Metrics for 2sin (example 3.3)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze45.0ms (0.4%)

Memory

-7.9MiB live, 65.8MiB 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)

sample6.6s (55.7%)

Memory

-201.1MiB live, 6 419.3MiB allocated

Samples

3.8s	26 276×	0	invalid
563.0ms	5 469×	0	valid
560.0ms	2 787×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 3.6s

ival-sin: 922.0ms (25.5% of total)

const: 641.0ms (17.7% of total)

ival-fabs: 359.0ms (9.9% of total)

ival-mult: 336.0ms (9.3% of total)

ival-sub: 310.0ms (8.6% of total)

ival-<=: 286.0ms (7.9% of total)

ival-add: 274.0ms (7.6% of total)

ival-<: 240.0ms (6.6% of total)

ival-and: 111.0ms (3.1% of total)

adjust: 83.0ms (2.3% of total)

exact: 47.0ms (1.3% of total)

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

Bogosity

explain89.0ms (0.8%)

Memory

20.8MiB live, 143.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
225	4	(1.9811860374192144e-274 1.9285785995973788e-277)	3	(-1.955730387293147e-64 3.0075063931379935e-66)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
1	1	(-689.4189722907948 6.472153418687527e-12)	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	226	8
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	2	0

Confusion

	Predicted +	Predicted -
+	222	3
-	4	27

Precision

0.9823008849557522

Recall

0.9866666666666667

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	222	3	0
-	4	5	22

Precision?

0.9615384615384616

Recall?

1.0

Freqs

test

number	freq
0	30
1	224
2	2

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

19.0ms	188×	1	valid
15.0ms	322×	0	valid
3.0ms	2×	3	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-sin: 12.0ms (52.6% of total)

adjust: 4.0ms (17.5% of total)

ival-add: 3.0ms (13.2% of total)

ival-sub: 3.0ms (13.2% of total)

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

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

preprocess26.0ms (0.2%)

Memory

-1.1MiB live, 37.5MiB 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	312	35
5	383	35
6	469	35
7	509	35
8	521	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	110	7
8	159	7
9	175	7
10	183	7
0	183	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
▶	61.3%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0.1%)

Memory

5.8MiB live, 5.8MiB 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	110	18
8	159	18
9	175	18
10	183	18
0	183	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)

localize27.0ms (0.2%)

Memory

-10.6MiB live, 27.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x eps)
accuracy	0.0	(sin.f64 x)
accuracy	0.04838648533329809	(sin.f64 (+.f64 x eps))
accuracy	24.71987378640009	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

13.0ms	94×	1	valid
7.0ms	161×	0	valid
1.0ms	1×	3	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

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

ival-sin: 9.0ms (62.4% of total)

adjust: 2.0ms (13.9% of total)

ival-add: 2.0ms (13.9% of total)

ival-sub: 2.0ms (13.9% of total)

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

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

series4.0ms (0%)

Memory

2.9MiB live, 2.9MiB 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))

simplify201.0ms (1.7%)

Memory

-15.5MiB live, 134.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	291
1	314	291
2	781	284
3	2853	284
4	6191	283
0	8157	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)

rewrite177.0ms (1.5%)

Memory

35.2MiB live, 155.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	53	16
2	385	16
3	4851	16
0	8393	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))))
(/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 (-.f64 x eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (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))) (+.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)))))
(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 (-.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 (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 (/.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 (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 #s(literal 1 binary64) (+.f64 eps x))
(.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 (+.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 #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 (-.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)))

eval48.0ms (0.4%)

Memory: -33.2MiB live, 54.9MiB allocated
Compiler: Compiled 6 283 to 852 computations (86.4% saved)

prune6.0ms (0%)

Memory

15.5MiB live, 15.5MiB allocated

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	230	5	235
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	230	6	236

Accuracy

100.0%

Counts

236 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	61.3%	(-.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))))
▶	98.6%	#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)))
▶	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
▶	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 163 to 124 computations (23.9% saved)

simplify207.0ms (1.7%)

Memory

-7.4MiB live, 187.6MiB 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 (.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	1	(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
cost-diff	1	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
cost-diff	2	(+.f64 #s(literal 0 binary64) 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 (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))

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	633	193
5	951	193
6	1351	193
7	2342	193
8	2934	193
9	3111	190
10	3342	190
11	3680	190
12	5246	190
13	6492	190
0	8498	188

Stop Event

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

Calls

Call 1

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

localize190.0ms (1.6%)

Memory

6.8MiB live, 163.6MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(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	0.12109375	(fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
accuracy	0.8812591811044372	#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	30.066029541218906	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))
accuracy	0.0	(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
accuracy	0.0078125	(.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	0.06674207153200762	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
accuracy	0.0	(cos.f64 x)
accuracy	0.00390625	(*.f64 (cos.f64 x) eps)
accuracy	0.2987126785346021	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
accuracy	0.0	(sin.f64 eps)
accuracy	1.3039747939369242	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
accuracy	0.0	(cos.f64 x)
accuracy	0.00390625	(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
accuracy	0.009070031620653759	#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	0.01171875	(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)

Samples

163.0ms

256×

valid

Compiler

Compiled 180 to 37 computations (79.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 132.0ms

ival-cos: 55.0ms (41.5% of total)

ival-mult: 26.0ms (19.6% of total)

adjust: 19.0ms (14.4% of total)

ival-add: 12.0ms (9.1% of total)

ival-sin: 12.0ms (9.1% of total)

ival-sub: 5.0ms (3.8% of total)

ival-div: 2.0ms (1.5% of total)

exact: 1.0ms (0.8% of total)

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

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

series31.0ms (0.3%)

Memory

-5.1MiB live, 31.9MiB allocated

Counts

20 → 100

Calls

Call 1

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

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	eps	@	0	((- (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) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -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	((- (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) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -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	((- (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) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -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	((- (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) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -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	((- (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) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -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))

simplify150.0ms (1.3%)

Memory

-21.1MiB live, 117.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	390	1297
1	1196	1240
2	3329	1207
0	8008	1097

Stop Event

1×	iter limit
1×	node limit

Counts

100 → 99

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

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

rewrite168.0ms (1.4%)

Memory

8.7MiB live, 165.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	167
0	60	159
1	210	159
2	1642	159
0	8606	159

Stop Event

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

Counts

20 → 416

Calls

Call 1

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

eval66.0ms (0.6%)

Memory: 24.1MiB live, 99.3MiB allocated
Compiler: Compiled 17 081 to 2 255 computations (86.8% saved)

prune37.0ms (0.3%)

Memory

-10.8MiB live, 33.2MiB allocated

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	520	11	531
Fresh	0	0	0
Picked	3	2	5
Done	1	0	1
Total	524	13	537

Accuracy

100.0%

Counts

537 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	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))))
	99.9%	(.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))))
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -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)) eps (cos.f64 x)) eps))
	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -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)) eps (cos.f64 x)) eps))
▶	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
	99.5%	#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))
✓	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
▶	98.7%	#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 (fma.f64 #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))
▶	98.6%	#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)))

Compiler

Compiled 602 to 410 computations (31.9% saved)

simplify170.0ms (1.4%)

Memory

12.7MiB live, 120.5MiB 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 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x))
cost-diff	0	(fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #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 (.f64 x x) #s(literal 1/12 binary64) #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 (.f64 x x) #s(literal 1/12 binary64) #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 (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
cost-diff	0	(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos 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)) #s(literal 1 binary64)) eps))
cost-diff	0	(.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))
cost-diff	0	(.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))))
cost-diff	1	(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
cost-diff	1	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	430
0	87	424
1	150	424
2	384	424
3	897	424
4	1460	424
5	2118	424
6	2158	424
7	2350	424
8	2369	424
9	2408	424
10	2584	424
11	2886	424
12	2986	424
13	3277	424
14	4463	424
15	5479	421
16	5807	421
17	7765	421
0	8016	414

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

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

localize234.0ms (2%)

Memory

-19.8MiB live, 200.4MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)
accuracy	0.009070031620653759	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
accuracy	0.01171875	(.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)
accuracy	0.8753201751584465	#s(approx (* (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x))
accuracy	0.0078125	(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))
accuracy	0.01171875	(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
accuracy	0.2987126785346021	#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	0.7752701262662861	#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	0.0078125	(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)
accuracy	0.009070031620653759	#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	0.10546875	(*.f64 eps (+.f64 eps x))
accuracy	0.8812156633012919	#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	0.009070031620653759	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
accuracy	0.01171875	(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
accuracy	1.3110242855352325	#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
accuracy	0.0	(*.f64 eps eps)
accuracy	0.0	#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
accuracy	0.0078125	(.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))))
accuracy	0.06674207153200762	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))

Samples

109.0ms	162×	0	valid
68.0ms	94×	1	valid

Compiler

Compiled 267 to 52 computations (80.5% saved)

Precisions

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

ival-mult: 96.0ms (63.3% of total)

const: 18.0ms (11.9% of total)

ival-add: 14.0ms (9.2% of total)

adjust: 9.0ms (5.9% of total)

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

ival-cos: 4.0ms (2.6% 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-assert: 0.0ms (0% of total)

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

series28.0ms (0.2%)

Memory

7.8MiB live, 45.2MiB allocated

Counts

25 → 108

Calls

Call 1

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

Outputs
(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))))))
(* -1/2 eps)
(+ (* -1 x) (* -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 (* (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 (* -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)
(+ 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 (* -1/2 (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)))
(* 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))
1/24
(+ 1/24 (* -1/720 (pow x 2)))
-1/2
(- (* 1/24 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)
(cos (* -1/2 (+ eps (* 2 x))))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (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)
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* -1/2 (sin x))
(* eps x)
(* x (+ eps (/ (pow eps 2) x)))
(* -1/720 (pow x 2))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* -1/720 (pow x 4))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* 1/12 (pow x 3))
(* (pow x 3) (- 1/12 (* 1/2 (/ 1 (pow x 2)))))
(cos (* -1/2 (- eps (* -2 x))))
(* -1 (* x (+ 1 (* 1/2 (/ eps 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)))))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/12)))
(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)))))
(* 1/2 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 (* eps (sin x)))
(* eps (+ (* -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))))
(sin (* 1/2 eps))
(* (pow eps 2) (+ 1 (/ x eps)))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* -1 (* eps (+ 1/2 (/ x 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)))))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	eps	@	-inf	((cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 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)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) 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) (sin (* 1/2 (+ 0 eps))) (* eps eps) (* eps (+ eps x)) (+ (* -1/720 (* x x)) 1/24) (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* (+ (* (* x x) 1/12) -1/2) x))
7.0ms	x	@	-inf	((cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 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)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) 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) (sin (* 1/2 (+ 0 eps))) (* eps eps) (* eps (+ eps x)) (+ (* -1/720 (* x x)) 1/24) (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* (+ (* (* x x) 1/12) -1/2) x))
4.0ms	x	@	inf	((cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 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)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) 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) (sin (* 1/2 (+ 0 eps))) (* eps eps) (* eps (+ eps x)) (+ (* -1/720 (* x x)) 1/24) (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* (+ (* (* x x) 1/12) -1/2) x))
3.0ms	eps	@	inf	((cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 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)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) 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) (sin (* 1/2 (+ 0 eps))) (* eps eps) (* eps (+ eps x)) (+ (* -1/720 (* x x)) 1/24) (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* (+ (* (* x x) 1/12) -1/2) x))
3.0ms	eps	@	0	((cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 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)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) 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) (sin (* 1/2 (+ 0 eps))) (* eps eps) (* eps (+ eps x)) (+ (* -1/720 (* x x)) 1/24) (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* (+ (* (* x x) 1/12) -1/2) x))

simplify195.0ms (1.6%)

Memory

2.7MiB live, 191.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	371	1278
1	1115	1224
2	3043	1194
3	7478	1194
0	8686	1100

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 107

Calls

Call 1

Inputs
(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))))))
(* -1/2 eps)
(+ (* -1 x) (* -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 (* (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 (* -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)
(+ 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 (* -1/2 (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)))
(* 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))
1/24
(+ 1/24 (* -1/720 (pow x 2)))
-1/2
(- (* 1/24 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)
(cos (* -1/2 (+ eps (* 2 x))))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (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)
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* -1/2 (sin x))
(* eps x)
(* x (+ eps (/ (pow eps 2) x)))
(* -1/720 (pow x 2))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* -1/720 (pow x 4))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* 1/12 (pow x 3))
(* (pow x 3) (- 1/12 (* 1/2 (/ 1 (pow x 2)))))
(cos (* -1/2 (- eps (* -2 x))))
(* -1 (* x (+ 1 (* 1/2 (/ eps 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)))))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/12)))
(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)))))
(* 1/2 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 (* eps (sin x)))
(* eps (+ (* -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))))
(sin (* 1/2 eps))
(* (pow eps 2) (+ 1 (/ x eps)))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* -1 (* eps (+ 1/2 (/ x 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)))))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))

Outputs
(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)))
(* -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))
(* 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 (.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))))) x) x (.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)))
(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 (* (pow eps 2) x)))
(.f64 (fma.f64 (.f64 eps x) #s(literal -1/2 binary64) #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
#s(literal 1 binary64)
(+ 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)
(+ 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 (* -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))
(* x (- (* 1/12 (pow x 2)) 1/2))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #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)
1/24
#s(literal 1/24 binary64)
(+ 1/24 (* -1/720 (pow x 2)))
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
-1/2
#s(literal -1/2 binary64)
(- (* 1/24 (pow x 2)) 1/2)
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)
(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))
(cos (* -1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 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)
(* 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) (* -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 (* eps (pow x 2)))
(.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps)
(* (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)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(cos x)
(cos.f64 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 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (-.f64 #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)))
(* -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)
(* -1/720 (pow x 2))
(.f64 #s(literal -1/720 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/720 binary64)) x) x)
(* -1/720 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/720 binary64))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/720 binary64)))
(* (pow x 4) (- (* 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 4 binary64)))
(* 1/12 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/12 binary64))
(* (pow x 3) (- 1/12 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (pow.f64 x #s(literal 3 binary64)))
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 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))
(* 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)
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/12)))
(.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (pow.f64 x #s(literal 3 binary64)))
(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)
(* 1/2 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 (* 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)
(* -1/2 (* (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)
(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))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(* -1 (* eps (+ 1/2 (/ x eps))))
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps)
(* 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))
(* -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)
(* (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)

rewrite161.0ms (1.4%)

Memory

-2.3MiB live, 191.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	374
0	87	368
1	318	368
2	2671	368
0	8287	363

Stop Event

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

Counts

25 → 582

Calls

Call 1

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

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

eval123.0ms (1%)

Memory: -1.4MiB live, 210.5MiB allocated
Compiler: Compiled 29 269 to 3 411 computations (88.3% saved)

prune48.0ms (0.4%)

Memory

0.9MiB live, 40.4MiB allocated

Pruning

18 alts after pruning (12 fresh and 6 done)

	Pruned	Kept	Total
New	670	7	677
Fresh	1	5	6
Picked	1	4	5
Done	0	2	2
Total	672	18	690

Accuracy

100.0%

Counts

690 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	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 #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 #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))))
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -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)) eps (cos.f64 x)) eps))
	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -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)) eps (cos.f64 x)) eps))
✓	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
	99.5%	#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))
✓	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
✓	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
✓	98.7%	#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 (fma.f64 #s(approx (+ ( -1/720 (* x x)) 1/24) #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))
	98.6%	#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) (fma.f64 x eps (.f64 eps eps)) eps)))
	51.0%	#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 (.f64 (.f64 (+.f64 eps x) (-.f64 x eps)) (neg.f64 (.f64 eps eps))) (*.f64 (-.f64 x eps) (neg.f64 eps))) eps)))
✓	98.6%	#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)))
	98.6%	#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)))
▶	34.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) eps) (.f64 (+.f64 eps x) (-.f64 x eps))) (-.f64 eps #s(literal 0 binary64)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 eps #s(literal 0 binary64))))))
▶	5.2%	#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 x x) #s(literal -1/2 binary64)) eps))))

Compiler

Compiled 925 to 600 computations (35.1% saved)

simplify142.0ms (1.2%)

Memory

15.4MiB live, 88.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) eps) (.f64 (+.f64 eps x) (-.f64 x eps))) (-.f64 eps #s(literal 0 binary64)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 eps #s(literal 0 binary64))))))
cost-diff	2	(-.f64 eps #s(literal 0 binary64))
cost-diff	6	(fma.f64 (.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) eps) (.f64 (+.f64 eps x) (-.f64 x eps))) (-.f64 eps #s(literal 0 binary64)) (.f64 (-.f64 x eps) (.f64 eps eps)))
cost-diff	12	(/.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) eps) (.f64 (+.f64 eps x) (-.f64 x eps))) (-.f64 eps #s(literal 0 binary64)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 eps #s(literal 0 binary64))))
cost-diff	0	(fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* x x)) 1/24) #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 #s(approx (+ (* -1/720 (* x x)) 1/24) #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 #s(approx (+ ( -1/720 (* x x)) 1/24) #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 #s(approx (+ ( -1/720 (* x x)) 1/24) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x 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 x x) #s(literal -1/2 binary64)) eps)
cost-diff	0	#s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps))
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 x x) #s(literal -1/2 binary64)) eps)))
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 x x) #s(literal -1/2 binary64)) eps))))
cost-diff	0	(.f64 (fma.f64 #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 #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 #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 #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	73	618
0	105	594
1	196	590
2	533	574
3	1981	568
4	3169	538
5	5058	532
0	8292	515

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

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

localize286.0ms (2.4%)

Memory

-24.6MiB live, 138.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.11328125	(.f64 (-.f64 x eps) (.f64 eps eps))
accuracy	0.125	(*.f64 (-.f64 x eps) (-.f64 eps #s(literal 0 binary64)))
accuracy	0.8812156633012919	#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) eps) (.f64 (+.f64 eps x) (-.f64 x eps))) (-.f64 eps #s(literal 0 binary64)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 eps #s(literal 0 binary64)))))
accuracy	40.2663074054089	(/.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) eps) (.f64 (+.f64 eps x) (-.f64 x eps))) (-.f64 eps #s(literal 0 binary64)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 eps #s(literal 0 binary64))))
accuracy	0.0078125	(fma.f64 #s(approx (+ (* -1/720 (* x x)) 1/24) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64))
accuracy	0.2987126785346021	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(approx (+ ( -1/720 (* x x)) 1/24) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
accuracy	0.7752701262662861	#s(approx (cos x) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* x x)) 1/24) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
accuracy	1.1761669540372601	#s(approx (+ (* -1/720 (* x x)) 1/24) #s(literal 1/24 binary64))
accuracy	0.0	(*.f64 x x)
accuracy	0.00390625	(.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)
accuracy	0.2987126785346021	#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	0.8860778679208301	#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
accuracy	0.015625	(.f64 (.f64 x x) #s(literal -1/2 binary64))
accuracy	0.09375	(.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps)
accuracy	0.8812156633012919	#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps)))
accuracy	60.48593496906711	#s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps))
accuracy	0.0	#s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
accuracy	0.0	#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
accuracy	0.0078125	(.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 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
accuracy	0.06674207153200762	(cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))

Samples

121.0ms	162×	0	valid
90.0ms	94×	1	valid

Compiler

Compiled 349 to 64 computations (81.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 179.0ms

ival-div: 65.0ms (36.3% of total)

ival-mult: 44.0ms (24.6% of total)

ival-add: 17.0ms (9.5% of total)

ival-neg: 17.0ms (9.5% of total)

adjust: 11.0ms (6.1% of total)

const: 11.0ms (6.1% of total)

ival-sin: 6.0ms (3.4% of total)

ival-sub: 4.0ms (2.2% of total)

ival-cos: 4.0ms (2.2% of total)

exact: 1.0ms (0.6% of total)

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

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

series30.0ms (0.3%)

Memory

28.1MiB live, 28.1MiB allocated

Counts

29 → 143

Calls

Call 1

Inputs
(.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 #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 #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 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 #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 x x) #s(literal -1/2 binary64)) eps))))
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps)))
#s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps))
(.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) 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))
(.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 (cos x) (fma.f64 (fma.f64 #s(approx (+ ( -1/720 (* x x)) 1/24) #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 #s(approx (+ ( -1/720 (* x x)) 1/24) #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 #s(approx (+ (* -1/720 (* x x)) 1/24) #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(approx (+ (* -1/720 (* x x)) 1/24) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) eps) (.f64 (+.f64 eps x) (-.f64 x eps))) (-.f64 eps #s(literal 0 binary64)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 eps #s(literal 0 binary64))))
(fma.f64 (.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) eps) (.f64 (+.f64 eps x) (-.f64 x eps))) (-.f64 eps #s(literal 0 binary64)) (.f64 (-.f64 x eps) (.f64 eps eps)))
(-.f64 eps #s(literal 0 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) eps) (.f64 (+.f64 eps x) (-.f64 x eps))) (-.f64 eps #s(literal 0 binary64)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 eps #s(literal 0 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)))
(.f64 (.f64 x x) #s(literal -1/2 binary64))
(*.f64 x x)
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(literal 1/24 binary64))
(fma.f64 #s(approx (+ (* -1/720 (* x x)) 1/24) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64))
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) eps) (.f64 (+.f64 eps x) (-.f64 x eps))) (-.f64 eps #s(literal 0 binary64)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 eps #s(literal 0 binary64)))))
(*.f64 (-.f64 x eps) (-.f64 eps #s(literal 0 binary64)))
(.f64 (-.f64 x eps) (.f64 eps 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 (* eps (pow x 2)))
(+ 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 (* x (+ 1 (* -1 (/ (+ (* 1/2 (pow eps 4)) (pow eps 2)) (pow eps 2))))))
(+ eps (* x (+ 1 (+ (* -1 (/ (+ (* 1/2 (pow eps 4)) (pow eps 2)) (pow eps 2))) (* x (- (* 1/2 (+ eps (* -1 eps))) (* -1 (/ (+ 1 (* -1 (/ (+ (* 1/2 (pow eps 4)) (pow eps 2)) (pow eps 2)))) eps))))))))
(+ eps (* x (+ 1 (+ (* -1 (/ (+ (* 1/2 (pow eps 4)) (pow eps 2)) (pow eps 2))) (* x (- (+ (* 1/2 (+ eps (* -1 eps))) (* x (- 1/2 (* -1 (/ (- (* 1/2 (+ eps (* -1 eps))) (* -1 (/ (+ 1 (* -1 (/ (+ (* 1/2 (pow eps 4)) (pow eps 2)) (pow eps 2)))) eps))) eps))))) (* -1 (/ (+ 1 (* -1 (/ (+ (* 1/2 (pow eps 4)) (pow eps 2)) (pow eps 2)))) eps))))))))
(* -1 (pow eps 3))
(+ (* -1 (pow eps 3)) (* x (+ (* 1/2 (pow eps 4)) (pow eps 2))))
(+ (* -1 (pow eps 3)) (* x (+ (* -1/2 (* (pow eps 2) (* x (+ eps (* -1 eps))))) (+ (* 1/2 (pow eps 4)) (pow eps 2)))))
(+ (* -1 (pow eps 3)) (* x (+ (* 1/2 (pow eps 4)) (+ (* x (+ (* -1/2 (* (pow eps 2) x)) (* -1/2 (* (pow eps 2) (+ eps (* -1 eps)))))) (pow eps 2)))))
(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))))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(* -1/2 (pow x 2))
(pow x 2)
1/24
(+ 1/24 (* -1/720 (pow x 2)))
-1/2
(- (* 1/24 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)
(* -1 (pow eps 2))
(+ (* -1 (pow eps 2)) (* eps x))
(+ (* -1 (pow eps 3)) (* (pow eps 2) x))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* (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)
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 2) (- (+ (* -1/2 eps) (* -1/2 (/ (* eps (+ eps (* -1 eps))) x))) (* 1/2 (/ (pow eps 2) x))))
(* (pow x 2) (- (+ (* -1/2 eps) (+ (* -1/2 (/ (* eps (+ eps (* -1 eps))) x)) (+ (* 1/2 (/ (pow eps 3) (pow x 2))) (/ eps (pow x 2))))) (+ (* -1 (/ (* eps (- (* -1/2 (* eps (+ eps (* -1 eps)))) (* 1/2 (pow eps 2)))) (pow x 2))) (* 1/2 (/ (pow eps 2) x)))))
(* (pow x 2) (- (+ (* -1 (/ (pow eps 2) (pow x 3))) (+ (* -1/2 eps) (+ (* -1/2 (/ (* eps (+ eps (* -1 eps))) x)) (+ (* 1/2 (/ (pow eps 3) (pow x 2))) (/ eps (pow x 2)))))) (+ (* -1 (/ (* eps (- (* -1/2 (* eps (+ eps (* -1 eps)))) (* 1/2 (pow eps 2)))) (pow x 2))) (+ (* -1 (/ (* eps (- (+ eps (* 1/2 (pow eps 3))) (* -1 (* eps (- (* -1/2 (* eps (+ eps (* -1 eps)))) (* 1/2 (pow eps 2))))))) (pow x 3))) (* 1/2 (/ (pow eps 2) x))))))
(* -1/2 (* (pow eps 2) (pow x 3)))
(* (pow x 3) (+ (* -1/2 (/ (* (pow eps 2) (+ eps (* -1 eps))) x)) (* -1/2 (pow eps 2))))
(* (pow x 3) (+ (* -1/2 (/ (* (pow eps 2) (+ eps (* -1 eps))) x)) (+ (* -1/2 (pow eps 2)) (+ (* 1/2 (/ (pow eps 4) (pow x 2))) (/ (pow eps 2) (pow x 2))))))
(* (pow x 3) (+ (* -1 (/ (pow eps 3) (pow x 3))) (+ (* -1/2 (/ (* (pow eps 2) (+ eps (* -1 eps))) x)) (+ (* -1/2 (pow eps 2)) (+ (* 1/2 (/ (pow eps 4) (pow x 2))) (/ (pow eps 2) (pow x 2)))))))
(cos (* -1/2 (+ eps (* 2 x))))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* -1/720 (pow x 2))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* -1/720 (pow x 4))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* eps x)
(* x (+ eps (* -1 (/ (pow eps 2) x))))
(* (pow eps 2) x)
(* x (+ (* -1 (/ (pow eps 3) x)) (pow eps 2)))
(* 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)))
(* (pow x 2) (+ (* -1 (/ (- (+ (* -1 (- (* -1/2 (* eps (+ eps (* -1 eps)))) (* 1/2 (pow eps 2)))) (+ (* -1 (/ eps x)) (* -1/2 (/ (pow eps 3) x)))) (/ (* eps (- (* -1/2 (* eps (+ eps (* -1 eps)))) (* 1/2 (pow eps 2)))) x)) x)) (* -1/2 eps)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* -1/2 (* eps (+ eps (* -1 eps)))) (* 1/2 (pow eps 2)))) (* -1 (/ (- (+ (* -1 (- (+ (* -1 eps) (* -1/2 (pow eps 3))) (* eps (- (* -1/2 (* eps (+ eps (* -1 eps)))) (* 1/2 (pow eps 2)))))) (* -1 (/ (pow eps 2) x))) (/ (* eps (- (+ (* -1 eps) (* -1/2 (pow eps 3))) (* eps (- (* -1/2 (* eps (+ eps (* -1 eps)))) (* 1/2 (pow eps 2)))))) x)) x))) x)) (* -1/2 eps)))
(* -1 (* (pow x 3) (+ (* 1/2 (/ (* (pow eps 2) (+ eps (* -1 eps))) x)) (* 1/2 (pow eps 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (pow eps 2)) (* -1/2 (pow eps 4))) x)) (* -1/2 (* (pow eps 2) (+ eps (* -1 eps))))) x)) (* 1/2 (pow eps 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (pow eps 2)) (+ (* -1/2 (pow eps 4)) (/ (pow eps 3) x))) x)) (* -1/2 (* (pow eps 2) (+ eps (* -1 eps))))) x)) (* 1/2 (pow eps 2)))))
(cos (* -1/2 (- eps (* -2 x))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* -1 (* x (+ (* -1 eps) (/ (pow eps 2) x))))
(* -1 (* x (+ (* -1 (pow eps 2)) (/ (pow eps 3) 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)))))
(/ (* eps (+ x (* -1/2 (pow x 3)))) x)
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (- (* -1/2 (+ x (* -1 x))) (+ (* -1 (/ (+ x (* -1/2 (pow x 3))) (pow x 2))) (/ 1 x)))))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (- (+ (* -1/2 (+ x (* -1 x))) (* eps (- 1/2 (* -1 (/ (- (* -1/2 (+ x (* -1 x))) (+ (* -1 (/ (+ x (* -1/2 (pow x 3))) (pow x 2))) (/ 1 x))) x))))) (+ (* -1 (/ (+ x (* -1/2 (pow x 3))) (pow x 2))) (/ 1 x)))))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (- (+ (* -1/2 (+ x (* -1 x))) (* eps (- (+ 1/2 (/ (* eps (- 1/2 (* -1 (/ (- (* -1/2 (+ x (* -1 x))) (+ (* -1 (/ (+ x (* -1/2 (pow x 3))) (pow x 2))) (/ 1 x))) x)))) x)) (* -1 (/ (- (* -1/2 (+ x (* -1 x))) (+ (* -1 (/ (+ x (* -1/2 (pow x 3))) (pow x 2))) (/ 1 x))) x))))) (+ (* -1 (/ (+ x (* -1/2 (pow x 3))) (pow x 2))) (/ 1 x)))))))
(* (pow eps 2) (+ x (* -1/2 (pow x 3))))
(* (pow eps 2) (+ x (+ (* -1/2 (pow x 3)) (* eps (- (* -1/2 (* x (+ x (* -1 x)))) 1)))))
(* (pow eps 2) (+ x (+ (* -1/2 (pow x 3)) (* eps (- (+ (* -1/2 (* x (+ x (* -1 x)))) (* 1/2 (* eps x))) 1)))))
(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 (+ x (* -1 eps)))
(* (pow eps 2) (+ x (* -1 eps)))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(* -1/48 (pow eps 3))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* -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))))
(* (pow eps 2) (- (+ (* -1 (/ (- (* -1/2 (* x (+ x (* -1 x)))) 1) eps)) (* -1/2 x)) (* 1/2 (/ (pow x 2) eps))))
(* (pow eps 2) (- (+ (* -1 (/ (+ x (* -1/2 (pow x 3))) (pow eps 2))) (+ (* -1 (/ (- (* -1/2 (* x (+ x (* -1 x)))) 1) eps)) (* -1/2 x))) (+ (* -1 (/ (* x (- (* -1 (- (* -1/2 (* x (+ x (* -1 x)))) 1)) (* 1/2 (pow x 2)))) (pow eps 2))) (* 1/2 (/ (pow x 2) eps)))))
(* (pow eps 2) (- (+ (* -1 (/ (+ x (* -1/2 (pow x 3))) (pow eps 2))) (+ (* -1 (/ (- (* -1/2 (* x (+ x (* -1 x)))) 1) eps)) (+ (* -1/2 x) (/ (* x (- (* -1 (+ x (* -1/2 (pow x 3)))) (* -1 (* x (- (* -1 (- (* -1/2 (* x (+ x (* -1 x)))) 1)) (* 1/2 (pow x 2))))))) (pow eps 3))))) (+ (* -1 (/ (* x (- (* -1 (- (* -1/2 (* x (+ x (* -1 x)))) 1)) (* 1/2 (pow x 2)))) (pow eps 2))) (* 1/2 (/ (pow x 2) eps)))))
(* 1/2 (* (pow eps 4) x))
(* (pow eps 4) (- (+ (* -1/2 (/ (* x (+ x (* -1 x))) eps)) (* 1/2 x)) (/ 1 eps)))
(* (pow eps 4) (- (+ (* -1/2 (/ (* x (+ x (* -1 x))) eps)) (+ (* -1/2 (/ (pow x 3) (pow eps 2))) (+ (* 1/2 x) (/ x (pow eps 2))))) (/ 1 eps)))
(* eps (- (* -1 (/ x eps)) 1/2))
(* (pow eps 2) (- (/ x eps) 1))
(* (pow eps 3) (- (/ x eps) 1))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))
(- (sin (- x (* -1 eps))) (sin x))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* (pow eps 2) (- (+ (* -1/2 x) (+ (* -1/2 (/ (* x (+ x (* -1 x))) eps)) (/ 1 eps))) (* 1/2 (/ (pow x 2) eps))))
(* (pow eps 2) (+ (* -1 (/ (- (+ (* -1 (- (+ 1 (* -1/2 (* x (+ x (* -1 x))))) (* 1/2 (pow x 2)))) (+ (* -1/2 (/ (pow x 3) eps)) (/ x eps))) (/ (* x (- (+ 1 (* -1/2 (* x (+ x (* -1 x))))) (* 1/2 (pow x 2)))) eps)) eps)) (* -1/2 x)))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (- (+ 1 (* -1/2 (* x (+ x (* -1 x))))) (* 1/2 (pow x 2)))) (* -1 (/ (+ (* -1 (- (+ x (* -1/2 (pow x 3))) (* x (- (+ 1 (* -1/2 (* x (+ x (* -1 x))))) (* 1/2 (pow x 2)))))) (* -1 (/ (* x (- (+ x (* -1/2 (pow x 3))) (* x (- (+ 1 (* -1/2 (* x (+ x (* -1 x))))) (* 1/2 (pow x 2)))))) eps))) eps))) eps)) (* -1/2 x)))
(* (pow eps 4) (+ (* -1 (/ (+ 1 (* -1/2 (* x (+ x (* -1 x))))) eps)) (* 1/2 x)))
(* (pow eps 4) (+ (* -1 (/ (+ 1 (+ (* -1 (/ (+ x (* -1/2 (pow x 3))) eps)) (* -1/2 (* x (+ x (* -1 x)))))) eps)) (* 1/2 x)))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* -1 (* (pow eps 3) (+ 1 (* -1 (/ x eps)))))

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	eps	@	inf	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* -1/48 (* 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) (* (* (* x x) -1/2) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (/ (+ (* (* (* (* -1/2 x) eps) (* (+ eps x) (- x eps))) (- eps 0)) (* (- x eps) (* eps eps))) (* (- x eps) (- eps 0))) (+ (* (* (* (* -1/2 x) eps) (* (+ eps x) (- x eps))) (- eps 0)) (* (- x eps) (* eps eps))) (- eps 0) (- (sin (+ x eps)) (sin x)) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* x x) -1/2) (* x x) (+ (* -1/720 (* x x)) 1/24) (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (* (- x eps) (- eps 0)) (* (- x eps) (* eps eps)))
5.0ms	x	@	inf	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* -1/48 (* 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) (* (* (* x x) -1/2) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (/ (+ (* (* (* (* -1/2 x) eps) (* (+ eps x) (- x eps))) (- eps 0)) (* (- x eps) (* eps eps))) (* (- x eps) (- eps 0))) (+ (* (* (* (* -1/2 x) eps) (* (+ eps x) (- x eps))) (- eps 0)) (* (- x eps) (* eps eps))) (- eps 0) (- (sin (+ x eps)) (sin x)) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* x x) -1/2) (* x x) (+ (* -1/720 (* x x)) 1/24) (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (* (- x eps) (- eps 0)) (* (- x eps) (* eps eps)))
5.0ms	eps	@	-inf	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* -1/48 (* 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) (* (* (* x x) -1/2) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (/ (+ (* (* (* (* -1/2 x) eps) (* (+ eps x) (- x eps))) (- eps 0)) (* (- x eps) (* eps eps))) (* (- x eps) (- eps 0))) (+ (* (* (* (* -1/2 x) eps) (* (+ eps x) (- x eps))) (- eps 0)) (* (- x eps) (* eps eps))) (- eps 0) (- (sin (+ x eps)) (sin x)) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* x x) -1/2) (* x x) (+ (* -1/720 (* x x)) 1/24) (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (* (- x eps) (- eps 0)) (* (- x eps) (* eps eps)))
5.0ms	x	@	-inf	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* -1/48 (* 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) (* (* (* x x) -1/2) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (/ (+ (* (* (* (* -1/2 x) eps) (* (+ eps x) (- x eps))) (- eps 0)) (* (- x eps) (* eps eps))) (* (- x eps) (- eps 0))) (+ (* (* (* (* -1/2 x) eps) (* (+ eps x) (- x eps))) (- eps 0)) (* (- x eps) (* eps eps))) (- eps 0) (- (sin (+ x eps)) (sin x)) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* x x) -1/2) (* x x) (+ (* -1/720 (* x x)) 1/24) (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (* (- x eps) (- eps 0)) (* (- x eps) (* eps eps)))
4.0ms	eps	@	0	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 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) (* (* (* x x) -1/2) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (/ (+ (* (* (* (* -1/2 x) eps) (* (+ eps x) (- x eps))) (- eps 0)) (* (- x eps) (* eps eps))) (* (- x eps) (- eps 0))) (+ (* (* (* (* -1/2 x) eps) (* (+ eps x) (- x eps))) (- eps 0)) (* (- x eps) (* eps eps))) (- eps 0) (- (sin (+ x eps)) (sin x)) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* x x) -1/2) (* x x) (+ (* -1/720 (* x x)) 1/24) (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (* (- x eps) (- eps 0)) (* (- x eps) (* eps eps)))

simplify184.0ms (1.6%)

Memory

-16.6MiB live, 100.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	638	2421
1	2045	2088
2	7134	2038
0	8604	1881

Stop Event

1×	iter limit
1×	node limit

Counts

143 → 142

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 (* eps (pow x 2)))
(+ 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 (* x (+ 1 (* -1 (/ (+ (* 1/2 (pow eps 4)) (pow eps 2)) (pow eps 2))))))
(+ eps (* x (+ 1 (+ (* -1 (/ (+ (* 1/2 (pow eps 4)) (pow eps 2)) (pow eps 2))) (* x (- (* 1/2 (+ eps (* -1 eps))) (* -1 (/ (+ 1 (* -1 (/ (+ (* 1/2 (pow eps 4)) (pow eps 2)) (pow eps 2)))) eps))))))))
(+ eps (* x (+ 1 (+ (* -1 (/ (+ (* 1/2 (pow eps 4)) (pow eps 2)) (pow eps 2))) (* x (- (+ (* 1/2 (+ eps (* -1 eps))) (* x (- 1/2 (* -1 (/ (- (* 1/2 (+ eps (* -1 eps))) (* -1 (/ (+ 1 (* -1 (/ (+ (* 1/2 (pow eps 4)) (pow eps 2)) (pow eps 2)))) eps))) eps))))) (* -1 (/ (+ 1 (* -1 (/ (+ (* 1/2 (pow eps 4)) (pow eps 2)) (pow eps 2)))) eps))))))))
(* -1 (pow eps 3))
(+ (* -1 (pow eps 3)) (* x (+ (* 1/2 (pow eps 4)) (pow eps 2))))
(+ (* -1 (pow eps 3)) (* x (+ (* -1/2 (* (pow eps 2) (* x (+ eps (* -1 eps))))) (+ (* 1/2 (pow eps 4)) (pow eps 2)))))
(+ (* -1 (pow eps 3)) (* x (+ (* 1/2 (pow eps 4)) (+ (* x (+ (* -1/2 (* (pow eps 2) x)) (* -1/2 (* (pow eps 2) (+ eps (* -1 eps)))))) (pow eps 2)))))
(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))))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(* -1/2 (pow x 2))
(pow x 2)
1/24
(+ 1/24 (* -1/720 (pow x 2)))
-1/2
(- (* 1/24 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)
(* -1 (pow eps 2))
(+ (* -1 (pow eps 2)) (* eps x))
(+ (* -1 (pow eps 3)) (* (pow eps 2) x))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* (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)
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 2) (- (+ (* -1/2 eps) (* -1/2 (/ (* eps (+ eps (* -1 eps))) x))) (* 1/2 (/ (pow eps 2) x))))
(* (pow x 2) (- (+ (* -1/2 eps) (+ (* -1/2 (/ (* eps (+ eps (* -1 eps))) x)) (+ (* 1/2 (/ (pow eps 3) (pow x 2))) (/ eps (pow x 2))))) (+ (* -1 (/ (* eps (- (* -1/2 (* eps (+ eps (* -1 eps)))) (* 1/2 (pow eps 2)))) (pow x 2))) (* 1/2 (/ (pow eps 2) x)))))
(* (pow x 2) (- (+ (* -1 (/ (pow eps 2) (pow x 3))) (+ (* -1/2 eps) (+ (* -1/2 (/ (* eps (+ eps (* -1 eps))) x)) (+ (* 1/2 (/ (pow eps 3) (pow x 2))) (/ eps (pow x 2)))))) (+ (* -1 (/ (* eps (- (* -1/2 (* eps (+ eps (* -1 eps)))) (* 1/2 (pow eps 2)))) (pow x 2))) (+ (* -1 (/ (* eps (- (+ eps (* 1/2 (pow eps 3))) (* -1 (* eps (- (* -1/2 (* eps (+ eps (* -1 eps)))) (* 1/2 (pow eps 2))))))) (pow x 3))) (* 1/2 (/ (pow eps 2) x))))))
(* -1/2 (* (pow eps 2) (pow x 3)))
(* (pow x 3) (+ (* -1/2 (/ (* (pow eps 2) (+ eps (* -1 eps))) x)) (* -1/2 (pow eps 2))))
(* (pow x 3) (+ (* -1/2 (/ (* (pow eps 2) (+ eps (* -1 eps))) x)) (+ (* -1/2 (pow eps 2)) (+ (* 1/2 (/ (pow eps 4) (pow x 2))) (/ (pow eps 2) (pow x 2))))))
(* (pow x 3) (+ (* -1 (/ (pow eps 3) (pow x 3))) (+ (* -1/2 (/ (* (pow eps 2) (+ eps (* -1 eps))) x)) (+ (* -1/2 (pow eps 2)) (+ (* 1/2 (/ (pow eps 4) (pow x 2))) (/ (pow eps 2) (pow x 2)))))))
(cos (* -1/2 (+ eps (* 2 x))))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* -1/720 (pow x 2))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* -1/720 (pow x 4))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* eps x)
(* x (+ eps (* -1 (/ (pow eps 2) x))))
(* (pow eps 2) x)
(* x (+ (* -1 (/ (pow eps 3) x)) (pow eps 2)))
(* 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)))
(* (pow x 2) (+ (* -1 (/ (- (+ (* -1 (- (* -1/2 (* eps (+ eps (* -1 eps)))) (* 1/2 (pow eps 2)))) (+ (* -1 (/ eps x)) (* -1/2 (/ (pow eps 3) x)))) (/ (* eps (- (* -1/2 (* eps (+ eps (* -1 eps)))) (* 1/2 (pow eps 2)))) x)) x)) (* -1/2 eps)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* -1/2 (* eps (+ eps (* -1 eps)))) (* 1/2 (pow eps 2)))) (* -1 (/ (- (+ (* -1 (- (+ (* -1 eps) (* -1/2 (pow eps 3))) (* eps (- (* -1/2 (* eps (+ eps (* -1 eps)))) (* 1/2 (pow eps 2)))))) (* -1 (/ (pow eps 2) x))) (/ (* eps (- (+ (* -1 eps) (* -1/2 (pow eps 3))) (* eps (- (* -1/2 (* eps (+ eps (* -1 eps)))) (* 1/2 (pow eps 2)))))) x)) x))) x)) (* -1/2 eps)))
(* -1 (* (pow x 3) (+ (* 1/2 (/ (* (pow eps 2) (+ eps (* -1 eps))) x)) (* 1/2 (pow eps 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (pow eps 2)) (* -1/2 (pow eps 4))) x)) (* -1/2 (* (pow eps 2) (+ eps (* -1 eps))))) x)) (* 1/2 (pow eps 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (pow eps 2)) (+ (* -1/2 (pow eps 4)) (/ (pow eps 3) x))) x)) (* -1/2 (* (pow eps 2) (+ eps (* -1 eps))))) x)) (* 1/2 (pow eps 2)))))
(cos (* -1/2 (- eps (* -2 x))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* -1 (* x (+ (* -1 eps) (/ (pow eps 2) x))))
(* -1 (* x (+ (* -1 (pow eps 2)) (/ (pow eps 3) 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)))))
(/ (* eps (+ x (* -1/2 (pow x 3)))) x)
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (- (* -1/2 (+ x (* -1 x))) (+ (* -1 (/ (+ x (* -1/2 (pow x 3))) (pow x 2))) (/ 1 x)))))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (- (+ (* -1/2 (+ x (* -1 x))) (* eps (- 1/2 (* -1 (/ (- (* -1/2 (+ x (* -1 x))) (+ (* -1 (/ (+ x (* -1/2 (pow x 3))) (pow x 2))) (/ 1 x))) x))))) (+ (* -1 (/ (+ x (* -1/2 (pow x 3))) (pow x 2))) (/ 1 x)))))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (- (+ (* -1/2 (+ x (* -1 x))) (* eps (- (+ 1/2 (/ (* eps (- 1/2 (* -1 (/ (- (* -1/2 (+ x (* -1 x))) (+ (* -1 (/ (+ x (* -1/2 (pow x 3))) (pow x 2))) (/ 1 x))) x)))) x)) (* -1 (/ (- (* -1/2 (+ x (* -1 x))) (+ (* -1 (/ (+ x (* -1/2 (pow x 3))) (pow x 2))) (/ 1 x))) x))))) (+ (* -1 (/ (+ x (* -1/2 (pow x 3))) (pow x 2))) (/ 1 x)))))))
(* (pow eps 2) (+ x (* -1/2 (pow x 3))))
(* (pow eps 2) (+ x (+ (* -1/2 (pow x 3)) (* eps (- (* -1/2 (* x (+ x (* -1 x)))) 1)))))
(* (pow eps 2) (+ x (+ (* -1/2 (pow x 3)) (* eps (- (+ (* -1/2 (* x (+ x (* -1 x)))) (* 1/2 (* eps x))) 1)))))
(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 (+ x (* -1 eps)))
(* (pow eps 2) (+ x (* -1 eps)))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(* -1/48 (pow eps 3))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* -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))))
(* (pow eps 2) (- (+ (* -1 (/ (- (* -1/2 (* x (+ x (* -1 x)))) 1) eps)) (* -1/2 x)) (* 1/2 (/ (pow x 2) eps))))
(* (pow eps 2) (- (+ (* -1 (/ (+ x (* -1/2 (pow x 3))) (pow eps 2))) (+ (* -1 (/ (- (* -1/2 (* x (+ x (* -1 x)))) 1) eps)) (* -1/2 x))) (+ (* -1 (/ (* x (- (* -1 (- (* -1/2 (* x (+ x (* -1 x)))) 1)) (* 1/2 (pow x 2)))) (pow eps 2))) (* 1/2 (/ (pow x 2) eps)))))
(* (pow eps 2) (- (+ (* -1 (/ (+ x (* -1/2 (pow x 3))) (pow eps 2))) (+ (* -1 (/ (- (* -1/2 (* x (+ x (* -1 x)))) 1) eps)) (+ (* -1/2 x) (/ (* x (- (* -1 (+ x (* -1/2 (pow x 3)))) (* -1 (* x (- (* -1 (- (* -1/2 (* x (+ x (* -1 x)))) 1)) (* 1/2 (pow x 2))))))) (pow eps 3))))) (+ (* -1 (/ (* x (- (* -1 (- (* -1/2 (* x (+ x (* -1 x)))) 1)) (* 1/2 (pow x 2)))) (pow eps 2))) (* 1/2 (/ (pow x 2) eps)))))
(* 1/2 (* (pow eps 4) x))
(* (pow eps 4) (- (+ (* -1/2 (/ (* x (+ x (* -1 x))) eps)) (* 1/2 x)) (/ 1 eps)))
(* (pow eps 4) (- (+ (* -1/2 (/ (* x (+ x (* -1 x))) eps)) (+ (* -1/2 (/ (pow x 3) (pow eps 2))) (+ (* 1/2 x) (/ x (pow eps 2))))) (/ 1 eps)))
(* eps (- (* -1 (/ x eps)) 1/2))
(* (pow eps 2) (- (/ x eps) 1))
(* (pow eps 3) (- (/ x eps) 1))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))
(- (sin (- x (* -1 eps))) (sin x))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* (pow eps 2) (- (+ (* -1/2 x) (+ (* -1/2 (/ (* x (+ x (* -1 x))) eps)) (/ 1 eps))) (* 1/2 (/ (pow x 2) eps))))
(* (pow eps 2) (+ (* -1 (/ (- (+ (* -1 (- (+ 1 (* -1/2 (* x (+ x (* -1 x))))) (* 1/2 (pow x 2)))) (+ (* -1/2 (/ (pow x 3) eps)) (/ x eps))) (/ (* x (- (+ 1 (* -1/2 (* x (+ x (* -1 x))))) (* 1/2 (pow x 2)))) eps)) eps)) (* -1/2 x)))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (- (+ 1 (* -1/2 (* x (+ x (* -1 x))))) (* 1/2 (pow x 2)))) (* -1 (/ (+ (* -1 (- (+ x (* -1/2 (pow x 3))) (* x (- (+ 1 (* -1/2 (* x (+ x (* -1 x))))) (* 1/2 (pow x 2)))))) (* -1 (/ (* x (- (+ x (* -1/2 (pow x 3))) (* x (- (+ 1 (* -1/2 (* x (+ x (* -1 x))))) (* 1/2 (pow x 2)))))) eps))) eps))) eps)) (* -1/2 x)))
(* (pow eps 4) (+ (* -1 (/ (+ 1 (* -1/2 (* x (+ x (* -1 x))))) eps)) (* 1/2 x)))
(* (pow eps 4) (+ (* -1 (/ (+ 1 (+ (* -1 (/ (+ x (* -1/2 (pow x 3))) eps)) (* -1/2 (* x (+ x (* -1 x)))))) eps)) (* 1/2 x)))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* -1 (* (pow eps 3) (+ 1 (* -1 (/ x eps)))))

Outputs
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) #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 eps #s(literal 1/2 binary64))))) #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 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) x (.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 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64)))
(+ (* 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 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64) (.f64 (.f64 x x) (fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))))
(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 (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 (* (pow eps 2) x)))
(fma.f64 (.f64 (.f64 eps eps) x) #s(literal -1/2 binary64) eps)
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(.f64 (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) #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 eps (+.f64 x eps)) #s(literal -1/2 binary64) (.f64 (.f64 #s(literal 1/12 binary64) (.f64 (*.f64 eps eps) x)) x)) x eps)
(* -1/2 (* eps (pow x 2)))
(.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps)
(+ eps (* -1/2 (* eps (pow x 2))))
(fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.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 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/720 binary64) (*.f64 #s(literal 1/24 binary64) eps)) 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 (.f64 x x) #s(literal 1/24 binary64) #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 (.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 (* x (+ 1 (* -1 (/ (+ (* 1/2 (pow eps 4)) (pow eps 2)) (pow eps 2))))))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/2 binary64) (*.f64 eps eps)) eps) eps)) x eps)
(+ eps (* x (+ 1 (+ (* -1 (/ (+ (* 1/2 (pow eps 4)) (pow eps 2)) (pow eps 2))) (* x (- (* 1/2 (+ eps (* -1 eps))) (* -1 (/ (+ 1 (* -1 (/ (+ (* 1/2 (pow eps 4)) (pow eps 2)) (pow eps 2)))) eps))))))))
(fma.f64 (fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/2 binary64) (.f64 eps eps)) eps) eps)) eps) x (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/2 binary64) (.f64 eps eps)) eps) eps))) x eps)
(+ eps (* x (+ 1 (+ (* -1 (/ (+ (* 1/2 (pow eps 4)) (pow eps 2)) (pow eps 2))) (* x (- (+ (* 1/2 (+ eps (* -1 eps))) (* x (- 1/2 (* -1 (/ (- (* 1/2 (+ eps (* -1 eps))) (* -1 (/ (+ 1 (* -1 (/ (+ (* 1/2 (pow eps 4)) (pow eps 2)) (pow eps 2)))) eps))) eps))))) (* -1 (/ (+ 1 (* -1 (/ (+ (* 1/2 (pow eps 4)) (pow eps 2)) (pow eps 2)))) eps))))))))
(fma.f64 (fma.f64 (fma.f64 (+.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/2 binary64) (.f64 eps eps)) eps) eps)) eps) eps) #s(literal 1/2 binary64)) x (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/2 binary64) (.f64 eps eps)) eps) eps)) eps)) x (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/2 binary64) (*.f64 eps eps)) eps) eps))) x eps)
(* -1 (pow eps 3))
(neg.f64 (pow.f64 eps #s(literal 3 binary64)))
(+ (* -1 (pow eps 3)) (* x (+ (* 1/2 (pow eps 4)) (pow eps 2))))
(fma.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/2 binary64) (*.f64 eps eps)) x (neg.f64 (pow.f64 eps #s(literal 3 binary64))))
(+ (* -1 (pow eps 3)) (* x (+ (* -1/2 (* (pow eps 2) (* x (+ eps (* -1 eps))))) (+ (* 1/2 (pow eps 4)) (pow eps 2)))))
(fma.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/2 binary64) (*.f64 eps eps)) x (neg.f64 (pow.f64 eps #s(literal 3 binary64))))
(+ (* -1 (pow eps 3)) (* x (+ (* 1/2 (pow eps 4)) (+ (* x (+ (* -1/2 (* (pow eps 2) x)) (* -1/2 (* (pow eps 2) (+ eps (* -1 eps)))))) (pow eps 2)))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) (pow.f64 eps #s(literal 4 binary64)) (.f64 (*.f64 (-.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/2 binary64) x) eps) eps) eps))
(cos (* -1/2 eps))
(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(fma.f64 (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal -1/2 binary64) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal -1/2 binary64))) x (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(* -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))
(* -1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/2 binary64))
(pow x 2)
(*.f64 x x)
1/24
#s(literal 1/24 binary64)
(+ 1/24 (* -1/720 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
-1/2
#s(literal -1/2 binary64)
(- (* 1/24 (pow x 2)) 1/2)
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)
(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))
(* -1 (pow eps 2))
(*.f64 (neg.f64 eps) eps)
(+ (* -1 (pow eps 2)) (* eps x))
(*.f64 (-.f64 x eps) eps)
(+ (* -1 (pow eps 3)) (* (pow eps 2) x))
(.f64 (.f64 (-.f64 x eps) eps) eps)
(* 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 eps #s(literal 1/2 binary64))))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.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)
(* (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 eps (*.f64 x x))) x) x)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(cos x)
(cos.f64 x)
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(* -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 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/720 binary64))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 2) (- (+ (* -1/2 eps) (* -1/2 (/ (* eps (+ eps (* -1 eps))) x))) (* 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 (/ (* eps (+ eps (* -1 eps))) x)) (+ (* 1/2 (/ (pow eps 3) (pow x 2))) (/ eps (pow x 2))))) (+ (* -1 (/ (* eps (- (* -1/2 (* eps (+ eps (* -1 eps)))) (* 1/2 (pow eps 2)))) (pow x 2))) (* 1/2 (/ (pow eps 2) x)))))
(.f64 (-.f64 (fma.f64 #s(literal -1/2 binary64) eps (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (pow.f64 eps #s(literal 3 binary64)) x) (/.f64 eps (.f64 x x)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (pow.f64 eps #s(literal 3 binary64)) x) (.f64 (/.f64 (.f64 eps eps) x) #s(literal 1/2 binary64)))) (*.f64 x x))
(* (pow x 2) (- (+ (* -1 (/ (pow eps 2) (pow x 3))) (+ (* -1/2 eps) (+ (* -1/2 (/ (* eps (+ eps (* -1 eps))) x)) (+ (* 1/2 (/ (pow eps 3) (pow x 2))) (/ eps (pow x 2)))))) (+ (* -1 (/ (* eps (- (* -1/2 (* eps (+ eps (* -1 eps)))) (* 1/2 (pow eps 2)))) (pow x 2))) (+ (* -1 (/ (* eps (- (+ eps (* 1/2 (pow eps 3))) (* -1 (* eps (- (* -1/2 (* eps (+ eps (* -1 eps)))) (* 1/2 (pow eps 2))))))) (pow x 3))) (* 1/2 (/ (pow eps 2) x))))))
(.f64 (-.f64 (fma.f64 (neg.f64 eps) (/.f64 eps (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal -1/2 binary64) eps (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (pow.f64 eps #s(literal 3 binary64)) x) (/.f64 eps (.f64 x x))))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (pow.f64 eps #s(literal 3 binary64)) x) (fma.f64 (/.f64 (.f64 eps eps) x) #s(literal 1/2 binary64) (.f64 (neg.f64 eps) (/.f64 eps (pow.f64 x #s(literal 3 binary64))))))) (*.f64 x x))
(* -1/2 (* (pow eps 2) (pow x 3)))
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(.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) (*.f64 eps eps))
(* (pow eps 2) (+ (* -1 (/ (- (+ (* -1 (- (+ 1 (* -1/2 (* x (+ x (* -1 x))))) (* 1/2 (pow x 2)))) (+ (* -1/2 (/ (pow x 3) eps)) (/ x eps))) (/ (* x (- (+ 1 (* -1/2 (* x (+ x (* -1 x))))) (* 1/2 (pow x 2)))) eps)) eps)) (* -1/2 x)))
(.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (-.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) eps) #s(literal -1/2 binary64) (/.f64 x eps)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/2 binary64) x) eps)) (neg.f64 eps))) eps) eps)
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (- (+ 1 (* -1/2 (* x (+ x (* -1 x))))) (* 1/2 (pow x 2)))) (* -1 (/ (+ (* -1 (- (+ x (* -1/2 (pow x 3))) (* x (- (+ 1 (* -1/2 (* x (+ x (* -1 x))))) (* 1/2 (pow x 2)))))) (* -1 (/ (* x (- (+ x (* -1/2 (pow x 3))) (* x (- (+ 1 (* -1/2 (* x (+ x (* -1 x))))) (* 1/2 (pow x 2)))))) eps))) eps))) eps)) (* -1/2 x)))
(.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) (*.f64 eps eps))
(* (pow eps 4) (+ (* -1 (/ (+ 1 (* -1/2 (* x (+ x (* -1 x))))) eps)) (* 1/2 x)))
(*.f64 (fma.f64 x #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) eps)) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (+ (* -1 (/ (+ 1 (+ (* -1 (/ (+ x (* -1/2 (pow x 3))) eps)) (* -1/2 (* x (+ x (* -1 x)))))) eps)) (* 1/2 x)))
(*.f64 (fma.f64 x #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/2 binary64) x) eps)) (neg.f64 eps))) (pow.f64 eps #s(literal 4 binary64)))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(* -1 (* eps (+ 1/2 (/ x eps))))
(*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) (neg.f64 eps))
(* -1 (* (pow eps 3) (+ 1 (* -1 (/ x eps)))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x eps)) (neg.f64 (pow.f64 eps #s(literal 3 binary64))))

rewrite235.0ms (2%)

Memory

19.3MiB live, 135.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	537
0	105	513
1	397	509
2	3730	461
0	10169	441

Stop Event

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

Counts

29 → 620

Calls

Call 1

Inputs
(.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 #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 #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 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 #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 x x) #s(literal -1/2 binary64)) eps))))
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps)))
#s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps))
(.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) 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))
(.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 (cos x) (fma.f64 (fma.f64 #s(approx (+ ( -1/720 (* x x)) 1/24) #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 #s(approx (+ ( -1/720 (* x x)) 1/24) #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 #s(approx (+ (* -1/720 (* x x)) 1/24) #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(approx (+ (* -1/720 (* x x)) 1/24) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) eps) (.f64 (+.f64 eps x) (-.f64 x eps))) (-.f64 eps #s(literal 0 binary64)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 eps #s(literal 0 binary64))))
(fma.f64 (.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) eps) (.f64 (+.f64 eps x) (-.f64 x eps))) (-.f64 eps #s(literal 0 binary64)) (.f64 (-.f64 x eps) (.f64 eps eps)))
(-.f64 eps #s(literal 0 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) eps) (.f64 (+.f64 eps x) (-.f64 x eps))) (-.f64 eps #s(literal 0 binary64)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 eps #s(literal 0 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)))
(.f64 (.f64 x x) #s(literal -1/2 binary64))
(*.f64 x x)
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(literal 1/24 binary64))
(fma.f64 #s(approx (+ (* -1/720 (* x x)) 1/24) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64))
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) eps) (.f64 (+.f64 eps x) (-.f64 x eps))) (-.f64 eps #s(literal 0 binary64)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 eps #s(literal 0 binary64)))))
(*.f64 (-.f64 x eps) (-.f64 eps #s(literal 0 binary64)))
(.f64 (-.f64 x eps) (.f64 eps 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 (.f64 eps eps) #s(literal -1/48 binary64) #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 (.f64 eps eps) #s(literal -1/48 binary64) #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 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))))
(.f64 (.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #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 (.f64 eps eps) #s(literal -1/48 binary64) #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 (.f64 eps eps) #s(literal -1/48 binary64) #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 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)
(.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)))
(/.f64 (.f64 (fma.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64)) eps) (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal -1/2 binary64)))
(/.f64 (.f64 (fma.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/110592 binary64) #s(literal 1/8 binary64)) eps) (fma.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 eps eps) #s(literal -1/96 binary64)))))
(/.f64 (.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64))) eps)
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64))) (neg.f64 eps))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64))) (*.f64 eps eps))
(/.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) (*.f64 eps eps)) eps)
(/.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))
(/.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))
(/.f64 (.f64 eps (fma.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64))) (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal -1/2 binary64)))
(/.f64 (.f64 eps (fma.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/110592 binary64) #s(literal 1/8 binary64))) (fma.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 eps eps) #s(literal -1/96 binary64)))))
(/.f64 (.f64 (fma.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64)) (.f64 eps eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal -1/2 binary64)) eps))
(/.f64 (.f64 (fma.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64)) (neg.f64 (.f64 eps eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal -1/2 binary64)) (neg.f64 eps)))
(/.f64 (.f64 (fma.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64)) (pow.f64 eps #s(literal 3 binary64))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal -1/2 binary64)) (.f64 eps eps)))
(/.f64 (.f64 (fma.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/110592 binary64) #s(literal 1/8 binary64)) (.f64 eps eps)) (.f64 (fma.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 eps eps) #s(literal -1/96 binary64)))) eps))
(/.f64 (.f64 (fma.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/110592 binary64) #s(literal 1/8 binary64)) (neg.f64 (.f64 eps eps))) (.f64 (fma.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 eps eps) #s(literal -1/96 binary64)))) (neg.f64 eps)))
(/.f64 (.f64 (fma.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/110592 binary64) #s(literal 1/8 binary64)) (pow.f64 eps #s(literal 3 binary64))) (.f64 (fma.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps eps) #s(literal -1/96 binary64)))) (*.f64 eps eps)))
(/.f64 (.f64 (.f64 eps eps) (fma.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64))) (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal -1/2 binary64))))
(/.f64 (.f64 (.f64 eps eps) (fma.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/110592 binary64) #s(literal 1/8 binary64))) (.f64 eps (fma.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 eps eps) #s(literal -1/96 binary64))))))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (fma.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64))) (.f64 (neg.f64 eps) (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal -1/2 binary64))))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (fma.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/110592 binary64) #s(literal 1/8 binary64))) (.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 eps eps) #s(literal -1/96 binary64))))))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal -1/2 binary64))))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/110592 binary64) #s(literal 1/8 binary64))) (.f64 (.f64 eps eps) (fma.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 eps eps) #s(literal -1/96 binary64))))))
(fma.f64 (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) eps (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps (.f64 #s(literal 0 binary64) (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64))))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) #s(literal 0 binary64)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) #s(literal 0 binary64) (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))
(fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) (.f64 #s(literal 0 binary64) (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64))))
(fma.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) #s(literal 0 binary64)))
(fma.f64 eps #s(literal 1/2 binary64) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) eps))
(fma.f64 eps #s(literal 1/2 binary64) (.f64 eps (.f64 (*.f64 eps eps) #s(literal -1/48 binary64))))
(fma.f64 #s(literal 0 binary64) (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))
(fma.f64 #s(literal 1/2 binary64) eps (.f64 (.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) eps))
(fma.f64 #s(literal 1/2 binary64) eps (.f64 eps (.f64 (*.f64 eps eps) #s(literal -1/48 binary64))))
(+.f64 (.f64 #s(literal 0 binary64) (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))
(+.f64 (.f64 (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) eps) (.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) #s(literal 0 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))
(+.f64 (.f64 eps (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) (.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) eps))
(+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps (.f64 (.f64 eps eps) #s(literal -1/48 binary64))))
(+.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps) (.f64 #s(literal 0 binary64) (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64))))
(+.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) #s(literal 0 binary64)))
#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 x x) #s(literal -1/2 binary64)) eps))))
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps)))
#s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps))
(.f64 (.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))
(.f64 (.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))
(.f64 (.f64 x eps) (*.f64 #s(literal -1/2 binary64) x))
(.f64 (.f64 #s(literal -1/2 binary64) eps) (*.f64 x x))
(.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps)
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(.f64 (-.f64 x eps) (.f64 eps eps))
(.f64 (.f64 eps eps) (-.f64 x eps))
(.f64 eps (.f64 (-.f64 x eps) eps))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (.f64 eps eps)) (fma.f64 (+.f64 x eps) eps (*.f64 x x)))
(/.f64 (.f64 (.f64 (-.f64 x eps) eps) (*.f64 eps eps)) eps)
(/.f64 (.f64 (.f64 (-.f64 x eps) eps) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))
(/.f64 (.f64 (.f64 (-.f64 x eps) eps) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))
(/.f64 (.f64 (.f64 eps eps) (*.f64 (-.f64 x eps) (+.f64 x eps))) (+.f64 x eps))
(/.f64 (.f64 (.f64 eps eps) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 (+.f64 x eps) eps (*.f64 x x)))
(/.f64 (.f64 (.f64 (-.f64 x eps) (+.f64 x eps)) (*.f64 eps eps)) (+.f64 x eps))
(fma.f64 (.f64 (-.f64 x eps) eps) eps (.f64 #s(literal 0 binary64) (*.f64 (-.f64 x eps) eps)))
(fma.f64 (.f64 (-.f64 x eps) eps) eps (.f64 (*.f64 (-.f64 x eps) eps) #s(literal 0 binary64)))
(fma.f64 (.f64 (-.f64 x eps) eps) #s(literal 0 binary64) (.f64 (*.f64 (-.f64 x eps) eps) eps))
(fma.f64 (-.f64 x eps) (.f64 eps eps) (.f64 #s(literal 0 binary64) (*.f64 (-.f64 x eps) eps)))
(fma.f64 (-.f64 x eps) (.f64 eps eps) (.f64 (*.f64 (-.f64 x eps) eps) #s(literal 0 binary64)))
(fma.f64 x (*.f64 eps eps) (pow.f64 (neg.f64 eps) #s(literal 3 binary64)))
(fma.f64 (.f64 eps eps) (-.f64 x eps) (.f64 #s(literal 0 binary64) (*.f64 (-.f64 x eps) eps)))
(fma.f64 (.f64 eps eps) (-.f64 x eps) (.f64 (*.f64 (-.f64 x eps) eps) #s(literal 0 binary64)))
(fma.f64 (*.f64 eps eps) x (pow.f64 (neg.f64 eps) #s(literal 3 binary64)))
(fma.f64 eps (.f64 (-.f64 x eps) eps) (.f64 #s(literal 0 binary64) (*.f64 (-.f64 x eps) eps)))
(fma.f64 eps (.f64 (-.f64 x eps) eps) (.f64 (*.f64 (-.f64 x eps) eps) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) (.f64 (-.f64 x eps) eps) (.f64 (*.f64 (-.f64 x eps) eps) eps))
(+.f64 (.f64 #s(literal 0 binary64) (.f64 (-.f64 x eps) eps)) (.f64 (.f64 (-.f64 x eps) eps) eps))
(+.f64 (.f64 (.f64 (-.f64 x eps) eps) #s(literal 0 binary64)) (.f64 (.f64 (-.f64 x eps) eps) eps))
(+.f64 (.f64 (.f64 eps eps) x) (pow.f64 (neg.f64 eps) #s(literal 3 binary64)))
(+.f64 (.f64 x (.f64 eps eps)) (pow.f64 (neg.f64 eps) #s(literal 3 binary64)))
(+.f64 (.f64 (.f64 (-.f64 x eps) eps) eps) (.f64 #s(literal 0 binary64) (.f64 (-.f64 x eps) eps)))
(+.f64 (.f64 (.f64 (-.f64 x eps) eps) eps) (.f64 (.f64 (-.f64 x eps) eps) #s(literal 0 binary64)))

eval214.0ms (1.8%)

Memory: -32.9MiB live, 126.4MiB allocated
Compiler: Compiled 41 815 to 4 028 computations (90.4% saved)

prune42.0ms (0.4%)

Memory

19.0MiB live, 57.6MiB allocated

Pruning

19 alts after pruning (11 fresh and 8 done)

	Pruned	Kept	Total
New	824	7	831
Fresh	3	4	7
Picked	2	3	5
Done	1	5	6
Total	830	19	849

Accuracy

100.0%

Counts

849 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	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 #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 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)))))
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -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)) eps (cos.f64 x)) eps))
	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -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)) eps (cos.f64 x)) eps))
	99.5%	#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))
✓	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
✓	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
✓	98.7%	#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 (fma.f64 #s(approx (+ ( -1/720 (* x x)) 1/24) #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) (+.f64 (.f64 (.f64 (fma.f64 #s(approx (+ ( -1/720 (* x x)) 1/24) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x) x) #s(literal 1 binary64))) eps))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 (.f64 x (+.f64 x eps)) eps) #s(literal -1/2 binary64) eps)))
	51.0%	#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 (.f64 (.f64 (+.f64 eps x) (-.f64 x eps)) (neg.f64 (.f64 eps eps))) (*.f64 (-.f64 x eps) (neg.f64 eps))) eps)))
✓	98.6%	#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)))
	28.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) eps) (.f64 (+.f64 eps x) (-.f64 x eps))) (-.f64 eps #s(literal 0 binary64)) (.f64 (-.f64 x eps) (.f64 eps eps))) (/.f64 (.f64 (.f64 (-.f64 x eps) (+.f64 x eps)) (.f64 eps eps)) (.f64 (+.f64 x eps) eps)))))
	38.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (/.f64 (.f64 eps (fma.f64 (.f64 (.f64 (-.f64 x eps) (+.f64 x eps)) eps) (.f64 #s(literal -1/2 binary64) x) (*.f64 (-.f64 x eps) eps))) (-.f64 x eps)) eps)))
	34.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (/.f64 (.f64 eps (fma.f64 (.f64 (.f64 (-.f64 x eps) (+.f64 x eps)) eps) (.f64 #s(literal -1/2 binary64) x) (.f64 (-.f64 x eps) eps))) (.f64 (-.f64 x eps) eps))))
	98.6%	#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) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps))))
✓	5.2%	#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 x x) #s(literal -1/2 binary64)) eps))))

Compiler

Compiled 1 551 to 612 computations (60.5% saved)

regimes33.0ms (0.3%)

Memory

-7.4MiB live, 29.7MiB allocated

Counts

31 → 1

Calls

Call 1

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

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

Calls

3 calls:

14.0ms	x
9.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes36.0ms (0.3%)

Memory

-12.1MiB live, 34.6MiB allocated

Counts

28 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

19.0ms	x
8.0ms	(-.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

23.5MiB live, 23.5MiB allocated

Counts

23 → 1

Calls

Call 1

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

7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	eps
6.0ms	x

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)

regimes45.0ms (0.4%)

Memory

-14.5MiB live, 24.2MiB allocated

Counts

20 → 1

Calls

Call 1

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

Outputs
#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))

Calls

3 calls:

32.0ms	eps
6.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	x

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`eps`
99.5%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes18.0ms (0.1%)

Memory

22.9MiB live, 22.9MiB allocated

Counts

19 → 1

Calls

Call 1

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

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

Calls

3 calls:

6.0ms	eps
6.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	x

Results

Accuracy	Segments	Branch
99.5%	1	`eps`
99.5%	1	`x`
99.5%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes45.0ms (0.4%)

Memory

-9.9MiB live, 26.9MiB allocated

Counts

18 → 1

Calls

Call 1

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

34.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	x
5.0ms	eps

Results

Accuracy	Segments	Branch
98.7%	1	`x`
98.7%	1	`eps`
98.7%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes11.0ms (0.1%)

Memory

16.7MiB live, 16.7MiB allocated

Counts

11 → 1

Calls

Call 1

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

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

Results

Accuracy	Segments	Branch
98.6%	1	`eps`
98.6%	1	`x`
98.6%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes12.0ms (0.1%)

Memory

-28.2MiB live, 10.2MiB allocated

Counts

5 → 1

Calls

Call 1

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

Calls

3 calls:

8.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms	eps
2.0ms	x

Results

Accuracy	Segments	Branch
98.6%	1	`x`
98.6%	1	`eps`
98.6%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory

8.1MiB live, 8.1MiB allocated

Accuracy

Total -59.4b remaining (-4558.1%)

Threshold costs -59.4b (-4558.1%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

Calls

3 calls:

1.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
1.0ms	eps
1.0ms	x

Results

Accuracy	Segments	Branch
98.0%	1	`eps`
98.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.0%	1	`x`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify399.0ms (3.4%)

Memory

-9.9MiB live, 31.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	227
1	116	227
2	258	227
3	595	227
4	831	227
5	902	227
6	934	227
7	1098	227
8	1187	227
9	1301	227
10	1843	227
11	3227	227
12	4234	227
13	4433	227
14	4530	227
15	4675	227
16	5313	227
17	5626	227
18	5679	227
19	5708	227
20	5708	227
21	5710	227
22	5710	227
23	7119	227
24	7745	227
25	7745	227
26	7816	227
27	7839	227
28	7839	227
29	7845	227
30	7855	227
31	7855	227
32	7855	227
33	7855	227
34	7861	227
35	7900	227

Stop Event

1×	node limit

Calls

Call 1

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

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

soundness971.0ms (8.2%)

Memory

9.0MiB live, 810.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	638	2421
1	2045	2088
2	7134	2038
0	8604	1881
0	390	1297
1	1196	1240
2	3329	1207
0	8008	1097
0	107	291
1	314	291
2	781	284
3	2853	284
4	6191	283
0	8157	253
0	6	16
0	10	16
1	53	16
2	385	16
3	4851	16
0	8393	16
0	371	1278
1	1115	1224
2	3043	1194
3	7478	1194
0	8686	1100

Stop Event

1×	fuel
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
1×	iter limit
1×	node limit

Compiler

Compiled 418 to 247 computations (40.9% saved)

preprocess86.0ms (0.7%)

Memory: 8.7MiB live, 85.1MiB allocated
Compiler: Compiled 506 to 200 computations (60.5% 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	312	35
5	383	35
6	469	35
7	509	35
8	521	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	110	7
8	159	7
9	175	7
10	183	7
0	183	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	110	18
8	159	18
9	175	18
10	183	18
0	183	18

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	312	35
5	383	35
6	469	35
7	509	35
8	521	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	110	7
8	159	7
9	175	7
10	183	7
0	183	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	110	18
8	159	18
9	175	18
10	183	18
0	183	18

start0.0ms (0%)

analyze45.0ms (0.4%)

sample6.6s (55.7%)

explain89.0ms (0.8%)

preprocess26.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0.1%)

localize27.0ms (0.2%)

series4.0ms (0%)

simplify201.0ms (1.7%)

rewrite177.0ms (1.5%)

eval48.0ms (0.4%)

prune6.0ms (0%)

simplify207.0ms (1.7%)

localize190.0ms (1.6%)

series31.0ms (0.3%)

simplify150.0ms (1.3%)

rewrite168.0ms (1.4%)

eval66.0ms (0.6%)

prune37.0ms (0.3%)

simplify170.0ms (1.4%)

localize234.0ms (2%)

series28.0ms (0.2%)

simplify195.0ms (1.6%)

rewrite161.0ms (1.4%)

eval123.0ms (1%)

prune48.0ms (0.4%)

simplify142.0ms (1.2%)

localize286.0ms (2.4%)

series30.0ms (0.3%)

simplify184.0ms (1.6%)

rewrite235.0ms (2%)

eval214.0ms (1.8%)

prune42.0ms (0.4%)

regimes33.0ms (0.3%)

regimes36.0ms (0.3%)

regimes21.0ms (0.2%)

regimes45.0ms (0.4%)

regimes18.0ms (0.1%)

regimes45.0ms (0.4%)

regimes11.0ms (0.1%)

regimes12.0ms (0.1%)

regimes4.0ms (0%)

simplify399.0ms (3.4%)

soundness971.0ms (8.2%)

preprocess86.0ms (0.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	312	35
5	383	35
6	469	35
7	509	35
8	521	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	110	7
8	159	7
9	175	7
10	183	7
0	183	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	110	18
8	159	18
9	175	18
10	183	18
0	183	18