Metrics for 2sin (example 3.3)

analyze62.0ms (0.4%)

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: 11.0ms (27.5% of total)

...c/correct-round.rkt:119:19: 9.0ms (22.5% of total)

ival-add: 5.0ms (12.5% of total)

ival-mult: 3.0ms (7.5% of total)

ival-fabs: 3.0ms (7.5% of total)

ival-<=: 3.0ms (7.5% of total)

ival-<: 3.0ms (7.5% of total)

ival-sub: 2.0ms (5% of total)

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

const: 1.0ms (2.5% of total)

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

sample6.5s (46.1%)

Results

3.3s	26063×	0	precondition
1.3s	4547×	1	valid
475.0ms	3709×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 3.7s

...c/correct-round.rkt:119:19: 818.0ms (22.1% of total)

ival-sin: 685.0ms (18.5% of total)

ival-<=: 414.0ms (11.2% of total)

ival-<: 369.0ms (10% of total)

ival-mult: 323.0ms (8.7% of total)

ival-add: 309.0ms (8.3% of total)

ival-fabs: 277.0ms (7.5% of total)

ival-sub: 224.0ms (6.1% of total)

ival-and: 130.0ms (3.5% of total)

backward-pass: 105.0ms (2.8% of total)

const: 49.0ms (1.3% of total)

Bogosity

preprocess44.0ms (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))

explain101.0ms (0.7%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
228	3	(-4.28718533615325e-244 2.596565261760719e-246)	4	(-3.078977089395929e-248 4.894015027365364e-250)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
3	0	-	0	-	`(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

44.0ms	282×	1	valid
15.0ms	230×	0	valid

Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-sin: 12.0ms (43.8% of total)

ival-add: 6.0ms (21.9% of total)

backward-pass: 5.0ms (18.3% of total)

ival-sub: 4.0ms (14.6% of total)

const: 0.0ms (0% 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
▶	62.0%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify13.0ms (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	99.8%	(sin.f64 (+.f64 x eps))
✓	accuracy	62.3%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Results

23.0ms	141×	1	valid
7.0ms	115×	0	valid

Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-sin: 7.0ms (50.2% of total)

ival-add: 3.0ms (21.5% of total)

ival-sub: 2.0ms (14.3% of total)

backward-pass: 2.0ms (14.3% 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	(+ x eps)
0.0ms	x	@	-inf	(- (sin (+ x eps)) (sin x))

rewrite344.0ms (2.4%)

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)

simplify229.0ms (1.6%)

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)

eval34.0ms (0.2%)

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

prune30.0ms (0.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	253	8	261
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	253	9	262

Accuracy

100.0%

Counts

262 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	35.4%	(-.f64 (sin.f64 (/.f64 (-.f64 (.f64 x x) (.f64 eps eps)) (-.f64 x eps))) (sin.f64 x))
	60.6%	(-.f64 (sin.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64))))))
✓	62.0%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	60.2%	(-.f64 (sin.f64 (+.f64 x eps)) 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))
▶	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))))
▶	99.8%	(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
	98.9%	(*.f64 eps (cos.f64 x))
▶	97.0%	(sin.f64 eps)

Compiler

Compiled 217 to 146 computations (32.7% saved)

simplify225.0ms (1.6%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	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	256	(.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	256	(.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))
✓	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 eps)
✓	cost-diff	0	(sin.f64 (+.f64 x eps))
✓	cost-diff	0	(-.f64 (sin.f64 (+.f64 x eps)) x)
✓	cost-diff	0	(sin.f64 eps)
✓	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))))

Rules

1914×	`fnmsub-define`
1772×	`fma-define`
1512×	`--lowering--.f32`
1512×	`--lowering--.f64`
1422×	`-lowering-.f32`

Iterations

Useful iterations: 10 (0.0ms)

Iter	Nodes	Cost
0	32	192
1	69	185
2	212	185
3	909	185
4	1489	183
5	2353	183
6	2805	183
7	3308	183
8	3457	183
9	3675	183
10	4230	175
11	6643	175
0	8111	175

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize215.0ms (1.5%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	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	99.9%	(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
✓	accuracy	100.0%	(.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 (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
✓	accuracy	100.0%	(*.f64 eps (sin.f64 x))
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	99.8%	(sin.f64 (+.f64 x eps))
✓	accuracy	63.5%	(-.f64 (sin.f64 (+.f64 x eps)) x)
✓	accuracy	100.0%	(sin.f64 eps)
✓	accuracy	100.0%	(+.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)))
✓	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))

Results

109.0ms	135×	1	valid
51.0ms	121×	0	valid

Compiler

Compiled 211 to 33 computations (84.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 99.0ms

ival-mult: 38.0ms (38.5% of total)

backward-pass: 16.0ms (16.2% of total)

ival-add: 11.0ms (11.2% of total)

ival-sin: 11.0ms (11.2% of total)

...c/correct-round.rkt:119:19: 8.0ms (8.1% of total)

ival-cos: 6.0ms (6.1% of total)

ival-div: 5.0ms (5.1% of total)

ival-sub: 2.0ms (2% of total)

const: 1.0ms (1% of total)

series45.0ms (0.3%)

Counts

18 → 360

Calls

Call 1

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

Outputs
#<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)) (* -1/6 (* eps (cos x)))))))>
#<alt (* -1/6 (* (pow eps 3) (cos x)))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* -1/6 (* (pow eps 3) (cos x)))>
#<alt (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))>
#<alt (+ (* 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)))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (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)) (* -1/6 (* eps (cos x))))))>
#<alt (* -1/6 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* -1/6 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 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 (* -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 (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 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)) (* -1/6 (* x (cos eps)))))) 1)))>
#<alt (* -1 x)>
#<alt (* x (- (/ (sin (+ eps x)) x) 1))>
#<alt (* x (- (/ (sin (+ eps x)) x) 1))>
#<alt (* x (- (/ (sin (+ eps x)) x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) x)))))>
#<alt (* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) x)))))>
#<alt (* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) x)))))>
#<alt (- (sin x) x)>
#<alt (- (+ (sin x) (* eps (cos x))) x)>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) x)>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) x)>
#<alt (- (sin (+ eps x)) x)>
#<alt (- (sin (+ eps x)) x)>
#<alt (- (sin (+ eps x)) x)>
#<alt (- (sin (+ eps x)) x)>
#<alt (- (sin (- x (* -1 eps))) x)>
#<alt (- (sin (- x (* -1 eps))) x)>
#<alt (- (sin (- x (* -1 eps))) x)>
#<alt (- (sin (- x (* -1 eps))) 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 (* 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 (* 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 (* -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) (* -1/2 (* 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)>

Calls

90 calls:

Time	Variable		Point	Expression
12.0ms	x	@	inf	(cos (/ (+ eps (* x 2)) 2))
8.0ms	eps	@	inf	(* (* eps eps) -1/6)
3.0ms	x	@	0	(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
2.0ms	x	@	-inf	(* eps (+ (* -1/2 (* eps (sin x))) (* (+ (* (* eps eps) -1/6) 1) (cos x))))
1.0ms	x	@	inf	(* eps (+ (* -1/2 (* eps (sin x))) (* (+ (* (* eps eps) -1/6) 1) (cos x))))

rewrite386.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

4122×	`-lowering-.f32`
4122×	`-lowering-.f64`
2698×	`+-lowering-+.f64`
2698×	`+-lowering-+.f32`
2456×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	32	130
1	173	125
2	1806	125
0	8654	125

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 335

Calls

Call 1

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

Outputs
(+.f64 (.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 (+.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))) #s(literal 0 binary64)))
(+.f64 (.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 #s(literal 0 binary64) (+.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 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 eps (cos.f64 x))) (.f64 (.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))))
(+.f64 (.f64 (.f64 eps (sin.f64 x)) (.f64 eps #s(literal -1/2 binary64))) (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 eps (cos.f64 x))))
(+.f64 (.f64 (+.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))) #s(literal 0 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 (.f64 #s(literal 0 binary64) (+.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 #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)))))
(fma.f64 eps (.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)) (.f64 eps (cos.f64 x))))
(fma.f64 eps (.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 eps #s(literal -1/2 binary64))))
(fma.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 (+.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))) #s(literal 0 binary64)))
(fma.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 #s(literal 0 binary64) (+.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)))))
(fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps (sin.f64 x)) eps) (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 eps (cos.f64 x))))
(fma.f64 (.f64 eps (sin.f64 x)) (.f64 eps #s(literal -1/2 binary64)) (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 eps (cos.f64 x))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))) eps (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 eps (cos.f64 x))))
(fma.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 eps (cos.f64 x)) (.f64 (.f64 eps (sin.f64 x)) (.f64 eps #s(literal -1/2 binary64))))
(fma.f64 (cos.f64 x) (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) (.f64 (.f64 eps (sin.f64 x)) (.f64 eps #s(literal -1/2 binary64))))
(fma.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) eps (.f64 (.f64 eps (sin.f64 x)) (.f64 eps #s(literal -1/2 binary64))))
(fma.f64 (+.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 (.f64 (+.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))) #s(literal 0 binary64)))
(fma.f64 (+.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 (.f64 #s(literal 0 binary64) (+.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)))))
(fma.f64 (+.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))) #s(literal 0 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)))))
(fma.f64 #s(literal 0 binary64) (+.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 #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)))))
(fma.f64 (.f64 eps (cos.f64 x)) (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (.f64 eps (sin.f64 x)) (.f64 eps #s(literal -1/2 binary64))))
(fma.f64 (.f64 eps #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)) (.f64 eps (cos.f64 x))))
(fma.f64 (.f64 eps (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64))) (cos.f64 x) (.f64 (.f64 eps (sin.f64 x)) (.f64 eps #s(literal -1/2 binary64))))
(fma.f64 (.f64 eps (.f64 eps (sin.f64 x))) #s(literal -1/2 binary64) (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 eps (cos.f64 x))))
(fma.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x) (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 eps (cos.f64 x))))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 3 binary64))) (pow.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #s(literal 3 binary64)))) (.f64 (.f64 eps eps) (+.f64 (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))) (.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (-.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))))))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) (.f64 (.f64 eps 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 (.f64 (.f64 eps eps) (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 3 binary64))) (pow.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #s(literal 3 binary64)))) (.f64 eps (+.f64 (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))) (.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (-.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))))))
(/.f64 (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 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 (.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 3 binary64))) (pow.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #s(literal 3 binary64))) (.f64 eps (.f64 eps eps))) (.f64 (+.f64 (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))) (.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (-.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))))) (*.f64 eps eps)))
(/.f64 (.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 3 binary64))) (pow.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #s(literal 3 binary64))) (.f64 eps eps)) (.f64 (+.f64 (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))) (.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (-.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))) eps))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64))))) (.f64 eps (.f64 eps eps))) (.f64 (-.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 eps)))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64))))) (.f64 eps eps)) (.f64 (-.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))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 eps (sin.f64 x)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 eps (cos.f64 x))) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (.f64 eps (sin.f64 x)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 eps (cos.f64 x))) #s(literal 2 binary64)) (.f64 (.f64 (.f64 eps (sin.f64 x)) (.f64 eps #s(literal -1/2 binary64))) (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 eps (cos.f64 x)))))))
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(/.f64 (+.f64 (.f64 (.f64 (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))) (.f64 eps eps)) (.f64 eps (.f64 (.f64 eps (.f64 eps eps)) (cos.f64 x)))) (.f64 eps (.f64 eps eps)))
(/.f64 (+.f64 (.f64 (.f64 (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))) eps) (.f64 eps (.f64 (.f64 eps eps) (cos.f64 x)))) (*.f64 eps eps))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (cos.f64 x)))
(.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (cos.f64 x)) eps)
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))) (cos.f64 x))
(+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))))
(-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (+.f64 (cos.f64 x) (.f64 #s(literal 1/2 binary64) (.f64 eps (sin.f64 x))))) (/.f64 (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))) (+.f64 (cos.f64 x) (.f64 #s(literal 1/2 binary64) (.f64 eps (sin.f64 x))))))
(fma.f64 eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) (cos.f64 x))
(fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))
(fma.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x))
(fma.f64 (*.f64 eps (sin.f64 x)) #s(literal -1/2 binary64) (cos.f64 x))
(fma.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x) (cos.f64 x))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))) (cos.f64 x)))) (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 eps (sin.f64 x)) #s(literal 3 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 x) (.f64 #s(literal 1/2 binary64) (.f64 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 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))))))
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 3 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))) (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (cos.f64 x)))))
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 3 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))) (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (cos.f64 x)))))
(/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))))) (+.f64 (cos.f64 x) (.f64 #s(literal 1/2 binary64) (.f64 eps (sin.f64 x)))))
(/.f64 (neg.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 3 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))) (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (cos.f64 x))))))
(/.f64 (neg.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))))) (neg.f64 (+.f64 (cos.f64 x) (.f64 #s(literal 1/2 binary64) (.f64 eps (sin.f64 x))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #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 (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))) (cos.f64 x)))
(pow.f64 (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))) (cos.f64 x)))) (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 eps (sin.f64 x)) #s(literal 3 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (cos.f64 x) (.f64 #s(literal 1/2 binary64) (.f64 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 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))))) #s(literal -1 binary64))
(.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 3 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))) (cos.f64 x))))))
(.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))))) (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 x) (.f64 #s(literal 1/2 binary64) (*.f64 eps (sin.f64 x))))))
(cos.f64 x)
(/.f64 (.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64)))))))) #s(literal 2 binary64))
(/.f64 (.f64 (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64))))))) #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 x #s(literal 2 binary64))) #s(literal 2 binary64)))))
(.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (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 (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 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)))) (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 x #s(literal 2 binary64))) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64)))))))))
(/.f64 (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64))))))) #s(literal 2 binary64))
(/.f64 (neg.f64 (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64)))))))) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64)))))))) #s(literal -1 binary64))
(.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (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))) (sin.f64 (/.f64 eps #s(literal 2 binary64))))
(.f64 (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64))))))) #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 (.f64 eps eps) (.f64 #s(literal 2 binary64) eps))
(/.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 #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))
(pow.f64 (/.f64 (/.f64 #s(literal 2 binary64) eps) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 eps #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 eps #s(literal 2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal -1/2 binary64))
(*.f64 #s(literal 1/2 binary64) eps)
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (.f64 eps (.f64 eps eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (.f64 eps eps)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) 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 (.f64 eps eps) #s(literal -1/6 binary64))
(.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 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))
(.f64 (.f64 eps #s(literal -1/6 binary64)) eps)
(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal -2 binary64)))
(*.f64 x #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) x)

simplify385.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

5784×	`-lowering-.f32`
5784×	`-lowering-.f64`
2288×	`+-lowering-+.f64`
2288×	`+-lowering-+.f32`
1620×	`neg-lowering-neg.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	393	3347
1	1360	3070
2	4607	3062
0	8652	3062

Stop Event

1×	iter limit
1×	node limit

Counts

360 → 360

Calls

Call 1

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

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)) (* -1/6 (* eps (cos x)))))))
(.f64 eps (+.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 eps (+.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(* -1/6 (* (pow eps 3) (cos x)))
(.f64 (cos.f64 x) (.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(.f64 eps (.f64 (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 eps eps)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) (+.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) (/.f64 (/.f64 (cos.f64 x) eps) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) (+.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) (/.f64 (/.f64 (cos.f64 x) eps) eps))))
(* -1/6 (* (pow eps 3) (cos x)))
(.f64 (cos.f64 x) (.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps))))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(.f64 eps (.f64 (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 eps eps)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(.f64 (+.f64 (.f64 (cos.f64 x) #s(literal 1/6 binary64)) (/.f64 (-.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) (/.f64 (cos.f64 x) eps)) eps)) (-.f64 #s(literal 0 binary64) (.f64 eps (*.f64 eps eps))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(.f64 (+.f64 (.f64 (cos.f64 x) #s(literal 1/6 binary64)) (/.f64 (-.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) (/.f64 (cos.f64 x) eps)) eps)) (-.f64 #s(literal 0 binary64) (.f64 eps (*.f64 eps eps))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))))
(+ (* 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)))))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 x (+.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 eps (+.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 eps (+.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 eps (+.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 eps (+.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 eps (+.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 eps (+.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 eps (+.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 eps (+.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+.f64 (cos.f64 x) (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
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(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 eps eps) #s(literal -1/48 binary64))))
(* 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 (.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))))))))
(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))
(* -1/6 (pow eps 2))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(* -1/6 (pow eps 2))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(* -1/6 (pow eps 2))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(* -1/6 (pow eps 2))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(* -1/6 (pow eps 2))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(* -1/6 (pow eps 2))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(* -1/6 (pow eps 2))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(* -1/6 (pow eps 2))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(* -1/6 (pow eps 2))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(* -1/6 (pow eps 2))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(* -1/6 (pow eps 2))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(* -1/6 (pow eps 2))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+.f64 (cos.f64 x) (.f64 eps (.f64 #s(literal -1/2 binary64) (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 (cos.f64 x) (.f64 eps #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 (.f64 eps (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 (.f64 x #s(literal -1/2 binary64)) (cos.f64 (.f64 eps #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))

eval94.0ms (0.7%)

Compiler: Compiled 15881 to 1493 computations (90.6% saved)

prune70.0ms (0.5%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	764	14	778
Fresh	2	1	3
Picked	3	2	5
Done	1	0	1
Total	770	17	787

Accuracy

100.0%

Counts

787 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 eps (cos.f64 x))) (.f64 (.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))))
	99.8%	(+.f64 (.f64 (.f64 eps (sin.f64 x)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (cos.f64 x)))
	97.4%	(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))))
	97.0%	(+.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
	97.4%	(+.f64 eps (.f64 x (.f64 #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) #s(literal -1/48 binary64)))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
	99.8%	(.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))
	99.8%	(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
▶	97.4%	(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))))) #s(literal 1 binary64))))
✓	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))))
▶	98.7%	(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
✓	99.8%	(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
	97.4%	(.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 #s(literal 1/12 binary64) (.f64 eps x))))))))
▶	97.4%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
	97.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
	98.9%	(*.f64 eps (cos.f64 x))
▶	97.0%	eps

Compiler

Compiled 508 to 332 computations (34.6% saved)

simplify296.0ms (2.1%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Rules

6642×	`fma-define`
6252×	`fma-lowering-fma.f32`
6252×	`fma-lowering-fma.f64`
3040×	`sum3-define`
2580×	`sum4-define`

Iterations

Useful iterations: 12 (0.0ms)

Iter	Nodes	Cost
0	35	264
1	115	253
2	331	251
3	941	249
4	2638	249
5	4382	249
6	5919	249
7	6366	249
8	6438	249
9	6438	249
10	7734	249
11	7920	249
12	7920	246
0	10477	246

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(+ (* (+ (* (* eps eps) -1/6) 1) (* eps (cos x))) (* (* eps (sin x)) (* eps -1/2)))
(* (+ (* (* eps eps) -1/6) 1) (* eps (cos x)))
(+ (* (* eps eps) -1/6) 1)
(* (* eps eps) -1/6)
(* eps eps)
eps
-1/6
1
(* eps (cos x))
(cos x)
x
(* (* eps (sin x)) (* eps -1/2))
(* eps (sin x))
(sin x)
(* eps -1/2)
-1/2
eps
(* eps (+ 1 (* x (* -1/2 (+ eps x)))))
eps
(+ 1 (* x (* -1/2 (+ eps x))))
1
(* x (* -1/2 (+ eps x)))
x
(* -1/2 (+ eps x))
-1/2
(+ eps x)
(* eps (+ (* -1/6 (* eps eps)) (+ (* x (+ (* eps -1/2) (* x (+ -1/2 (* (* eps eps) 1/12))))) 1)))
eps
(+ (* -1/6 (* eps eps)) (+ (* x (+ (* eps -1/2) (* x (+ -1/2 (* (* eps eps) 1/12))))) 1))
(* -1/6 (* eps eps))
-1/6
(* eps eps)
(+ (* x (+ (* eps -1/2) (* x (+ -1/2 (* (* eps eps) 1/12))))) 1)
(* x (+ (* eps -1/2) (* x (+ -1/2 (* (* eps eps) 1/12)))))
x
(+ (* eps -1/2) (* x (+ -1/2 (* (* eps eps) 1/12))))
(* eps -1/2)
-1/2
(* x (+ -1/2 (* (* eps eps) 1/12)))
(+ -1/2 (* (* eps eps) 1/12))
(* (* eps eps) 1/12)
1/12
1
(* 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

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

localize160.0ms (1.1%)

Localize:

Found 16 expressions of interest:

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

Results

107.0ms	254×	0	valid
2.0ms	2×	1	valid

Compiler

Compiled 281 to 36 computations (87.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 62.0ms

ival-mult: 34.0ms (54.4% of total)

ival-add: 13.0ms (20.8% of total)

...c/correct-round.rkt:119:19: 10.0ms (16% of total)

ival-sin: 2.0ms (3.2% of total)

ival-cos: 2.0ms (3.2% of total)

const: 1.0ms (1.6% of total)

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

series37.0ms (0.3%)

Counts

21 → 432

Calls

Call 1

Inputs
#<alt (+ (* (+ (* (* eps eps) -1/6) 1) (* eps (cos x))) (* (* eps (sin x)) (* eps -1/2)))>
#<alt (* (+ (* (* eps eps) -1/6) 1) (* eps (cos x)))>
#<alt (+ (* (* eps eps) -1/6) 1)>
#<alt (* (* eps eps) -1/6)>
#<alt (* eps (+ 1 (* x (* -1/2 (+ eps x)))))>
#<alt (+ 1 (* x (* -1/2 (+ eps x))))>
#<alt (* x (* -1/2 (+ eps x)))>
#<alt (* -1/2 (+ eps x))>
#<alt (* eps (+ (* -1/6 (* eps eps)) (+ (* x (+ (* eps -1/2) (* x (+ -1/2 (* (* eps eps) 1/12))))) 1)))>
#<alt (+ (* -1/6 (* eps eps)) (+ (* x (+ (* eps -1/2) (* x (+ -1/2 (* (* eps eps) 1/12))))) 1))>
#<alt (* -1/6 (* eps eps))>
#<alt (* eps eps)>
#<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 (sin x)) (* eps -1/2))>
#<alt (* eps (sin x))>
#<alt (* (* eps eps) 1/12)>
#<alt (* x (+ (* eps -1/2) (* x (+ -1/2 (* (* eps eps) 1/12)))))>
#<alt (+ (* eps -1/2) (* x (+ -1/2 (* (* eps eps) 1/12))))>

Outputs
#<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)) (* -1/6 (* eps (cos x)))))))>
#<alt (* -1/6 (* (pow eps 3) (cos x)))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))>
#<alt (* -1/6 (* (pow eps 3) (cos x)))>
#<alt (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))>
#<alt (+ (* 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)))))))>
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))>
#<alt (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))>
#<alt (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))>
#<alt (* -1/6 (* (pow eps 3) (cos x)))>
#<alt (* (pow eps 3) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* (pow eps 3) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* (pow eps 3) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* -1/6 (* (pow eps 3) (cos x)))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (cos x) (pow eps 2))) (* 1/6 (cos x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (cos x) (pow eps 2))) (* 1/6 (cos x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (cos x) (pow eps 2))) (* 1/6 (cos x)))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (+ (* -1/2 (* eps (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))) (* eps (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/24 (* eps (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* (pow x 2) (+ (* -1/720 (* eps (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))) (* 1/24 (* eps (+ 1 (* -1/6 (pow eps 2))))))))))>
#<alt (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* eps (* (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 (* -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 (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -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 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))>
#<alt 1>
#<alt (+ 1 (* -1/2 (* eps x)))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))>
#<alt (* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))>
#<alt (* -1/2 (* eps x))>
#<alt (* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))>
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))>
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))>
#<alt (* -1/2 (* eps x))>
#<alt (* x (+ (* -1/2 eps) (* -1/2 x)))>
#<alt (* x (+ (* -1/2 eps) (* -1/2 x)))>
#<alt (* x (+ (* -1/2 eps) (* -1/2 x)))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))>
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))>
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))>
#<alt (* -1/2 (* eps x))>
#<alt (* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))>
#<alt (* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))>
#<alt (* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))>
#<alt (* -1/2 x)>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (* -1/2 eps)>
#<alt (* eps (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* eps (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* eps (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* -1/2 eps)>
#<alt (* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))>
#<alt (* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))>
#<alt (* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (* -1/2 x)>
#<alt (* x (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* x (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* x (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* -1/2 x)>
#<alt (* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))>
#<alt (* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))>
#<alt (* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))>
#<alt (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))>
#<alt (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))>
#<alt (* (pow eps 3) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 3) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))>
#<alt (* (pow eps 3) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))>
#<alt (* (pow eps 3) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))>
#<alt (* (pow eps 3) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (- (* 1/12 (pow x 2)) 1/6)) (* 1/2 (/ x eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (- (* 1/12 (pow x 2)) 1/6)) (* -1 (/ (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (- (* 1/12 (pow x 2)) 1/6)) (* -1 (/ (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))) eps)))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))>
#<alt (* eps (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))>
#<alt (* (pow x 2) (+ (* -1/2 (/ (pow eps 2) x)) (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) (pow x 2)))))>
#<alt (* (pow x 2) (+ (* -1/2 (/ (pow eps 2) x)) (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) (pow x 2)))))>
#<alt (* eps (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x)) (* 1/2 (pow eps 2))) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x)) (* 1/2 (pow eps 2))) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))>
#<alt (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))>
#<alt (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))>
#<alt (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))>
#<alt (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 1/2))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 1/2))>
#<alt (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))>
#<alt (* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))>
#<alt (* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))>
#<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 (* -1/6 (pow eps 2))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps x))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps x))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps x))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 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) (* 1/24 (* eps (pow x 2))))))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (/ (* eps (cos x)) x)))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (/ (* eps (cos x)) x)))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (/ (* eps (cos x)) x)))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1 (* x (+ (* -1 (/ (* eps (cos x)) x)) (* 1/2 (pow eps 2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (* eps (cos x)) x)) (* 1/2 (pow eps 2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (* eps (cos x)) x)) (* 1/2 (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 (- (* 1/24 (pow x 2)) 1/2)))))>
#<alt (* -1/2 (* eps x))>
#<alt (* x (+ (* -1/2 eps) (/ (cos x) x)))>
#<alt (* x (+ (* -1/2 eps) (/ (cos x) x)))>
#<alt (* x (+ (* -1/2 eps) (/ (cos x) x)))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1 (* x (+ (* -1 (/ (cos x) x)) (* 1/2 eps))))>
#<alt (* -1 (* x (+ (* -1 (/ (cos x) x)) (* 1/2 eps))))>
#<alt (* -1 (* x (+ (* -1 (/ (cos x) x)) (* 1/2 eps))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps x)))>
#<alt (+ (cos x) (* -1/2 (* eps x)))>
#<alt (+ (cos x) (* -1/2 (* eps x)))>
#<alt (* -1/2 (* eps x))>
#<alt (* eps (+ (* -1/2 x) (/ (cos x) eps)))>
#<alt (* eps (+ (* -1/2 x) (/ (cos x) eps)))>
#<alt (* eps (+ (* -1/2 x) (/ (cos x) eps)))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 x))))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 x))))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 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 x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2)))))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (* (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* 1/12 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (pow eps 2)) (* 1/10080 (* (pow eps 2) (pow x 2)))))))))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (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 (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 (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* -1/2 (* eps x))>
#<alt (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))>
#<alt (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))>
#<alt (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))>
#<alt (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))>
#<alt (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))>
#<alt (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* 1/12 (* eps (pow x 2))))))>
#<alt (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* 1/12 (* eps (pow x 2))))))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2)))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2)))))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))))>
#<alt (* -1/2 x)>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2)))>
#<alt (+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2)))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (- (* 1/12 x) (* 1/2 (/ 1 eps))))>
#<alt (* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/12 x)) (* 1/2 (/ 1 eps))))>
#<alt (* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/12 x)) (* 1/2 (/ 1 eps))))>
#<alt (* 1/12 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (- (* 1/12 x) (* 1/2 (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ x eps))) eps)) (* 1/12 x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ x eps))) eps)) (* 1/12 x)))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))>
#<alt (* x (- (* 1/12 (pow eps 2)) 1/2))>
#<alt (* x (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))>
#<alt (* x (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))>
#<alt (* x (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))>
#<alt (* x (- (* 1/12 (pow eps 2)) 1/2))>
#<alt (* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x)))))>
#<alt (* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x)))))>
#<alt (* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x)))))>

Calls

108 calls:

Time	Variable		Point	Expression
5.0ms	x	@	0	(* eps (+ (* -1/6 (* eps eps)) (+ (* x (+ (* eps -1/2) (* x (+ -1/2 (* (* eps eps) 1/12))))) 1)))
5.0ms	eps	@	0	(* eps (+ (* -1/6 (* eps eps)) (+ (* x (+ (* eps -1/2) (* x (+ -1/2 (* (* eps eps) 1/12))))) 1)))
1.0ms	x	@	inf	(+ (* (+ (* (* eps eps) -1/6) 1) (* eps (cos x))) (* (* eps (sin x)) (* eps -1/2)))
1.0ms	x	@	-inf	(+ (* (+ (* (* eps eps) -1/6) 1) (* eps (cos x))) (* (* eps (sin x)) (* eps -1/2)))
1.0ms	eps	@	-inf	(* eps (+ 1 (* x (* -1/2 (+ eps x)))))

rewrite414.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

4132×	`-lowering-.f32`
4132×	`-lowering-.f64`
2642×	`/-lowering-/.f32`
2642×	`/-lowering-/.f64`
2634×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	35	191
1	227	183
2	2136	183
0	9411	183

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 563

Calls

Call 1

Inputs
(+ (* (+ (* (* eps eps) -1/6) 1) (* eps (cos x))) (* (* eps (sin x)) (* eps -1/2)))
(* (+ (* (* eps eps) -1/6) 1) (* eps (cos x)))
(+ (* (* eps eps) -1/6) 1)
(* (* eps eps) -1/6)
(* eps (+ 1 (* x (* -1/2 (+ eps x)))))
(+ 1 (* x (* -1/2 (+ eps x))))
(* x (* -1/2 (+ eps x)))
(* -1/2 (+ eps x))
(* eps (+ (* -1/6 (* eps eps)) (+ (* x (+ (* eps -1/2) (* x (+ -1/2 (* (* eps eps) 1/12))))) 1)))
(+ (* -1/6 (* eps eps)) (+ (* x (+ (* eps -1/2) (* x (+ -1/2 (* (* eps eps) 1/12))))) 1))
(* -1/6 (* eps eps))
(* eps eps)
(* eps (+ (cos x) (* eps (* x -1/2))))
(+ (cos x) (* eps (* x -1/2)))
(cos x)
(* eps (* x -1/2))
(* (* eps (sin x)) (* eps -1/2))
(* eps (sin x))
(* (* eps eps) 1/12)
(* x (+ (* eps -1/2) (* x (+ -1/2 (* (* eps eps) 1/12)))))
(+ (* eps -1/2) (* x (+ -1/2 (* (* eps eps) 1/12))))

Outputs
(+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (.f64 eps (cos.f64 x))) (.f64 (sin.f64 x) (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(+.f64 (.f64 (sin.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (*.f64 eps (cos.f64 x))))
(-.f64 (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64))))) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64))))))) (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (.f64 eps (cos.f64 x))) (.f64 (sin.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))) (/.f64 (pow.f64 (.f64 (sin.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) #s(literal 2 binary64)) (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (.f64 eps (cos.f64 x))) (.f64 (sin.f64 x) (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))))
(-.f64 (/.f64 (pow.f64 (.f64 (sin.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) #s(literal 2 binary64)) (-.f64 (.f64 (sin.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (.f64 eps (cos.f64 x))))) (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64))))) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64))))))) (-.f64 (.f64 (sin.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (*.f64 eps (cos.f64 x))))))
(fma.f64 eps (.f64 (sin.f64 x) (.f64 eps #s(literal -1/2 binary64))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (.f64 eps (cos.f64 x))))
(fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (.f64 eps (cos.f64 x))))
(fma.f64 eps (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64))))) (.f64 (sin.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
(fma.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (.f64 eps (cos.f64 x)) (.f64 (sin.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
(fma.f64 (cos.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64))))) (.f64 (sin.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
(fma.f64 (.f64 eps (cos.f64 x)) (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (.f64 (sin.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
(fma.f64 (sin.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (.f64 eps (cos.f64 x))))
(fma.f64 (.f64 eps (sin.f64 x)) (.f64 eps #s(literal -1/2 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (.f64 eps (cos.f64 x))))
(fma.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (sin.f64 x))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (.f64 eps (cos.f64 x))))
(fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps (sin.f64 x)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (.f64 eps (cos.f64 x))))
(fma.f64 (.f64 eps (.f64 eps (sin.f64 x))) #s(literal -1/2 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (.f64 eps (cos.f64 x))))
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(fma.f64 (+.f64 eps x) #s(literal -1/2 binary64) (.f64 x (.f64 eps (*.f64 eps #s(literal 1/12 binary64)))))
(fma.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) x (*.f64 eps #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (-.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (.f64 eps #s(literal -1/2 binary64))))) (+.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (*.f64 x x))))))
(/.f64 (+.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 x x))))) (+.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (-.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (.f64 eps #s(literal -1/2 binary64))))))
(/.f64 (+.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 x x))))) (+.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 x x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (.f64 eps (.f64 x #s(literal -1/2 binary64))) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))))))
(/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 x x)))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 eps #s(literal 1/12 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (-.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (.f64 eps #s(literal -1/2 binary64))))) (+.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 x x))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (*.f64 x x)))))))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 x x)))))) (neg.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (-.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (.f64 eps #s(literal -1/2 binary64)))))))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 x x)))))) (neg.f64 (+.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 x x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (.f64 eps (.f64 x #s(literal -1/2 binary64))) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 x x))))) (neg.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 eps #s(literal 1/12 binary64))))))))
(/.f64 (-.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 x x))) (.f64 (.f64 eps eps) #s(literal 1/4 binary64))) (-.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (*.f64 eps #s(literal -1/2 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))))) (.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 x x))))) (.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 x x))))))) (neg.f64 (neg.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (-.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (.f64 eps #s(literal -1/2 binary64))))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 x x)))))) (neg.f64 (neg.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 eps #s(literal 1/12 binary64)))))))))
(/.f64 (neg.f64 (-.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 x x))) (.f64 (.f64 eps eps) #s(literal 1/4 binary64)))) (neg.f64 (-.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (*.f64 eps #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)))) (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x x))) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/1728 binary64)))) (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) (.f64 #s(literal -1/2 binary64) (+.f64 eps x))) (-.f64 (.f64 (.f64 x (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 x (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) (.f64 x (.f64 eps (*.f64 eps #s(literal 1/12 binary64))))))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (pow.f64 (+.f64 (.f64 x (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 eps #s(literal -1/2 binary64))) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 x #s(literal -1/2 binary64))) (-.f64 (.f64 (+.f64 (.f64 x (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 eps #s(literal -1/2 binary64))) (+.f64 (.f64 x (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 eps #s(literal -1/2 binary64)))) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 (.f64 x (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (*.f64 eps #s(literal -1/2 binary64)))))))
(pow.f64 (/.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (-.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (.f64 eps #s(literal -1/2 binary64))))) (+.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 x x)))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (*.f64 x x))))) #s(literal -1 binary64))
(.f64 (+.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (-.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (*.f64 eps #s(literal -1/2 binary64)))))))
(.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))))))

simplify282.0ms (2%)

Algorithm

1×	egg-herbie

Rules

5600×	`-lowering-.f32`
5600×	`-lowering-.f64`
2218×	`+-lowering-+.f64`
2218×	`+-lowering-+.f32`
1348×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	384	4521
1	1376	4292
2	5291	4171
0	8348	4171

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 432

Calls

Call 1

Inputs
(* 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)))))))
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))
(* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))
(* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* (pow eps 3) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* (pow eps 3) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* -1/6 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos x) (pow eps 2))) (* 1/6 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos x) (pow eps 2))) (* 1/6 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos x) (pow eps 2))) (* 1/6 (cos x)))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* eps (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/24 (* eps (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* (pow x 2) (+ (* -1/720 (* eps (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))) (* 1/24 (* eps (+ 1 (* -1/6 (pow eps 2))))))))))
(* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* eps (* (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))
(* -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))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -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 (* eps x)) (* -1/2 (pow eps 2)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/2 (* eps x))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(* -1/2 (* eps x))
(* x (+ (* -1/2 eps) (* -1/2 x)))
(* x (+ (* -1/2 eps) (* -1/2 x)))
(* x (+ (* -1/2 eps) (* -1/2 x)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* -1/2 (pow x 2))
(+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))
(+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))
(+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))
(* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))
(* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))
(* -1/2 (* eps x))
(* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))
(* -1/2 x)
(+ (* -1/2 eps) (* -1/2 x))
(+ (* -1/2 eps) (* -1/2 x))
(+ (* -1/2 eps) (* -1/2 x))
(* -1/2 eps)
(* eps (- (* -1/2 (/ x eps)) 1/2))
(* eps (- (* -1/2 (/ x eps)) 1/2))
(* eps (- (* -1/2 (/ x eps)) 1/2))
(* -1/2 eps)
(* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))
(* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))
(* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))
(* -1/2 eps)
(+ (* -1/2 eps) (* -1/2 x))
(+ (* -1/2 eps) (* -1/2 x))
(+ (* -1/2 eps) (* -1/2 x))
(* -1/2 x)
(* x (- (* -1/2 (/ eps x)) 1/2))
(* x (- (* -1/2 (/ eps x)) 1/2))
(* x (- (* -1/2 (/ eps x)) 1/2))
(* -1/2 x)
(* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))
(* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))
(* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
(* (pow eps 3) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 3) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 3) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(* (pow eps 3) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(* (pow eps 3) (- (* 1/12 (pow x 2)) 1/6))
(* -1 (* (pow eps 3) (+ (* -1 (- (* 1/12 (pow x 2)) 1/6)) (* 1/2 (/ x eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (* 1/12 (pow x 2)) 1/6)) (* -1 (/ (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (* 1/12 (pow x 2)) 1/6)) (* -1 (/ (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))) eps)))))
(* 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 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(* eps (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2)))
(* (pow x 2) (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))
(* (pow x 2) (+ (* -1/2 (/ (pow eps 2) x)) (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) (pow x 2)))))
(* (pow x 2) (+ (* -1/2 (/ (pow eps 2) x)) (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) (pow x 2)))))
(* eps (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2)))
(* (pow x 2) (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x)) (* 1/2 (pow eps 2))) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x)) (* 1/2 (pow eps 2))) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))
(+ 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) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 1/2))
(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))
(* -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))
(* -1/6 (pow eps 2))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 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))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) x))
(* x (+ (* -1/2 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2)))))
(* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (* (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))))
(* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* 1/12 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (pow eps 2)) (* 1/10080 (* (pow eps 2) (pow x 2)))))))))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (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))
(* 1/12 (pow eps 2))
(* 1/12 (pow eps 2))
(* 1/12 (pow eps 2))
(* 1/12 (pow eps 2))
(* 1/12 (pow eps 2))
(* 1/12 (pow eps 2))
(* 1/12 (pow eps 2))
(* 1/12 (pow eps 2))
(* 1/12 (pow eps 2))
(* 1/12 (pow eps 2))
(* 1/12 (pow eps 2))
(* 1/12 (pow eps 2))
(* -1/2 (* eps x))
(* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))
(* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))
(* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))
(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* -1/2 (pow x 2))
(+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))
(+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* 1/12 (* eps (pow x 2))))))
(+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* 1/12 (* eps (pow x 2))))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(* (pow eps 2) (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))))
(* (pow eps 2) (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2)))))
(* (pow eps 2) (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2)))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(* (pow eps 2) (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))))
(* -1/2 x)
(+ (* -1/2 eps) (* -1/2 x))
(+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2)))
(+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2)))
(* 1/12 (* (pow eps 2) x))
(* (pow eps 2) (- (* 1/12 x) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/12 x)) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/12 x)) (* 1/2 (/ 1 eps))))
(* 1/12 (* (pow eps 2) x))
(* (pow eps 2) (- (* 1/12 x) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ x eps))) eps)) (* 1/12 x)))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ x eps))) eps)) (* 1/12 x)))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))
(+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))
(+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))
(* x (- (* 1/12 (pow eps 2)) 1/2))
(* x (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* x (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* x (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* x (- (* 1/12 (pow eps 2)) 1/2))
(* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x)))))
(* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x)))))
(* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x)))))

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)) (* -1/6 (* eps (cos x)))))))
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(* -1/2 (* (pow eps 2) (sin x)))
(.f64 (sin.f64 x) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) (sin x)))
(.f64 (sin.f64 x) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) (sin x)))
(.f64 (sin.f64 x) (.f64 eps (*.f64 eps #s(literal -1/2 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))
(* 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 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(.f64 x (+.f64 eps (.f64 (.f64 eps (.f64 x x)) (+.f64 #s(literal -1/6 binary64) (.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 eps (+.f64 (.f64 (*.f64 x x) #s(literal -1/5040 binary64)) #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))
(* 1/12 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/12 binary64))
(* 1/12 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/12 binary64))
(* 1/12 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/12 binary64))
(* 1/12 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/12 binary64))
(* 1/12 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/12 binary64))
(* 1/12 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/12 binary64))
(* 1/12 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/12 binary64))
(* 1/12 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/12 binary64))
(* 1/12 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/12 binary64))
(* 1/12 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/12 binary64))
(* 1/12 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/12 binary64))
(* 1/12 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/12 binary64))
(* -1/2 (* eps x))
(.f64 eps (.f64 x #s(literal -1/2 binary64)))
(* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))
(.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))))
(* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))
(.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))))
(* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))
(.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))))
(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (.f64 eps #s(literal 1/12 binary64))))))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (.f64 eps #s(literal 1/12 binary64))))))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (.f64 eps #s(literal 1/12 binary64))))))
(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (.f64 eps #s(literal 1/12 binary64))))))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (.f64 eps #s(literal 1/12 binary64))))))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (.f64 eps #s(literal 1/12 binary64))))))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))
(.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))
(+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* 1/12 (* eps (pow x 2))))))
(.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))))
(+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* 1/12 (* eps (pow x 2))))))
(.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 x (.f64 (.f64 eps eps) #s(literal 1/12 binary64))))
(* (pow eps 2) (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))))
(.f64 eps (.f64 eps (.f64 x (+.f64 (.f64 x #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) eps)))))
(* (pow eps 2) (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2)))))
(.f64 (.f64 eps eps) (+.f64 (/.f64 (.f64 x #s(literal -1/2 binary64)) eps) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps))))))
(* (pow eps 2) (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2)))))
(.f64 (.f64 eps eps) (+.f64 (/.f64 (.f64 x #s(literal -1/2 binary64)) eps) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps))))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 x (.f64 (.f64 eps eps) #s(literal 1/12 binary64))))
(* (pow eps 2) (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))))
(.f64 eps (.f64 eps (.f64 x (+.f64 (.f64 x #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) eps)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))))
(.f64 (.f64 eps eps) (-.f64 (.f64 x (.f64 x #s(literal 1/12 binary64))) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 (/.f64 x eps) #s(literal 1 binary64)))) eps)))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))))
(.f64 (.f64 eps eps) (-.f64 (.f64 x (.f64 x #s(literal 1/12 binary64))) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 (/.f64 x eps) #s(literal 1 binary64)))) eps)))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(+ (* -1/2 eps) (* -1/2 x))
(*.f64 #s(literal -1/2 binary64) (+.f64 eps x))
(+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2)))
(+.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 x #s(literal 1/12 binary64))))))
(+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2)))
(+.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 x #s(literal 1/12 binary64))))))
(* 1/12 (* (pow eps 2) x))
(.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))
(* (pow eps 2) (- (* 1/12 x) (* 1/2 (/ 1 eps))))
(.f64 (.f64 eps eps) (+.f64 (*.f64 x #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) eps)))
(* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/12 x)) (* 1/2 (/ 1 eps))))
(.f64 (.f64 eps eps) (+.f64 (.f64 x (+.f64 #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) (/.f64 #s(literal -1/2 binary64) eps)))
(* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/12 x)) (* 1/2 (/ 1 eps))))
(.f64 (.f64 eps eps) (+.f64 (.f64 x (+.f64 #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) (/.f64 #s(literal -1/2 binary64) eps)))
(* 1/12 (* (pow eps 2) x))
(.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))
(* (pow eps 2) (- (* 1/12 x) (* 1/2 (/ 1 eps))))
(.f64 (.f64 eps eps) (+.f64 (*.f64 x #s(literal 1/12 binary64)) (/.f64 #s(literal -1/2 binary64) eps)))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ x eps))) eps)) (* 1/12 x)))
(.f64 eps (.f64 eps (+.f64 (.f64 x #s(literal 1/12 binary64)) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) eps)) eps))))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ x eps))) eps)) (* 1/12 x)))
(.f64 eps (.f64 eps (+.f64 (.f64 x #s(literal 1/12 binary64)) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) eps)) eps))))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))
(+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))))
(+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))
(+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))))
(+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))
(+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))))
(* x (- (* 1/12 (pow eps 2)) 1/2))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))
(* x (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (*.f64 eps #s(literal 1/12 binary64))))))
(* x (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (*.f64 eps #s(literal 1/12 binary64))))))
(* x (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (*.f64 eps #s(literal 1/12 binary64))))))
(* x (- (* 1/12 (pow eps 2)) 1/2))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))
(* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x)))))
(.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 eps x)) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) #s(literal -1/12 binary64)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x)))))
(.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 eps x)) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) #s(literal -1/12 binary64)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x)))))
(.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 eps x)) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) #s(literal -1/12 binary64)))) (-.f64 #s(literal 0 binary64) x))

eval132.0ms (0.9%)

Compiler: Compiled 41077 to 2647 computations (93.6% saved)

prune100.0ms (0.7%)

Pruning

24 alts after pruning (18 fresh and 6 done)

	Pruned	Kept	Total
New	1037	11	1048
Fresh	3	7	10
Picked	1	4	5
Done	0	2	2
Total	1041	24	1065

Accuracy

100.0%

Counts

1065 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	26.8%	(/.f64 (+.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)))) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 (.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps))))
✓	100.0%	(+.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 eps (cos.f64 x))) (.f64 (.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))))
	99.8%	(+.f64 (.f64 (.f64 eps (sin.f64 x)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (cos.f64 x)))
	97.4%	(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))))
	97.4%	(+.f64 eps (.f64 x (.f64 #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) #s(literal -1/48 binary64)))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
	99.8%	(.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))
▶	99.8%	(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
	50.9%	(.f64 (.f64 eps eps) (+.f64 (/.f64 (cos.f64 x) eps) (*.f64 x #s(literal -1/2 binary64))))
▶	5.3%	(.f64 x (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
▶	97.8%	(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
	97.4%	(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #s(literal 1 binary64))))
✓	97.4%	(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))))) #s(literal 1 binary64))))
	44.7%	(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 x (.f64 (.f64 eps eps) (+.f64 (.f64 x (+.f64 #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) (/.f64 #s(literal -1/2 binary64) eps)))) #s(literal 1 binary64))))
✓	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))))
✓	98.7%	(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
✓	99.8%	(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
	97.4%	(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/12 binary64))))))))
	97.5%	(.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))))))))
	97.4%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
▶	97.4%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) eps))))))
	97.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
▶	98.9%	(*.f64 eps (cos.f64 x))
✓	97.0%	eps

Compiler

Compiled 843 to 503 computations (40.3% saved)

simplify144.0ms (1%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(cos.f64 x)
✓	cost-diff	0	(*.f64 eps (cos.f64 x))
✓	cost-diff	0	(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))))
✓	cost-diff	128	(+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))) (.f64 eps (.f64 x #s(literal -1/2 binary64))))
✓	cost-diff	128	(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
✓	cost-diff	256	(.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) eps)))
✓	cost-diff	256	(.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) eps))))
✓	cost-diff	256	(+.f64 #s(literal 1 binary64) (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) eps)))))
✓	cost-diff	256	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) eps))))))
✓	cost-diff	0	(*.f64 x #s(literal -1/2 binary64))
✓	cost-diff	0	(.f64 eps (.f64 x #s(literal -1/2 binary64)))
✓	cost-diff	0	(.f64 x (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
✓	cost-diff	0	(*.f64 eps #s(literal 1/2 binary64))
✓	cost-diff	0	(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
✓	cost-diff	0	(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
✓	cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))

Rules

2524×	`-lowering-.f32`
2524×	`-lowering-.f64`
1500×	`fma-define`
1152×	`+-lowering-+.f64`
1152×	`+-lowering-+.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	287
1	106	260
2	327	260
3	1027	242
4	3812	242
5	6716	242
6	7801	242
0	8081	242

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (* (sin (* eps 1/2)) (cos (+ x (* eps 1/2)))) 2)
(* (sin (* eps 1/2)) (cos (+ x (* eps 1/2))))
(sin (* eps 1/2))
(* eps 1/2)
eps
1/2
(cos (+ x (* eps 1/2)))
(+ x (* eps 1/2))
x
2
(* x (* eps (* x -1/2)))
x
(* eps (* x -1/2))
eps
(* x -1/2)
-1/2
(* eps (+ 1 (* x (* eps (+ -1/2 (/ (* x -1/2) eps))))))
eps
(+ 1 (* x (* eps (+ -1/2 (/ (* x -1/2) eps)))))
1
(* x (* eps (+ -1/2 (/ (* x -1/2) eps))))
x
(* eps (+ -1/2 (/ (* x -1/2) eps)))
(+ -1/2 (/ (* x -1/2) eps))
-1/2
(/ (* x -1/2) eps)
(* x -1/2)
(* eps (+ (+ 1 (* (* x x) (+ -1/2 (* x (* x (+ 1/24 (* (* x x) -1/720))))))) (* eps (* x -1/2))))
eps
(+ (+ 1 (* (* x x) (+ -1/2 (* x (* x (+ 1/24 (* (* x x) -1/720))))))) (* eps (* x -1/2)))
(+ 1 (* (* x x) (+ -1/2 (* x (* x (+ 1/24 (* (* x x) -1/720)))))))
1
(* (* x x) (+ -1/2 (* x (* x (+ 1/24 (* (* x x) -1/720))))))
(* x x)
x
(+ -1/2 (* x (* x (+ 1/24 (* (* x x) -1/720)))))
-1/2
(* x (* x (+ 1/24 (* (* x x) -1/720))))
(* x (+ 1/24 (* (* x x) -1/720)))
(+ 1/24 (* (* x x) -1/720))
1/24
(* (* x x) -1/720)
-1/720
(* eps (* x -1/2))
(* x -1/2)
(* eps (cos x))
eps
(cos x)
x

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

localize157.0ms (1.1%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(*.f64 eps (cos.f64 x))
✓	accuracy	100.0%	(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))
✓	accuracy	99.8%	(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))
✓	accuracy	99.8%	(.f64 (.f64 x x) #s(literal -1/720 binary64))
✓	accuracy	99.4%	(.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64))))
✓	accuracy	100.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) eps))))))
✓	accuracy	100.0%	(+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) eps))
✓	accuracy	99.8%	(.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) eps))))
✓	accuracy	99.7%	(.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) eps)))
✓	accuracy	100.0%	(*.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(.f64 eps (.f64 x #s(literal -1/2 binary64)))
✓	accuracy	99.8%	(.f64 x (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
✓	accuracy	100.0%	(*.f64 eps #s(literal 1/2 binary64))
✓	accuracy	100.0%	(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
✓	accuracy	99.9%	(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))

Results

93.0ms	252×	0	valid
8.0ms	4×	5	exit

Compiler

Compiled 292 to 36 computations (87.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 56.0ms

ival-mult: 28.0ms (49.9% of total)

ival-add: 10.0ms (17.8% of total)

...c/correct-round.rkt:119:19: 7.0ms (12.5% of total)

ival-cos: 4.0ms (7.1% of total)

ival-div: 2.0ms (3.6% of total)

backward-pass: 2.0ms (3.6% of total)

ival-sin: 2.0ms (3.6% of total)

const: 1.0ms (1.8% of total)

series28.0ms (0.2%)

Counts

22 → 420

Calls

Call 1

Inputs
#<alt (* (* (sin (* eps 1/2)) (cos (+ x (* eps 1/2)))) 2)>
#<alt (* (sin (* eps 1/2)) (cos (+ x (* eps 1/2))))>
#<alt (sin (* eps 1/2))>
#<alt (* eps 1/2)>
#<alt (* x (* eps (* x -1/2)))>
#<alt (* eps (* x -1/2))>
#<alt (* x -1/2)>
#<alt (* eps (+ 1 (* x (* eps (+ -1/2 (/ (* x -1/2) eps))))))>
#<alt (+ 1 (* x (* eps (+ -1/2 (/ (* x -1/2) eps)))))>
#<alt (* x (* eps (+ -1/2 (/ (* x -1/2) eps))))>
#<alt (* eps (+ -1/2 (/ (* x -1/2) eps)))>
#<alt (* eps (+ (+ 1 (* (* x x) (+ -1/2 (* x (* x (+ 1/24 (* (* x x) -1/720))))))) (* eps (* x -1/2))))>
#<alt (+ (+ 1 (* (* x x) (+ -1/2 (* x (* x (+ 1/24 (* (* x x) -1/720))))))) (* eps (* x -1/2)))>
#<alt (+ 1 (* (* x x) (+ -1/2 (* x (* x (+ 1/24 (* (* x x) -1/720)))))))>
#<alt (* (* x x) (+ -1/2 (* x (* x (+ 1/24 (* (* x x) -1/720))))))>
#<alt (* eps (cos x))>
#<alt (cos x)>
#<alt (cos (+ x (* eps 1/2)))>
#<alt (+ -1/2 (/ (* x -1/2) eps))>
#<alt (* x (+ 1/24 (* (* x x) -1/720)))>
#<alt (* (* x x) -1/720)>
#<alt (* x (* x (+ 1/24 (* (* x x) -1/720))))>

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 (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- x (* -1/2 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))>
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))>
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))>
#<alt (* (cos (- (* 1/2 eps) (* -1 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 (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -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 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))>
#<alt 1>
#<alt (+ 1 (* -1/2 (* eps x)))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))>
#<alt (* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))>
#<alt (* -1/2 (* eps x))>
#<alt (* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))>
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))>
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))>
#<alt (* -1/2 (* eps x))>
#<alt (* x (+ (* -1/2 eps) (* -1/2 x)))>
#<alt (* x (+ (* -1/2 eps) (* -1/2 x)))>
#<alt (* x (+ (* -1/2 eps) (* -1/2 x)))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))>
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))>
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))>
#<alt (* -1/2 (* eps x))>
#<alt (* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))>
#<alt (* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))>
#<alt (* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))>
#<alt (* -1/2 x)>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (* -1/2 eps)>
#<alt (* eps (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* eps (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* eps (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* -1/2 eps)>
#<alt (* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))>
#<alt (* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))>
#<alt (* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (* -1/2 x)>
#<alt (* x (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* x (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* x (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* -1/2 x)>
#<alt (* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))>
#<alt (* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))>
#<alt (* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) eps))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) 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) (* 1/24 (* eps (pow x 2))))))))>
#<alt (* -1/720 (* eps (pow x 6)))>
#<alt (* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))>
#<alt (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))>
#<alt (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/2 (/ (pow eps 2) (pow x 5))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))))>
#<alt (* -1/720 (* eps (pow x 6)))>
#<alt (* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))>
#<alt (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))>
#<alt (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/2 (/ (pow eps 2) (pow x 5))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 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 (- (* 1/24 (pow x 2)) 1/2)))))>
#<alt (* -1/720 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* -1/2 (/ eps (pow x 5))) (* 1/24 (/ 1 (pow x 2)))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* -1/720 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* -1/2 (/ eps (pow x 5))) (* 1/24 (/ 1 (pow x 2)))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* -1/2 (* eps x))>
#<alt (* eps (+ (* -1/2 x) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) eps))))>
#<alt (* eps (+ (* -1/2 x) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) eps))))>
#<alt (* eps (+ (* -1/2 x) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) eps))))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) eps)) (* 1/2 x))))>
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) eps)) (* 1/2 x))))>
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) eps)) (* 1/2 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 (* -1/720 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* -1/720 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))>
#<alt (* -1/720 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* -1/720 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<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 (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 (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<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 (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt -1/2>
#<alt (- (* -1/2 (/ x eps)) 1/2)>
#<alt (- (* -1/2 (/ x eps)) 1/2)>
#<alt (- (* -1/2 (/ x eps)) 1/2)>
#<alt (* -1/2 (/ x eps))>
#<alt (* -1 (* x (+ (* 1/2 (/ 1 eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (+ (* 1/2 (/ 1 eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (+ (* 1/2 (/ 1 eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1/2 (/ x eps))>
#<alt (* -1 (* x (+ (* 1/2 (/ 1 eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (+ (* 1/2 (/ 1 eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (+ (* 1/2 (/ 1 eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1/2 (/ x eps))>
#<alt (/ (+ (* -1/2 eps) (* -1/2 x)) eps)>
#<alt (/ (+ (* -1/2 eps) (* -1/2 x)) eps)>
#<alt (/ (+ (* -1/2 eps) (* -1/2 x)) eps)>
#<alt -1/2>
#<alt (- (* -1/2 (/ x eps)) 1/2)>
#<alt (- (* -1/2 (/ x eps)) 1/2)>
#<alt (- (* -1/2 (/ x eps)) 1/2)>
#<alt -1/2>
#<alt (- (* -1/2 (/ x eps)) 1/2)>
#<alt (- (* -1/2 (/ x eps)) 1/2)>
#<alt (- (* -1/2 (/ x eps)) 1/2)>
#<alt (* 1/24 x)>
#<alt (* x (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* x (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* x (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* -1/720 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* -1/720 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* -1/720 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* -1/720 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>

Calls

105 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	0	(* eps (+ (+ 1 (* (* x x) (+ -1/2 (* x (* x (+ 1/24 (* (* x x) -1/720))))))) (* eps (* x -1/2))))
1.0ms	eps	@	-inf	(* eps (+ 1 (* x (* eps (+ -1/2 (/ (* x -1/2) eps))))))
1.0ms	eps	@	0	(* x (* eps (* x -1/2)))
1.0ms	eps	@	0	(* eps (+ 1 (* x (* eps (+ -1/2 (/ (* x -1/2) eps))))))
1.0ms	eps	@	inf	(* (* (sin (* eps 1/2)) (cos (+ x (* eps 1/2)))) 2)

rewrite310.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

2916×	`-lowering-.f32`
2916×	`-lowering-.f64`
2812×	`fma-lowering-fma.f32`
2812×	`fma-lowering-fma.f64`
2162×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	35	224
1	209	201
2	1931	201
0	8289	201

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 431

Calls

Call 1

Inputs
(* (* (sin (* eps 1/2)) (cos (+ x (* eps 1/2)))) 2)
(* (sin (* eps 1/2)) (cos (+ x (* eps 1/2))))
(sin (* eps 1/2))
(* eps 1/2)
(* x (* eps (* x -1/2)))
(* eps (* x -1/2))
(* x -1/2)
(* eps (+ 1 (* x (* eps (+ -1/2 (/ (* x -1/2) eps))))))
(+ 1 (* x (* eps (+ -1/2 (/ (* x -1/2) eps)))))
(* x (* eps (+ -1/2 (/ (* x -1/2) eps))))
(* eps (+ -1/2 (/ (* x -1/2) eps)))
(* eps (+ (+ 1 (* (* x x) (+ -1/2 (* x (* x (+ 1/24 (* (* x x) -1/720))))))) (* eps (* x -1/2))))
(+ (+ 1 (* (* x x) (+ -1/2 (* x (* x (+ 1/24 (* (* x x) -1/720))))))) (* eps (* x -1/2)))
(+ 1 (* (* x x) (+ -1/2 (* x (* x (+ 1/24 (* (* x x) -1/720)))))))
(* (* x x) (+ -1/2 (* x (* x (+ 1/24 (* (* x x) -1/720))))))
(* eps (cos x))
(cos x)
(cos (+ x (* eps 1/2)))
(+ -1/2 (/ (* x -1/2) eps))
(* x (+ 1/24 (* (* x x) -1/720)))
(* (* x x) -1/720)
(* x (* x (+ 1/24 (* (* x x) -1/720))))

Outputs
(/.f64 (.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))))) #s(literal 2 binary64))
(/.f64 (.f64 (+.f64 (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (neg.f64 (.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))))) #s(literal -2 binary64))
(/.f64 (neg.f64 (.f64 (+.f64 (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))) #s(literal 2 binary64))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) x)) #s(literal 2 binary64)))
(.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))))
(.f64 (.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) x)) #s(literal 2 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))))))
(/.f64 (+.f64 (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x)))) #s(literal 2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x)))))))
(/.f64 (neg.f64 (+.f64 (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))))) #s(literal -2 binary64))
(/.f64 (neg.f64 (neg.f64 (+.f64 (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x)))))) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))))) #s(literal -1 binary64))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) x)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(.f64 (+.f64 (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))) #s(literal 1/2 binary64))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) eps)
(.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(.f64 x (.f64 x (*.f64 eps #s(literal -1/2 binary64))))
(.f64 (.f64 x #s(literal -1/2 binary64)) (*.f64 eps x))
(.f64 (.f64 x (*.f64 eps #s(literal -1/2 binary64))) x)
(.f64 (.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps)
(.f64 (.f64 eps x) (*.f64 x #s(literal -1/2 binary64)))
(.f64 (.f64 x (*.f64 eps x)) #s(literal -1/2 binary64))
(.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64))
(.f64 eps (.f64 x #s(literal -1/2 binary64)))
(.f64 x (.f64 eps #s(literal -1/2 binary64)))
(.f64 #s(literal -1/2 binary64) (.f64 eps x))
(.f64 (.f64 x #s(literal -1/2 binary64)) eps)
(.f64 (.f64 eps #s(literal -1/2 binary64)) x)
(.f64 (.f64 eps x) #s(literal -1/2 binary64))
(*.f64 x #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) x)
(+.f64 eps (.f64 eps (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
(+.f64 (.f64 eps (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))) eps)
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps (.f64 eps (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))) (/.f64 (.f64 (.f64 eps (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))) (.f64 eps (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))) (-.f64 eps (.f64 eps (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))))
(fma.f64 eps #s(literal 1 binary64) (.f64 eps (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
(fma.f64 eps (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) eps)
(fma.f64 x (.f64 (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) eps) eps)
(fma.f64 #s(literal 1 binary64) eps (.f64 eps (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
(fma.f64 (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (.f64 eps x) eps)
(fma.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) eps eps)
(fma.f64 (.f64 eps x) (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) eps)
(fma.f64 (.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) x eps)
(fma.f64 (.f64 eps (.f64 eps x)) (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) eps)) eps)
(/.f64 (+.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (.f64 (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))) (.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))))) (+.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))) (.f64 eps (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))) (.f64 eps (.f64 eps (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))))))
(/.f64 (-.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))) (.f64 eps (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))) (-.f64 eps (.f64 eps (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))))
(/.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (-.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) #s(literal 1 binary64)))))
(/.f64 (.f64 eps (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))) eps) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (-.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) #s(literal 1 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))) eps) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (+.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (.f64 (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))) (.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps)))))) (neg.f64 (+.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))) (.f64 eps (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))) (.f64 eps (.f64 eps (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))))))
(/.f64 (neg.f64 (-.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))) (.f64 eps (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))))) (neg.f64 (-.f64 eps (.f64 eps (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))))
(/.f64 (neg.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))))) (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (-.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (.f64 eps (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))))) (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))) eps)) (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (-.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) #s(literal 1 binary64))))))
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(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))) eps)
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(+.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))) (/.f64 (.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))))
(-.f64 (/.f64 (.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))) (-.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) #s(literal 1 binary64))))
(fma.f64 eps (.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) eps)) x) #s(literal 1 binary64))
(fma.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) #s(literal 1 binary64))
(fma.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) eps)) (.f64 eps x) #s(literal 1 binary64))
(fma.f64 (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) x #s(literal 1 binary64))
(fma.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) #s(literal 1 binary64) #s(literal 1 binary64))
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(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 x #s(literal -1/2 binary64))) (.f64 eps eps)))) (neg.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) eps))))
(/.f64 (-.f64 (/.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 x #s(literal -1/2 binary64))) (.f64 eps eps)) #s(literal 1/4 binary64)) (-.f64 (/.f64 (*.f64 x #s(literal -1/2 binary64)) eps) #s(literal -1/2 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) eps))) (.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) eps)) (/.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 x #s(literal -1/2 binary64))) (.f64 eps eps)))) (.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) eps)) (-.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) eps))))
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(pow.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (/.f64 (.f64 x #s(literal -1/2 binary64)) eps) #s(literal -1/2 binary64)) (/.f64 eps (.f64 x #s(literal -1/2 binary64))))) (+.f64 #s(literal -1/8 binary64) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (.f64 eps (*.f64 eps eps))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) eps)) (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 x #s(literal -1/2 binary64))) (*.f64 eps eps)))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (/.f64 (.f64 x #s(literal -1/2 binary64)) eps) #s(literal -1/2 binary64)) (/.f64 eps (.f64 x #s(literal -1/2 binary64)))))))
(.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 x #s(literal -1/2 binary64))) (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) eps))))
(+.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x (.f64 x (.f64 x #s(literal -1/720 binary64)))))
(+.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 x #s(literal 1/24 binary64)))
(-.f64 (/.f64 (.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x #s(literal 1/24 binary64))) (-.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x (.f64 x (.f64 x #s(literal -1/720 binary64)))))) (/.f64 (.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/720 binary64))))) (-.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x (.f64 x (.f64 x #s(literal -1/720 binary64)))))))
(fma.f64 x #s(literal 1/24 binary64) (.f64 x (.f64 x (*.f64 x #s(literal -1/720 binary64)))))
(fma.f64 x (.f64 x (.f64 x #s(literal -1/720 binary64))) (*.f64 x #s(literal 1/24 binary64)))
(fma.f64 (.f64 x x) (.f64 x #s(literal -1/720 binary64)) (*.f64 x #s(literal 1/24 binary64)))
(fma.f64 #s(literal 1/24 binary64) x (.f64 x (.f64 x (*.f64 x #s(literal -1/720 binary64)))))
(fma.f64 #s(literal -1/720 binary64) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/24 binary64)))
(fma.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) x (*.f64 x #s(literal 1/24 binary64)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal -1/720 binary64) (*.f64 x #s(literal 1/24 binary64)))
(fma.f64 (.f64 x #s(literal -1/720 binary64)) (.f64 x x) (*.f64 x #s(literal 1/24 binary64)))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64))))) (+.f64 (.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x #s(literal 1/24 binary64))) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/720 binary64))))) (.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x (.f64 x (*.f64 x #s(literal -1/720 binary64))))))))
(/.f64 (-.f64 (.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x #s(literal 1/24 binary64))) (.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/720 binary64)))))) (-.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x (.f64 x (.f64 x #s(literal -1/720 binary64))))))
(/.f64 (.f64 x (+.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64))))) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) #s(literal 1/24 binary64)))))
(/.f64 (.f64 x (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)))) (+.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/720 binary64) (*.f64 x x))))
(/.f64 (.f64 (+.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)))) x) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) #s(literal 1/24 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64))) x) (+.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/720 binary64) (*.f64 x x))))
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(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)))))) (neg.f64 (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) #s(literal 1/24 binary64))))))
(/.f64 (neg.f64 (.f64 x (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64))))) (neg.f64 (+.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/720 binary64) (*.f64 x x)))))
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(.f64 (.f64 x x) #s(literal -1/720 binary64))
(.f64 #s(literal -1/720 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal -1/720 binary64)) x)
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(fma.f64 (.f64 x x) #s(literal 1/24 binary64) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal -1/720 binary64)))))
(fma.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -1/720 binary64))) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))
(fma.f64 #s(literal 1/24 binary64) (.f64 x x) (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (*.f64 x x)))
(fma.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (.f64 x x) (.f64 #s(literal 1/24 binary64) (*.f64 x x)))
(fma.f64 (.f64 x #s(literal 1/24 binary64)) x (.f64 (.f64 x (.f64 x (*.f64 x #s(literal -1/720 binary64)))) x))
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(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))))
(.f64 (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 x x))
(.f64 (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))) x)

simplify552.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

4680×	`-lowering-.f32`
4680×	`-lowering-.f64`
3510×	`+-lowering-+.f64`
3510×	`+-lowering-+.f32`
1080×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	338	4022
1	1157	3837
2	3711	3720
3	7951	3720
0	8099	3720

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 420

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 (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 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)
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -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 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -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 (* eps x)) (* -1/2 (pow eps 2)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/2 (* eps x))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(* -1/2 (* eps x))
(* x (+ (* -1/2 eps) (* -1/2 x)))
(* x (+ (* -1/2 eps) (* -1/2 x)))
(* x (+ (* -1/2 eps) (* -1/2 x)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* -1/2 (pow x 2))
(+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))
(+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))
(+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))
(* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))
(* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))
(* -1/2 (* eps x))
(* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))
(* -1/2 x)
(+ (* -1/2 eps) (* -1/2 x))
(+ (* -1/2 eps) (* -1/2 x))
(+ (* -1/2 eps) (* -1/2 x))
(* -1/2 eps)
(* eps (- (* -1/2 (/ x eps)) 1/2))
(* eps (- (* -1/2 (/ x eps)) 1/2))
(* eps (- (* -1/2 (/ x eps)) 1/2))
(* -1/2 eps)
(* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))
(* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))
(* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))
(* -1/2 eps)
(+ (* -1/2 eps) (* -1/2 x))
(+ (* -1/2 eps) (* -1/2 x))
(+ (* -1/2 eps) (* -1/2 x))
(* -1/2 x)
(* x (- (* -1/2 (/ eps x)) 1/2))
(* x (- (* -1/2 (/ eps x)) 1/2))
(* x (- (* -1/2 (/ eps x)) 1/2))
(* -1/2 x)
(* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))
(* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))
(* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) eps))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) 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))))))))
(* -1/720 (* eps (pow x 6)))
(* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/2 (/ (pow eps 2) (pow x 5))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))))
(* -1/720 (* eps (pow x 6)))
(* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/2 (/ (pow eps 2) (pow x 5))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 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)))))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* -1/2 (/ eps (pow x 5))) (* 1/24 (/ 1 (pow x 2)))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* -1/2 (/ eps (pow x 5))) (* 1/24 (/ 1 (pow x 2)))) (+ 1/720 (/ 1/2 (pow x 4)))))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+ 1 (+ (* -1/2 (* eps x)) (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(+ 1 (+ (* -1/2 (* eps x)) (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(+ 1 (+ (* -1/2 (* eps x)) (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) eps))))
(* eps (+ (* -1/2 x) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) eps))))
(* eps (+ (* -1/2 x) (+ (/ 1 eps) (/ (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) eps))))
(* -1/2 (* eps x))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) eps)) (* 1/2 x))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) eps)) (* 1/2 x))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) 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)))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* 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)
(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 (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(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 (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
-1/2
(- (* -1/2 (/ x eps)) 1/2)
(- (* -1/2 (/ x eps)) 1/2)
(- (* -1/2 (/ x eps)) 1/2)
(* -1/2 (/ x eps))
(* -1 (* x (+ (* 1/2 (/ 1 eps)) (* 1/2 (/ 1 x)))))
(* -1 (* x (+ (* 1/2 (/ 1 eps)) (* 1/2 (/ 1 x)))))
(* -1 (* x (+ (* 1/2 (/ 1 eps)) (* 1/2 (/ 1 x)))))
(* -1/2 (/ x eps))
(* -1 (* x (+ (* 1/2 (/ 1 eps)) (* 1/2 (/ 1 x)))))
(* -1 (* x (+ (* 1/2 (/ 1 eps)) (* 1/2 (/ 1 x)))))
(* -1 (* x (+ (* 1/2 (/ 1 eps)) (* 1/2 (/ 1 x)))))
(* -1/2 (/ x eps))
(/ (+ (* -1/2 eps) (* -1/2 x)) eps)
(/ (+ (* -1/2 eps) (* -1/2 x)) eps)
(/ (+ (* -1/2 eps) (* -1/2 x)) eps)
-1/2
(- (* -1/2 (/ x eps)) 1/2)
(- (* -1/2 (/ x eps)) 1/2)
(- (* -1/2 (/ x eps)) 1/2)
-1/2
(- (* -1/2 (/ x eps)) 1/2)
(- (* -1/2 (/ x eps)) 1/2)
(- (* -1/2 (/ x eps)) 1/2)
(* 1/24 x)
(* x (+ 1/24 (* -1/720 (pow x 2))))
(* x (+ 1/24 (* -1/720 (pow x 2))))
(* x (+ 1/24 (* -1/720 (pow x 2))))
(* -1/720 (pow x 3))
(* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* -1/720 (pow x 3))
(* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(* -1/720 (pow x 4))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* -1/720 (pow x 4))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))

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 (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 eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 eps #s(literal 1/24 binary64)))))))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 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 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (+.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 x #s(literal -2 binary64)) (sin.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)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
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(.f64 x (.f64 (*.f64 x x) #s(literal -1/720 binary64)))
(* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x)))))
(* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x)))))
(* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x)))))
(* -1/720 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/720 binary64)))
(* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x)))))
(* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x)))))
(* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x)))))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* 1/24 (pow x 2))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))
(* -1/720 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -1/720 binary64))))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(* -1/720 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -1/720 binary64))))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))))

eval114.0ms (0.8%)

Compiler: Compiled 25614 to 2156 computations (91.6% saved)

prune87.0ms (0.6%)

Pruning

29 alts after pruning (18 fresh and 11 done)

	Pruned	Kept	Total
New	915	8	923
Fresh	3	10	13
Picked	0	5	5
Done	0	6	6
Total	918	29	947

Accuracy

100.0%

Counts

947 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
	26.8%	(/.f64 (+.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)))) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 (.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps))))
✓	100.0%	(+.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 eps (cos.f64 x))) (.f64 (.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))))
	99.8%	(+.f64 (.f64 (.f64 eps (sin.f64 x)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (cos.f64 x)))
	97.4%	(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))))
	97.7%	(+.f64 eps (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))))
	97.4%	(+.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps x)))))
	99.8%	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64))))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
	99.8%	(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
✓	99.8%	(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
✓	5.3%	(.f64 x (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
	97.8%	(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64))))) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) #s(literal 1/24 binary64)))))))) (.f64 eps (.f64 x #s(literal -1/2 binary64)))))
	48.2%	(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x))))))) (.f64 eps (.f64 x #s(literal -1/2 binary64)))))
✓	97.8%	(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
	97.4%	(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #s(literal 1 binary64))))
✓	97.4%	(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))))) #s(literal 1 binary64))))
	44.7%	(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 x (.f64 (.f64 eps eps) (+.f64 (.f64 x (+.f64 #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) (/.f64 #s(literal -1/2 binary64) eps)))) #s(literal 1 binary64))))
✓	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))))
✓	98.7%	(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
✓	99.8%	(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
	97.4%	(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/12 binary64))))))))
	97.5%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))))
	97.8%	(.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) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))))))
	97.5%	(.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))))))))
	97.7%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 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)))))))))
	97.4%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
✓	97.4%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) eps))))))
	97.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
✓	98.9%	(*.f64 eps (cos.f64 x))
✓	97.0%	eps

Compiler

Compiled 1361 to 608 computations (55.3% saved)

regimes42.0ms (0.3%)

Counts

42 → 1

Calls

Call 1

Inputs
eps
(.f64 x (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(+.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) eps))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #s(literal 1 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 #s(literal 1/12 binary64) (.f64 eps 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 x x) #s(literal 1/24 binary64))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 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 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/12 binary64))))))))
(+.f64 eps (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 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) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))))) #s(literal 1 binary64))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 x (.f64 (.f64 eps eps) (+.f64 (.f64 x (+.f64 #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) (/.f64 #s(literal -1/2 binary64) eps)))) #s(literal 1 binary64))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x))))))) (.f64 eps (.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64))))) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) #s(literal 1/24 binary64)))))))) (.f64 eps (.f64 x #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)))) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 (.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(-.f64 (sin.f64 (+.f64 x eps)) x)
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 (.f64 eps eps) (+.f64 (/.f64 (cos.f64 x) eps) (*.f64 x #s(literal -1/2 binary64))))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 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 (sin.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64))))))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64))))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps 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)) (sin.f64 x))
(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(+.f64 (.f64 (.f64 eps (sin.f64 x)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (cos.f64 x)))
(-.f64 (sin.f64 (/.f64 (-.f64 (.f64 x x) (.f64 eps eps)) (-.f64 x eps))) (sin.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 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 eps (cos.f64 x))) (.f64 (.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))))

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

Calls

3 calls:

15.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
11.0ms	eps
11.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`eps`
100.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes38.0ms (0.3%)

Counts

41 → 1

Calls

Call 1

Inputs
eps
(.f64 x (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(+.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) eps))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #s(literal 1 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 #s(literal 1/12 binary64) (.f64 eps 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 x x) #s(literal 1/24 binary64))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 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 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/12 binary64))))))))
(+.f64 eps (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 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) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))))) #s(literal 1 binary64))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 x (.f64 (.f64 eps eps) (+.f64 (.f64 x (+.f64 #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) (/.f64 #s(literal -1/2 binary64) eps)))) #s(literal 1 binary64))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x))))))) (.f64 eps (.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64))))) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) #s(literal 1/24 binary64)))))))) (.f64 eps (.f64 x #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)))) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 (.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(-.f64 (sin.f64 (+.f64 x eps)) x)
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 (.f64 eps eps) (+.f64 (/.f64 (cos.f64 x) eps) (*.f64 x #s(literal -1/2 binary64))))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 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 (sin.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64))))))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64))))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps 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)) (sin.f64 x))
(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(+.f64 (.f64 (.f64 eps (sin.f64 x)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (cos.f64 x)))
(-.f64 (sin.f64 (/.f64 (-.f64 (.f64 x x) (.f64 eps eps)) (-.f64 x eps))) (sin.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))))

Outputs
(.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))))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`eps`
100.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes39.0ms (0.3%)

Counts

40 → 1

Calls

Call 1

Inputs
eps
(.f64 x (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(+.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) eps))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #s(literal 1 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 #s(literal 1/12 binary64) (.f64 eps 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 x x) #s(literal 1/24 binary64))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 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 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/12 binary64))))))))
(+.f64 eps (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 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) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))))) #s(literal 1 binary64))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 x (.f64 (.f64 eps eps) (+.f64 (.f64 x (+.f64 #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) (/.f64 #s(literal -1/2 binary64) eps)))) #s(literal 1 binary64))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x))))))) (.f64 eps (.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64))))) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) #s(literal 1/24 binary64)))))))) (.f64 eps (.f64 x #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)))) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 (.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(-.f64 (sin.f64 (+.f64 x eps)) x)
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 (.f64 eps eps) (+.f64 (/.f64 (cos.f64 x) eps) (*.f64 x #s(literal -1/2 binary64))))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 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 (sin.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64))))))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64))))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps 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)) (sin.f64 x))
(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(+.f64 (.f64 (.f64 eps (sin.f64 x)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (cos.f64 x)))
(-.f64 (sin.f64 (/.f64 (-.f64 (.f64 x x) (.f64 eps eps)) (-.f64 x eps))) (sin.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))

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

Calls

3 calls:

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

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)

regimes33.0ms (0.2%)

Counts

36 → 1

Calls

Call 1

Inputs
eps
(.f64 x (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(+.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) eps))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #s(literal 1 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 #s(literal 1/12 binary64) (.f64 eps 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 x x) #s(literal 1/24 binary64))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 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 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/12 binary64))))))))
(+.f64 eps (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 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) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))))) #s(literal 1 binary64))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 x (.f64 (.f64 eps eps) (+.f64 (.f64 x (+.f64 #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) (/.f64 #s(literal -1/2 binary64) eps)))) #s(literal 1 binary64))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x))))))) (.f64 eps (.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64))))) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) #s(literal 1/24 binary64)))))))) (.f64 eps (.f64 x #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)))) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 (.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(-.f64 (sin.f64 (+.f64 x eps)) x)
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 (.f64 eps eps) (+.f64 (/.f64 (cos.f64 x) eps) (*.f64 x #s(literal -1/2 binary64))))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 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 (sin.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64))))))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64))))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps 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)) (sin.f64 x))
(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))

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

Calls

3 calls:

10.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
10.0ms	x
10.0ms	eps

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)

regimes23.0ms (0.2%)

Counts

32 → 1

Calls

Call 1

Inputs
eps
(.f64 x (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(+.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) eps))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #s(literal 1 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 #s(literal 1/12 binary64) (.f64 eps 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 x x) #s(literal 1/24 binary64))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 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 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/12 binary64))))))))
(+.f64 eps (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 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) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))))) #s(literal 1 binary64))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 x (.f64 (.f64 eps eps) (+.f64 (.f64 x (+.f64 #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) (/.f64 #s(literal -1/2 binary64) eps)))) #s(literal 1 binary64))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x))))))) (.f64 eps (.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64))))) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) #s(literal 1/24 binary64)))))))) (.f64 eps (.f64 x #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)))) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 (.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(-.f64 (sin.f64 (+.f64 x eps)) x)
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 (.f64 eps eps) (+.f64 (/.f64 (cos.f64 x) eps) (*.f64 x #s(literal -1/2 binary64))))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 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 (sin.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64))))))

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

Calls

2 calls:

10.0ms	eps
9.0ms	x

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes22.0ms (0.2%)

Counts

29 → 1

Calls

Call 1

Inputs
eps
(.f64 x (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(+.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) eps))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #s(literal 1 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 #s(literal 1/12 binary64) (.f64 eps 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 x x) #s(literal 1/24 binary64))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 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 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/12 binary64))))))))
(+.f64 eps (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 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) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))))) #s(literal 1 binary64))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 x (.f64 (.f64 eps eps) (+.f64 (.f64 x (+.f64 #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) (/.f64 #s(literal -1/2 binary64) eps)))) #s(literal 1 binary64))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x))))))) (.f64 eps (.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64))))) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) #s(literal 1/24 binary64)))))))) (.f64 eps (.f64 x #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)))) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 (.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(-.f64 (sin.f64 (+.f64 x eps)) x)
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 (.f64 eps eps) (+.f64 (/.f64 (cos.f64 x) eps) (*.f64 x #s(literal -1/2 binary64))))

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

Calls

2 calls:

10.0ms	x
8.0ms	eps

Results

Accuracy	Segments	Branch
98.9%	1	`x`
98.9%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes16.0ms (0.1%)

Counts

25 → 1

Calls

Call 1

Inputs
eps
(.f64 x (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(+.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) eps))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #s(literal 1 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 #s(literal 1/12 binary64) (.f64 eps 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 x x) #s(literal 1/24 binary64))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 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 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/12 binary64))))))))
(+.f64 eps (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 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) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))))) #s(literal 1 binary64))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) (+.f64 (.f64 x (.f64 (.f64 eps eps) (+.f64 (.f64 x (+.f64 #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) (/.f64 #s(literal -1/2 binary64) eps)))) #s(literal 1 binary64))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x))))))) (.f64 eps (.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64))))) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) #s(literal 1/24 binary64)))))))) (.f64 eps (.f64 x #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)))) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 (.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (.f64 eps (.f64 x (.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps))))
(sin.f64 eps)

Outputs

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

Calls

2 calls:

7.0ms	x
7.0ms	eps

Results

Accuracy	Segments	Branch
97.8%	1	`x`
97.8%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes15.0ms (0.1%)

Counts

18 → 1

Calls

Call 1

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

Outputs

(*.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) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))))))

Calls

2 calls:

8.0ms	eps
5.0ms	x

Results

Accuracy	Segments	Branch
97.8%	1	`x`
97.8%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes11.0ms (0.1%)

Counts

16 → 1

Calls

Call 1

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

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

Calls

2 calls:

5.0ms	x
5.0ms	eps

Results

Accuracy	Segments	Branch
97.7%	1	`x`
97.7%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes12.0ms (0.1%)

Counts

13 → 1

Calls

Call 1

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

Outputs
(.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))))))))

Calls

2 calls:

7.0ms	eps
4.0ms	x

Results

Accuracy	Segments	Branch
97.5%	1	`eps`
97.5%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes9.0ms (0.1%)

Counts

12 → 1

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	x
4.0ms	eps

Results

Accuracy	Segments	Branch
97.5%	1	`x`
97.5%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes7.0ms (0%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	eps
3.0ms	x

Results

Accuracy	Segments	Branch
97.4%	1	`x`
97.4%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	x
2.0ms	eps

Results

Accuracy	Segments	Branch
97.4%	1	`x`
97.4%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0%)

Counts

4 → 1

Calls

Call 1

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

Outputs
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))

Calls

2 calls:

2.0ms	x
2.0ms	eps

Results

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

Accuracy

Total -58.8b remaining (-3065.3%)

Threshold costs -58.8b (-3065.3%)

Counts

2 → 1

Calls

Call 1

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

Outputs
eps

Calls

2 calls:

1.0ms	x
1.0ms	eps

Results

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

88×	`*-commutative_binary64`
44×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	84	224
1	155	224

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness2.1s (14.8%)

Rules

5784×	`-lowering-.f32`
5784×	`-lowering-.f64`
5600×	`-lowering-.f32`
5600×	`-lowering-.f64`
4680×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	338	4022
1	1157	3837
2	3711	3720
3	7951	3720
0	8099	3720
0	384	4521
1	1376	4292
2	5291	4171
0	8348	4171
0	32	130
1	173	125
2	1806	125
0	8654	125
0	393	3347
1	1360	3070
2	4607	3062
0	8652	3062
0	6	16
1	49	16
2	402	16
3	5232	16
0	8309	16
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
1×	iter limit
1×	node limit

Compiler

Compiled 662 to 376 computations (43.2% saved)

preprocess81.0ms (0.6%)

Compiler: Compiled 500 to 190 computations (62% 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

analyze62.0ms (0.4%)

sample6.5s (46.1%)

preprocess44.0ms (0.3%)

explain101.0ms (0.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify13.0ms (0.1%)

localize39.0ms (0.3%)

series4.0ms (0%)

rewrite344.0ms (2.4%)

simplify229.0ms (1.6%)

eval34.0ms (0.2%)

prune30.0ms (0.2%)

simplify225.0ms (1.6%)

localize215.0ms (1.5%)

series45.0ms (0.3%)

rewrite386.0ms (2.7%)

simplify385.0ms (2.7%)

eval94.0ms (0.7%)

prune70.0ms (0.5%)

simplify296.0ms (2.1%)

localize160.0ms (1.1%)

series37.0ms (0.3%)

rewrite414.0ms (2.9%)

simplify282.0ms (2%)

eval132.0ms (0.9%)

prune100.0ms (0.7%)

simplify144.0ms (1%)

localize157.0ms (1.1%)

series28.0ms (0.2%)

rewrite310.0ms (2.2%)

simplify552.0ms (3.9%)

eval114.0ms (0.8%)

prune87.0ms (0.6%)

regimes42.0ms (0.3%)

regimes38.0ms (0.3%)

regimes39.0ms (0.3%)

regimes33.0ms (0.2%)

regimes23.0ms (0.2%)

regimes22.0ms (0.2%)

regimes16.0ms (0.1%)

regimes15.0ms (0.1%)

regimes11.0ms (0.1%)

regimes12.0ms (0.1%)

regimes9.0ms (0.1%)

regimes7.0ms (0%)

regimes5.0ms (0%)

regimes4.0ms (0%)

regimes3.0ms (0%)

simplify14.0ms (0.1%)

soundness2.1s (14.8%)

preprocess81.0ms (0.6%)

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