Metrics for 2sin (example 3.3)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze42.0ms (0.4%)

Memory

8.5MiB live, 50.8MiB allocated

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%	49.4%	0%	25.3%	0%	3
0%	0%	25.3%	49.4%	0%	25.3%	0%	4
0%	0%	19%	49.4%	0%	31.6%	0%	5
0%	0%	15.8%	49.4%	0%	34.8%	0%	6
0%	0%	11.1%	49.4%	0%	39.5%	0%	7
0%	0%	8.7%	49.4%	0%	41.9%	0%	8
0%	0%	5.9%	49.4%	0%	44.6%	0%	9
0%	0%	4.5%	49.4%	0%	46%	0%	10
0%	0%	3.1%	49.4%	0%	47.5%	0%	11
0%	0%	2.7%	49.4%	0%	47.9%	0%	12

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample6.1s (56.3%)

Memory

134.1MiB live, 6 776.6MiB allocated

Samples

3.3s	26 139×	0	invalid
790.0ms	5 500×	0	valid
558.0ms	2 756×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 3.4s

const: 661.0ms (19.7% of total)

ival-sin: 644.0ms (19.2% of total)

ival-add: 366.0ms (10.9% of total)

ival-<=: 336.0ms (10% of total)

ival-fabs: 305.0ms (9.1% of total)

ival-mult: 294.0ms (8.8% of total)

ival-sub: 258.0ms (7.7% of total)

ival-<: 186.0ms (5.5% of total)

adjust: 139.0ms (4.1% of total)

ival-and: 105.0ms (3.1% of total)

exact: 48.0ms (1.4% of total)

ival-assert: 14.0ms (0.4% of total)

Bogosity

explain125.0ms (1.1%)

Memory

-27.0MiB live, 136.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
223	2	(4.9684126565015066e-220 4.500062827463338e-223)	3	(-2.7047159038723304e-190 5.820920694496905e-192)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
2	0	-	0	-	`(sin.f64 (+.f64 x eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`	cancellation	222	8
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	2	0

Confusion

	Predicted +	Predicted -
+	220	3
-	2	31

Precision

0.990990990990991

Recall

0.9865470852017937

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	220	3	0
-	2	5	26

Precision?

0.9695652173913043

Recall?

1.0

Freqs

test

number	freq
0	34
1	220
2	2

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

25.0ms	198×	1	valid
16.0ms	308×	0	valid
2.0ms	4×	3	valid
0.0ms	2×	2	valid

Compiler

Compiled 83 to 34 computations (59% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-sin: 11.0ms (45.6% of total)

ival-sub: 5.0ms (20.7% of total)

adjust: 4.0ms (16.6% of total)

ival-add: 3.0ms (12.4% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

preprocess23.0ms (0.2%)

Memory

-9.6MiB live, 28.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.4%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0.1%)

Memory

6.6MiB live, 6.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize26.0ms (0.2%)

Memory

-4.9MiB live, 32.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(sin.f64 x)
accuracy	0.07434796408644774	(sin.f64 (+.f64 x eps))
accuracy	25.272279659742747	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

10.0ms	154×	0	valid
10.0ms	99×	1	valid
1.0ms	2×	3	valid
0.0ms	1×	2	valid

Compiler

Compiled 38 to 14 computations (63.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-sin: 5.0ms (41.9% of total)

ival-sub: 3.0ms (25.1% of total)

adjust: 2.0ms (16.8% of total)

ival-add: 2.0ms (16.8% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series4.0ms (0%)

Memory

5.5MiB live, 5.5MiB allocated

Counts

4 → 31

Calls

Call 1

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

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

Calls

6 calls:

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

simplify144.0ms (1.3%)

Memory

13.8MiB live, 169.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	291
1	314	291
2	779	284
3	2842	284
4	6177	284
0	8125	253

Stop Event

1×	iter limit
1×	node limit

Counts

31 → 29

Calls

Call 1

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

Outputs
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (cos eps)))
(fma.f64 (cos.f64 eps) x (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) x (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 eps) x) #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (cos.f64 eps)) x (sin.f64 eps))
eps
(+ eps x)
(+.f64 eps x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) x)
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(sin x)
(sin.f64 x)
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps)) eps (cos.f64 x)) eps)
(+ (sin x) (* eps (cos x)))
(fma.f64 (cos.f64 x) eps (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(fma.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps (sin.f64 x))
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)

rewrite175.0ms (1.6%)

Memory

-13.6MiB live, 140.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	53	16
2	380	16
3	4766	16
0	8210	16

Stop Event

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

Counts

4 → 214

Calls

Call 1

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

Outputs
(*.f64 (pow.f64 (/.f64 (fma.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (sin.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 9 binary64)) (pow.f64 (sin.f64 x) #s(literal 9 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)) (+.f64 (pow.f64 (.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (sin.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 (.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) #s(literal -1 binary64)) (pow.f64 (/.f64 (.f64 (cos.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal -2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))) #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x))))
(.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)))) (fma.f64 (.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) (-.f64 (.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64))))
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(/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 (-.f64 eps x)) (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64))))
(neg.f64 (sin.f64 (/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (-.f64 x eps))))
(neg.f64 (sin.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(neg.f64 (sin.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (neg.f64 (-.f64 x eps)))))
(neg.f64 (sin.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x))))))
(fma.f64 (sin.f64 (.f64 x (/.f64 x (-.f64 x eps)))) (cos.f64 (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps))))) (.f64 (cos.f64 (.f64 x (/.f64 x (-.f64 x eps)))) (sin.f64 (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))))
(fma.f64 (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 (+.f64 eps x))) #s(literal 1/2 binary64) (*.f64 (sin.f64 eps) (cos.f64 x)))
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x)))
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (cos.f64 eps) (sin.f64 x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (sin.f64 eps) (cos.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x)))
(sin.f64 (+.f64 eps x))
(-.f64 (.f64 (sin.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (cos.f64 (/.f64 (.f64 x x) (-.f64 eps x)))) (.f64 (cos.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (sin.f64 (/.f64 (.f64 x x) (-.f64 eps x)))))
(-.f64 (/.f64 (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 x eps))) (/.f64 (pow.f64 (.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 x eps))))
(-.f64 (.f64 (sin.f64 (.f64 x (/.f64 x (-.f64 x eps)))) (cos.f64 (.f64 eps (/.f64 eps (-.f64 x eps))))) (.f64 (cos.f64 (.f64 x (/.f64 x (-.f64 x eps)))) (sin.f64 (.f64 eps (/.f64 eps (-.f64 x eps))))))
(+.f64 (.f64 (sin.f64 (.f64 x (/.f64 x (-.f64 x eps)))) (cos.f64 (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))) (.f64 (cos.f64 (.f64 x (/.f64 x (-.f64 x eps)))) (sin.f64 (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))))
(+.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (.f64 (cos.f64 eps) (sin.f64 x)))
(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x)))
(exp.f64 (*.f64 (log.f64 (sin.f64 (+.f64 eps x))) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 x eps) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 eps eps (.f64 x x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 x eps) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (+.f64 eps x) (*.f64 x x)))
(.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (-.f64 eps x) eps) #s(literal 2 binary64)))) (-.f64 (.f64 x x) (.f64 (-.f64 eps x) eps)))
(.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 eps x) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (.f64 (-.f64 eps x) eps) (-.f64 (.f64 (-.f64 eps x) eps) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x))
(.f64 (.f64 (+.f64 eps x) (-.f64 eps x)) (pow.f64 (-.f64 eps x) #s(literal -1 binary64)))
(.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (pow.f64 (pow.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (.f64 (-.f64 x eps) (+.f64 eps x)))
(.f64 (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))
(*.f64 #s(literal 1 binary64) (+.f64 eps x))
(.f64 (neg.f64 (.f64 (-.f64 x eps) (+.f64 eps x))) (pow.f64 (neg.f64 (-.f64 x eps)) #s(literal -1 binary64)))
(.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (neg.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x))) #s(literal -1 binary64)))
(.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)))
(.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (/.f64 (+.f64 eps x) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (.f64 (+.f64 eps x) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64))))
(.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64)))
(*.f64 (+.f64 eps x) (/.f64 (-.f64 x eps) (-.f64 x eps)))
(.f64 (+.f64 eps x) (.f64 (-.f64 x eps) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))))
(pow.f64 (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 eps eps (.f64 x x)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 (.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))))
(/.f64 (-.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64)) (pow.f64 (.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 2 binary64))) (fma.f64 x (/.f64 x (-.f64 x eps)) (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 x eps) #s(literal -3 binary64))) (.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 (-.f64 x eps) #s(literal -3 binary64)))) (+.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 2 binary64)) (.f64 (.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps)))))))
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (neg.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)))) (neg.f64 (neg.f64 (-.f64 x eps))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 eps eps (*.f64 x x)) (-.f64 x eps)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps eps (.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (-.f64 x eps)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (.f64 eps x) #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (.f64 x x))))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (fma.f64 (-.f64 eps x) eps (.f64 x x)))
(/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x eps)) (.f64 (-.f64 x eps) (.f64 eps eps))) (pow.f64 (-.f64 x eps) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (.f64 (-.f64 x eps) (fma.f64 eps eps (.f64 x x))))
(/.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (-.f64 eps x))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (.f64 (-.f64 x eps) (fma.f64 (.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 eps x) #s(literal -1 binary64)))
(/.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 x eps))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))
(neg.f64 (/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (-.f64 x eps)))
(neg.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(neg.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (neg.f64 (-.f64 x eps))))
(neg.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(fma.f64 (/.f64 (.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (+.f64 eps x) (.f64 x x)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 (/.f64 (.f64 x x) (.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 (.f64 x x) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))
(-.f64 (.f64 x (/.f64 x (-.f64 x eps))) (.f64 eps (/.f64 eps (-.f64 x eps))))
(+.f64 (.f64 x (/.f64 x (-.f64 x eps))) (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))
(+.f64 eps x)
(+.f64 x eps)
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(pow.f64 (sin.f64 x) #s(literal 1 binary64))
(sin.f64 x)
(exp.f64 (*.f64 (log.f64 (sin.f64 x)) #s(literal 1 binary64)))

eval45.0ms (0.4%)

Memory: -4.6MiB live, 42.9MiB allocated
Compiler: Compiled 6 283 to 852 computations (86.4% saved)

prune6.0ms (0.1%)

Memory

13.9MiB live, 13.9MiB allocated

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	229	6	235
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	229	7	236

Accuracy

99.9%

Counts

236 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x))))
✓	60.4%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	99.9%	(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
▶	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
▶	99.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
▶	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 189 to 142 computations (24.9% saved)

simplify163.0ms (1.5%)

Memory

-20.2MiB live, 93.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (sin.f64 eps) x)
cost-diff	0	(fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
cost-diff	0	(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
cost-diff	0	(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
cost-diff	0	(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
cost-diff	0	(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
cost-diff	0	(cos.f64 x)
cost-diff	0	(*.f64 (cos.f64 x) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
cost-diff	0	(sin.f64 eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
cost-diff	0	(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
cost-diff	128	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
cost-diff	192	(+.f64 #s(literal 0 binary64) eps)
cost-diff	576	(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	203
0	60	193
1	99	193
2	182	193
3	359	193
4	629	193
5	953	193
6	1323	193
7	2172	193
8	2772	193
9	3025	190
10	3260	190
11	3602	190
12	5183	190
13	6421	190
0	8038	188

Stop Event

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

Calls

Call 1

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

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

localize201.0ms (1.8%)

Memory

31.2MiB live, 188.9MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
accuracy	0.16796875	(fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
accuracy	0.987684136344057	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
accuracy	34.042320585196954	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
accuracy	0	(cos.f64 x)
accuracy	0.0078125	(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
accuracy	0.01171875	(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
accuracy	0.27185438823275765	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
accuracy	0	(cos.f64 x)
accuracy	0.015625	(*.f64 (cos.f64 x) eps)
accuracy	0.5556812310534159	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
accuracy	0	(sin.f64 eps)
accuracy	1.224765317795204	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
accuracy	0	(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))
accuracy	0	(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
accuracy	0.01171875	(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
accuracy	0.06595174075693216	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))

Samples

171.0ms	253×	1	valid
1.0ms	3×	0	valid

Compiler

Compiled 383 to 73 computations (80.9% saved)

Precisions

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

ival-cos: 57.0ms (40.6% of total)

ival-mult: 30.0ms (21.3% of total)

adjust: 18.0ms (12.8% of total)

ival-sub: 11.0ms (7.8% of total)

ival-sin: 11.0ms (7.8% of total)

ival-add: 10.0ms (7.1% of total)

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

exact: 1.0ms (0.7% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series33.0ms (0.3%)

Memory

-20.4MiB live, 22.4MiB allocated

Counts

20 → 100

Calls

Call 1

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

Outputs
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
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))))))
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)))
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* -1/2 x)
(* x (- (* 1/12 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(- (cos eps) 1)
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(* x (sin eps))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(cos (* -1/2 (+ eps (* 2 x))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(cos x)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (sin x))
(* -1/2 (* (pow x 2) (sin eps)))
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))) (/ 1 x)))
(* -1/2 (* x (sin eps)))
(* x (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(cos (* -1/2 (- eps (* -2 x))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))
(* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps)))))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6)))))))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 eps) (* -1/2 x)))
(* eps (+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2))))
(* eps (+ (* -1/2 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/12 x))) 1/2))))
(* eps x)
(* eps (+ x (* -1/6 (* (pow eps 2) x))))
(* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* 1/120 (* (pow eps 2) x))))))
(* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) x)) (* 1/120 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))))
(* -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))
(* eps (- (* -1 (/ x eps)) 1/2))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(sin (* 1/2 eps))
(* -1 (* eps (+ 1/2 (/ x eps))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))

Calls

6 calls:

Time	Variable		Point	Expression
11.0ms	eps	@	0	((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (sin (* 1/2 (+ 0 eps))) (* 1/2 (+ 0 eps)) (- (cos eps) 1))
5.0ms	x	@	inf	((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (sin (* 1/2 (+ 0 eps))) (* 1/2 (+ 0 eps)) (- (cos eps) 1))
4.0ms	x	@	-inf	((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (sin (* 1/2 (+ 0 eps))) (* 1/2 (+ 0 eps)) (- (cos eps) 1))
4.0ms	eps	@	-inf	((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (sin (* 1/2 (+ 0 eps))) (* 1/2 (+ 0 eps)) (- (cos eps) 1))
4.0ms	x	@	0	((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (sin (* 1/2 (+ 0 eps))) (* 1/2 (+ 0 eps)) (- (cos eps) 1))

simplify226.0ms (2.1%)

Memory

8.0MiB live, 164.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	390	1307
1	1196	1242
2	3299	1207
3	7968	1207
0	8344	1097

Stop Event

1×	iter limit
1×	node limit

Counts

100 → 99

Calls

Call 1

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

Outputs
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1 x) (* -1/2 eps))
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
(cos (* -1/2 eps))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(fma.f64 (fma.f64 (fma.f64 x (.f64 #s(literal -1/6 binary64) x) #s(literal 1 binary64)) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (.f64 #s(literal -1/2 binary64) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(fma.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) x) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (+.f64 #s(literal 2 binary64) (*.f64 x (neg.f64 x)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (.f64 x x) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (-.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(fma.f64 (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (*.f64 x x) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ eps (* -1/2 (* (pow eps 2) x)))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps)
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(fma.f64 (fma.f64 (.f64 x (.f64 (.f64 eps eps) x)) #s(literal 1/12 binary64) (.f64 (*.f64 eps (+.f64 eps x)) #s(literal -1/2 binary64))) x eps)
(+ 1 (* -1/2 (* eps x)))
(fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 eps x) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* x (- (* 1/12 (pow x 2)) 1/2))
(.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/10080 binary64) (.f64 x x) #s(literal -1/240 binary64)) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)
(- (cos eps) 1)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(* x (sin eps))
(*.f64 (sin.f64 eps) x)
(* -1 x)
(neg.f64 x)
(* x (- (* -1/2 (/ eps x)) 1))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)) x)
(cos (* -1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(cos x)
(cos.f64 x)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (* (pow x 2) (sin eps)))
(.f64 (.f64 (*.f64 (sin.f64 eps) x) x) #s(literal -1/2 binary64))
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))
(.f64 (.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x)) x) x)
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))) (/ 1 x)))
(.f64 (+.f64 (/.f64 (/.f64 (sin.f64 eps) x) x) (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x))) (.f64 x x))
(* -1/2 (* x (sin eps)))
(.f64 (.f64 (sin.f64 eps) #s(literal -1/2 binary64)) x)
(* x (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))
(*.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x)) x)
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 x))
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))
(.f64 (.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) x))) x)) x) x)
(* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps)))))
(*.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x)) x)
(cos (* -1 x))
(cos.f64 x)
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/8 binary64))) eps (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/8 binary64))) eps (cos.f64 x))
(* eps (cos (* -1 x)))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/24 binary64) eps) (neg.f64 (sin.f64 x)) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps)) eps (cos.f64 x)) eps)
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps)
(* eps (+ 1 (* -1/2 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (+.f64 eps x) #s(literal 1 binary64)) eps)
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
(.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/6 binary64)) eps) eps (fma.f64 (.f64 #s(literal -1/2 binary64) x) (+.f64 eps x) #s(literal 1 binary64))) eps)
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6)))))))
(.f64 (fma.f64 (.f64 (fma.f64 x (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) #s(literal -1/6 binary64)) eps) eps (fma.f64 (.f64 #s(literal -1/2 binary64) x) (+.f64 eps x) #s(literal 1 binary64))) eps)
(* -1/2 (* eps x))
(.f64 (.f64 eps x) #s(literal -1/2 binary64))
(* eps (+ (* -1/2 eps) (* -1/2 x)))
(.f64 (.f64 eps (+.f64 eps x)) #s(literal -1/2 binary64))
(* eps (+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) eps (*.f64 #s(literal -1/2 binary64) x)) eps)
(* eps (+ (* -1/2 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/12 x))) 1/2))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64)) eps (*.f64 #s(literal -1/2 binary64) x)) eps)
(* eps x)
(*.f64 eps x)
(* eps (+ x (* -1/6 (* (pow eps 2) x))))
(*.f64 x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps))
(* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* 1/120 (* (pow eps 2) x))))))
(.f64 (fma.f64 (.f64 x (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 eps eps) x) eps)
(* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) x)) (* 1/120 x)))))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (.f64 (.f64 x (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64))) eps) eps (.f64 #s(literal -1/6 binary64) x)) (*.f64 eps x))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* -1/2 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/40320 binary64) (.f64 eps eps) #s(literal -1/720 binary64)) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)
(* eps (- (* -1 (/ x eps)) 1/2))
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps)
(* -1/2 (* (pow eps 2) (sin x)))
(.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps)
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) (.f64 eps eps))
(* -1/2 (* eps (sin x)))
(.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(* -1 (* eps (+ 1/2 (/ x eps))))
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps)
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)

rewrite184.0ms (1.7%)

Memory

0.6MiB live, 194.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	167
0	60	159
1	210	159
2	1636	159
0	8543	159

Stop Event

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

Counts

20 → 416

Calls

Call 1

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

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

eval74.0ms (0.7%)

Memory: -5.3MiB live, 124.3MiB allocated
Compiler: Compiled 17 094 to 2 262 computations (86.8% saved)

prune18.0ms (0.2%)

Memory

3.2MiB live, 42.3MiB allocated

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	518	14	532
Fresh	0	1	1
Picked	4	1	5
Done	1	0	1
Total	523	16	539

Accuracy

99.9%

Counts

539 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x))))
	74.0%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps)))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
▶	99.9%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.9%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.6%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	59.5%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
▶	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
✓	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
▶	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
▶	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
▶	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (*.f64 x x) eps)))

Compiler

Compiled 726 to 505 computations (30.4% saved)

simplify184.0ms (1.7%)

Memory

21.5MiB live, 140.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (* (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x))
cost-diff	0	(fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x))
cost-diff	0	(.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
cost-diff	0	#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
cost-diff	0	(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
cost-diff	0	(*.f64 #s(literal -1/2 binary64) x)
cost-diff	0	(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)
cost-diff	0	#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
cost-diff	0	#s(approx (cos x) #s(literal 1 binary64))
cost-diff	0	(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
cost-diff	0	(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
cost-diff	0	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
cost-diff	128	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
cost-diff	576	(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	441
0	91	435
1	158	435
2	419	435
3	1040	435
4	1809	435
5	2327	435
6	2381	435
7	2617	435
8	2632	435
9	2667	435
10	2882	435
11	3099	435
12	3190	435
13	3654	435
14	5374	435
15	6451	435
16	7158	432
17	7491	432
18	7727	432
0	8225	428

Stop Event

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

Calls

Call 1

Inputs
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
#s(literal 1/3840 binary64)
(*.f64 eps eps)
eps
#s(literal -1/48 binary64)
#s(literal 1/2 binary64)
#s(literal 2 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(fma.f64 #s(literal 2 binary64) x eps)
x
#s(literal -2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)
#s(approx (cos x) #s(literal 1 binary64))
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
(*.f64 eps (+.f64 eps x))
eps
(+.f64 eps x)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64))
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(literal -1/720 binary64)
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x))
#s(approx (* (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x))
(.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)
(fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/2 binary64))
#s(literal 1/12 binary64)
(*.f64 x x)
x
#s(literal -1/2 binary64)
eps
(cos.f64 x)

Outputs
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
(fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))
#s(literal 1/3840 binary64)
(*.f64 eps eps)
eps
#s(literal -1/48 binary64)
#s(literal 1/2 binary64)
#s(literal 2 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(neg.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
x
#s(literal -2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)
#s(approx (cos x) #s(literal 1 binary64))
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 (+.f64 x eps) eps) (.f64 #s(literal -1/2 binary64) x) eps)))
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps))
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 (+.f64 x eps) eps) (.f64 #s(literal -1/2 binary64) x) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)
(fma.f64 (.f64 (+.f64 x eps) eps) (.f64 #s(literal -1/2 binary64) x) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
(*.f64 eps (+.f64 eps x))
(*.f64 (+.f64 x eps) eps)
eps
(+.f64 eps x)
(+.f64 x eps)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64))
(fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64))
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
#s(literal -1/720 binary64)
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x))
#s(approx (* (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x))
(.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)
(fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/2 binary64))
#s(literal 1/12 binary64)
(*.f64 x x)
x
#s(literal -1/2 binary64)
eps
(cos.f64 x)

localize195.0ms (1.8%)

Memory

-12.2MiB live, 182.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)
accuracy	0.015625	(fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/2 binary64))
accuracy	0.27185438823275765	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
accuracy	1.0014668064417382	#s(approx (* (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x))
accuracy	0.010097509768442016	(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
accuracy	0.015625	(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
accuracy	0.5556812310534159	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
accuracy	0.8589910300980649	#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
accuracy	0.00390625	(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)
accuracy	0.16015625	(*.f64 eps (+.f64 eps x))
accuracy	0.27185438823275765	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
accuracy	0.9876841364955697	#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps))
accuracy	0.015625	(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)
accuracy	0.5556812310534159	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
accuracy	1.2332101865596485	#s(approx (cos x) #s(literal 1 binary64))
accuracy	0	#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
accuracy	0.00390625	(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
accuracy	0.01171875	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
accuracy	0.06595174075693216	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))

Samples

64.0ms	159×	0	valid
61.0ms	97×	1	valid

Compiler

Compiled 714 to 115 computations (83.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 94.0ms

ival-mult: 37.0ms (39.3% of total)

const: 17.0ms (18.1% of total)

ival-add: 16.0ms (17% of total)

adjust: 9.0ms (9.6% of total)

ival-sin: 6.0ms (6.4% of total)

ival-cos: 4.0ms (4.3% of total)

ival-div: 2.0ms (2.1% of total)

ival-sub: 2.0ms (2.1% of total)

exact: 1.0ms (1.1% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series22.0ms (0.2%)

Memory

-15.4MiB live, 22.8MiB allocated

Counts

23 → 103

Calls

Call 1

Inputs
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x))
#s(approx (* (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x))
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(*.f64 eps (+.f64 eps x))
(fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/2 binary64))

Outputs
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
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))))))
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)))
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(* -1/2 x)
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* x (- (* 1/12 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(pow eps 2)
(+ (* eps x) (pow eps 2))
-1/2
(- (* 1/12 (pow x 2)) 1/2)
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(cos (* -1/2 (+ eps (* 2 x))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(cos x)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (sin x))
(* eps x)
(* x (+ eps (/ (pow eps 2) x)))
(* 1/12 (pow x 2))
(* (pow x 2) (- 1/12 (* 1/2 (/ 1 (pow x 2)))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(cos (* -1/2 (- eps (* -2 x))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
-1/48
(- (* 1/3840 (pow eps 2)) 1/48)
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* eps (+ eps x))
(* eps (- (* -1 (/ x eps)) 1/2))
(* 2 (sin (* 1/2 eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* 1/3840 (pow eps 2))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(sin (* 1/2 eps))
(* (pow eps 2) (+ 1 (/ x eps)))
(* -1 (* eps (+ 1/2 (/ x eps))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(- (sin (- x (* -1 eps))) (sin x))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	inf	((/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (+ (* 1/3840 (* eps eps)) -1/48) (sin (* 1/2 (+ 0 eps))) (* eps (+ eps x)) (+ (* 1/12 (* x x)) -1/2))
3.0ms	x	@	inf	((/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (+ (* 1/3840 (* eps eps)) -1/48) (sin (* 1/2 (+ 0 eps))) (* eps (+ eps x)) (+ (* 1/12 (* x x)) -1/2))
3.0ms	eps	@	-inf	((/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (+ (* 1/3840 (* eps eps)) -1/48) (sin (* 1/2 (+ 0 eps))) (* eps (+ eps x)) (+ (* 1/12 (* x x)) -1/2))
3.0ms	x	@	-inf	((/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (+ (* 1/3840 (* eps eps)) -1/48) (sin (* 1/2 (+ 0 eps))) (* eps (+ eps x)) (+ (* 1/12 (* x x)) -1/2))
2.0ms	eps	@	0	((/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (+ (* 1/3840 (* eps eps)) -1/48) (sin (* 1/2 (+ 0 eps))) (* eps (+ eps x)) (+ (* 1/12 (* x x)) -1/2))

simplify161.0ms (1.5%)

Memory

34.5MiB live, 188.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	365	1221
1	1103	1167
2	2971	1137
3	7249	1137
0	8433	1045

Stop Event

1×	iter limit
1×	node limit

Counts

103 → 102

Calls

Call 1

Inputs
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
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))))))
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)))
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(* -1/2 x)
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* x (- (* 1/12 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(pow eps 2)
(+ (* eps x) (pow eps 2))
-1/2
(- (* 1/12 (pow x 2)) 1/2)
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(cos (* -1/2 (+ eps (* 2 x))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(cos x)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (sin x))
(* eps x)
(* x (+ eps (/ (pow eps 2) x)))
(* 1/12 (pow x 2))
(* (pow x 2) (- 1/12 (* 1/2 (/ 1 (pow x 2)))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(cos (* -1/2 (- eps (* -2 x))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
-1/48
(- (* 1/3840 (pow eps 2)) 1/48)
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* eps (+ eps x))
(* eps (- (* -1 (/ x eps)) 1/2))
(* 2 (sin (* 1/2 eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* 1/3840 (pow eps 2))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(sin (* 1/2 eps))
(* (pow eps 2) (+ 1 (/ x eps)))
(* -1 (* eps (+ 1/2 (/ x eps))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(- (sin (- x (* -1 eps))) (sin x))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))

Outputs
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1 x) (* -1/2 eps))
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
(cos (* -1/2 eps))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(fma.f64 (fma.f64 (fma.f64 x (.f64 #s(literal -1/6 binary64) x) #s(literal 1 binary64)) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (.f64 #s(literal -1/2 binary64) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (+.f64 #s(literal 2 binary64) (.f64 (neg.f64 x) x)) (.f64 (.f64 (.f64 #s(literal 2 binary64) x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64) (.f64 (.f64 x x) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (.f64 #s(literal -1/3 binary64) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (neg.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(fma.f64 (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (*.f64 x x) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ eps (* -1/2 (* (pow eps 2) x)))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64)) eps)
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (+.f64 eps x) #s(literal 1 binary64)) eps)
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(fma.f64 (fma.f64 (.f64 x #s(literal 1/12 binary64)) (.f64 (.f64 eps eps) x) (.f64 (*.f64 #s(literal -1/2 binary64) eps) (+.f64 eps x))) x eps)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(+ 1 (* -1/2 (* eps x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 eps x) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(* x (- (* 1/12 (pow x 2)) 1/2))
(.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/10080 binary64) (.f64 x x) #s(literal -1/240 binary64)) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)
(pow eps 2)
(*.f64 eps eps)
(+ (* eps x) (pow eps 2))
(*.f64 (+.f64 eps x) eps)
-1/2
#s(literal -1/2 binary64)
(- (* 1/12 (pow x 2)) 1/2)
(fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* -1 x)
(neg.f64 x)
(* x (- (* -1/2 (/ eps x)) 1))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)) x)
(cos (* -1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(cos x)
(cos.f64 x)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps)
(* -1/2 (* eps (pow x 2)))
(.f64 (.f64 (*.f64 eps x) #s(literal -1/2 binary64)) x)
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(.f64 (.f64 (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)) (*.f64 x x))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(.f64 (.f64 (fma.f64 (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64) (/.f64 (/.f64 eps x) x)) x) x)
(* -1/720 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/720 binary64))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/720 binary64)) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/720 binary64)) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/720 binary64)) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64))))) (pow.f64 x #s(literal 6 binary64)))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* eps x)
(*.f64 eps x)
(* x (+ eps (/ (pow eps 2) x)))
(*.f64 (fma.f64 eps (/.f64 eps x) eps) x)
(* 1/12 (pow x 2))
(.f64 #s(literal 1/12 binary64) (.f64 x x))
(* (pow x 2) (- 1/12 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x) x)
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 x))
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) eps (/.f64 #s(literal -1 binary64) x))) (neg.f64 x))) x) x)
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 eps (/.f64 eps x) eps) x)
(cos (* -1 x))
(cos.f64 x)
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/8 binary64))) eps (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/8 binary64))) eps (cos.f64 x))
(* eps (cos (* -1 x)))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/24 binary64) eps) (neg.f64 (sin.f64 x)) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ 1 (* -1/24 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/1920 binary64) (*.f64 eps eps) #s(literal -1/24 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps)) eps (cos.f64 x)) eps)
(* eps (+ 1 (* -1/2 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (+.f64 eps x) #s(literal 1 binary64)) eps)
-1/48
#s(literal -1/48 binary64)
(- (* 1/3840 (pow eps 2)) 1/48)
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ eps x))
(*.f64 (+.f64 eps x) eps)
(* eps (- (* -1 (/ x eps)) 1/2))
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps)
(* 2 (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(* -1/2 (* (pow eps 2) (sin x)))
(.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps)
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) (.f64 eps eps))
(* -1/2 (* (pow eps 2) x))
(.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x)
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 x (/.f64 x eps) x) (/.f64 #s(literal 1 binary64) eps)) eps) eps)
(* -1/2 (* eps (sin x)))
(.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)
(* 1/3840 (pow eps 2))
(.f64 #s(literal 1/3840 binary64) (.f64 eps eps))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(.f64 (.f64 (-.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal 1/48 binary64) (*.f64 eps eps))) eps) eps)
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(* (pow eps 2) (+ 1 (/ x eps)))
(*.f64 eps (fma.f64 (/.f64 x eps) eps eps))
(* -1 (* eps (+ 1/2 (/ x eps))))
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps)
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (neg.f64 eps))) eps) eps)
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)

rewrite259.0ms (2.4%)

Memory

-19.5MiB live, 143.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	352
0	91	346
1	340	346
2	2874	346
0	8732	344

Stop Event

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

Counts

23 → 520

Calls

Call 1

Inputs
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x))
#s(approx (* (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x))
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(*.f64 eps (+.f64 eps x))
(fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/2 binary64))

Outputs
(.f64 (pow.f64 (/.f64 #s(literal -2 binary64) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps))) #s(literal -1 binary64)) (pow.f64 (-.f64 (.f64 x #s(literal 2 binary64)) eps) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal -2 binary64) (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))) #s(literal -1 binary64)))
(*.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) #s(literal 1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (pow.f64 (pow.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))
(.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal -2 binary64) (fma.f64 x #s(literal 2 binary64) eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal -2 binary64) (fma.f64 x #s(literal 2 binary64) eps)) #s(literal -1 binary64))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #s(literal -1/2 binary64))) (neg.f64 (-.f64 (.f64 x #s(literal 2 binary64)) eps)))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1/2 binary64))) (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)))) #s(literal 2 binary64))
(/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #s(literal -1/2 binary64)) (-.f64 (.f64 x #s(literal 2 binary64)) eps))
(/.f64 (.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1/2 binary64)) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps))) (neg.f64 (.f64 #s(literal -2 binary64) (-.f64 (.f64 x #s(literal 2 binary64)) eps))))
(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (.f64 #s(literal -2 binary64) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps))) #s(literal -2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 #s(literal -2 binary64) (fma.f64 x #s(literal 2 binary64) eps)) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal -2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))
(/.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) (.f64 #s(literal -2 binary64) (-.f64 (.f64 x #s(literal 2 binary64)) eps)))
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (.f64 #s(literal -2 binary64) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal -2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -2 binary64) (fma.f64 x #s(literal 2 binary64) eps)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))
(/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))
(neg.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal -2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal -1 binary64)))
(cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))
(cos.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))
(.f64 (.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
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(fma.f64 eps eps (*.f64 eps x))
(fma.f64 eps x (*.f64 eps eps))
(fma.f64 x eps (*.f64 eps eps))
(+.f64 (.f64 #s(literal 0 binary64) (+.f64 eps x)) (.f64 (+.f64 eps x) eps))
(+.f64 (.f64 (+.f64 eps x) #s(literal 0 binary64)) (.f64 (+.f64 eps x) eps))
(+.f64 (.f64 eps x) (.f64 eps eps))
(+.f64 (.f64 (+.f64 eps x) eps) (.f64 #s(literal 0 binary64) (+.f64 eps x)))
(+.f64 (.f64 (+.f64 eps x) eps) (.f64 (+.f64 eps x) #s(literal 0 binary64)))
(+.f64 (.f64 eps eps) (.f64 eps x))
(.f64 (fma.f64 #s(literal 1/144 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) (pow.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal 1/1728 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64)) (pow.f64 (fma.f64 #s(literal 1/144 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 x x) #s(literal -1/24 binary64)))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/144 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/144 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))) (fma.f64 #s(literal 1/1728 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64))) #s(literal -1 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/144 binary64) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (-.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/12 binary64) (*.f64 x x)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/144 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/1728 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/144 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/144 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal 1/2 binary64))) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/144 binary64) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/12 binary64) (*.f64 x x))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/144 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64))) (neg.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/1728 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/144 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 (*.f64 x x) #s(literal -1/24 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/1728 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64))) (neg.f64 (fma.f64 #s(literal 1/144 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/144 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/144 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))) (fma.f64 #s(literal 1/1728 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64)))))
(/.f64 (fma.f64 #s(literal 1/144 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) (fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(/.f64 (fma.f64 #s(literal 1/1728 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/144 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 (*.f64 x x) #s(literal -1/24 binary64)))))
(/.f64 (fma.f64 #s(literal 1/1728 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64)) (fma.f64 #s(literal 1/144 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/144 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/144 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))) (fma.f64 #s(literal 1/1728 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64))))
(fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))
(fma.f64 x (*.f64 #s(literal 1/12 binary64) x) #s(literal -1/2 binary64))
(-.f64 (/.f64 (.f64 #s(literal 1/144 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal 1/2 binary64))))
(+.f64 (.f64 #s(literal 1/12 binary64) (.f64 x x)) #s(literal -1/2 binary64))
(+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/12 binary64) (.f64 x x)))

eval117.0ms (1.1%)

Memory: 8.9MiB live, 93.1MiB allocated
Compiler: Compiled 26 888 to 3 039 computations (88.7% saved)

prune23.0ms (0.2%)

Memory

-2.0MiB live, 36.6MiB allocated

Pruning

19 alts after pruning (14 fresh and 5 done)

	Pruned	Kept	Total
New	604	6	610
Fresh	2	8	10
Picked	1	4	5
Done	0	1	1
Total	607	19	626

Accuracy

99.9%

Counts

626 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x))))
	74.0%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps)))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
▶	99.9%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
	99.9%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(approx (+ ( 1/3840 (* eps eps)) -1/48) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
▶	99.6%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	59.5%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
✓	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 #s(approx (+ ( 1/12 (* x x)) -1/2) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
✓	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
✓	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
▶	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
✓	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
✓	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
	5.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) #s(literal -1/2 binary64)) x))))
▶	5.7%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (*.f64 x x) eps)))

Compiler

Compiled 896 to 611 computations (31.8% saved)

simplify169.0ms (1.5%)

Memory

-6.3MiB live, 70.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
cost-diff	0	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
cost-diff	128	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
cost-diff	576	(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
cost-diff	0	#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
cost-diff	0	(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
cost-diff	0	#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
cost-diff	0	(.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
cost-diff	0	(.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x)
cost-diff	0	#s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))
cost-diff	0	#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x)))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
cost-diff	0	(.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
cost-diff	0	#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
cost-diff	0	(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
cost-diff	0	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	502
0	99	489
1	170	489
2	413	489
3	992	489
4	1575	489
5	1804	489
6	2166	489
7	3989	489
8	5824	484
9	6828	484
10	7423	484
0	8126	474

Stop Event

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

Calls

Call 1

Inputs
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
#s(literal 1/3840 binary64)
(*.f64 eps eps)
eps
#s(literal -1/48 binary64)
#s(literal 1/2 binary64)
#s(literal 2 binary64)
(cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))
#s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
#s(literal -1/2 binary64)
(neg.f64 x)
x
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x)))
#s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))
(.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x)
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(*.f64 eps eps)
eps
#s(literal -1/2 binary64)
x
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(*.f64 x x)
x
#s(literal -1/2 binary64)
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
(fma.f64 #s(literal 1/12 binary64) (*.f64 eps x) #s(literal -1/2 binary64))
#s(literal 1/12 binary64)
(*.f64 eps x)
eps
x
#s(literal -1/2 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal 1 binary64)
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
#s(literal 2 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(fma.f64 #s(literal 2 binary64) x eps)
x
#s(literal -2 binary64)

Outputs
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(.f64 (.f64 (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
(fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))
#s(literal 1/3840 binary64)
(*.f64 eps eps)
eps
#s(literal -1/48 binary64)
#s(literal 1/2 binary64)
#s(literal 2 binary64)
(cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))
#s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
#s(literal -1/2 binary64)
(neg.f64 x)
x
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) x))))
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x)))
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) x)))
#s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))
#s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) x))
(.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x)
(.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) x)
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(*.f64 eps eps)
eps
#s(literal -1/2 binary64)
x
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(*.f64 x x)
x
#s(literal -1/2 binary64)
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 x eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)
(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 x eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 x eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(fma.f64 (fma.f64 (fma.f64 (.f64 x eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
(fma.f64 (fma.f64 (.f64 x eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
(fma.f64 #s(literal 1/12 binary64) (*.f64 eps x) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))
#s(literal 1/12 binary64)
(*.f64 eps x)
(*.f64 x eps)
eps
x
#s(literal -1/2 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal 1 binary64)
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
eps
#s(literal 2 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
x
#s(literal -2 binary64)

localize261.0ms (2.4%)

Memory

-1.6MiB live, 153.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 #s(literal 1/2 binary64) eps)
accuracy	0.01171875	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
accuracy	0.06595174075693216	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
accuracy	0.25240991158493065	#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps))
accuracy	0.0078125	(fma.f64 #s(literal 1/12 binary64) (*.f64 eps x) #s(literal -1/2 binary64))
accuracy	0.01171875	(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)
accuracy	0.27185438823275765	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
accuracy	1.0171101834039122	#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
accuracy	0	(*.f64 x x)
accuracy	0.015625	(.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)
accuracy	0.5556812310534159	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
accuracy	0.9912875068578391	#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
accuracy	0.08984375	(.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x)
accuracy	0.27185438823275765	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
accuracy	0.9876841364955697	#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x)))
accuracy	60.36241388843338	#s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))
accuracy	0	#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
accuracy	0.00390625	(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
accuracy	0.01171875	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
accuracy	0.06595174075693216	(cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))

Samples

150.0ms	98×	1	valid
58.0ms	157×	0	valid
1.0ms	1×	3	valid

Compiler

Compiled 814 to 130 computations (84% saved)

Precisions

Click to see histograms. Total time spent on operations: 149.0ms

ival-add: 59.0ms (39.6% of total)

ival-mult: 53.0ms (35.6% of total)

const: 11.0ms (7.4% of total)

adjust: 10.0ms (6.7% of total)

ival-sin: 6.0ms (4% of total)

ival-cos: 4.0ms (2.7% of total)

ival-div: 2.0ms (1.3% of total)

ival-sub: 2.0ms (1.3% of total)

exact: 1.0ms (0.7% of total)

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

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series28.0ms (0.3%)

Memory

32.4MiB live, 32.4MiB allocated

Counts

26 → 110

Calls

Call 1

Inputs
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x)))
#s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))
(.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
(*.f64 x x)
(fma.f64 #s(literal 1/12 binary64) (*.f64 eps x) #s(literal -1/2 binary64))
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)

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

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	x	@	0	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* (+ (* 1/3840 (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* (* (* eps eps) -1/2) x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (+ (* (+ (* 1/12 (* eps x)) -1/2) x) (* -1/2 eps)) x) 1) (/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2)) (+ (* 1/3840 (* eps eps)) -1/48) (* x x) (+ (* 1/12 (* eps x)) -1/2) (sin (* 1/2 (+ 0 eps))) (* 1/2 eps))
4.0ms	eps	@	-inf	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* (+ (* 1/3840 (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* (* (* eps eps) -1/2) x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (+ (* (+ (* 1/12 (* eps x)) -1/2) x) (* -1/2 eps)) x) 1) (/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2)) (+ (* 1/3840 (* eps eps)) -1/48) (* x x) (+ (* 1/12 (* eps x)) -1/2) (sin (* 1/2 (+ 0 eps))) (* 1/2 eps))
4.0ms	eps	@	inf	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* (+ (* 1/3840 (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* (* (* eps eps) -1/2) x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (+ (* (+ (* 1/12 (* eps x)) -1/2) x) (* -1/2 eps)) x) 1) (/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2)) (+ (* 1/3840 (* eps eps)) -1/48) (* x x) (+ (* 1/12 (* eps x)) -1/2) (sin (* 1/2 (+ 0 eps))) (* 1/2 eps))
4.0ms	x	@	-inf	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* (+ (* 1/3840 (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* (* (* eps eps) -1/2) x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (+ (* (+ (* 1/12 (* eps x)) -1/2) x) (* -1/2 eps)) x) 1) (/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2)) (+ (* 1/3840 (* eps eps)) -1/48) (* x x) (+ (* 1/12 (* eps x)) -1/2) (sin (* 1/2 (+ 0 eps))) (* 1/2 eps))
4.0ms	x	@	inf	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* (+ (* 1/3840 (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* (* (* eps eps) -1/2) x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (+ (* (+ (* 1/12 (* eps x)) -1/2) x) (* -1/2 eps)) x) 1) (/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2)) (+ (* 1/3840 (* eps eps)) -1/48) (* x x) (+ (* 1/12 (* eps x)) -1/2) (sin (* 1/2 (+ 0 eps))) (* 1/2 eps))

simplify225.0ms (2.1%)

Memory

-16.2MiB live, 97.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	403	1372
1	1242	1305
2	3640	1266
0	8306	1156

Stop Event

1×	iter limit
1×	node limit

Counts

110 → 109

Calls

Call 1

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

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

rewrite238.0ms (2.2%)

Memory

4.0MiB live, 136.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	416
0	99	404
1	350	404
2	2825	404
0	9131	396

Stop Event

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

Counts

26 → 304

Calls

Call 1

Inputs
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x)))
#s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))
(.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
(*.f64 x x)
(fma.f64 #s(literal 1/12 binary64) (*.f64 eps x) #s(literal -1/2 binary64))
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)

Outputs
(.f64 (.f64 (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) #s(literal 2 binary64)) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(.f64 (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) (.f64 #s(literal 2 binary64) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 (.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (.f64 (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64)) eps)) (neg.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/8 binary64)) eps)) (neg.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) eps) (*.f64 eps #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (.f64 (neg.f64 (.f64 eps eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)))) (neg.f64 (neg.f64 eps)))
(/.f64 (neg.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)))) (neg.f64 (.f64 eps eps)))
(/.f64 (neg.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) (neg.f64 (.f64 eps eps)))) (neg.f64 (neg.f64 eps)))
(/.f64 (neg.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (.f64 eps eps)))
(/.f64 (neg.f64 (.f64 eps (fma.f64 (pow.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64)))) (neg.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (.f64 eps (fma.f64 (pow.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) eps) (*.f64 eps #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64)) (neg.f64 (.f64 eps eps)))) (neg.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) (neg.f64 eps))))
(/.f64 (neg.f64 (.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 eps eps))))
(/.f64 (neg.f64 (.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/8 binary64)) (neg.f64 (.f64 eps eps)))) (neg.f64 (.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) eps) (*.f64 eps #s(literal 1/2 binary64)))) (neg.f64 eps))))
(/.f64 (neg.f64 (.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/8 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) eps) (.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps))))
(/.f64 (neg.f64 (.f64 (neg.f64 (.f64 eps eps)) (fma.f64 (pow.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64)))) (neg.f64 (.f64 (neg.f64 eps) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (.f64 (neg.f64 (.f64 eps eps)) (fma.f64 (pow.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (.f64 (neg.f64 eps) (-.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) eps) (*.f64 eps #s(literal 1/2 binary64)))))))
(/.f64 (neg.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (pow.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64)))) (neg.f64 (.f64 (.f64 eps eps) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (pow.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (.f64 (.f64 eps eps) (-.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) eps) (*.f64 eps #s(literal 1/2 binary64)))))))
(/.f64 (.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64)) eps) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)))
(/.f64 (.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/8 binary64)) eps) (-.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) eps) (*.f64 eps #s(literal 1/2 binary64)))))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64))) (neg.f64 eps))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64))) (.f64 eps eps))
(/.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) (neg.f64 (.f64 eps eps))) (neg.f64 eps))
(/.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) (pow.f64 eps #s(literal 3 binary64))) (.f64 eps eps))
(/.f64 (.f64 eps (fma.f64 (pow.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64))) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)))
(/.f64 (.f64 eps (fma.f64 (pow.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/8 binary64))) (-.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) eps) (*.f64 eps #s(literal 1/2 binary64)))))
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(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (.f64 x eps) #s(literal 1/12 binary64)) #s(literal 2 binary64)))) (neg.f64 (-.f64 #s(literal -1/2 binary64) (.f64 (.f64 x eps) #s(literal 1/12 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/144 binary64) (pow.f64 (.f64 x eps) #s(literal 2 binary64)) #s(literal -1/4 binary64)))) (neg.f64 (neg.f64 (fma.f64 (.f64 x eps) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 x eps) #s(literal 3 binary64)) #s(literal 1/1728 binary64) #s(literal -1/8 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/144 binary64) (pow.f64 (.f64 x eps) #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x eps) #s(literal -1/24 binary64)))))))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 (.f64 x eps) #s(literal 1/12 binary64)) #s(literal 2 binary64)) (fma.f64 (.f64 x eps) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) (.f64 (fma.f64 (.f64 x eps) #s(literal 1/12 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (.f64 (fma.f64 (.f64 x eps) #s(literal 1/12 binary64) #s(literal 1/2 binary64)) (fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (.f64 x eps) #s(literal 1/12 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal -1/2 binary64) (.f64 (.f64 x eps) #s(literal 1/12 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/144 binary64) (pow.f64 (.f64 x eps) #s(literal 2 binary64)) #s(literal -1/4 binary64))) (neg.f64 (fma.f64 (.f64 x eps) #s(literal 1/12 binary64) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 x eps) #s(literal 3 binary64)) #s(literal 1/1728 binary64) #s(literal -1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 (.f64 x eps) #s(literal 1/12 binary64)) #s(literal 2 binary64)) (.f64 (*.f64 x eps) #s(literal -1/24 binary64))))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 x eps) #s(literal 3 binary64)) #s(literal 1/1728 binary64) #s(literal -1/8 binary64))) (neg.f64 (fma.f64 #s(literal 1/144 binary64) (pow.f64 (.f64 x eps) #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x eps) #s(literal -1/24 binary64))))))
(/.f64 (fma.f64 #s(literal 1/144 binary64) (pow.f64 (.f64 x eps) #s(literal 2 binary64)) #s(literal -1/4 binary64)) (fma.f64 (.f64 x eps) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (.f64 x eps) #s(literal 1/12 binary64) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/144 binary64) (pow.f64 (.f64 x eps) #s(literal 2 binary64)) #s(literal -1/4 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/144 binary64) (pow.f64 (.f64 x eps) #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x eps) #s(literal -1/24 binary64)))) (fma.f64 (pow.f64 (.f64 x eps) #s(literal 3 binary64)) #s(literal 1/1728 binary64) #s(literal -1/8 binary64)))))
(/.f64 (fma.f64 (pow.f64 (.f64 x eps) #s(literal 3 binary64)) #s(literal 1/1728 binary64) #s(literal -1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 (.f64 x eps) #s(literal 1/12 binary64)) #s(literal 2 binary64)) (.f64 (*.f64 x eps) #s(literal -1/24 binary64)))))
(/.f64 (fma.f64 (pow.f64 (.f64 x eps) #s(literal 3 binary64)) #s(literal 1/1728 binary64) #s(literal -1/8 binary64)) (fma.f64 #s(literal 1/144 binary64) (pow.f64 (.f64 x eps) #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x eps) #s(literal -1/24 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x eps) #s(literal 1/12 binary64) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/144 binary64) (pow.f64 (.f64 x eps) #s(literal 2 binary64)) #s(literal -1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/144 binary64) (pow.f64 (.f64 x eps) #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x eps) #s(literal -1/24 binary64)))) (fma.f64 (pow.f64 (.f64 x eps) #s(literal 3 binary64)) #s(literal 1/1728 binary64) #s(literal -1/8 binary64))))
(fma.f64 (*.f64 #s(literal 1/12 binary64) x) eps #s(literal -1/2 binary64))
(fma.f64 (*.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64))
(fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/12 binary64) (*.f64 x eps) #s(literal -1/2 binary64))
(fma.f64 x (*.f64 #s(literal 1/12 binary64) eps) #s(literal -1/2 binary64))
(fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 x eps) #s(literal 1/12 binary64)) #s(literal 2 binary64)) (fma.f64 (.f64 x eps) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 x eps) #s(literal 1/12 binary64) #s(literal 1/2 binary64))))
(+.f64 (.f64 (.f64 x eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x eps) #s(literal 1/12 binary64)))
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) eps)
(/.f64 (neg.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(literal 1/2 binary64))) (neg.f64 (neg.f64 eps)))
(/.f64 (neg.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/2 binary64))) (neg.f64 (.f64 eps eps)))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (neg.f64 (.f64 eps eps)))) (neg.f64 (neg.f64 eps)))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (.f64 eps eps)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 eps #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 eps #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (+.f64 #s(literal 0 binary64) (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (+.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (.f64 eps #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 #s(literal 0 binary64) (.f64 eps #s(literal 1/2 binary64)))))))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(literal 1/2 binary64)) (neg.f64 eps))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))
(/.f64 (.f64 #s(literal 1/2 binary64) (neg.f64 (.f64 eps eps))) (neg.f64 eps))
(/.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 3 binary64))) (.f64 eps eps))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 eps #s(literal 1/2 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (.f64 eps #s(literal 1/2 binary64))))
(/.f64 (+.f64 #s(literal 0 binary64) (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/8 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (.f64 eps #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 #s(literal 0 binary64) (.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 1/2 binary64) eps #s(literal 0 binary64))
(+.f64 (*.f64 eps #s(literal 1/2 binary64)) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/2 binary64)))

eval71.0ms (0.7%)

Memory: 8.7MiB live, 83.0MiB allocated
Compiler: Compiled 15 249 to 1 977 computations (87% saved)

prune49.0ms (0.4%)

Memory

-5.0MiB live, 44.3MiB allocated

Pruning

18 alts after pruning (10 fresh and 8 done)

	Pruned	Kept	Total
New	389	5	394
Fresh	4	5	9
Picked	1	4	5
Done	1	4	5
Total	395	18	413

Accuracy

99.9%

Counts

413 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x))))
	40.3%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (/.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) (pow.f64 eps #s(literal 3 binary64))) (.f64 eps eps))) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
	60.0%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (/.f64 (.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64)) (neg.f64 (.f64 eps eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) (neg.f64 eps)))) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
✓	99.9%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
	99.9%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(approx (+ ( 1/3840 (* eps eps)) -1/48) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
	99.6%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 #s(approx (+ ( 1/12 (* x x)) -1/2) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
✓	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
✓	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
✓	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
✓	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
✓	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
✓	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
	5.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) #s(literal -1/2 binary64)) x))))
✓	5.7%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (*.f64 x x) eps)))

Compiler

Compiled 1 396 to 591 computations (57.7% saved)

regimes32.0ms (0.3%)

Memory

-24.5MiB live, 51.8MiB allocated

Counts

32 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 #s(approx (+ ( 1/12 (* x x)) -1/2) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(approx (+ ( 1/3840 (* eps eps)) -1/48) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(approx (+ ( 1/3840 (* eps eps)) -1/48) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (/.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) (pow.f64 eps #s(literal 3 binary64))) (.f64 eps eps))) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (/.f64 (.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64)) (neg.f64 (.f64 eps eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) (neg.f64 eps)))) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps)))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x))))

Outputs

(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))

Calls

3 calls:

10.0ms	x
9.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
8.0ms	eps

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`eps`
99.9%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes21.0ms (0.2%)

Memory

-0.9MiB live, 37.0MiB allocated

Counts

22 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 #s(approx (+ ( 1/12 (* x x)) -1/2) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(approx (+ ( 1/3840 (* eps eps)) -1/48) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(approx (+ ( 1/3840 (* eps eps)) -1/48) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))

Outputs

(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(approx (+ (* 1/3840 (* eps eps)) -1/48) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))

Calls

3 calls:

8.0ms	x
6.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	eps

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`eps`
99.9%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes23.0ms (0.2%)

Memory

-7.4MiB live, 33.7MiB allocated

Counts

19 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 #s(approx (+ ( 1/12 (* x x)) -1/2) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))

Outputs

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

Calls

3 calls:

5.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	eps
5.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes14.0ms (0.1%)

Memory

34.6MiB live, 34.6MiB allocated

Counts

15 → 1

Calls

Call 1

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

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))

Calls

3 calls:

5.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	x
4.0ms	eps

Results

Accuracy	Segments	Branch
99.1%	1	`x`
99.1%	1	`eps`
99.1%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes14.0ms (0.1%)

Memory

-12.7MiB live, 24.7MiB allocated

Counts

12 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

5.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	x
4.0ms	eps

Results

Accuracy	Segments	Branch
98.5%	1	`x`
98.5%	1	`eps`
98.5%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes13.0ms (0.1%)

Memory

-14.7MiB live, 23.7MiB allocated

Counts

10 → 1

Calls

Call 1

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

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

Calls

3 calls:

5.0ms	x
4.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	eps

Results

Accuracy	Segments	Branch
98.5%	1	`x`
98.5%	1	`eps`
98.5%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes9.0ms (0.1%)

Memory

18.3MiB live, 18.3MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

3.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	eps
3.0ms	x

Results

Accuracy	Segments	Branch
98.5%	1	`x`
98.5%	1	`eps`
98.5%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0.1%)

Memory

13.1MiB live, 13.1MiB allocated

Accuracy

Total -59.7b remaining (-4870.9%)

Threshold costs -59.7b (-4870.9%)

Counts

3 → 1

Calls

Call 1

Inputs

#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))

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

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

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

Calls

3 calls:

2.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms	x
2.0ms	eps

Results

Accuracy	Segments	Branch
98.1%	1	`x`
98.1%	1	`eps`
98.1%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify29.0ms (0.3%)

Memory

-15.7MiB live, 63.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	223
1	98	223
2	100	223
3	101	223

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(approx (+ ( 1/3840 (* eps eps)) -1/48) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))

Outputs
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(.f64 (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) (.f64 #s(literal 2 binary64) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(approx (+ ( 1/3840 (* eps eps)) -1/48) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ ( 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 (+.f64 x eps) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))

soundness996.0ms (9.1%)

Memory

2.8MiB live, 714.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	390	1307
1	1196	1242
2	3299	1207
3	7968	1207
0	8344	1097
0	403	1372
1	1242	1305
2	3640	1266
0	8306	1156
0	6	16
0	10	16
1	53	16
2	380	16
3	4766	16
0	8210	16
0	365	1221
1	1103	1167
2	2971	1137
3	7249	1137
0	8433	1045
0	107	291
1	314	291
2	779	284
3	2842	284
4	6177	284
0	8125	253

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

Compiler

Compiled 495 to 302 computations (39% saved)

preprocess120.0ms (1.1%)

Memory: 12.9MiB live, 136.5MiB allocated
Compiler: Compiled 490 to 202 computations (58.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18

start0.0ms (0%)

analyze42.0ms (0.4%)

sample6.1s (56.3%)

explain125.0ms (1.1%)

preprocess23.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0.1%)

localize26.0ms (0.2%)

series4.0ms (0%)

simplify144.0ms (1.3%)

rewrite175.0ms (1.6%)

eval45.0ms (0.4%)

prune6.0ms (0.1%)

simplify163.0ms (1.5%)

localize201.0ms (1.8%)

series33.0ms (0.3%)

simplify226.0ms (2.1%)

rewrite184.0ms (1.7%)

eval74.0ms (0.7%)

prune18.0ms (0.2%)

simplify184.0ms (1.7%)

localize195.0ms (1.8%)

series22.0ms (0.2%)

simplify161.0ms (1.5%)

rewrite259.0ms (2.4%)

eval117.0ms (1.1%)

prune23.0ms (0.2%)

simplify169.0ms (1.5%)

localize261.0ms (2.4%)

series28.0ms (0.3%)

simplify225.0ms (2.1%)

rewrite238.0ms (2.2%)

eval71.0ms (0.7%)

prune49.0ms (0.4%)

regimes32.0ms (0.3%)

regimes21.0ms (0.2%)

regimes23.0ms (0.2%)

regimes14.0ms (0.1%)

regimes14.0ms (0.1%)

regimes13.0ms (0.1%)

regimes9.0ms (0.1%)

regimes6.0ms (0.1%)

simplify29.0ms (0.3%)

soundness996.0ms (9.1%)

preprocess120.0ms (1.1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18