Metrics for 2cos (problem 3.3.5)

analyze68.0ms (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: 41.0ms

ival-cos: 10.0ms (24.3% of total)

...c/correct-round.rkt:119:19: 7.0ms (17% of total)

ival-<=: 7.0ms (17% of total)

ival-add: 5.0ms (12.1% of total)

ival-mult: 3.0ms (7.3% of total)

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

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

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

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

const: 0.0ms (0% of total)

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

sample9.6s (56.9%)

Results

3.5s	5801×	2	valid
3.4s	26157×	0	precondition
938.0ms	2378×	1	valid
12.0ms	77×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.0s

ival-cos: 2.3s (38.5% of total)

...c/correct-round.rkt:119:19: 913.0ms (15.1% of total)

ival-<: 580.0ms (9.6% of total)

backward-pass: 420.0ms (7% of total)

ival-add: 371.0ms (6.1% of total)

ival-mult: 343.0ms (5.7% of total)

ival-fabs: 306.0ms (5.1% of total)

ival-sub: 280.0ms (4.6% of total)

ival-<=: 259.0ms (4.3% of total)

ival-and: 195.0ms (3.2% of total)

const: 47.0ms (0.8% of total)

Bogosity

preprocess60.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

414×	`fnmadd-define`
382×	`sum3-define`
370×	`fmsub-define`
356×	`fnmsub-define`
316×	`fmm-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	48
1	43	44
2	89	42
3	178	42
4	438	42
5	863	42
6	1279	42
7	1611	42
8	1749	42
9	1832	42
10	1850	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
(- (cos (+ x eps)) (cos x))

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

Call 2

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

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

explain265.0ms (1.6%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
140	1	(8.181070398398997e-155 9.336452202973445e-170)	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
2	0	-	-	`(cos.f64 (+.f64 x eps))`
0	0	-	-	`x`
0	0	-	-	`(+.f64 x eps)`
0	0	-	-	`(cos.f64 x)`
0	0	-	-	`eps`

Results

178.0ms	348×	2	valid
47.0ms	158×	1	valid
1.0ms	6×	0	valid

Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 152.0ms

ival-cos: 112.0ms (73.7% of total)

backward-pass: 21.0ms (13.8% of total)

ival-add: 10.0ms (6.6% of total)

ival-sub: 9.0ms (5.9% of total)

const: 1.0ms (0.7% 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
▶	52.4%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

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

localize124.0ms (0.7%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	99.9%	(cos.f64 (+.f64 x eps))
✓	accuracy	52.5%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

95.0ms	174×	2	valid
19.0ms	79×	1	valid
0.0ms	3×	0	valid

Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 71.0ms

ival-cos: 51.0ms (72.1% of total)

backward-pass: 10.0ms (14.1% of total)

ival-add: 5.0ms (7.1% of total)

ival-sub: 5.0ms (7.1% of total)

const: 0.0ms (0% of total)

series4.0ms (0%)

Counts

4 → 84

Calls

Call 1

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

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

Calls

21 calls:

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

rewrite277.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

2774×	`-lowering-.f32`
2774×	`-lowering-.f64`
2148×	`/-lowering-/.f32`
2148×	`/-lowering-/.f64`
1850×	`sum5-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	50	16
2	412	16
3	5247	16
0	8062	16

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 173

Calls

Call 1

Inputs
(- (cos (+ x eps)) (cos x))
(cos (+ x eps))
(+ x eps)
(cos x)

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

simplify157.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

3196×	`-lowering-.f32`
3196×	`-lowering-.f64`
1368×	`fnmadd-define`
1248×	`neg-lowering-neg.f64`
1248×	`neg-lowering-neg.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	105	481
1	304	458
2	777	457
3	2938	457
0	8476	457

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

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

Outputs
(- (cos eps) 1)
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(-.f64 (cos.f64 eps) (+.f64 (*.f64 x (sin.f64 eps)) #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(+.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (.f64 x (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 eps) #s(literal -1/2 binary64)))) (sin.f64 eps))))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(+.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 eps) #s(literal -1/2 binary64)))) (.f64 (sin.f64 eps) (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64))))))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* -1 (* eps (sin x)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (sin.f64 x)))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos eps)
(cos.f64 eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(-.f64 (cos.f64 eps) (*.f64 x (sin.f64 eps)))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+.f64 (cos.f64 eps) (.f64 x (-.f64 (.f64 (cos.f64 eps) (*.f64 x #s(literal -1/2 binary64))) (sin.f64 eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(+.f64 (cos.f64 eps) (.f64 x (+.f64 (.f64 (cos.f64 eps) (.f64 x #s(literal -1/2 binary64))) (.f64 (sin.f64 eps) (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64))))))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1 (* eps (sin x))))
(-.f64 (cos.f64 x) (*.f64 eps (sin.f64 x)))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+.f64 (cos.f64 x) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))))))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
(cos (- x (* -1 eps)))
(cos.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)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x))))))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)

eval43.0ms (0.3%)

Compiler: Compiled 6681 to 740 computations (88.9% saved)

prune28.0ms (0.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	248	9	257
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	248	10	258

Accuracy

99.8%

Counts

258 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.5%	(-.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
	82.1%	(-.f64 (+.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 (cos.f64 x) (cos.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps)))
	51.2%	(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x)))))))
▶	51.1%	(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
✓	52.4%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	81.1%	(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
▶	51.0%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
▶	99.6%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
	99.4%	(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (sin.f64 x)))
▶	99.0%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))

Compiler

Compiled 291 to 200 computations (31.3% saved)

simplify131.0ms (0.8%)

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(cos.f64 x)
✓	cost-diff	0	(*.f64 (cos.f64 x) (cos.f64 eps))
✓	cost-diff	0	(-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (.f64 (sin.f64 x) (sin.f64 eps)))
✓	cost-diff	6400	(-.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
✓	cost-diff	0	(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
✓	cost-diff	0	(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
✓	cost-diff	0	(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
✓	cost-diff	0	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
✓	cost-diff	0	(+.f64 x eps)
✓	cost-diff	0	(cos.f64 (+.f64 x eps))
✓	cost-diff	0	(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
✓	cost-diff	0	(cos.f64 eps)
✓	cost-diff	0	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
✓	cost-diff	0	(sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)))
✓	cost-diff	0	(.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
✓	cost-diff	0	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
✓	cost-diff	128	(+.f64 eps #s(literal 0 binary64))

Rules

2152×	`fnmadd-define`
2056×	`sum5-define`
1698×	`sum3-define`
1528×	`sum4-define`
1472×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	188
1	77	177
2	194	177
3	540	177
4	1345	177
5	2511	177
6	5555	177
0	8109	177

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize599.0ms (3.6%)

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (.f64 (sin.f64 x) (sin.f64 eps)))
✓	accuracy	100.0%	(*.f64 (sin.f64 x) (sin.f64 eps))
✓	accuracy	100.0%	(*.f64 (cos.f64 x) (cos.f64 eps))
✓	accuracy	52.5%	(-.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
✓	accuracy	100.0%	(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
✓	accuracy	99.8%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
✓	accuracy	100.0%	(.f64 x (.f64 x #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal -1/2 binary64))
✓	accuracy	99.9%	(cos.f64 (+.f64 x eps))
✓	accuracy	53.2%	(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
✓	accuracy	100.0%	(cos.f64 eps)
✓	accuracy	53.3%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
✓	accuracy	100.0%	(sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)))
✓	accuracy	100.0%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
✓	accuracy	99.8%	(sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
✓	accuracy	99.8%	(.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))

Results

405.0ms	172×	2	valid
126.0ms	79×	1	valid
7.0ms	2×	3	valid
2.0ms	3×	0	valid

Compiler

Compiled 205 to 37 computations (82% saved)

Precisions

Click to see histograms. Total time spent on operations: 339.0ms

ival-cos: 94.0ms (27.7% of total)

ival-sin: 89.0ms (26.3% of total)

ival-mult: 67.0ms (19.8% of total)

backward-pass: 47.0ms (13.9% of total)

ival-add: 17.0ms (5% of total)

ival-sub: 13.0ms (3.8% of total)

ival-div: 8.0ms (2.4% of total)

const: 2.0ms (0.6% of total)

series31.0ms (0.2%)

Counts

22 → 420

Calls

Call 1

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

Outputs
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (pow (sin (* 1/2 eps)) 2)>
#<alt (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<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 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow eps 2)))>
#<alt (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (- (+ 1/2 (/ (cos (+ eps x)) (pow x 2))) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- (+ 1/2 (/ (cos (+ eps x)) (pow x 2))) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- (+ 1/2 (/ (cos (+ eps x)) (pow x 2))) (/ 1 (pow x 2))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (- (+ 1/2 (/ (cos (- eps (* -1 x))) (pow x 2))) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- (+ 1/2 (/ (cos (- eps (* -1 x))) (pow x 2))) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- (+ 1/2 (/ (cos (- eps (* -1 x))) (pow x 2))) (/ 1 (pow x 2))))>
#<alt (- (cos x) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (+ (cos x) (* -1 (* eps (sin x)))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (cos eps)>
#<alt (+ (cos eps) (* -1 (* x (sin eps))))>
#<alt (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))>
#<alt (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- 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 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* -1 (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))>
#<alt (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))>
#<alt (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt -1/2>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
#<alt (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)>
#<alt (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (cos eps)>
#<alt (+ (cos eps) (* -1 (* x (sin eps))))>
#<alt (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))>
#<alt (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (cos eps)>
#<alt (+ (cos eps) (* -1/2 (* (pow x 2) (cos eps))))>
#<alt (+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* 1/24 (* (pow x 2) (cos eps))))))>
#<alt (+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos eps))) (* 1/24 (cos eps)))))))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* (pow eps 2) (cos x))))>
#<alt (+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x))))))>
#<alt (+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x)))))))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos 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 (sin x)>
#<alt (+ (sin x) (* 1/2 (* eps (cos x))))>
#<alt (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))>
#<alt (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -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 (* -1/2 x)>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* x (sin eps))>
#<alt (* x (+ (sin eps) (* -1/6 (* (pow x 2) (sin eps)))))>
#<alt (* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* 1/120 (* (pow x 2) (sin eps)))))))>
#<alt (* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin eps))) (* 1/120 (sin eps))))))))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (+ (sin x) (* -1/6 (* (pow eps 2) (sin x)))))>
#<alt (* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* 1/120 (* (pow eps 2) (sin x)))))))>
#<alt (* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (sin x))) (* 1/120 (sin x))))))))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>

Calls

105 calls:

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

rewrite269.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

2812×	`fma-lowering-fma.f32`
2812×	`fma-lowering-fma.f64`
2112×	`-lowering-.f32`
2112×	`-lowering-.f64`
1686×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	132
1	214	124
2	2237	124
0	8264	124

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 430

Calls

Call 1

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

Outputs
eps
(+.f64 eps #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) eps)
(-.f64 eps #s(literal 0 binary64))
(-.f64 eps (/.f64 #s(literal 0 binary64) eps))
(fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 0 binary64))
(fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (neg.f64 (/.f64 #s(literal 0 binary64) eps)))
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64))
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) (neg.f64 (/.f64 #s(literal 0 binary64) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 eps eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))
(/.f64 (.f64 eps (.f64 eps eps)) (*.f64 eps eps))
(/.f64 (*.f64 eps eps) eps)
(/.f64 (neg.f64 (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (neg.f64 (.f64 eps (.f64 eps eps))) (neg.f64 (*.f64 eps eps)))
(pow.f64 eps #s(literal 1 binary64))
(pow.f64 (/.f64 eps (*.f64 eps eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64))
(.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
(.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
(/.f64 (.f64 #s(literal -2 binary64) (-.f64 (cos.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))))))) #s(literal 2 binary64))
(/.f64 (.f64 (-.f64 (cos.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))))) #s(literal -2 binary64)) #s(literal 2 binary64))
(.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) #s(literal -2 binary64)))
(.f64 (sin.f64 (/.f64 (+.f64 eps (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal -2 binary64)))
(.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) 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)))) (sin.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))))
(-.f64 (/.f64 (cos.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) #s(literal 2 binary64)) (/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))))) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))))))))
(/.f64 (-.f64 (cos.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (/.f64 (+.f64 eps (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (/.f64 eps #s(literal 2 binary64)))) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))))) #s(literal 2 binary64))
(/.f64 (neg.f64 (-.f64 (cos.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))))))) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))))))) #s(literal -1 binary64))
(.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))))
(.f64 (sin.f64 (/.f64 (+.f64 eps (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (sin.f64 (/.f64 eps #s(literal 2 binary64))))
(.f64 (-.f64 (cos.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))))) #s(literal 1/2 binary64))
(sin.f64 (/.f64 eps #s(literal 2 binary64)))
(neg.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (+.f64 (cos.f64 eps) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 eps) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 eps) #s(literal -1 binary64)))) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) #s(literal -1 binary64))))
(/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 eps) #s(literal -1 binary64)))))
(/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #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 #s(literal 2 binary64) eps)))) (*.f64 (cos.f64 eps) #s(literal -1 binary64)))))
(/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) #s(literal -1 binary64)) (+.f64 (cos.f64 eps) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (-.f64 #s(literal -1 binary64) (cos.f64 eps)))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 3 binary64)))) (neg.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 eps) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) #s(literal -1 binary64))) (neg.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64))))
(pow.f64 (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 eps) #s(literal -1 binary64)))) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) #s(literal -1 binary64))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #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 #s(literal 2 binary64) eps)))) (-.f64 #s(literal 1 binary64) (.f64 (cos.f64 eps) #s(literal -1 binary64))))))
(.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 eps) #s(literal 1 binary64))))
(+.f64 (.f64 (cos.f64 eps) #s(literal 1 binary64)) (.f64 (sin.f64 eps) #s(literal 0 binary64)))
(+.f64 (fma.f64 (cos.f64 eps) #s(literal 1 binary64) (neg.f64 (.f64 #s(literal 0 binary64) (sin.f64 eps)))) (fma.f64 #s(literal 0 binary64) (sin.f64 eps) (.f64 #s(literal 0 binary64) (sin.f64 eps))))
(+.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 eps) (neg.f64 (.f64 (sin.f64 eps) #s(literal 0 binary64)))) (fma.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) #s(literal 0 binary64) (.f64 (sin.f64 eps) #s(literal 0 binary64))))
(+.f64 (.f64 (cos.f64 eps) (cos.f64 (/.f64 #s(literal 0 binary64) eps))) (.f64 (sin.f64 eps) (sin.f64 (/.f64 #s(literal 0 binary64) eps))))
(cos.f64 eps)
(-.f64 (.f64 (cos.f64 eps) #s(literal 1 binary64)) (.f64 (sin.f64 eps) #s(literal 0 binary64)))
(-.f64 (.f64 #s(literal 1 binary64) (cos.f64 eps)) (.f64 #s(literal 0 binary64) (sin.f64 eps)))
(fma.f64 (cos.f64 eps) #s(literal 1 binary64) (neg.f64 (*.f64 (sin.f64 eps) #s(literal 0 binary64))))
(fma.f64 #s(literal 1 binary64) (cos.f64 eps) (neg.f64 (*.f64 #s(literal 0 binary64) (sin.f64 eps))))
(+.f64 (cos.f64 (+.f64 eps x)) (+.f64 #s(literal -1 binary64) (neg.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)))))
(+.f64 (cos.f64 (+.f64 eps x)) (+.f64 (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps))) (+.f64 #s(literal -1 binary64) (neg.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x))))))
(+.f64 (cos.f64 (+.f64 eps x)) (-.f64 (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))))
(+.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (-.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))))
(+.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)))) (cos.f64 (+.f64 eps x)))
(+.f64 (+.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x))))
(+.f64 (+.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (.f64 (neg.f64 x) (.f64 x #s(literal -1/2 binary64))))
(+.f64 (+.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (.f64 (neg.f64 (.f64 x #s(literal -1/2 binary64))) x))
(+.f64 (+.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (.f64 (neg.f64 (.f64 x x)) #s(literal -1/2 binary64)))
(+.f64 (fma.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 (-.f64 x eps))))) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))))))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64)))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)))))))
(+.f64 (fma.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 (-.f64 x eps))))) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64)))))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x))))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64))))))
(+.f64 (fma.f64 (.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 (-.f64 x eps))) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))))))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64)))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)))))))
(+.f64 (fma.f64 (.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 (-.f64 x eps))) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64)))))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x))))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64))))))
(-.f64 (cos.f64 (+.f64 eps x)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x))))
(-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (-.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (+.f64 #s(literal -1 binary64) (neg.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x))))))
(-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (+.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))))
(-.f64 (+.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(-.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x))) (+.f64 (cos.f64 (+.f64 eps x)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x))))))) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x))))) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x))) (+.f64 (cos.f64 (+.f64 eps x)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x))))))))
(-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (+.f64 (cos.f64 (+.f64 eps x)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x))))) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))) (+.f64 (cos.f64 (+.f64 eps x)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(-.f64 (-.f64 (cos.f64 (+.f64 eps x)) (.f64 #s(literal -1/2 binary64) (.f64 x x))) #s(literal 1 binary64))
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(cos.f64 (+.f64 eps x))
(-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (sin.f64 x) (sin.f64 eps)))
(-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (-.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps)))))
(-.f64 (/.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 (-.f64 x eps))))) (/.f64 (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64)) (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 (-.f64 x eps))))))
(-.f64 (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (cos.f64 (-.f64 x eps))) (/.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps))))) (cos.f64 (-.f64 x eps))))
(-.f64 (.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64)) (.f64 (sin.f64 (+.f64 eps x)) #s(literal 0 binary64)))
(-.f64 (.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (.f64 #s(literal 0 binary64) (sin.f64 (+.f64 eps x))))
(-.f64 (.f64 (cos.f64 eps) (cos.f64 (+.f64 #s(literal 0 binary64) x))) (.f64 (sin.f64 eps) (sin.f64 (+.f64 #s(literal 0 binary64) x))))
(-.f64 (.f64 (cos.f64 (+.f64 x #s(literal 0 binary64))) (cos.f64 eps)) (.f64 (sin.f64 (+.f64 x #s(literal 0 binary64))) (sin.f64 eps)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))))
(fma.f64 (cos.f64 eps) (cos.f64 x) (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(fma.f64 (cos.f64 eps) (cos.f64 x) (neg.f64 (-.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (sin.f64 x) (sin.f64 eps))))))
(fma.f64 #s(literal -1 binary64) (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))))
(fma.f64 (cos.f64 x) (cos.f64 eps) (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (-.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (sin.f64 x) (sin.f64 eps))))))
(fma.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 (sin.f64 eps) (-.f64 #s(literal 0 binary64) (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) (sin.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps))) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))))
(fma.f64 (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps))) #s(literal 1/2 binary64) (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(fma.f64 (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps))) #s(literal 1/2 binary64) (neg.f64 (-.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (sin.f64 x) (sin.f64 eps))))))
(fma.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 (-.f64 x eps))))) (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (sin.f64 x) (sin.f64 eps))))
(fma.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 (-.f64 x eps))))) (+.f64 (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps))) (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(fma.f64 (.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 (-.f64 x eps))) (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (sin.f64 x) (sin.f64 eps))))
(fma.f64 (.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 (-.f64 x eps))) (+.f64 (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps))) (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 (-.f64 x eps)))) (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (-.f64 x eps)) (*.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x)))))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 (-.f64 x eps)))))
(/.f64 (*.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x))) (cos.f64 (-.f64 x eps)))
(/.f64 (-.f64 (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps))) (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x)))) #s(literal 2 binary64))
(/.f64 (-.f64 (.f64 (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps))) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x))))) #s(literal 4 binary64))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 (-.f64 x eps))))))
(/.f64 (neg.f64 (*.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x)))) (neg.f64 (cos.f64 (-.f64 x eps))))
(/.f64 (+.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps))) #s(literal 3 binary64))) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (-.f64 (pow.f64 (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps))) #s(literal 2 binary64)) (.f64 (cos.f64 (+.f64 eps x)) (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (sin.f64 x) (sin.f64 eps)))))))
(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) #s(literal 3 binary64))) (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (-.f64 (pow.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps)))))))
(/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (pow.f64 (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps))) #s(literal 2 binary64))) (-.f64 (cos.f64 (+.f64 eps x)) (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps)))))
(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (pow.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) #s(literal 2 binary64))) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps)))))
(pow.f64 (/.f64 (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 (-.f64 x eps)))) (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (cos.f64 (-.f64 x eps)) (*.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x)))) #s(literal -1 binary64))
(.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 (-.f64 x eps))))))
(.f64 (.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 (-.f64 x eps))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps)))))
(/.f64 (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps))) #s(literal 2 binary64))
(/.f64 (neg.f64 (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps)))) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps)))) #s(literal -1 binary64))
(*.f64 (cos.f64 eps) (cos.f64 x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(*.f64 (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps))) #s(literal 1/2 binary64))
(cos.f64 x)
(sin.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))
(neg.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal -2 binary64))))
(*.f64 x #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) x)
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal -1/2 binary64)) x)
(.f64 (.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(.f64 (.f64 x x) #s(literal -1/2 binary64))
(.f64 (.f64 #s(literal 1 binary64) x) (*.f64 x #s(literal -1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64))) x)
(.f64 (.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(-.f64 (/.f64 (cos.f64 (-.f64 x eps)) #s(literal 2 binary64)) (/.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x)))))
(/.f64 (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64))
(/.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x)))) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x)))) #s(literal -1 binary64))
(*.f64 (sin.f64 x) (sin.f64 eps))
(*.f64 (sin.f64 eps) (sin.f64 x))
(*.f64 (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x))) #s(literal 1/2 binary64))

simplify244.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

5622×	`-lowering-.f32`
5622×	`-lowering-.f64`
2858×	`+-lowering-+.f64`
2858×	`+-lowering-+.f32`
1538×	`neg-lowering-neg.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	413	3751
1	1405	3297
2	4557	3270
0	8443	3270

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 420

Calls

Call 1

Inputs
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* 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 (pow eps 2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
1
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* 1/2 (pow x 2))
(* (pow x 2) (- (+ 1/2 (/ (cos (+ eps x)) (pow x 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (+ 1/2 (/ (cos (+ eps x)) (pow x 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (+ 1/2 (/ (cos (+ eps x)) (pow x 2))) (/ 1 (pow x 2))))
(* 1/2 (pow x 2))
(* (pow x 2) (- (+ 1/2 (/ (cos (- eps (* -1 x))) (pow x 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (+ 1/2 (/ (cos (- eps (* -1 x))) (pow x 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (+ 1/2 (/ (cos (- eps (* -1 x))) (pow x 2))) (/ 1 (pow x 2))))
(- (cos x) (+ 1 (* -1/2 (pow x 2))))
(- (+ (cos x) (* -1 (* eps (sin x)))) (+ 1 (* -1/2 (pow x 2))))
(- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (+ 1 (* -1/2 (pow x 2))))
(- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (+ 1 (* -1/2 (pow x 2))))
(- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))
(- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))
(- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))
(- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))
(- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))
(- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))
(- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))
(- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- 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)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* -1/2 (pow x 2)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* eps (cos x)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin 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 (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 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(* -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 (cos x)))
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(cos eps)
(+ (cos eps) (* -1/2 (* (pow x 2) (cos eps))))
(+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* 1/24 (* (pow x 2) (cos eps))))))
(+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos eps))) (* 1/24 (cos eps)))))))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(cos x)
(+ (cos x) (* -1/2 (* (pow eps 2) (cos x))))
(+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x))))))
(+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x)))))))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos 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)
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -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)
(* -1/2 x)
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* x (sin eps))
(* x (+ (sin eps) (* -1/6 (* (pow x 2) (sin eps)))))
(* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* 1/120 (* (pow x 2) (sin eps)))))))
(* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin eps))) (* 1/120 (sin eps))))))))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* eps (sin x))
(* eps (+ (sin x) (* -1/6 (* (pow eps 2) (sin x)))))
(* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* 1/120 (* (pow eps 2) (sin x)))))))
(* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (sin x))) (* 1/120 (sin x))))))))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))

Outputs
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))) (sin.f64 x)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
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(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))) (cos.f64 eps))
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(* (cos eps) (cos x))
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1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
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(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
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(cos x)
(cos.f64 x)
(cos x)
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(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(sin x)
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(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
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(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
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(sin (* 1/2 (+ eps (* 2 x))))
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(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 eps))
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(+.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (+.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (*.f64 x #s(literal -1/6 binary64))))))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (- eps (* -2 x))))
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(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
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(* -1/2 x)
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(* -1/2 x)
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(* -1/2 x)
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(.f64 x (.f64 x #s(literal -1/2 binary64)))
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(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* x (sin eps))
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(.f64 x (.f64 (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 x x)) #s(literal 1 binary64)) (sin.f64 eps)))
(* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* 1/120 (* (pow x 2) (sin eps)))))))
(.f64 x (+.f64 (sin.f64 eps) (.f64 (.f64 x x) (.f64 (sin.f64 eps) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64)))))))
(* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin eps))) (* 1/120 (sin eps))))))))
(.f64 x (+.f64 (.f64 (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 x x)) #s(literal 1 binary64)) (sin.f64 eps)) (.f64 (.f64 (sin.f64 eps) (+.f64 (.f64 (.f64 x x) #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) (.f64 (.f64 x x) (*.f64 x x)))))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
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(*.f64 (sin.f64 x) (sin.f64 eps))
(* eps (sin x))
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(* eps (+ (sin x) (* -1/6 (* (pow eps 2) (sin x)))))
(.f64 eps (.f64 (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) #s(literal 1 binary64)) (sin.f64 x)))
(* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* 1/120 (* (pow eps 2) (sin x)))))))
(.f64 eps (+.f64 (sin.f64 x) (.f64 eps (.f64 eps (.f64 (sin.f64 x) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 eps eps) #s(literal 1/120 binary64))))))))
(* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (sin x))) (* 1/120 (sin x))))))))
(.f64 eps (+.f64 (.f64 (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) #s(literal 1 binary64)) (sin.f64 x)) (.f64 (.f64 (sin.f64 x) (+.f64 (.f64 (.f64 eps eps) #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) (.f64 (.f64 eps eps) (*.f64 eps eps)))))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))

eval86.0ms (0.5%)

Compiler: Compiled 18792 to 1700 computations (91% saved)

prune83.0ms (0.5%)

Pruning

27 alts after pruning (23 fresh and 4 done)

	Pruned	Kept	Total
New	876	21	897
Fresh	2	2	4
Picked	2	3	5
Done	0	1	1
Total	880	27	907

Accuracy

100.0%

Counts

907 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	18.5%	(/.f64 (.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 3 binary64))) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (.f64 eps (.f64 eps eps))) (.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 #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (.f64 (sin.f64 x) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x)))) (.f64 eps eps)))
▶	84.8%	(/.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x)) (.f64 eps eps)) eps)
✓	52.5%	(-.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
	82.1%	(-.f64 (+.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 (cos.f64 x) (cos.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps)))
	97.3%	(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 eps x))
✓	52.4%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	81.1%	(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
	97.8%	(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (-.f64 (.f64 x (+.f64 (.f64 eps (.f64 x #s(literal 1/6 binary64))) (.f64 #s(literal 1/4 binary64) (.f64 eps eps)))) eps)))
	97.3%	(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) eps)))
	97.9%	(+.f64 (.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (+.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))) (.f64 (+.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 (.f64 (.f64 x #s(literal 1/3 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 x x)))
✓	51.0%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
▶	50.7%	(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
	99.4%	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
	99.0%	(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
▶	99.5%	(.f64 (.f64 (sin.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
	97.7%	(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
	98.9%	(.f64 eps (/.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 #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (pow.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) (-.f64 #s(literal 0 binary64) (sin.f64 x)))))
	99.4%	(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))) (sin.f64 x)))
	99.3%	(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))
✓	99.0%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
▶	98.5%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
	97.4%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
	97.9%	(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))
▶	97.4%	(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 #s(literal 1/4 binary64) x))))))
	98.9%	(.f64 eps (.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))))
	50.0%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
	52.0%	(.f64 #s(literal -1/2 binary64) (.f64 eps eps))

Compiler

Compiled 940 to 598 computations (36.4% saved)

simplify162.0ms (1%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps))
✓	cost-diff	0	(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x))
✓	cost-diff	0	(.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x)) (.f64 eps eps))
✓	cost-diff	256	(/.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x)) (.f64 eps eps)) eps)
✓	cost-diff	0	(sin.f64 x)
✓	cost-diff	0	(*.f64 eps #s(literal -1/2 binary64))
✓	cost-diff	0	(-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x))
✓	cost-diff	0	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 #s(literal 1/4 binary64) x))))
✓	cost-diff	0	(*.f64 eps #s(literal -1/2 binary64))
✓	cost-diff	0	(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 #s(literal 1/4 binary64) x))))))
✓	cost-diff	128	(+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 #s(literal 1/4 binary64) x)))))
✓	cost-diff	128	(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
✓	cost-diff	0	(sin.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal 2 binary64)))
✓	cost-diff	0	(.f64 (sin.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
✓	cost-diff	0	(.f64 (.f64 (sin.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))

Rules

2144×	`-lowering-.f32`
2144×	`-lowering-.f64`
1838×	`/-lowering-/.f32`
1838×	`/-lowering-/.f64`
1520×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	37	198
1	91	189
2	284	186
3	774	181
4	2286	179
5	5698	179
0	8012	179

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (* (sin (/ (/ 1 (/ 1 eps)) 2)) (sin (/ (+ eps (* x 2)) 2))) -2)
(* (sin (/ (/ 1 (/ 1 eps)) 2)) (sin (/ (+ eps (* x 2)) 2)))
(sin (/ (/ 1 (/ 1 eps)) 2))
(/ (/ 1 (/ 1 eps)) 2)
(/ 1 (/ 1 eps))
1
(/ 1 eps)
eps
2
(sin (/ (+ eps (* x 2)) 2))
(/ (+ eps (* x 2)) 2)
(+ eps (* x 2))
(* x 2)
x
-2
(+ 1 -1)
1
-1
(* eps (+ (* eps -1/2) (* x (+ -1 (* eps (* 1/4 x))))))
eps
(+ (* eps -1/2) (* x (+ -1 (* eps (* 1/4 x)))))
(* eps -1/2)
-1/2
(* x (+ -1 (* eps (* 1/4 x))))
x
(+ -1 (* eps (* 1/4 x)))
-1
(* eps (* 1/4 x))
(* 1/4 x)
1/4
(* eps (- (* eps -1/2) (sin x)))
eps
(- (* eps -1/2) (sin x))
(* eps -1/2)
-1/2
(sin x)
x
(/ (* (- (* -1/2 (* (cos x) eps)) (sin x)) (* eps eps)) eps)
(* (- (* -1/2 (* (cos x) eps)) (sin x)) (* eps eps))
(- (* -1/2 (* (cos x) eps)) (sin x))
(* -1/2 (* (cos x) eps))
-1/2
(* (cos x) eps)
(cos x)
x
eps
(sin x)
(* eps eps)

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

localize167.0ms (1%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 (cos.f64 x) eps)
✓	accuracy	100.0%	(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x))
✓	accuracy	99.8%	(.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x)) (.f64 eps eps))
✓	accuracy	85.8%	(/.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x)) (.f64 eps eps)) eps)
✓	accuracy	100.0%	(*.f64 eps #s(literal -1/2 binary64))
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x))
✓	accuracy	99.8%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
✓	accuracy	100.0%	(*.f64 #s(literal 1/4 binary64) x)
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 #s(literal 1/4 binary64) x))))
✓	accuracy	100.0%	(+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 #s(literal 1/4 binary64) x)))))
✓	accuracy	99.8%	(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 #s(literal 1/4 binary64) x))))))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
✓	accuracy	100.0%	(.f64 (.f64 (sin.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
✓	accuracy	99.8%	(sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
✓	accuracy	99.8%	(.f64 (sin.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))

Results

115.0ms	252×	0	valid
5.0ms	2×	3	valid
1.0ms	1×	2	valid
1.0ms	1×	1	valid

Compiler

Compiled 234 to 37 computations (84.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 52.0ms

ival-mult: 19.0ms (36.6% of total)

ival-div: 13.0ms (25% of total)

ival-sin: 7.0ms (13.5% of total)

ival-add: 5.0ms (9.6% of total)

ival-sub: 3.0ms (5.8% of total)

ival-cos: 3.0ms (5.8% of total)

const: 1.0ms (1.9% of total)

backward-pass: 1.0ms (1.9% of total)

series20.0ms (0.1%)

Counts

19 → 372

Calls

Call 1

Inputs
#<alt (/ 1 (/ 1 eps))>
#<alt (* (* (sin (/ (/ 1 (/ 1 eps)) 2)) (sin (/ (+ eps (* x 2)) 2))) -2)>
#<alt (* (sin (/ (/ 1 (/ 1 eps)) 2)) (sin (/ (+ eps (* x 2)) 2)))>
#<alt (sin (/ (/ 1 (/ 1 eps)) 2))>
#<alt (+ 1 -1)>
#<alt (+ (* eps -1/2) (* x (+ -1 (* eps (* 1/4 x)))))>
#<alt (* eps (+ (* eps -1/2) (* x (+ -1 (* eps (* 1/4 x))))))>
#<alt (* eps -1/2)>
#<alt (* x (+ -1 (* eps (* 1/4 x))))>
#<alt (* eps (- (* eps -1/2) (sin x)))>
#<alt (- (* eps -1/2) (sin x))>
#<alt (sin x)>
#<alt (/ (* (- (* -1/2 (* (cos x) eps)) (sin x)) (* eps eps)) eps)>
#<alt (* (- (* -1/2 (* (cos x) eps)) (sin x)) (* eps eps))>
#<alt (- (* -1/2 (* (cos x) eps)) (sin x))>
#<alt (* -1/2 (* (cos x) eps))>
#<alt (sin (/ (+ eps (* x 2)) 2))>
#<alt (* 1/4 x)>
#<alt (* (cos x) eps)>

Outputs
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (pow (sin (* 1/2 eps)) 2)>
#<alt (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<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 x)>
#<alt (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2)))>
#<alt (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2)))>
#<alt (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2)))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* -1 (* eps (+ 1/2 (* -1/4 (pow x 2)))))>
#<alt (* -1 (* eps (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps)))))>
#<alt (* -1 (* eps (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps)))))>
#<alt (* -1 (* eps (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps)))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))>
#<alt (* 1/4 (* eps (pow x 2)))>
#<alt (* (pow x 2) (- (* 1/4 eps) (/ 1 x)))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x)))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x)))>
#<alt (* 1/4 (* eps (pow x 2)))>
#<alt (* (pow x 2) (- (* 1/4 eps) (/ 1 x)))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)))>
#<alt (* -1 (* eps x))>
#<alt (* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))>
#<alt (* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))>
#<alt (* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))>
#<alt (* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* -1 (* (pow eps 2) (+ 1/2 (* -1/4 (pow x 2)))))>
#<alt (* (pow eps 2) (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (* -1 (/ x eps))))>
#<alt (* (pow eps 2) (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (* -1 (/ x eps))))>
#<alt (* (pow eps 2) (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (* -1 (/ x eps))))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))>
#<alt (* 1/4 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2)))))>
#<alt (* (pow x 2) (+ (* -1 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2)))))>
#<alt (* 1/4 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))))>
#<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 x)>
#<alt (* x (- (* 1/4 (* eps x)) 1))>
#<alt (* x (- (* 1/4 (* eps x)) 1))>
#<alt (* x (- (* 1/4 (* eps x)) 1))>
#<alt (* 1/4 (* eps (pow x 2)))>
#<alt (* (pow x 2) (- (* 1/4 eps) (/ 1 x)))>
#<alt (* (pow x 2) (- (* 1/4 eps) (/ 1 x)))>
#<alt (* (pow x 2) (- (* 1/4 eps) (/ 1 x)))>
#<alt (* 1/4 (* eps (pow x 2)))>
#<alt (* (pow x 2) (- (* 1/4 eps) (/ 1 x)))>
#<alt (* (pow x 2) (- (* 1/4 eps) (/ 1 x)))>
#<alt (* (pow x 2) (- (* 1/4 eps) (/ 1 x)))>
#<alt (* -1 x)>
#<alt (+ (* -1 x) (* 1/4 (* eps (pow x 2))))>
#<alt (+ (* -1 x) (* 1/4 (* eps (pow x 2))))>
#<alt (+ (* -1 x) (* 1/4 (* eps (pow x 2))))>
#<alt (* 1/4 (* eps (pow x 2)))>
#<alt (* eps (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))))>
#<alt (* eps (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))))>
#<alt (* eps (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))))>
#<alt (* 1/4 (* eps (pow x 2)))>
#<alt (* -1 (* eps (+ (* -1/4 (pow x 2)) (/ x eps))))>
#<alt (* -1 (* eps (+ (* -1/4 (pow x 2)) (/ x eps))))>
#<alt (* -1 (* eps (+ (* -1/4 (pow x 2)) (/ x eps))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 eps)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 eps)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 eps)))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))>
#<alt (* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))>
#<alt (* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))>
#<alt (* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))>
#<alt (* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))))))>
#<alt (* eps (- (* -1/2 eps) (sin x)))>
#<alt (* eps (- (* -1/2 eps) (sin x)))>
#<alt (* eps (- (* -1/2 eps) (sin x)))>
#<alt (* eps (- (* -1/2 eps) (sin x)))>
#<alt (* eps (- (* -1/2 eps) (sin x)))>
#<alt (* eps (- (* -1/2 eps) (sin x)))>
#<alt (* eps (- (* -1/2 eps) (sin x)))>
#<alt (* eps (- (* -1/2 eps) (sin x)))>
#<alt (* -1 (sin x))>
#<alt (- (* -1/2 eps) (sin x))>
#<alt (- (* -1/2 eps) (sin x))>
#<alt (- (* -1/2 eps) (sin x))>
#<alt (* -1/2 eps)>
#<alt (* eps (- (* -1 (/ (sin x) eps)) 1/2))>
#<alt (* eps (- (* -1 (/ (sin x) eps)) 1/2))>
#<alt (* eps (- (* -1 (/ (sin x) eps)) 1/2))>
#<alt (* -1/2 eps)>
#<alt (* -1 (* eps (+ 1/2 (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ 1/2 (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ 1/2 (/ (sin x) eps))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))>
#<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 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)>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (pow eps 3))>
#<alt (+ (* -1 (* (pow eps 2) x)) (* -1/2 (pow eps 3)))>
#<alt (+ (* -1/2 (pow eps 3)) (* x (+ (* -1 (pow eps 2)) (* 1/4 (* (pow eps 3) x)))))>
#<alt (+ (* -1/2 (pow eps 3)) (* x (+ (* -1 (pow eps 2)) (* x (+ (* 1/6 (* (pow eps 2) x)) (* 1/4 (pow eps 3)))))))>
#<alt (* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* -1 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* (pow eps 2) (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* (pow eps 2) (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* -1/2 (* (pow eps 3) (cos x)))>
#<alt (* (pow eps 3) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 3) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 3) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (* (pow eps 3) (cos x)))>
#<alt (* -1 (* (pow eps 3) (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1 (* (pow eps 3) (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1 (* (pow eps 3) (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (* -1 (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))>
#<alt (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))>
#<alt (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (sin x)>
#<alt (+ (sin x) (* 1/2 (* eps (cos x))))>
#<alt (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))>
#<alt (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 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 (* 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))>

Calls

93 calls:

Time	Variable		Point	Expression
4.0ms	x	@	inf	(* 1/4 x)
1.0ms	eps	@	inf	(+ (* eps -1/2) (* x (+ -1 (* eps (* 1/4 x)))))
1.0ms	x	@	0	(* eps (- (* eps -1/2) (sin x)))
1.0ms	eps	@	0	(+ (* eps -1/2) (* x (+ -1 (* eps (* 1/4 x)))))
0.0ms	eps	@	-inf	(+ (* eps -1/2) (* x (+ -1 (* eps (* 1/4 x)))))

rewrite270.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

3804×	`-lowering-.f32`
3804×	`-lowering-.f64`
2576×	`/-lowering-/.f32`
2576×	`/-lowering-/.f64`
2198×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	139
1	188	133
2	1746	130
0	8207	130

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 368

Calls

Call 1

Inputs
(/ 1 (/ 1 eps))
(* (* (sin (/ (/ 1 (/ 1 eps)) 2)) (sin (/ (+ eps (* x 2)) 2))) -2)
(* (sin (/ (/ 1 (/ 1 eps)) 2)) (sin (/ (+ eps (* x 2)) 2)))
(sin (/ (/ 1 (/ 1 eps)) 2))
(+ 1 -1)
(+ (* eps -1/2) (* x (+ -1 (* eps (* 1/4 x)))))
(* eps (+ (* eps -1/2) (* x (+ -1 (* eps (* 1/4 x))))))
(* eps -1/2)
(* x (+ -1 (* eps (* 1/4 x))))
(* eps (- (* eps -1/2) (sin x)))
(- (* eps -1/2) (sin x))
(sin x)
(/ (* (- (* -1/2 (* (cos x) eps)) (sin x)) (* eps eps)) eps)
(* (- (* -1/2 (* (cos x) eps)) (sin x)) (* eps eps))
(- (* -1/2 (* (cos x) eps)) (sin x))
(* -1/2 (* (cos x) eps))
(sin (/ (+ eps (* x 2)) 2))
(* 1/4 x)
(* (cos x) eps)

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

simplify234.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

5272×	`-lowering-.f32`
5272×	`-lowering-.f64`
3542×	`+-lowering-+.f64`
3542×	`+-lowering-+.f32`
1324×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	368	3461
1	1284	3040
2	4107	2933
0	8063	2933

Stop Event

1×	iter limit
1×	node limit

Counts

372 → 372

Calls

Call 1

Inputs
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* 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 x)
(+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2)))
(+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2)))
(+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2)))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* -1 (* eps (+ 1/2 (* -1/4 (pow x 2)))))
(* -1 (* eps (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps)))))
(* -1 (* eps (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps)))))
(* -1 (* eps (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps)))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (- (* 1/4 eps) (/ 1 x)))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x)))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x)))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (- (* 1/4 eps) (/ 1 x)))
(* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)))
(* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)))
(* -1 (* eps x))
(* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* -1 (* (pow eps 2) (+ 1/2 (* -1/4 (pow x 2)))))
(* (pow eps 2) (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (* -1 (/ x eps))))
(* (pow eps 2) (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (* -1 (/ x eps))))
(* (pow eps 2) (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (* -1 (/ x eps))))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))
(* (pow x 2) (+ (* -1 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2)))))
(* (pow x 2) (+ (* -1 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2)))))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))
(* (pow x 2) (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))))
(* (pow x 2) (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))))
(* -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 x)
(* x (- (* 1/4 (* eps x)) 1))
(* x (- (* 1/4 (* eps x)) 1))
(* x (- (* 1/4 (* eps x)) 1))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (- (* 1/4 eps) (/ 1 x)))
(* (pow x 2) (- (* 1/4 eps) (/ 1 x)))
(* (pow x 2) (- (* 1/4 eps) (/ 1 x)))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (- (* 1/4 eps) (/ 1 x)))
(* (pow x 2) (- (* 1/4 eps) (/ 1 x)))
(* (pow x 2) (- (* 1/4 eps) (/ 1 x)))
(* -1 x)
(+ (* -1 x) (* 1/4 (* eps (pow x 2))))
(+ (* -1 x) (* 1/4 (* eps (pow x 2))))
(+ (* -1 x) (* 1/4 (* eps (pow x 2))))
(* 1/4 (* eps (pow x 2)))
(* eps (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))))
(* eps (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))))
(* eps (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))))
(* 1/4 (* eps (pow x 2)))
(* -1 (* eps (+ (* -1/4 (pow x 2)) (/ x eps))))
(* -1 (* eps (+ (* -1/4 (pow x 2)) (/ x eps))))
(* -1 (* eps (+ (* -1/4 (pow x 2)) (/ x eps))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 eps)))
(* eps (+ (* -1 (sin x)) (* -1/2 eps)))
(* eps (+ (* -1 (sin x)) (* -1/2 eps)))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))))))
(* eps (- (* -1/2 eps) (sin x)))
(* eps (- (* -1/2 eps) (sin x)))
(* eps (- (* -1/2 eps) (sin x)))
(* eps (- (* -1/2 eps) (sin x)))
(* eps (- (* -1/2 eps) (sin x)))
(* eps (- (* -1/2 eps) (sin x)))
(* eps (- (* -1/2 eps) (sin x)))
(* eps (- (* -1/2 eps) (sin x)))
(* -1 (sin x))
(- (* -1/2 eps) (sin x))
(- (* -1/2 eps) (sin x))
(- (* -1/2 eps) (sin x))
(* -1/2 eps)
(* eps (- (* -1 (/ (sin x) eps)) 1/2))
(* eps (- (* -1 (/ (sin x) eps)) 1/2))
(* eps (- (* -1 (/ (sin x) eps)) 1/2))
(* -1/2 eps)
(* -1 (* eps (+ 1/2 (/ (sin x) eps))))
(* -1 (* eps (+ 1/2 (/ (sin x) eps))))
(* -1 (* eps (+ 1/2 (/ (sin x) eps))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* -1/2 eps) (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))
(- (* -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))
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)
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (pow eps 3))
(+ (* -1 (* (pow eps 2) x)) (* -1/2 (pow eps 3)))
(+ (* -1/2 (pow eps 3)) (* x (+ (* -1 (pow eps 2)) (* 1/4 (* (pow eps 3) x)))))
(+ (* -1/2 (pow eps 3)) (* x (+ (* -1 (pow eps 2)) (* x (+ (* 1/6 (* (pow eps 2) x)) (* 1/4 (pow eps 3)))))))
(* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))
(* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))
(* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))
(* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))
(* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))
(* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))
(* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))
(* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))
(* -1 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* (pow eps 2) (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* (pow eps 2) (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* -1/2 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* (pow eps 3) (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* (pow eps 3) (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* eps (cos x)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(* -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 (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 (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 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))
(* 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))

Outputs
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) (sin.f64 x)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (pow (sin (* 1/2 eps)) 2))
(.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (+.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+.f64 (.f64 (.f64 (.f64 x #s(literal -2 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (+.f64 (.f64 x x) #s(literal -2 binary64))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(+.f64 (.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (.f64 x (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal -2 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64))))) (.f64 x (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* 1/2 (* eps (sin x)))
(.f64 eps (.f64 (sin.f64 x) #s(literal 1/2 binary64)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 eps (+.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) (.f64 (.f64 eps (cos.f64 x)) #s(literal 1/4 binary64))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(.f64 eps (+.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) (.f64 eps (+.f64 (.f64 (.f64 eps (sin.f64 x)) #s(literal -1/12 binary64)) (.f64 (cos.f64 x) #s(literal 1/4 binary64))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(.f64 eps (+.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) (.f64 eps (+.f64 (.f64 (cos.f64 x) #s(literal 1/4 binary64)) (.f64 eps (+.f64 (.f64 (sin.f64 x) #s(literal -1/12 binary64)) (.f64 (.f64 eps (cos.f64 x)) #s(literal -1/48 binary64))))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(pow (sin (* 1/2 eps)) 2)
(pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (+.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 x (+.f64 (.f64 x (.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (.f64 (*.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 x)
(-.f64 #s(literal 0 binary64) x)
(+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2)))
(-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/4 binary64))))) x)
(+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2)))
(-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/4 binary64))))) x)
(+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2)))
(-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/4 binary64))))) x)
(* eps (- (* 1/4 (pow x 2)) 1/2))
(.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/4 binary64)))))
(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(* -1 (* eps (+ 1/2 (* -1/4 (pow x 2)))))
(.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/4 binary64)))))
(* -1 (* eps (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps)))))
(.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(* -1 (* eps (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps)))))
(.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(* -1 (* eps (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps)))))
(.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(+ (* -1 x) (* -1/2 eps))
(-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/4 binary64))))) x)
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/4 binary64))))) x)
(* 1/4 (* eps (pow x 2)))
(.f64 eps (.f64 x (*.f64 x #s(literal 1/4 binary64))))
(* (pow x 2) (- (* 1/4 eps) (/ 1 x)))
(.f64 (.f64 x x) (+.f64 (*.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x)))
(.f64 (.f64 x x) (+.f64 (.f64 eps (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))) (/.f64 #s(literal -1 binary64) x)))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x)))
(.f64 (.f64 x x) (+.f64 (.f64 eps (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))) (/.f64 #s(literal -1 binary64) x)))
(* 1/4 (* eps (pow x 2)))
(.f64 eps (.f64 x (*.f64 x #s(literal 1/4 binary64))))
(* (pow x 2) (- (* 1/4 eps) (/ 1 x)))
(.f64 (.f64 x x) (+.f64 (*.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)))
(* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)))
(.f64 (.f64 x x) (-.f64 (.f64 eps #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal 1/2 binary64)) x)) x)))
(* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)))
(.f64 (.f64 x x) (-.f64 (.f64 eps #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal 1/2 binary64)) x)) x)))
(* -1 (* eps x))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) x))
(* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) x))
(* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) x))
(* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))))
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
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(+ (* -1/2 (pow eps 3)) (* x (+ (* -1 (pow eps 2)) (* x (+ (* 1/6 (* (pow eps 2) x)) (* 1/4 (pow eps 3)))))))
(+.f64 (.f64 (.f64 x x) (.f64 (.f64 eps eps) (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))))
(* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))))
(* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))))
(* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))))
(* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))))
(* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))))
(* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))))
(* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))))
(* -1 (* (pow eps 2) (sin x)))
(-.f64 #s(literal 0 binary64) (.f64 eps (.f64 eps (sin.f64 x))))
(* (pow eps 2) (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))))
(* (pow eps 2) (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))))
(* (pow eps 2) (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))))
(* -1/2 (* (pow eps 3) (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (cos.f64 x)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)) (.f64 eps (.f64 eps eps)))
(* (pow eps 3) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)) (.f64 eps (.f64 eps eps)))
(* (pow eps 3) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)) (.f64 eps (.f64 eps eps)))
(* -1/2 (* (pow eps 3) (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (cos.f64 x)))))
(* -1 (* (pow eps 3) (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)) (.f64 eps (.f64 eps eps)))
(* -1 (* (pow eps 3) (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)) (.f64 eps (.f64 eps eps)))
(* -1 (* (pow eps 3) (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)) (.f64 eps (.f64 eps eps)))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(+ (* -1 x) (* -1/2 eps))
(-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/4 binary64))))) x)
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/6 binary64)))))))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(* -1 (sin x))
(-.f64 #s(literal 0 binary64) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/4 binary64)))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/48 binary64))))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal -1/48 binary64) (.f64 (*.f64 x x) #s(literal 1/1440 binary64))))))))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(sin x)
(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+.f64 (sin.f64 x) (.f64 (.f64 eps (cos.f64 x)) #s(literal 1/2 binary64)))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+.f64 (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal -1/8 binary64))) #s(literal 1 binary64)) (sin.f64 x)) (.f64 (*.f64 eps (cos.f64 x)) #s(literal 1/2 binary64)))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(+.f64 (sin.f64 x) (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal -1/8 binary64))) (.f64 (cos.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+.f64 (.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(+.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (+.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal -1/2 binary64))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64)))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(* 1/4 x)
(*.f64 x #s(literal 1/4 binary64))
(* 1/4 x)
(*.f64 x #s(literal 1/4 binary64))
(* 1/4 x)
(*.f64 x #s(literal 1/4 binary64))
(* 1/4 x)
(*.f64 x #s(literal 1/4 binary64))
(* 1/4 x)
(*.f64 x #s(literal 1/4 binary64))
(* 1/4 x)
(*.f64 x #s(literal 1/4 binary64))
(* 1/4 x)
(*.f64 x #s(literal 1/4 binary64))
(* 1/4 x)
(*.f64 x #s(literal 1/4 binary64))
(* 1/4 x)
(*.f64 x #s(literal 1/4 binary64))
(* 1/4 x)
(*.f64 x #s(literal 1/4 binary64))
(* 1/4 x)
(*.f64 x #s(literal 1/4 binary64))
(* 1/4 x)
(*.f64 x #s(literal 1/4 binary64))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal -1/2 binary64))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+.f64 eps (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(+.f64 eps (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 (.f64 x x) #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))))))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))

eval71.0ms (0.4%)

Compiler: Compiled 15839 to 1604 computations (89.9% saved)

prune95.0ms (0.6%)

Pruning

35 alts after pruning (30 fresh and 5 done)

	Pruned	Kept	Total
New	749	21	770
Fresh	9	9	18
Picked	4	1	5
Done	0	4	4
Total	762	35	797

Accuracy

100.0%

Counts

797 → 35

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	95.3%	(/.f64 (+.f64 (.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 eps #s(literal 1/4 binary64))))) (/.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 #s(literal 1 binary64) eps) (.f64 eps #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
	97.3%	(/.f64 (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 eps #s(literal 1/4 binary64)))))) (/.f64 #s(literal 1 binary64) eps))
▶	83.3%	(/.f64 (.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (*.f64 eps eps)) eps)
✓	52.5%	(-.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
	82.1%	(-.f64 (+.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 (cos.f64 x) (cos.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps)))
	97.3%	(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 eps x))
✓	52.4%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	81.1%	(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
	80.1%	(-.f64 #s(literal 0 binary64) (*.f64 eps x))
	97.9%	(+.f64 (.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
▶	97.8%	(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))))
✓	51.0%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
	99.4%	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
	99.0%	(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
	99.3%	(.f64 (.f64 (sin.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal 2 binary64))) (+.f64 (sin.f64 x) (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal -1/8 binary64))) (.f64 (cos.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))))))) #s(literal -2 binary64))
	50.4%	(.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))) (/.f64 eps x)))
	80.1%	(.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x))))
	96.1%	(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
▶	99.4%	(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) (sin.f64 x)))
	99.3%	(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))
	97.4%	(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) x))
✓	99.0%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
	97.8%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64))))))))
	98.1%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
	97.8%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))))
✓	98.5%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
	97.4%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
	97.2%	(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (+.f64 (*.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)))))
	97.9%	(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))
	98.5%	(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps))))
	97.3%	(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps))))))
	51.0%	(.f64 eps (.f64 eps (.f64 x (.f64 x #s(literal 1/4 binary64)))))
	52.0%	(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
	50.0%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
▶	50.7%	#s(literal 0 binary64)

Compiler

Compiled 1072 to 727 computations (32.2% saved)

simplify174.0ms (1%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 (.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 eps #s(literal 1/4 binary64))))) (/.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 #s(literal 1 binary64) eps) (.f64 eps #s(literal -1/2 binary64))))
✓	cost-diff	256	(.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 eps #s(literal 1/4 binary64))))) (/.f64 #s(literal 1 binary64) eps))
✓	cost-diff	256	(/.f64 (+.f64 (.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 eps #s(literal 1/4 binary64))))) (/.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 #s(literal 1 binary64) eps) (.f64 eps #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
✓	cost-diff	384	(.f64 (/.f64 #s(literal 1 binary64) eps) (.f64 eps #s(literal -1/2 binary64)))
✓	cost-diff	0	(.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)))))
✓	cost-diff	0	(*.f64 eps eps)
✓	cost-diff	0	(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
✓	cost-diff	128	(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))))
✓	cost-diff	0	(*.f64 eps #s(literal -1/2 binary64))
✓	cost-diff	0	(-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
✓	cost-diff	0	(.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (*.f64 eps eps))
✓	cost-diff	256	(/.f64 (.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (*.f64 eps eps)) eps)
✓	cost-diff	0	(+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))
✓	cost-diff	0	(.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
✓	cost-diff	0	(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) (sin.f64 x)))
✓	cost-diff	6272	(-.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) (sin.f64 x))

Rules

3774×	`-lowering-.f32`
3774×	`-lowering-.f64`
2646×	`/-lowering-/.f32`
2646×	`/-lowering-/.f64`
1836×	`+-lowering-+.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	43	290
1	133	263
2	398	258
3	1041	249
4	3004	245
0	8323	245

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* eps (- (* eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x)))
eps
(- (* eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x))
(* eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2))))
(+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))
(* eps (* (sin x) 1/6))
(* (sin x) 1/6)
(sin x)
x
1/6
(* (cos x) (+ (* eps (* eps 1/24)) -1/2))
(cos x)
(+ (* eps (* eps 1/24)) -1/2)
(* eps (* eps 1/24))
(* eps 1/24)
1/24
-1/2
0
(/ (* (- (* eps -1/2) x) (* eps eps)) eps)
(* (- (* eps -1/2) x) (* eps eps))
(- (* eps -1/2) x)
(* eps -1/2)
eps
-1/2
x
(* eps eps)
(+ (* -1/2 (* eps eps)) (* x (* eps (+ -1 (* (* x x) 1/6)))))
(* -1/2 (* eps eps))
-1/2
(* eps eps)
eps
(* x (* eps (+ -1 (* (* x x) 1/6))))
x
(* eps (+ -1 (* (* x x) 1/6)))
(+ -1 (* (* x x) 1/6))
-1
(* (* x x) 1/6)
(* x x)
1/6
(/ (+ (* (* x (+ -1 (* x (* eps 1/4)))) (/ 1 eps)) (* (/ 1 eps) (* eps -1/2))) (/ 1 (* eps eps)))
(+ (* (* x (+ -1 (* x (* eps 1/4)))) (/ 1 eps)) (* (/ 1 eps) (* eps -1/2)))
(* (* x (+ -1 (* x (* eps 1/4)))) (/ 1 eps))
(* x (+ -1 (* x (* eps 1/4))))
x
(+ -1 (* x (* eps 1/4)))
-1
(* x (* eps 1/4))
(* eps 1/4)
eps
1/4
(/ 1 eps)
1
(* (/ 1 eps) (* eps -1/2))
(* eps -1/2)
-1/2
(/ 1 (* eps eps))
(* eps eps)

Outputs
(* eps (- (* eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x)))
(.f64 eps (+.f64 (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) (.f64 eps (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
eps
(- (* eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x))
(+.f64 (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) (.f64 eps (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))))
(* eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2))))
(.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
(+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))
(+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))
(* eps (* (sin x) 1/6))
(.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)))
(* (sin x) 1/6)
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
(sin x)
(sin.f64 x)
x
1/6
#s(literal 1/6 binary64)
(* (cos x) (+ (* eps (* eps 1/24)) -1/2))
(.f64 (cos.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))
(cos x)
(cos.f64 x)
(+ (* eps (* eps 1/24)) -1/2)
(+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))
(* eps (* eps 1/24))
(.f64 eps (.f64 eps #s(literal 1/24 binary64)))
(* eps 1/24)
(*.f64 eps #s(literal 1/24 binary64))
1/24
#s(literal 1/24 binary64)
-1/2
#s(literal -1/2 binary64)
0
#s(literal 0 binary64)
(/ (* (- (* eps -1/2) x) (* eps eps)) eps)
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(* (- (* eps -1/2) x) (* eps eps))
(.f64 eps (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(- (* eps -1/2) x)
(-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
eps
-1/2
#s(literal -1/2 binary64)
x
(* eps eps)
(*.f64 eps eps)
(+ (* -1/2 (* eps eps)) (* x (* eps (+ -1 (* (* x x) 1/6)))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (*.f64 x x))))))
(* -1/2 (* eps eps))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
-1/2
#s(literal -1/2 binary64)
(* eps eps)
(*.f64 eps eps)
eps
(* x (* eps (+ -1 (* (* x x) 1/6))))
(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))
x
(* eps (+ -1 (* (* x x) 1/6)))
(.f64 eps (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (*.f64 x x))))
(+ -1 (* (* x x) 1/6))
(+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x)))
-1
#s(literal -1 binary64)
(* (* x x) 1/6)
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* x x)
(*.f64 x x)
1/6
#s(literal 1/6 binary64)
(/ (+ (* (* x (+ -1 (* x (* eps 1/4)))) (/ 1 eps)) (* (/ 1 eps) (* eps -1/2))) (/ 1 (* eps eps)))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) x))
(+ (* (* x (+ -1 (* x (* eps 1/4)))) (/ 1 eps)) (* (/ 1 eps) (* eps -1/2)))
(+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps))))
(* (* x (+ -1 (* x (* eps 1/4)))) (/ 1 eps))
(.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))
(* x (+ -1 (* x (* eps 1/4))))
(.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 eps #s(literal 1/4 binary64)))))
x
(+ -1 (* x (* eps 1/4)))
(+.f64 #s(literal -1 binary64) (.f64 x (.f64 eps #s(literal 1/4 binary64))))
-1
#s(literal -1 binary64)
(* x (* eps 1/4))
(.f64 x (.f64 eps #s(literal 1/4 binary64)))
(* eps 1/4)
(*.f64 eps #s(literal 1/4 binary64))
eps
1/4
#s(literal 1/4 binary64)
(/ 1 eps)
(/.f64 #s(literal 1 binary64) eps)
1
#s(literal 1 binary64)
(* (/ 1 eps) (* eps -1/2))
#s(literal -1/2 binary64)
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(/ 1 (* eps eps))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(* eps eps)
(*.f64 eps eps)

localize202.0ms (1.2%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
✓	accuracy	99.7%	(.f64 (/.f64 #s(literal 1 binary64) eps) (.f64 eps #s(literal -1/2 binary64)))
✓	accuracy	99.6%	(.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 eps #s(literal 1/4 binary64))))) (/.f64 #s(literal 1 binary64) eps))
✓	accuracy	97.9%	(/.f64 (+.f64 (.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 eps #s(literal 1/4 binary64))))) (/.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 #s(literal 1 binary64) eps) (.f64 eps #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
✓	accuracy	100.0%	(.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)))))
✓	accuracy	100.0%	(.f64 eps (+.f64 #s(literal -1 binary64) (.f64 (*.f64 x x) #s(literal 1/6 binary64))))
✓	accuracy	99.7%	(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))))
✓	accuracy	99.7%	(.f64 (.f64 x x) #s(literal 1/6 binary64))
✓	accuracy	100.0%	(*.f64 eps eps)
✓	accuracy	100.0%	(*.f64 eps #s(literal -1/2 binary64))
✓	accuracy	99.8%	(.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (*.f64 eps eps))
✓	accuracy	85.8%	(/.f64 (.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (*.f64 eps eps)) eps)
✓	accuracy	99.8%	(.f64 eps (.f64 eps #s(literal 1/24 binary64)))
✓	accuracy	99.8%	(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) (sin.f64 x)))
✓	accuracy	99.5%	(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
✓	accuracy	99.4%	(*.f64 eps #s(literal 1/24 binary64))

Results

137.0ms	252×	0	valid
6.0ms	2×	3	valid
2.0ms	1×	2	valid
1.0ms	1×	1	valid

Compiler

Compiled 341 to 44 computations (87.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 66.0ms

ival-mult: 32.0ms (48.8% of total)

ival-div: 8.0ms (12.2% of total)

...c/correct-round.rkt:119:19: 8.0ms (12.2% of total)

ival-add: 7.0ms (10.7% of total)

ival-sub: 3.0ms (4.6% of total)

ival-cos: 3.0ms (4.6% of total)

ival-sin: 3.0ms (4.6% of total)

const: 1.0ms (1.5% of total)

backward-pass: 1.0ms (1.5% of total)

series28.0ms (0.2%)

Counts

22 → 420

Calls

Call 1

Inputs
#<alt (- (* eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x))>
#<alt (* eps (- (* eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x)))>
#<alt (* eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2))))>
#<alt (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))>
#<alt (/ (* (- (* eps -1/2) x) (* eps eps)) eps)>
#<alt (* (- (* eps -1/2) x) (* eps eps))>
#<alt (- (* eps -1/2) x)>
#<alt (* eps -1/2)>
#<alt (+ (* -1/2 (* eps eps)) (* x (* eps (+ -1 (* (* x x) 1/6)))))>
#<alt (* -1/2 (* eps eps))>
#<alt (* eps eps)>
#<alt (* x (* eps (+ -1 (* (* x x) 1/6))))>
#<alt (* (/ 1 eps) (* eps -1/2))>
#<alt (/ (+ (* (* x (+ -1 (* x (* eps 1/4)))) (/ 1 eps)) (* (/ 1 eps) (* eps -1/2))) (/ 1 (* eps eps)))>
#<alt (* (* x (+ -1 (* x (* eps 1/4)))) (/ 1 eps))>
#<alt (+ (* (* x (+ -1 (* x (* eps 1/4)))) (/ 1 eps)) (* (/ 1 eps) (* eps -1/2)))>
#<alt (* eps 1/24)>
#<alt (* (sin x) 1/6)>
#<alt (* eps (* eps 1/24))>
#<alt (* (* x x) 1/6)>
#<alt (* eps (+ -1 (* (* x x) 1/6)))>
#<alt (/ 1 (* eps eps))>

Outputs
#<alt (* -1 (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))>
#<alt (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))>
#<alt (* 1/24 (* (pow eps 3) (cos x)))>
#<alt (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))>
#<alt (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))>
#<alt (* 1/24 (* (pow eps 3) (cos x)))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))>
#<alt (* eps (- (* 1/24 (pow eps 2)) 1/2))>
#<alt (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))>
#<alt (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))>
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#<alt (* 1/4 (pow x 2))>
#<alt (* (pow x 2) (- 1/4 (/ 1 (* eps x))))>
#<alt (* (pow x 2) (- 1/4 (/ 1 (* eps x))))>
#<alt (* (pow x 2) (- 1/4 (/ 1 (* eps x))))>
#<alt (* -1 (/ x eps))>
#<alt (/ (+ (* -1 x) (* 1/4 (* eps (pow x 2)))) eps)>
#<alt (/ (+ (* -1 x) (* 1/4 (* eps (pow x 2)))) eps)>
#<alt (/ (+ (* -1 x) (* 1/4 (* eps (pow x 2)))) eps)>
#<alt (* 1/4 (pow x 2))>
#<alt (+ (* -1 (/ x eps)) (* 1/4 (pow x 2)))>
#<alt (+ (* -1 (/ x eps)) (* 1/4 (pow x 2)))>
#<alt (+ (* -1 (/ x eps)) (* 1/4 (pow x 2)))>
#<alt (* 1/4 (pow x 2))>
#<alt (+ (* -1 (/ x eps)) (* 1/4 (pow x 2)))>
#<alt (+ (* -1 (/ x eps)) (* 1/4 (pow x 2)))>
#<alt (+ (* -1 (/ x eps)) (* 1/4 (pow x 2)))>
#<alt -1/2>
#<alt (- (* -1 (/ x eps)) 1/2)>
#<alt (- (* x (- (* 1/4 x) (/ 1 eps))) 1/2)>
#<alt (- (* x (- (* 1/4 x) (/ 1 eps))) 1/2)>
#<alt (* 1/4 (pow x 2))>
#<alt (* (pow x 2) (- 1/4 (/ 1 (* eps x))))>
#<alt (* (pow x 2) (+ 1/4 (* -1 (/ (+ (/ 1 eps) (* 1/2 (/ 1 x))) x))))>
#<alt (* (pow x 2) (+ 1/4 (* -1 (/ (+ (/ 1 eps) (* 1/2 (/ 1 x))) x))))>
#<alt (* 1/4 (pow x 2))>
#<alt (* (pow x 2) (- 1/4 (/ 1 (* eps x))))>
#<alt (* (pow x 2) (+ 1/4 (* -1 (/ (+ (/ 1 eps) (* 1/2 (/ 1 x))) x))))>
#<alt (* (pow x 2) (+ 1/4 (* -1 (/ (+ (/ 1 eps) (* 1/2 (/ 1 x))) x))))>
#<alt (* -1 (/ x eps))>
#<alt (/ (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))) eps)>
#<alt (/ (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))) eps)>
#<alt (/ (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))) eps)>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
#<alt (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2)>
#<alt (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2)>
#<alt (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2)>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
#<alt (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2)>
#<alt (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2)>
#<alt (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* -1/36 (pow x 2))))>
#<alt (* x (+ 1/6 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/36))))>
#<alt (* x (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/30240 (pow x 2)))) 1/36))))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* -1 eps)>
#<alt (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))>
#<alt (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))>
#<alt (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))>
#<alt (* 1/6 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* 1/6 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (/ 1 (pow eps 2))>
#<alt (/ 1 (pow eps 2))>
#<alt (/ 1 (pow eps 2))>
#<alt (/ 1 (pow eps 2))>
#<alt (/ 1 (pow eps 2))>
#<alt (/ 1 (pow eps 2))>
#<alt (/ 1 (pow eps 2))>
#<alt (/ 1 (pow eps 2))>
#<alt (/ 1 (pow eps 2))>
#<alt (/ 1 (pow eps 2))>
#<alt (/ 1 (pow eps 2))>
#<alt (/ 1 (pow eps 2))>

Calls

105 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	(/ (+ (* (* x (+ -1 (* x (* eps 1/4)))) (/ 1 eps)) (* (/ 1 eps) (* eps -1/2))) (/ 1 (* eps eps)))
1.0ms	x	@	inf	(- (* eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x))
1.0ms	x	@	-inf	(- (* eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x))
1.0ms	eps	@	-inf	(/ (+ (* (* x (+ -1 (* x (* eps 1/4)))) (/ 1 eps)) (* (/ 1 eps) (* eps -1/2))) (/ 1 (* eps eps)))
1.0ms	eps	@	0	(+ (* -1/2 (* eps eps)) (* x (* eps (+ -1 (* (* x x) 1/6)))))

rewrite313.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

4102×	`-lowering-.f32`
4102×	`-lowering-.f64`
2842×	`/-lowering-/.f32`
2842×	`/-lowering-/.f64`
2112×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	208
1	257	179
2	2439	177
0	9212	177

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 547

Calls

Call 1

Inputs
(- (* eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x))
(* eps (- (* eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x)))
(* eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2))))
(+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))
(/ (* (- (* eps -1/2) x) (* eps eps)) eps)
(* (- (* eps -1/2) x) (* eps eps))
(- (* eps -1/2) x)
(* eps -1/2)
(+ (* -1/2 (* eps eps)) (* x (* eps (+ -1 (* (* x x) 1/6)))))
(* -1/2 (* eps eps))
(* eps eps)
(* x (* eps (+ -1 (* (* x x) 1/6))))
(* (/ 1 eps) (* eps -1/2))
(/ (+ (* (* x (+ -1 (* x (* eps 1/4)))) (/ 1 eps)) (* (/ 1 eps) (* eps -1/2))) (/ 1 (* eps eps)))
(* (* x (+ -1 (* x (* eps 1/4)))) (/ 1 eps))
(+ (* (* x (+ -1 (* x (* eps 1/4)))) (/ 1 eps)) (* (/ 1 eps) (* eps -1/2)))
(* eps 1/24)
(* (sin x) 1/6)
(* eps (* eps 1/24))
(* (* x x) 1/6)
(* eps (+ -1 (* (* x x) 1/6)))
(/ 1 (* eps eps))

Outputs
(+.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(+.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))
(+.f64 (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 eps eps)) (-.f64 (.f64 (cos.f64 x) (.f64 (+.f64 (.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) eps)) (sin.f64 x)))
(-.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) (sin.f64 x))
(-.f64 (/.f64 (pow.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (.f64 (sin.f64 x) (+.f64 (sin.f64 x) (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (.f64 (sin.f64 x) (+.f64 (sin.f64 x) (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))))))
(-.f64 (/.f64 (pow.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (+.f64 (sin.f64 x) (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))))
(-.f64 (/.f64 (pow.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (-.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))) (/.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 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))))
(fma.f64 eps (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (-.f64 (.f64 (cos.f64 x) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) eps)) (sin.f64 x)))
(fma.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 eps eps) (-.f64 (.f64 (cos.f64 x) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) eps)) (sin.f64 x)))
(fma.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps (-.f64 (.f64 (cos.f64 x) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) eps)) (sin.f64 x)))
(fma.f64 (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) eps (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (-.f64 (.f64 (cos.f64 x) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) eps)) (sin.f64 x)))
(fma.f64 #s(literal -1 binary64) (sin.f64 x) (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))
(fma.f64 (.f64 eps (sin.f64 x)) (.f64 #s(literal 1/6 binary64) eps) (-.f64 (.f64 (cos.f64 x) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) eps)) (sin.f64 x)))
(fma.f64 (.f64 eps (.f64 eps (sin.f64 x))) #s(literal 1/6 binary64) (-.f64 (.f64 (cos.f64 x) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) eps)) (sin.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (pow.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (.f64 (sin.f64 x) (+.f64 (sin.f64 x) (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))))) (-.f64 (pow.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (sin.f64 x) (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))) (-.f64 (pow.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (.f64 (sin.f64 x) (+.f64 (sin.f64 x) (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))))) (-.f64 (pow.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sin.f64 x) (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))) (-.f64 (pow.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))))
(/.f64 (-.f64 (pow.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (.f64 (sin.f64 x) (+.f64 (sin.f64 x) (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))))))
(/.f64 (-.f64 (pow.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (-.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 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) (-.f64 #s(literal 0 binary64) (sin.f64 x))))))
(/.f64 (-.f64 (pow.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (+.f64 (sin.f64 x) (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))))
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(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
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(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(.f64 (.f64 eps #s(literal 1/24 binary64)) eps)
(.f64 (.f64 eps eps) #s(literal 1/24 binary64))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(.f64 (.f64 x #s(literal 1/6 binary64)) x)
(+.f64 (-.f64 #s(literal 0 binary64) eps) (.f64 eps (.f64 #s(literal 1/6 binary64) (*.f64 x x))))
(+.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (*.f64 x x))) (-.f64 #s(literal 0 binary64) eps))
(-.f64 (/.f64 (.f64 eps eps) (-.f64 (-.f64 #s(literal 0 binary64) eps) (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x))))) (/.f64 (.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x)))) (-.f64 (-.f64 #s(literal 0 binary64) eps) (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x))))))
(fma.f64 eps #s(literal -1 binary64) (.f64 eps (.f64 #s(literal 1/6 binary64) (*.f64 x x))))
(fma.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) eps))
(fma.f64 x (.f64 (.f64 x #s(literal 1/6 binary64)) eps) (-.f64 #s(literal 0 binary64) eps))
(fma.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) eps) (-.f64 #s(literal 0 binary64) eps))
(fma.f64 #s(literal -1 binary64) eps (.f64 eps (.f64 #s(literal 1/6 binary64) (*.f64 x x))))
(fma.f64 (.f64 x x) (.f64 #s(literal 1/6 binary64) eps) (-.f64 #s(literal 0 binary64) eps))
(fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) eps (-.f64 #s(literal 0 binary64) eps))
(fma.f64 (.f64 eps x) (.f64 x #s(literal 1/6 binary64)) (-.f64 #s(literal 0 binary64) eps))
(fma.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 x x) (-.f64 #s(literal 0 binary64) eps))
(fma.f64 (.f64 eps (.f64 x x)) #s(literal 1/6 binary64) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (+.f64 (.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps eps))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) (.f64 eps (.f64 eps eps)))) (+.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x)))) (.f64 (-.f64 #s(literal 0 binary64) eps) (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x)))))))
(/.f64 (-.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x))))) (-.f64 (-.f64 #s(literal 0 binary64) eps) (.f64 eps (.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
(/.f64 (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) #s(literal -1 binary64)))))
(/.f64 (.f64 eps (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)))) (+.f64 #s(literal -1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(/.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) eps) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) #s(literal -1 binary64)))))
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(/.f64 (neg.f64 (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))))) (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) #s(literal -1 binary64))))))
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(/.f64 (neg.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) eps)) (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) #s(literal -1 binary64))))))
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(.f64 eps (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (*.f64 x x))))
(.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (*.f64 x x))) eps)
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 eps)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 eps) #s(literal -2 binary64)))
(exp.f64 (+.f64 (.f64 (log.f64 eps) #s(literal -1 binary64)) (.f64 (log.f64 eps) #s(literal -1 binary64))))
(exp.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (log.f64 eps))))
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(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 eps eps)))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)))))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps))))
(/.f64 (/.f64 #s(literal 1 binary64) eps) eps)
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) eps)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) eps))) (neg.f64 (-.f64 #s(literal 0 binary64) eps)))
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(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 1 binary64))
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps))) #s(literal -1 binary64))
(pow.f64 (.f64 (.f64 eps eps) (*.f64 eps eps)) #s(literal -1/2 binary64))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps eps)))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
(*.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1 binary64) eps))
(*.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal -1 binary64) eps) (/.f64 #s(literal -1 binary64) eps))
(*.f64 (/.f64 #s(literal -1 binary64) eps) (/.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 eps #s(literal -1/2 binary64)) eps) (/.f64 (pow.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)))

simplify277.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

5252×	`-lowering-.f32`
5252×	`-lowering-.f64`
4068×	`+-lowering-+.f64`
4068×	`+-lowering-+.f32`
1352×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	337	4251
1	1169	3830
2	4002	3663
0	8321	3663

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 420

Calls

Call 1

Inputs
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
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(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
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(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* -1/2 (* eps (cos x)))
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(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
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(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* 1/24 (* (pow eps 3) (cos x)))
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(* eps (- (* 1/24 (pow eps 2)) 1/2))
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(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* -1/36 (* (pow eps 2) x)))))))
(* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))
(* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))
(* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))
(* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))
(* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))
(* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))
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(* -1/2 (cos x))
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(- (* 1/24 (pow eps 2)) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* -1/2 (* x (- (* 1/24 (pow eps 2)) 1/2))) (* 1/6 eps)))) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ (* -1/2 (- (* 1/24 (pow eps 2)) 1/2)) (* -1/36 (* eps x))))))) 1/2)
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
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(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(* -1 (* eps x))
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(* eps (+ (* -1 x) (* -1/2 eps)))
(* eps (+ (* -1 x) (* -1/2 eps)))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* -1/2 (pow eps 2))
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(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
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(* x (+ (* -1 eps) (* -1/2 (/ (pow eps 2) x))))
(* x (+ (* -1 eps) (* -1/2 (/ (pow eps 2) x))))
(* -1 (* eps x))
(* -1 (* x (+ eps (* 1/2 (/ (pow eps 2) x)))))
(* -1 (* x (+ eps (* 1/2 (/ (pow eps 2) x)))))
(* -1 (* x (+ eps (* 1/2 (/ (pow eps 2) x)))))
(* -1 (* (pow eps 2) x))
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(* (pow eps 2) (+ (* -1 x) (* -1/2 eps)))
(* (pow eps 2) (+ (* -1 x) (* -1/2 eps)))
(* -1/2 (pow eps 3))
(* (pow eps 3) (- (* -1 (/ x eps)) 1/2))
(* (pow eps 3) (- (* -1 (/ x eps)) 1/2))
(* (pow eps 3) (- (* -1 (/ x eps)) 1/2))
(* -1/2 (pow eps 3))
(* -1 (* (pow eps 3) (+ 1/2 (/ x eps))))
(* -1 (* (pow eps 3) (+ 1/2 (/ x eps))))
(* -1 (* (pow eps 3) (+ 1/2 (/ x eps))))
(* -1/2 (pow eps 3))
(+ (* -1 (* (pow eps 2) x)) (* -1/2 (pow eps 3)))
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(- (* -1/2 eps) x)
(- (* -1/2 eps) x)
(* -1/2 eps)
(* eps (- (* -1 (/ x eps)) 1/2))
(* eps (- (* -1 (/ x eps)) 1/2))
(* eps (- (* -1 (/ x eps)) 1/2))
(* -1/2 eps)
(* -1 (* eps (+ 1/2 (/ x eps))))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* -1 (* eps (+ 1/2 (/ x eps))))
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(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* -1/2 eps))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* x (- (* -1/2 (/ eps x)) 1))
(* x (- (* -1/2 (/ eps x)) 1))
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(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (+ (* -1/2 eps) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (+ (* -1/2 eps) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (+ (* -1/2 eps) (* x (- (* 1/6 (pow x 2)) 1))))
(* -1/2 (pow eps 2))
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(* (pow eps 2) (- (/ (* x (- (* 1/6 (pow x 2)) 1)) eps) 1/2))
(* (pow eps 2) (- (/ (* x (- (* 1/6 (pow x 2)) 1)) eps) 1/2))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (/ (* x (- (* 1/6 (pow x 2)) 1)) eps) 1/2))
(* (pow eps 2) (- (/ (* x (- (* 1/6 (pow x 2)) 1)) eps) 1/2))
(* (pow eps 2) (- (/ (* x (- (* 1/6 (pow x 2)) 1)) eps) 1/2))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))))
(* 1/6 (* eps (pow x 3)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (* 1/6 eps))))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (* 1/6 eps))))
(* 1/6 (* eps (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (+ (* 1/2 (/ (pow eps 2) (pow x 3))) (/ eps (pow x 2))))))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (+ (* 1/2 (/ (pow eps 2) (pow x 3))) (/ eps (pow x 2))))))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (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)
(pow eps 2)
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* 1/6 (* eps (pow x 3)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* 1/6 (* eps (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
-1/2
-1/2
-1/2
-1/2
-1/2
-1/2
-1/2
-1/2
-1/2
-1/2
-1/2
-1/2
(* -1/2 (pow eps 2))
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(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))
(* (pow x 2) (+ (* -1 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2)))))
(* (pow x 2) (+ (* -1 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2)))))
(* 1/4 (* (pow eps 2) (pow x 2)))
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(* -1 (* eps x))
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(/ (+ (* -1 x) (* 1/4 (* eps (pow x 2)))) eps)
(/ (+ (* -1 x) (* 1/4 (* eps (pow x 2)))) eps)
(* 1/4 (pow x 2))
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(+ (* -1 (/ x eps)) (* 1/4 (pow x 2)))
-1/2
(- (* -1 (/ x eps)) 1/2)
(- (* x (- (* 1/4 x) (/ 1 eps))) 1/2)
(- (* x (- (* 1/4 x) (/ 1 eps))) 1/2)
(* 1/4 (pow x 2))
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(/ (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))) eps)
(/ (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))) eps)
(- (* 1/4 (pow x 2)) 1/2)
(- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2)
(- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2)
(- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2)
(- (* 1/4 (pow x 2)) 1/2)
(- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2)
(- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2)
(- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/6 x)
(* x (+ 1/6 (* -1/36 (pow x 2))))
(* x (+ 1/6 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/36))))
(* x (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/30240 (pow x 2)))) 1/36))))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* -1 eps)
(+ (* -1 eps) (* 1/6 (* eps (pow x 2))))
(+ (* -1 eps) (* 1/6 (* eps (pow x 2))))
(+ (* -1 eps) (* 1/6 (* eps (pow x 2))))
(* 1/6 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* 1/6 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))

Outputs
(* -1 (sin x))
(-.f64 #s(literal 0 binary64) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 eps #s(literal 1/6 binary64))))))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(+.f64 (.f64 (.f64 eps (cos.f64 x)) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 eps #s(literal 1/6 binary64))))))
(* 1/24 (* (pow eps 3) (cos x)))
(.f64 (cos.f64 x) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) eps))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (/.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(.f64 eps (.f64 (.f64 eps eps) (+.f64 (/.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps) (.f64 (cos.f64 x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(.f64 eps (.f64 (.f64 eps eps) (+.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) (.f64 (/.f64 (sin.f64 x) eps) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps)))))))
(* 1/24 (* (pow eps 3) (cos x)))
(.f64 (cos.f64 x) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) eps))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (/.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(.f64 (-.f64 (.f64 (cos.f64 x) #s(literal -1/24 binary64)) (/.f64 (+.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 #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 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(.f64 (-.f64 (.f64 (cos.f64 x) #s(literal -1/24 binary64)) (/.f64 (-.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (/.f64 (+.f64 (/.f64 (sin.f64 x) eps) (.f64 (cos.f64 x) #s(literal 1/2 binary64))) eps)) eps)) (-.f64 #s(literal 0 binary64) (.f64 eps (.f64 eps eps))))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64))))))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))
(+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))) (.f64 eps #s(literal 1/6 binary64)))))))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))) (.f64 eps #s(literal 1/6 binary64)))) (.f64 (+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 eps #s(literal -1/36 binary64)))) (.f64 x x))))))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(+.f64 (.f64 (.f64 eps (cos.f64 x)) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 eps #s(literal 1/6 binary64))))))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(+.f64 (.f64 (.f64 eps (cos.f64 x)) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 eps #s(literal 1/6 binary64))))))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(+.f64 (.f64 (.f64 eps (cos.f64 x)) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 eps #s(literal 1/6 binary64))))))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(+.f64 (.f64 (.f64 eps (cos.f64 x)) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 eps #s(literal 1/6 binary64))))))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(+.f64 (.f64 (.f64 eps (cos.f64 x)) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 eps #s(literal 1/6 binary64))))))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(+.f64 (.f64 (.f64 eps (cos.f64 x)) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 eps #s(literal 1/6 binary64))))))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(+.f64 (.f64 (.f64 eps (cos.f64 x)) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 eps #s(literal 1/6 binary64))))))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(+.f64 (.f64 (.f64 eps (cos.f64 x)) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 eps #s(literal 1/6 binary64))))))
(* -1 (* eps (sin x)))
(*.f64 eps (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(.f64 eps (+.f64 (.f64 (.f64 eps (cos.f64 x)) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))
(* 1/24 (* (pow eps 4) (cos x)))
(.f64 (cos.f64 x) (.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64))))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(.f64 (+.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (/.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(.f64 (+.f64 (/.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps) (.f64 (cos.f64 x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps))))) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(.f64 (+.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) (.f64 (/.f64 (sin.f64 x) eps) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))))) (pow.f64 eps #s(literal 4 binary64)))
(* 1/24 (* (pow eps 4) (cos x)))
(.f64 (cos.f64 x) (.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64))))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(.f64 (+.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (/.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (/.f64 (+.f64 (.f64 (sin.f64 x) #s(literal -1/6 binary64)) (.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/2 binary64))) eps)))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (/.f64 (-.f64 (.f64 (sin.f64 x) #s(literal -1/6 binary64)) (/.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)) eps)) eps)))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))))
(+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 x (+.f64 (.f64 (.f64 eps eps) (.f64 x (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))))) (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64))))))))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+.f64 (.f64 x (.f64 x (+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))) (.f64 x (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 eps #s(literal -1/36 binary64))))))))) (.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64))))))))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(.f64 eps (+.f64 (.f64 (.f64 eps (cos.f64 x)) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(.f64 eps (+.f64 (.f64 (.f64 eps (cos.f64 x)) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(.f64 eps (+.f64 (.f64 (.f64 eps (cos.f64 x)) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(.f64 eps (+.f64 (.f64 (.f64 eps (cos.f64 x)) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(.f64 eps (+.f64 (.f64 (.f64 eps (cos.f64 x)) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(.f64 eps (+.f64 (.f64 (.f64 eps (cos.f64 x)) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(.f64 eps (+.f64 (.f64 (.f64 eps (cos.f64 x)) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(.f64 eps (+.f64 (.f64 (.f64 eps (cos.f64 x)) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))
(* 1/24 (* (pow eps 3) (cos x)))
(.f64 (cos.f64 x) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) eps))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
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(.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x eps))))
(* (pow x 2) (- 1/4 (/ 1 (* eps x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x eps))))
(* -1 (/ x eps))
(-.f64 #s(literal 0 binary64) (/.f64 x eps))
(/ (+ (* -1 x) (* 1/4 (* eps (pow x 2)))) eps)
(/.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 (*.f64 eps #s(literal 1/4 binary64)) x))) eps)
(/ (+ (* -1 x) (* 1/4 (* eps (pow x 2)))) eps)
(/.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 (*.f64 eps #s(literal 1/4 binary64)) x))) eps)
(/ (+ (* -1 x) (* 1/4 (* eps (pow x 2)))) eps)
(/.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 (*.f64 eps #s(literal 1/4 binary64)) x))) eps)
(* 1/4 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/4 binary64))
(+ (* -1 (/ x eps)) (* 1/4 (pow x 2)))
(.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))
(+ (* -1 (/ x eps)) (* 1/4 (pow x 2)))
(.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))
(+ (* -1 (/ x eps)) (* 1/4 (pow x 2)))
(.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))
(* 1/4 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/4 binary64))
(+ (* -1 (/ x eps)) (* 1/4 (pow x 2)))
(.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))
(+ (* -1 (/ x eps)) (* 1/4 (pow x 2)))
(.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))
(+ (* -1 (/ x eps)) (* 1/4 (pow x 2)))
(.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))
-1/2
#s(literal -1/2 binary64)
(- (* -1 (/ x eps)) 1/2)
(-.f64 #s(literal -1/2 binary64) (/.f64 x eps))
(- (* x (- (* 1/4 x) (/ 1 eps))) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps))))
(- (* x (- (* 1/4 x) (/ 1 eps))) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps))))
(* 1/4 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/4 binary64))
(* (pow x 2) (- 1/4 (/ 1 (* eps x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x eps))))
(* (pow x 2) (+ 1/4 (* -1 (/ (+ (/ 1 eps) (* 1/2 (/ 1 x))) x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) eps) (/.f64 #s(literal -1/2 binary64) x)) x)))
(* (pow x 2) (+ 1/4 (* -1 (/ (+ (/ 1 eps) (* 1/2 (/ 1 x))) x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) eps) (/.f64 #s(literal -1/2 binary64) x)) x)))
(* 1/4 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/4 binary64))
(* (pow x 2) (- 1/4 (/ 1 (* eps x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x eps))))
(* (pow x 2) (+ 1/4 (* -1 (/ (+ (/ 1 eps) (* 1/2 (/ 1 x))) x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) eps) (/.f64 #s(literal -1/2 binary64) x)) x)))
(* (pow x 2) (+ 1/4 (* -1 (/ (+ (/ 1 eps) (* 1/2 (/ 1 x))) x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) eps) (/.f64 #s(literal -1/2 binary64) x)) x)))
(* -1 (/ x eps))
(-.f64 #s(literal 0 binary64) (/.f64 x eps))
(/ (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))) eps)
(/.f64 (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/4 binary64)))) x) eps)
(/ (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))) eps)
(/.f64 (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/4 binary64)))) x) eps)
(/ (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))) eps)
(/.f64 (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/4 binary64)))) x) eps)
(- (* 1/4 (pow x 2)) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/4 binary64)))
(- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps))))
(- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps))))
(- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps))))
(- (* 1/4 (pow x 2)) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/4 binary64)))
(- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps))))
(- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps))))
(- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps))))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* -1/36 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x #s(literal -1/36 binary64)))))
(* x (+ 1/6 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/36))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/36 binary64) (.f64 (*.f64 x x) #s(literal 1/720 binary64))))))
(* x (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/30240 (pow x 2)))) 1/36))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/36 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (*.f64 x x) #s(literal -1/30240 binary64))))))))
(* 1/6 (sin x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
(* 1/6 (sin x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
(* 1/6 (sin x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
(* 1/6 (sin x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
(* 1/6 (sin x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
(* 1/6 (sin x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
(* 1/6 (sin x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
(* 1/6 (sin x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* eps (- (* 1/6 (pow x 2)) 1))
(.f64 eps (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(* eps (- (* 1/6 (pow x 2)) 1))
(.f64 eps (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(* eps (- (* 1/6 (pow x 2)) 1))
(.f64 eps (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(* eps (- (* 1/6 (pow x 2)) 1))
(.f64 eps (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(* eps (- (* 1/6 (pow x 2)) 1))
(.f64 eps (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(* eps (- (* 1/6 (pow x 2)) 1))
(.f64 eps (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(* eps (- (* 1/6 (pow x 2)) 1))
(.f64 eps (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(* eps (- (* 1/6 (pow x 2)) 1))
(.f64 eps (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(* eps (- (* 1/6 (pow x 2)) 1))
(.f64 eps (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(* eps (- (* 1/6 (pow x 2)) 1))
(.f64 eps (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(* eps (- (* 1/6 (pow x 2)) 1))
(.f64 eps (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(* eps (- (* 1/6 (pow x 2)) 1))
(.f64 eps (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(+ (* -1 eps) (* 1/6 (* eps (pow x 2))))
(.f64 eps (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(+ (* -1 eps) (* 1/6 (* eps (pow x 2))))
(.f64 eps (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(+ (* -1 eps) (* 1/6 (* eps (pow x 2))))
(.f64 eps (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(* 1/6 (* eps (pow x 2)))
(.f64 eps (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(.f64 x (.f64 x (.f64 eps (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))))))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(.f64 x (.f64 x (.f64 eps (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))))))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(.f64 x (.f64 x (.f64 eps (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))))))
(* 1/6 (* eps (pow x 2)))
(.f64 eps (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(.f64 x (.f64 x (.f64 eps (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))))))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(.f64 x (.f64 x (.f64 eps (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))))))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(.f64 x (.f64 x (.f64 eps (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))))))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))

eval107.0ms (0.6%)

Compiler: Compiled 30384 to 2370 computations (92.2% saved)

prune112.0ms (0.7%)

Pruning

36 alts after pruning (29 fresh and 7 done)

	Pruned	Kept	Total
New	1055	14	1069
Fresh	10	15	25
Picked	3	2	5
Done	0	5	5
Total	1068	36	1104

Accuracy

100.0%

Counts

1104 → 36

Alt Table

Click to see full alt table

Status	Accuracy	Program
	70.9%	(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 eps eps))) eps)
	97.3%	(/.f64 (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 eps #s(literal 1/4 binary64)))))) (/.f64 #s(literal 1 binary64) eps))
	95.8%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
	52.0%	(/.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
✓	52.5%	(-.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
	82.1%	(-.f64 (+.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 (cos.f64 x) (cos.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps)))
	97.3%	(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 eps x))
✓	52.4%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	80.1%	(-.f64 #s(literal 0 binary64) (*.f64 x eps))
	81.1%	(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
	97.9%	(+.f64 (.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
✓	97.8%	(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))))
✓	51.0%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
	97.4%	(.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)
	96.2%	(.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (.f64 eps eps))
	99.4%	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
	99.0%	(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
	99.3%	(.f64 (.f64 (sin.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal 2 binary64))) (+.f64 (sin.f64 x) (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal -1/8 binary64))) (.f64 (cos.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))))))) #s(literal -2 binary64))
	97.4%	(.f64 x (-.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) x) eps))
	50.5%	(.f64 x (.f64 eps (.f64 x (.f64 x #s(literal 1/6 binary64)))))
	99.1%	(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 eps (.f64 x #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) (sin.f64 x)))
	97.4%	(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) x))
✓	99.0%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
	97.8%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64))))))))
	98.1%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
	97.8%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))))
✓	98.5%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
	99.4%	(.f64 eps (+.f64 (.f64 (.f64 eps (cos.f64 x)) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))
	97.9%	(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))) (.f64 eps #s(literal 1/6 binary64)))) (.f64 (+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 eps #s(literal -1/36 binary64)))) (*.f64 x x)))))))
	97.9%	(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))
	80.4%	(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
	98.5%	(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps))))
	97.4%	(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
	52.0%	(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
	50.0%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
✓	50.7%	#s(literal 0 binary64)

Compiler

Compiled 1607 to 711 computations (55.8% saved)

regimes49.0ms (0.3%)

Counts

66 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(-.f64 #s(literal 0 binary64) (*.f64 x eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)
(/.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
(.f64 eps (.f64 eps (.f64 x (.f64 x #s(literal 1/4 binary64)))))
(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(.f64 x (.f64 eps (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (.f64 eps eps))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 eps x))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 eps eps))) eps)
(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(.f64 x (-.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) x) eps))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 (.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (*.f64 eps eps)) eps)
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) x))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) x))
(.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 #s(literal 1/4 binary64) x))))))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (+.f64 (*.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) eps)))
(/.f64 (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 eps #s(literal 1/4 binary64)))))) (/.f64 #s(literal 1 binary64) eps))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))
(.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))) (/.f64 eps x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64))))))))
(+.f64 (.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (-.f64 (.f64 x (+.f64 (.f64 eps (.f64 x #s(literal 1/6 binary64))) (.f64 #s(literal 1/4 binary64) (.f64 eps eps)))) eps)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(/.f64 (+.f64 (.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 eps #s(literal 1/4 binary64))))) (/.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 #s(literal 1 binary64) eps) (.f64 eps #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))) (.f64 eps #s(literal 1/6 binary64)))) (.f64 (+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 eps #s(literal -1/36 binary64)))) (*.f64 x x)))))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps))))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x)))))))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(.f64 eps (.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))))
(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(/.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x)) (.f64 eps eps)) eps)
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 eps (.f64 x #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) (sin.f64 x)))
(.f64 eps (+.f64 (.f64 (.f64 eps (cos.f64 x)) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))
(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))) (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (sin.f64 x)))
(.f64 (.f64 (sin.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal 2 binary64))) (+.f64 (sin.f64 x) (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal -1/8 binary64))) (.f64 (cos.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))))))) #s(literal -2 binary64))
(-.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
(-.f64 (+.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 (cos.f64 x) (cos.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps)))
(.f64 eps (/.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 #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (pow.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) (-.f64 #s(literal 0 binary64) (sin.f64 x)))))
(+.f64 (.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (+.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))) (.f64 (+.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 (.f64 (.f64 x #s(literal 1/3 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 x x)))
(/.f64 (.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 3 binary64))) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (.f64 eps (.f64 eps eps))) (.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 #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (.f64 (sin.f64 x) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x)))) (.f64 eps eps)))

Outputs

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

Calls

3 calls:

16.0ms	eps
16.0ms	x
12.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`eps`
99.6%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes39.0ms (0.2%)

Counts

52 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(-.f64 #s(literal 0 binary64) (*.f64 x eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)
(/.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
(.f64 eps (.f64 eps (.f64 x (.f64 x #s(literal 1/4 binary64)))))
(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(.f64 x (.f64 eps (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (.f64 eps eps))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 eps x))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 eps eps))) eps)
(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(.f64 x (-.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) x) eps))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 (.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (*.f64 eps eps)) eps)
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) x))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) x))
(.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 #s(literal 1/4 binary64) x))))))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (+.f64 (*.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) eps)))
(/.f64 (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 eps #s(literal 1/4 binary64)))))) (/.f64 #s(literal 1 binary64) eps))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))
(.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))) (/.f64 eps x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64))))))))
(+.f64 (.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (-.f64 (.f64 x (+.f64 (.f64 eps (.f64 x #s(literal 1/6 binary64))) (.f64 #s(literal 1/4 binary64) (.f64 eps eps)))) eps)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(/.f64 (+.f64 (.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 eps #s(literal 1/4 binary64))))) (/.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 #s(literal 1 binary64) eps) (.f64 eps #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))) (.f64 eps #s(literal 1/6 binary64)))) (.f64 (+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 eps #s(literal -1/36 binary64)))) (*.f64 x x)))))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps))))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x)))))))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(.f64 eps (.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))))
(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(/.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x)) (.f64 eps eps)) eps)

Outputs

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

Calls

3 calls:

13.0ms	x
12.0ms	eps
10.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`eps`
99.4%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes26.0ms (0.2%)

Counts

46 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(-.f64 #s(literal 0 binary64) (*.f64 x eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)
(/.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
(.f64 eps (.f64 eps (.f64 x (.f64 x #s(literal 1/4 binary64)))))
(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(.f64 x (.f64 eps (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (.f64 eps eps))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 eps x))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 eps eps))) eps)
(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(.f64 x (-.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) x) eps))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 (.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (*.f64 eps eps)) eps)
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) x))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) x))
(.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 #s(literal 1/4 binary64) x))))))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (+.f64 (*.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) eps)))
(/.f64 (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 eps #s(literal 1/4 binary64)))))) (/.f64 #s(literal 1 binary64) eps))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))
(.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))) (/.f64 eps x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64))))))))
(+.f64 (.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (-.f64 (.f64 x (+.f64 (.f64 eps (.f64 x #s(literal 1/6 binary64))) (.f64 #s(literal 1/4 binary64) (.f64 eps eps)))) eps)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(/.f64 (+.f64 (.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 eps #s(literal 1/4 binary64))))) (/.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 #s(literal 1 binary64) eps) (.f64 eps #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))) (.f64 eps #s(literal 1/6 binary64)))) (.f64 (+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 eps #s(literal -1/36 binary64)))) (*.f64 x x)))))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps))))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x)))))))

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

Calls

2 calls:

11.0ms	eps
11.0ms	x

Results

Accuracy	Segments	Branch
99.0%	1	`x`
99.0%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes25.0ms (0.1%)

Counts

44 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(-.f64 #s(literal 0 binary64) (*.f64 x eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)
(/.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
(.f64 eps (.f64 eps (.f64 x (.f64 x #s(literal 1/4 binary64)))))
(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(.f64 x (.f64 eps (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (.f64 eps eps))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 eps x))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 eps eps))) eps)
(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(.f64 x (-.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) x) eps))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 (.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (*.f64 eps eps)) eps)
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) x))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) x))
(.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 #s(literal 1/4 binary64) x))))))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (+.f64 (*.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) eps)))
(/.f64 (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 eps #s(literal 1/4 binary64)))))) (/.f64 #s(literal 1 binary64) eps))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))
(.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))) (/.f64 eps x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64))))))))
(+.f64 (.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (-.f64 (.f64 x (+.f64 (.f64 eps (.f64 x #s(literal 1/6 binary64))) (.f64 #s(literal 1/4 binary64) (.f64 eps eps)))) eps)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(/.f64 (+.f64 (.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 eps #s(literal 1/4 binary64))))) (/.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 #s(literal 1 binary64) eps) (.f64 eps #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))) (.f64 eps #s(literal 1/6 binary64)))) (.f64 (+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 eps #s(literal -1/36 binary64)))) (*.f64 x x)))))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps))))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))

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

Calls

2 calls:

11.0ms	x
11.0ms	eps

Results

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes24.0ms (0.1%)

Counts

41 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(-.f64 #s(literal 0 binary64) (*.f64 x eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)
(/.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
(.f64 eps (.f64 eps (.f64 x (.f64 x #s(literal 1/4 binary64)))))
(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(.f64 x (.f64 eps (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (.f64 eps eps))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 eps x))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 eps eps))) eps)
(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(.f64 x (-.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) x) eps))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 (.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (*.f64 eps eps)) eps)
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) x))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) x))
(.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 #s(literal 1/4 binary64) x))))))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (+.f64 (*.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) eps)))
(/.f64 (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 eps #s(literal 1/4 binary64)))))) (/.f64 #s(literal 1 binary64) eps))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))
(.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))) (/.f64 eps x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64))))))))
(+.f64 (.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (-.f64 (.f64 x (+.f64 (.f64 eps (.f64 x #s(literal 1/6 binary64))) (.f64 #s(literal 1/4 binary64) (.f64 eps eps)))) eps)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(/.f64 (+.f64 (.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 eps #s(literal 1/4 binary64))))) (/.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 #s(literal 1 binary64) eps) (.f64 eps #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))) (.f64 eps #s(literal 1/6 binary64)))) (.f64 (+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 eps #s(literal -1/36 binary64)))) (*.f64 x x)))))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))

Outputs

(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))

Calls

2 calls:

12.0ms	x
10.0ms	eps

Results

Accuracy	Segments	Branch
98.1%	1	`eps`
98.1%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes20.0ms (0.1%)

Counts

36 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(-.f64 #s(literal 0 binary64) (*.f64 x eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)
(/.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
(.f64 eps (.f64 eps (.f64 x (.f64 x #s(literal 1/4 binary64)))))
(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(.f64 x (.f64 eps (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (.f64 eps eps))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 eps x))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 eps eps))) eps)
(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(.f64 x (-.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) x) eps))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 (.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (*.f64 eps eps)) eps)
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) x))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) x))
(.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 #s(literal 1/4 binary64) x))))))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (+.f64 (*.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) eps)))
(/.f64 (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 eps #s(literal 1/4 binary64)))))) (/.f64 #s(literal 1 binary64) eps))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))
(.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))) (/.f64 eps x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64))))))))
(+.f64 (.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (-.f64 (.f64 x (+.f64 (.f64 eps (.f64 x #s(literal 1/6 binary64))) (.f64 #s(literal 1/4 binary64) (.f64 eps eps)))) eps)))

Outputs
(+.f64 (.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))

Calls

2 calls:

9.0ms	x
9.0ms	eps

Results

Accuracy	Segments	Branch
97.9%	1	`x`
97.9%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes19.0ms (0.1%)

Counts

34 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(-.f64 #s(literal 0 binary64) (*.f64 x eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)
(/.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
(.f64 eps (.f64 eps (.f64 x (.f64 x #s(literal 1/4 binary64)))))
(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(.f64 x (.f64 eps (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (.f64 eps eps))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 eps x))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 eps eps))) eps)
(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(.f64 x (-.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) x) eps))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 (.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (*.f64 eps eps)) eps)
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) x))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) x))
(.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 #s(literal 1/4 binary64) x))))))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (+.f64 (*.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) eps)))
(/.f64 (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 eps #s(literal 1/4 binary64)))))) (/.f64 #s(literal 1 binary64) eps))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))
(.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))) (/.f64 eps x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64))))))))

Outputs
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))

Calls

2 calls:

9.0ms	eps
9.0ms	x

Results

Accuracy	Segments	Branch
97.9%	1	`x`
97.9%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes18.0ms (0.1%)

Counts

31 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(-.f64 #s(literal 0 binary64) (*.f64 x eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)
(/.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
(.f64 eps (.f64 eps (.f64 x (.f64 x #s(literal 1/4 binary64)))))
(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(.f64 x (.f64 eps (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (.f64 eps eps))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 eps x))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 eps eps))) eps)
(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(.f64 x (-.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) x) eps))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 (.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (*.f64 eps eps)) eps)
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) x))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) x))
(.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 #s(literal 1/4 binary64) x))))))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (+.f64 (*.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) eps)))
(/.f64 (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 eps #s(literal 1/4 binary64)))))) (/.f64 #s(literal 1 binary64) eps))

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

Calls

2 calls:

9.0ms	eps
8.0ms	x

Results

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes14.0ms (0.1%)

Counts

25 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(-.f64 #s(literal 0 binary64) (*.f64 x eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)
(/.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
(.f64 eps (.f64 eps (.f64 x (.f64 x #s(literal 1/4 binary64)))))
(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(.f64 x (.f64 eps (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (.f64 eps eps))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 eps x))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 eps eps))) eps)
(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(.f64 x (-.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) x) eps))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 (.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (*.f64 eps eps)) eps)
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) x))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) x))
(.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 #s(literal 1/4 binary64) x))))))

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

Calls

2 calls:

7.0ms	x
7.0ms	eps

Results

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes10.0ms (0.1%)

Counts

17 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(-.f64 #s(literal 0 binary64) (*.f64 x eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)
(/.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
(.f64 eps (.f64 eps (.f64 x (.f64 x #s(literal 1/4 binary64)))))
(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(.f64 x (.f64 eps (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (.f64 eps eps))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 eps x))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 eps eps))) eps)
(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))

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

Calls

2 calls:

5.0ms	eps
5.0ms	x

Results

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0%)

Counts

7 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(-.f64 #s(literal 0 binary64) (*.f64 x eps))

Outputs
(-.f64 #s(literal 0 binary64) (*.f64 eps x))

Calls

2 calls:

3.0ms	x
3.0ms	eps

Results

Accuracy	Segments	Branch
80.1%	1	`x`
80.1%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

Counts

5 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))

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

Calls

2 calls:

2.0ms	eps
2.0ms	x

Results

Accuracy	Segments	Branch
52.0%	1	`eps`
53.9%	2	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0%)

Counts

3 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))

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

Calls

2 calls:

2.0ms	x
2.0ms	eps

Results

Accuracy	Segments	Branch
52.0%	1	`eps`
52.0%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))

Outputs
#s(literal 0 binary64)

Calls

2 calls:

2.0ms	eps
1.0ms	x

Results

Accuracy	Segments	Branch
50.7%	1	`x`
50.7%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch46.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
44.0ms	-6.656876252741639e-149	-3.915171681247036e-150

Results

36.0ms	86×	2	valid
4.0ms	24×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 126 to 94 computations (25.4% saved)

Precisions

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

ival-cos: 24.0ms (77% of total)

backward-pass: 3.0ms (9.6% of total)

ival-add: 2.0ms (6.4% of total)

ival-sub: 2.0ms (6.4% of total)

const: 0.0ms (0% of total)

simplify20.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

112×	`*-commutative_binary64`
74×	`+-commutative_binary64`
54×	`sub-neg_binary64`
44×	`neg-mul-1_binary64`
42×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	181
1	144	181
2	178	181
3	204	181
4	236	181
5	265	181
6	278	181
7	294	181
8	308	181
9	324	181
10	332	181
11	336	181
12	337	181

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(+.f64 (.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))))
(.f64 x (-.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) x) eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(if (<=.f64 x #s(literal -7601364747260185/115172193140305827399949785796761135587064246228529065807379342658863042065190089480167441564259605943037975312218134915154131611020654072038617988630148194691448832 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
#s(literal 0 binary64)

Outputs
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (sin.f64 (/.f64 (+.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 (+.f64 eps (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps))))))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (sin.f64 (/.f64 (+.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 (+.f64 eps (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (.f64 eps #s(literal 1/2 binary64))))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (-.f64 #s(literal -1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(+.f64 (.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))))))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (-.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))))
(.f64 x (-.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) x) eps))
(.f64 x (-.f64 (/.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x) eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(*.f64 eps (-.f64 #s(literal 0 binary64) x))
(if (<=.f64 x #s(literal -7601364747260185/115172193140305827399949785796761135587064246228529065807379342658863042065190089480167441564259605943037975312218134915154131611020654072038617988630148194691448832 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(if (<=.f64 x #s(literal -7601364747260185/115172193140305827399949785796761135587064246228529065807379342658863042065190089480167441564259605943037975312218134915154131611020654072038617988630148194691448832 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
#s(literal 0 binary64)

soundness2.1s (12.7%)

Rules

5622×	`-lowering-.f32`
5622×	`-lowering-.f64`
5272×	`-lowering-.f32`
5272×	`-lowering-.f64`
5252×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	337	4251
1	1169	3830
2	4002	3663
0	8321	3663
0	105	481
1	304	458
2	777	457
3	2938	457
0	8476	457
0	413	3751
1	1405	3297
2	4557	3270
0	8443	3270
0	368	3461
1	1284	3040
2	4107	2933
0	8063	2933
0	36	132
1	214	124
2	2237	124
0	8264	124
0	37	139
1	188	133
2	1746	130
0	8207	130
0	6	16
1	50	16
2	412	16
3	5247	16
0	8062	16

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
1×	iter limit
1×	node limit

Compiler

Compiled 585 to 359 computations (38.6% saved)

preprocess65.0ms (0.4%)

Compiler: Compiled 416 to 182 computations (56.3% 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	78	181
1	144	181
2	178	181
3	204	181
4	236	181
5	265	181
6	278	181
7	294	181
8	308	181
9	324	181
10	332	181
11	336	181
12	337	181

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	78	181
1	144	181
2	178	181
3	204	181
4	236	181
5	265	181
6	278	181
7	294	181
8	308	181
9	324	181
10	332	181
11	336	181
12	337	181

analyze68.0ms (0.4%)

sample9.6s (56.9%)

preprocess60.0ms (0.4%)

explain265.0ms (1.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify14.0ms (0.1%)

localize124.0ms (0.7%)

series4.0ms (0%)

rewrite277.0ms (1.7%)

simplify157.0ms (0.9%)

eval43.0ms (0.3%)

prune28.0ms (0.2%)

simplify131.0ms (0.8%)

localize599.0ms (3.6%)

series31.0ms (0.2%)

rewrite269.0ms (1.6%)

simplify244.0ms (1.5%)

eval86.0ms (0.5%)

prune83.0ms (0.5%)

simplify162.0ms (1%)

localize167.0ms (1%)

series20.0ms (0.1%)

rewrite270.0ms (1.6%)

simplify234.0ms (1.4%)

eval71.0ms (0.4%)

prune95.0ms (0.6%)

simplify174.0ms (1%)

localize202.0ms (1.2%)

series28.0ms (0.2%)

rewrite313.0ms (1.9%)

simplify277.0ms (1.6%)

eval107.0ms (0.6%)

prune112.0ms (0.7%)

regimes49.0ms (0.3%)

regimes39.0ms (0.2%)

regimes26.0ms (0.2%)

regimes25.0ms (0.1%)

regimes24.0ms (0.1%)

regimes20.0ms (0.1%)

regimes19.0ms (0.1%)

regimes18.0ms (0.1%)

regimes14.0ms (0.1%)

regimes10.0ms (0.1%)

regimes6.0ms (0%)

regimes5.0ms (0%)

regimes4.0ms (0%)

regimes4.0ms (0%)

bsearch46.0ms (0.3%)

simplify20.0ms (0.1%)

soundness2.1s (12.7%)

preprocess65.0ms (0.4%)

end0.0ms (0%)

Profiling

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

Iter	Nodes	Cost
0	78	181
1	144	181
2	178	181
3	204	181
4	236	181
5	265	181
6	278	181
7	294	181
8	308	181
9	324	181
10	332	181
11	336	181
12	337	181