x 2) (- (* 1/12 (* eps x)) 1/2))
(* 1/12 (* eps (pow x 3)))
(* (pow x 3) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(* (pow x 3) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(* (pow x 3) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(* 1/12 (* eps (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))
(* -1/2 (pow x 2))
(+ (* -1/2 (pow x 2)) (* 1/12 (* eps (pow x 3))))
(+ (* -1/2 (pow x 2)) (* 1/12 (* eps (pow x 3))))
(+ (* -1/2 (pow x 2)) (* 1/12 (* eps (pow x 3))))
(* 1/12 (* eps (pow x 3)))
(* eps (+ (* -1/2 (/ (pow x 2) eps)) (* 1/12 (pow x 3))))
(* eps (+ (* -1/2 (/ (pow x 2) eps)) (* 1/12 (pow x 3))))
(* eps (+ (* -1/2 (/ (pow x 2) eps)) (* 1/12 (pow x 3))))
(* 1/12 (* eps (pow x 3)))
(* -1 (* eps (+ (* -1/12 (pow x 3)) (* 1/2 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* -1/12 (pow x 3)) (* 1/2 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* -1/12 (pow x 3)) (* 1/2 (/ (pow x 2) eps)))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps x))))
(* eps (+ (cos x) (* -1/2 (* eps x))))
(* eps (+ (cos x) (* -1/2 (* eps x))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
(* -1/2 (* (pow eps 2) x))
(* x (+ (* -1/2 (pow eps 2)) (/ (* eps (cos x)) x)))
(* x (+ (* -1/2 (pow eps 2)) (/ (* eps (cos x)) x)))
(* x (+ (* -1/2 (pow eps 2)) (/ (* eps (cos x)) x)))
(* -1/2 (* (pow eps 2) x))
(* -1 (* x (+ (* -1 (/ (* eps (cos x)) x)) (* 1/2 (pow eps 2)))))
(* -1 (* x (+ (* -1 (/ (* eps (cos x)) x)) (* 1/2 (pow eps 2)))))
(* -1 (* x (+ (* -1 (/ (* eps (cos x)) x)) (* 1/2 (pow eps 2)))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/24 (pow x 2)) 1/2)))))
(* -1/2 (* eps x))
(* x (+ (* -1/2 eps) (/ (cos x) x)))
(* x (+ (* -1/2 eps) (/ (cos x) x)))
(* x (+ (* -1/2 eps) (/ (cos x) x)))
(* -1/2 (* eps x))
(* -1 (* x (+ (* -1 (/ (cos x) x)) (* 1/2 eps))))
(* -1 (* x (+ (* -1 (/ (cos x) x)) (* 1/2 eps))))
(* -1 (* x (+ (* -1 (/ (cos x) x)) (* 1/2 eps))))
(cos x)
(+ (cos x) (* -1/2 (* eps x)))
(+ (cos x) (* -1/2 (* eps x)))
(+ (cos x) (* -1/2 (* eps x)))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (/ (cos x) eps)))
(* eps (+ (* -1/2 x) (/ (cos x) eps)))
(* eps (+ (* -1/2 x) (/ (cos x) eps)))
(* -1/2 (* eps x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 x))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 x))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 x))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps x))
(* x (+ (* -1/2 eps) (* 1/12 (* eps (pow x 2)))))
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/240 (* eps (pow x 2))) (* 1/12 eps)))))
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/240 eps) (* 1/10080 (* eps (pow x 2)))))))))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps x)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* -1/48 eps)
(* eps (- (* 1/3840 (pow eps 2)) 1/48))
(* eps (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))
(* eps (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))
(* -1/645120 (pow eps 5))
(* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* -1/645120 (pow eps 5))
(* -1 (* (pow eps 5) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 5) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 5) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/110592 (pow eps 3))
(* (pow eps 3) (- (* 1/2949120 (pow eps 2)) 1/110592))
(* (pow eps 3) (- (* (pow eps 2) (+ 1/2949120 (* -31/4954521600 (pow eps 2)))) 1/110592))
(* (pow eps 3) (- (* (pow eps 2) (+ 1/2949120 (* (pow eps 2) (- (* 1/14680064000 (pow eps 2)) 31/4954521600)))) 1/110592))
(* -1/268485921865728000 (pow eps 15))
(* (pow eps 15) (- (* 1/532710162432000 (/ 1 (pow eps 2))) 1/268485921865728000))
(* (pow eps 15) (- (* 1/532710162432000 (/ 1 (pow eps 2))) (+ 1/268485921865728000 (/ 31/66588770304000 (pow eps 4)))))
(* (pow eps 15) (- (+ (* 1/532710162432000 (/ 1 (pow eps 2))) (* 1/14680064000 (/ 1 (pow eps 6)))) (+ 1/268485921865728000 (/ 31/66588770304000 (pow eps 4)))))
(* -1/268485921865728000 (pow eps 15))
(* -1 (* (pow eps 15) (- 1/268485921865728000 (* 1/532710162432000 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 15) (- (+ 1/268485921865728000 (/ 31/66588770304000 (pow eps 4))) (* 1/532710162432000 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 15) (- (+ 1/268485921865728000 (/ 31/66588770304000 (pow eps 4))) (+ (* 1/532710162432000 (/ 1 (pow eps 2))) (* 1/14680064000 (/ 1 (pow eps 6)))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(cos x)
(+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))
(+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))
(+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/24 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* 1/24 (+ 1 (* -1/6 (pow eps 2))))))))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))

Outputs
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (- (* -1/16 (cos x)) (* 1/48 (cos x)))))))))
(.f64 eps (+.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 2 (* eps (- (* 1/96 (sin x)) (* -1/96 (sin x))))) (* 2 (- (* -1/16 (cos x)) (* 1/48 (cos x))))))))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (.f64 eps #s(literal 2 binary64)) (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/48 binary64))) (.f64 (cos.f64 x) #s(literal -1/12 binary64))))))))
(* -1/322560 (* (pow eps 7) (cos (* 1/2 (+ eps (* 2 x))))))
(.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal -1/322560 binary64) (pow.f64 eps #s(literal 7 binary64))))
(* (pow eps 7) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (* 2 (/ (- (* 1/1280 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x)))))) (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (.f64 #s(literal -1/322560 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal 2 binary64) (/.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 1/3840 binary64)) (*.f64 eps eps)))))
(* (pow eps 7) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* 2 (/ (- (* -31/160 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* -336 (- (* 1/1280 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))))) (* -41/480 (cos (* 1/2 (+ eps (* 2 x))))))) (pow eps 4))) (* 2 (/ (- (* 1/1280 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x)))))) (pow eps 2))))))
(.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (.f64 #s(literal -1/322560 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal 2 binary64) (+.f64 (/.f64 (+.f64 (-.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -31/160 binary64)) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -7/80 binary64))) (.f64 #s(literal 41/480 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))) (pow.f64 eps #s(literal 4 binary64))) (/.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 1/3840 binary64)) (*.f64 eps eps))))))
(* (pow eps 7) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* 2 (/ (- (* -31/160 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* -336 (- (* 1/1280 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))))) (* -41/480 (cos (* 1/2 (+ eps (* 2 x))))))) (pow eps 4))) (+ (* 2 (/ (- (* 1/1280 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x)))))) (pow eps 2))) (* 2 (/ (- (* 567/20 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* -336 (- (* -31/160 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* -336 (- (* 1/1280 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))))) (* -41/480 (cos (* 1/2 (+ eps (* 2 x)))))))) (+ (* 13/2 (cos (* 1/2 (+ eps (* 2 x))))) (* 55104 (- (* 1/1280 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x)))))))))) (pow eps 6)))))))
(.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (.f64 #s(literal -1/322560 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal 2 binary64) (+.f64 (+.f64 (/.f64 (+.f64 (-.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -31/160 binary64)) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -7/80 binary64))) (.f64 #s(literal 41/480 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))) (pow.f64 eps #s(literal 4 binary64))) (/.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 1/3840 binary64)) (.f64 eps eps))) (/.f64 (-.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 567/20 binary64)) (+.f64 (.f64 #s(literal -336 binary64) (+.f64 (-.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -31/160 binary64)) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -7/80 binary64))) (.f64 #s(literal 41/480 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))) (+.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 13/2 binary64)) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 287/20 binary64))))) (pow.f64 eps #s(literal 6 binary64)))))))
(* -1/322560 (* (pow eps 7) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal -1/322560 binary64) (pow.f64 eps #s(literal 7 binary64))))
(* -1 (* (pow eps 7) (+ (* -2 (/ (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) (pow eps 2))) (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))
(-.f64 #s(literal 0 binary64) (.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (/.f64 (.f64 #s(literal -2 binary64) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 1/3840 binary64))) (.f64 eps eps)) (.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 1/322560 binary64)))))
(* -1 (* (pow eps 7) (+ (* -2 (/ (- (* -31/160 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (+ (* -336 (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))) (* -41/480 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))) (pow eps 4))) (+ (* -2 (/ (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) (pow eps 2))) (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))))
(.f64 (+.f64 (.f64 #s(literal -2 binary64) (+.f64 (/.f64 (+.f64 (-.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -31/160 binary64)) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -7/80 binary64))) (.f64 #s(literal 41/480 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))) (pow.f64 eps #s(literal 4 binary64))) (/.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 1/3840 binary64)) (.f64 eps eps)))) (.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 1/322560 binary64))) (neg.f64 (pow.f64 eps #s(literal 7 binary64))))
(* -1 (* (pow eps 7) (+ (* -2 (/ (- (* -31/160 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (+ (* -336 (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))) (* -41/480 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))) (pow eps 4))) (+ (* -2 (/ (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) (pow eps 2))) (+ (* -2 (/ (- (* 567/20 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (+ (* -336 (- (* -31/160 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (+ (* -336 (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))) (* -41/480 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))) (+ (* 13/2 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 55104 (- (* 1/1280 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))))) (pow eps 6))) (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))))
(.f64 (+.f64 (+.f64 (.f64 #s(literal -2 binary64) (+.f64 (/.f64 (+.f64 (-.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -31/160 binary64)) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -7/80 binary64))) (.f64 #s(literal 41/480 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))) (pow.f64 eps #s(literal 4 binary64))) (/.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 1/3840 binary64)) (.f64 eps eps)))) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 1/322560 binary64))) (/.f64 (.f64 (-.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 567/20 binary64)) (+.f64 (.f64 #s(literal -336 binary64) (+.f64 (-.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -31/160 binary64)) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -7/80 binary64))) (.f64 #s(literal 41/480 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))) (+.f64 (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 13/2 binary64)) (.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 287/20 binary64))))) #s(literal -2 binary64)) (pow.f64 eps #s(literal 6 binary64)))) (neg.f64 (pow.f64 eps #s(literal 7 binary64))))
(* 2 (/ (* eps (* (cos (* 1/2 eps)) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2))))))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64)) (+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64))) (.f64 (+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64)) (pow.f64 eps #s(literal 6 binary64))))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) eps))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps eps) (.f64 (+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64)) (+.f64 (.f64 (.f64 eps eps) (+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64))) #s(literal -1/2 binary64))))))
(+ (* -2 (/ (* eps (* x (* (sin (* 1/2 eps)) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3)))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2)))))) (* 2 (/ (* eps (* (cos (* 1/2 eps)) (+ 1/8 (* (pow eps 6) (pow (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) 3))))) (+ 1/4 (* (pow eps 2) (* (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (- (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) 1/2)))))))
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(* 1/2 (* eps (cos x)))
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eps
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eps
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(cos x)
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(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
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(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
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(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
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(cos x)
(cos.f64 x)
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(.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))

eval140.0ms (1%)

Compiler: Compiled 53806 to 2631 computations (95.1% saved)

prune105.0ms (0.7%)

Pruning

30 alts after pruning (21 fresh and 9 done)

	Pruned	Kept	Total
New	1001	8	1009
Fresh	3	13	16
Picked	2	3	5
Done	0	6	6
Total	1006	30	1036

Accuracy

100.0%

Counts

1036 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
	57.4%	(/.f64 (.f64 (+.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 (sin.f64 x) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64))))))) (*.f64 eps eps)) eps)
	99.1%	(+.f64 (.f64 (.f64 eps (sin.f64 x)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (cos.f64 x)))
	99.5%	(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
	97.0%	(+.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
	99.7%	(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps #s(literal 1/3840 binary64))))))) (.f64 eps (.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))))
	99.8%	(.f64 (.f64 (/.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 1/2949120 binary64) (.f64 (.f64 eps eps) #s(literal -31/4954521600 binary64))))) #s(literal -1/110592 binary64)) (.f64 eps (.f64 eps eps))))) eps) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))))) (-.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))))) #s(literal 1/2 binary64))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
✓	99.8%	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
	99.6%	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64)))))) (+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (+.f64 (.f64 (.f64 eps (sin.f64 x)) #s(literal 1/48 binary64)) (*.f64 (cos.f64 x) #s(literal -1/8 binary64)))))))) #s(literal 2 binary64))
✓	99.7%	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64)))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
	99.5%	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
	99.1%	(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
	55.9%	(.f64 (.f64 eps eps) (+.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 (cos.f64 x) eps)))
	97.2%	(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))) #s(literal -1/2 binary64)))) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
	96.8%	(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
✓	99.5%	(.f64 eps (+.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
	51.5%	(.f64 eps (+.f64 (.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))) (cos.f64 x)) (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
✓	99.4%	(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))) (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
✓	98.2%	(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
✓	99.1%	(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
	97.1%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64))))))))
	97.1%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))))
	96.7%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps (.f64 (*.f64 x x) #s(literal 1/12 binary64))) x)))
	96.9%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
	97.2%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
	97.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
✓	96.8%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
	5.1%	(.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64))))
	5.8%	(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
✓	98.5%	(*.f64 eps (cos.f64 x))
✓	96.9%	eps

Compiler

Compiled 1591 to 682 computations (57.1% saved)

regimes41.0ms (0.3%)

Counts

45 → 1

Calls

Call 1

Inputs
eps
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(+.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps (.f64 (*.f64 x x) #s(literal 1/12 binary64))) x)))
(.f64 eps (.f64 (.f64 x (.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps x) #s(literal 1/12 binary64))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64))))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))) #s(literal -1/2 binary64)))) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (+.f64 (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/6 binary64)))))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 (.f64 eps eps) (+.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 (cos.f64 x) eps)))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/120 binary64))))))))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64)))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps #s(literal 1/3840 binary64))))))) (.f64 eps (.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))))
(-.f64 (sin.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 x (*.f64 x #s(literal -1/5040 binary64))))))))))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (/.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 1/2949120 binary64) (.f64 (.f64 eps eps) #s(literal -31/4954521600 binary64))))) #s(literal -1/110592 binary64)) (.f64 eps (.f64 eps eps))))) eps) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))))) (-.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))))) #s(literal 1/2 binary64))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(.f64 (.f64 (/.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))) (.f64 (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))))))))) eps) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))))) (-.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64))))))) #s(literal 1/2 binary64))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(+.f64 (.f64 (.f64 eps (sin.f64 x)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (cos.f64 x)))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))) (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
(.f64 eps (+.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 (.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))) (cos.f64 x)) (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(/.f64 (.f64 (+.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 (sin.f64 x) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64))))))) (*.f64 eps eps)) eps)
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64)))))) (+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (+.f64 (.f64 (.f64 eps (sin.f64 x)) #s(literal 1/48 binary64)) (*.f64 (cos.f64 x) #s(literal -1/8 binary64)))))))) #s(literal 2 binary64))
(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/48 binary64))) (.f64 (cos.f64 x) #s(literal -1/8 binary64)))))))) #s(literal 2 binary64))

Outputs

(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))

Calls

3 calls:

13.0ms	x
13.0ms	eps
11.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`eps`
99.8%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes24.0ms (0.2%)

Counts

31 → 1

Calls

Call 1

Inputs
eps
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(+.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps (.f64 (*.f64 x x) #s(literal 1/12 binary64))) x)))
(.f64 eps (.f64 (.f64 x (.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps x) #s(literal 1/12 binary64))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64))))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))) #s(literal -1/2 binary64)))) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (+.f64 (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/6 binary64)))))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 (.f64 eps eps) (+.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 (cos.f64 x) eps)))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/120 binary64))))))))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64)))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps #s(literal 1/3840 binary64))))))) (.f64 eps (.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))))
(-.f64 (sin.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 x (*.f64 x #s(literal -1/5040 binary64))))))))))

Outputs

(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))

Calls

2 calls:

13.0ms	eps
8.0ms	x

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes19.0ms (0.1%)

Counts

28 → 1

Calls

Call 1

Inputs
eps
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(+.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps (.f64 (*.f64 x x) #s(literal 1/12 binary64))) x)))
(.f64 eps (.f64 (.f64 x (.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps x) #s(literal 1/12 binary64))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64))))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))) #s(literal -1/2 binary64)))) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (+.f64 (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/6 binary64)))))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 (.f64 eps eps) (+.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 (cos.f64 x) eps)))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/120 binary64))))))))

Outputs

(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))

Calls

2 calls:

10.0ms	eps
7.0ms	x

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes18.0ms (0.1%)

Counts

25 → 1

Calls

Call 1

Inputs
eps
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(+.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps (.f64 (*.f64 x x) #s(literal 1/12 binary64))) x)))
(.f64 eps (.f64 (.f64 x (.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps x) #s(literal 1/12 binary64))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64))))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))) #s(literal -1/2 binary64)))) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (+.f64 (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/6 binary64)))))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 (.f64 eps eps) (+.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 (cos.f64 x) eps)))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))

Outputs
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))

Calls

2 calls:

9.0ms	eps
7.0ms	x

Results

Accuracy	Segments	Branch
99.1%	1	`x`
99.1%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes17.0ms (0.1%)

Counts

24 → 1

Calls

Call 1

Inputs
eps
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(+.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps (.f64 (*.f64 x x) #s(literal 1/12 binary64))) x)))
(.f64 eps (.f64 (.f64 x (.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps x) #s(literal 1/12 binary64))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64))))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))) #s(literal -1/2 binary64)))) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (+.f64 (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/6 binary64)))))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 (.f64 eps eps) (+.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 (cos.f64 x) eps)))

Outputs
(*.f64 eps (cos.f64 x))

Calls

2 calls:

8.0ms	eps
6.0ms	x

Results

Accuracy	Segments	Branch
98.5%	1	`x`
98.5%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes20.0ms (0.1%)

Counts

21 → 1

Calls

Call 1

Inputs
eps
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(+.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps (.f64 (*.f64 x x) #s(literal 1/12 binary64))) x)))
(.f64 eps (.f64 (.f64 x (.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps x) #s(literal 1/12 binary64))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64))))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))) #s(literal -1/2 binary64)))) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (+.f64 (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/6 binary64)))))))))
(sin.f64 eps)

Outputs
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))

Calls

2 calls:

13.0ms	eps
6.0ms	x

Results

Accuracy	Segments	Branch
97.2%	1	`x`
97.2%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes13.0ms (0.1%)

Counts

14 → 1

Calls

Call 1

Inputs
eps
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(+.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps (.f64 (*.f64 x x) #s(literal 1/12 binary64))) x)))
(.f64 eps (.f64 (.f64 x (.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps x) #s(literal 1/12 binary64))))))))

Outputs
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))))

Calls

2 calls:

7.0ms	x
4.0ms	eps

Results

Accuracy	Segments	Branch
97.1%	1	`x`
97.1%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes7.0ms (0.1%)

Counts

10 → 1

Calls

Call 1

Inputs
eps
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(+.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps (.f64 (*.f64 x x) #s(literal 1/12 binary64))) x)))
(.f64 eps (.f64 (.f64 x (.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) x))))

Outputs
(+.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))

Calls

2 calls:

3.0ms	eps
3.0ms	x

Results

Accuracy	Segments	Branch
97.0%	1	`x`
97.0%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes9.0ms (0.1%)

Counts

7 → 1

Calls

Call 1

Inputs
eps
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))

Outputs
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))

Calls

2 calls:

6.0ms	eps
3.0ms	x

Results

Accuracy	Segments	Branch
97.0%	1	`x`
97.0%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

Accuracy

Total -58.8b remaining (-2923.2%)

Threshold costs -58.8b (-2923.2%)

Counts

5 → 1

Calls

Call 1

Inputs
eps
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))

Outputs
eps

Calls

2 calls:

2.0ms	eps
2.0ms	x

Results

Accuracy	Segments	Branch
96.9%	1	`x`
96.9%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

70×	`*-commutative_binary64`
30×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	151
1	118	151

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64)))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 eps (cos.f64 x))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))))
(+.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
eps

Outputs
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 eps (.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64)))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64))))))))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))))))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (.f64 eps #s(literal 1/2 binary64))))
(*.f64 eps (cos.f64 x))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))))
(+.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
eps

soundness1.7s (12%)

Rules

6668×	`-lowering-.f32`
6668×	`-lowering-.f64`
6664×	`-lowering-.f32`
6664×	`-lowering-.f64`
4300×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	567	6377
1	2015	6004
2	7657	6001
0	8417	6001
0	683	7865
1	2423	7086
0	8670	7086
0	6	16
1	49	16
2	402	16
3	5232	16
0	8309	16
0	507	4569
1	1753	4212
2	6161	4211
0	8038	4211
0	107	488
1	327	465
2	963	459
3	3572	459
0	8267	459

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 414 to 243 computations (41.3% saved)

preprocess61.0ms (0.4%)

Compiler: Compiled 354 to 160 computations (54.8% saved)

Iter	Nodes	Cost
0	6	18
1	9	18
2	14	18
3	21	18
4	31	18
5	63	18
6	122	18
7	210	18
8	295	18
9	401	18
10	479	18
11	485	18
0	485	18

Iter	Nodes	Cost
0	6	18
1	9	18
2	14	18
3	21	18
4	31	18
5	63	18
6	122	18
7	210	18
8	295	18
9	401	18
10	479	18
11	485	18
0	485	18

analyze103.0ms (0.7%)

sample6.8s (48.1%)

preprocess46.0ms (0.3%)

explain93.0ms (0.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify15.0ms (0.1%)

localize39.0ms (0.3%)

series4.0ms (0%)

rewrite284.0ms (2%)

simplify239.0ms (1.7%)

eval30.0ms (0.2%)

prune34.0ms (0.2%)

simplify144.0ms (1%)

localize299.0ms (2.1%)

series37.0ms (0.3%)

rewrite385.0ms (2.7%)

simplify249.0ms (1.8%)

eval134.0ms (0.9%)

prune100.0ms (0.7%)

simplify180.0ms (1.3%)

localize322.0ms (2.3%)

series45.0ms (0.3%)

rewrite347.0ms (2.4%)

simplify376.0ms (2.6%)

eval134.0ms (0.9%)

prune108.0ms (0.8%)

simplify284.0ms (2%)

localize326.0ms (2.3%)

series58.0ms (0.4%)

rewrite390.0ms (2.7%)

simplify371.0ms (2.6%)

eval140.0ms (1%)

prune105.0ms (0.7%)

regimes41.0ms (0.3%)

regimes24.0ms (0.2%)

regimes19.0ms (0.1%)

regimes18.0ms (0.1%)

regimes17.0ms (0.1%)

regimes20.0ms (0.1%)

regimes13.0ms (0.1%)

regimes7.0ms (0.1%)

regimes9.0ms (0.1%)

regimes5.0ms (0%)

simplify10.0ms (0.1%)

soundness1.7s (12%)

preprocess61.0ms (0.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	6	18
1	9	18
2	14	18
3	21	18
4	31	18
5	63	18
6	122	18
7	210	18
8	295	18
9	401	18
10	479	18
11	485	18
0	485	18