Metrics for 2sin (example 3.3)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze63.0ms (0.5%)

Memory

-19.3MiB live, 75.7MiB allocated; 8ms collecting garbage

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)

sample6.8s (58.9%)

Memory

54.7MiB live, 7 507.2MiB allocated; 2.6s collecting garbage

Samples

3.4s	26 314×	0	invalid
1.1s	5 115×	1	valid
392.0ms	3 141×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 3.3s

const: 715.0ms (21.7% of total)

ival-sin: 698.0ms (21.2% of total)

ival-add: 316.0ms (9.6% of total)

ival-mult: 278.0ms (8.4% of total)

ival-<: 263.0ms (8% of total)

adjust: 257.0ms (7.8% of total)

ival-fabs: 212.0ms (6.4% of total)

ival-sub: 201.0ms (6.1% of total)

ival-<=: 195.0ms (5.9% of total)

ival-and: 105.0ms (3.2% of total)

exact: 44.0ms (1.3% of total)

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

Bogosity

explain116.0ms (1%)

Memory

-31.7MiB live, 104.7MiB allocated; 18ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
226	2	(-2.149671592621115e-192 1.8925975972374645e-194)	6	(-7.931845447766479e-63 1.1558208663394699e-64)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
1	0	-	0	-	`(sin.f64 (+.f64 x eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`	cancellation	222	12
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	220	6
-	2	28

Precision

0.990990990990991

Recall

0.9734513274336283

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	220	6	0
-	2	6	22

Precision?

0.9658119658119658

Recall?

1.0

Freqs

test

number	freq
0	34
1	221
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

62.0ms	322×	1	valid
9.0ms	188×	0	valid
1.0ms	2×	3	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

ival-sin: 21.0ms (54.4% of total)

adjust: 10.0ms (25.9% of total)

ival-add: 4.0ms (10.4% of total)

ival-sub: 3.0ms (7.8% of total)

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

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

preprocess45.0ms (0.4%)

Memory

4.5MiB live, 50.8MiB allocated; 5ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	43
1	22	43
2	29	43
3	37	43
4	49	43
5	71	43
6	93	43
7	147	43
8	231	43
9	385	43
10	1010	43
11	4371	43
0	6	7
0	10	7
1	11	7
0	11	7

Stop Event

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

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: 0.2MiB live, 0.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated; 0ms collecting garbage

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)

simplify3.0ms (0%)

Memory

5.3MiB live, 5.3MiB allocated; 0ms collecting garbage

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	11	18
0	11	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)

localize32.0ms (0.3%)

Memory

12.6MiB live, 58.5MiB allocated; 3ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x eps)
accuracy	0.0	(sin.f64 x)
accuracy	0.03029252930532605	(sin.f64 (+.f64 x eps))
accuracy	24.72936043780375	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

21.0ms	161×	1	valid
4.0ms	94×	0	valid
0.0ms	1×	3	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

adjust: 6.0ms (33.9% of total)

ival-add: 5.0ms (28.2% of total)

ival-sin: 5.0ms (28.2% of total)

ival-sub: 2.0ms (11.3% of total)

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

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

series4.0ms (0%)

Memory

2.2MiB live, 2.2MiB allocated; 0ms collecting garbage

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))

simplify166.0ms (1.4%)

Memory

-21.7MiB live, 77.1MiB allocated; 9ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	303
1	366	303
2	1224	296
3	4149	296
4	7986	296
0	8046	267

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)) (-.f64 (.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 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/5040 binary64) (-.f64 (.f64 #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 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64)))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (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) eps) #s(literal -1/6 binary64))) 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) eps) #s(literal -1/2 binary64) (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 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64)))

rewrite196.0ms (1.7%)

Memory

11.6MiB live, 101.6MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	51	16
2	365	16
3	4452	16
0	8177	16

Stop Event

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

Counts

4 → 154

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

eval53.0ms (0.5%)

Memory: -13.6MiB live, 30.3MiB allocated; 6ms collecting garbage
Compiler: Compiled 5 510 to 734 computations (86.7% saved)

prune6.0ms (0.1%)

Memory

12.1MiB live, 12.1MiB allocated; 0ms collecting garbage

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	171	6	177
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	171	7	178

Accuracy

100.0%

Counts

178 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	37.5%	(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (-.f64 (.f64 (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))))) (.f64 (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))))))))
✓	61.3%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	60.7%	(-.f64 (sin.f64 #s(approx (+ x eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))) (sin.f64 x))
▶	100.0%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
▶	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
▶	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 397 to 156 computations (60.7% saved)

simplify172.0ms (1.5%)

Memory

15.9MiB live, 70.9MiB allocated; 6ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (+ x eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))
cost-diff	0	(sin.f64 #s(approx (+ x eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64)))))
cost-diff	0	(-.f64 (sin.f64 #s(approx (+ x eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))) (sin.f64 x))
cost-diff	3	(*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64)))
cost-diff	0	(*.f64 (sin.f64 x) eps)
cost-diff	0	(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
cost-diff	0	(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
cost-diff	0	(cos.f64 x)
cost-diff	0	(*.f64 (cos.f64 x) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
cost-diff	0	(sin.f64 eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
cost-diff	0	(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))
cost-diff	0	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #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	2	(+.f64 #s(literal 0 binary64) eps)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	212
0	61	202
1	101	202
2	212	202
3	548	199
4	1263	191
5	2604	191
6	6276	191
0	8071	187

Stop Event

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

Calls

Call 1

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

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

localize136.0ms (1.2%)

Memory

-0.2MiB live, 135.6MiB allocated; 9ms collecting garbage

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))
accuracy	0.02638627930532605	(sin.f64 #s(approx (+ x eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64)))))
accuracy	0.24609375	(*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64)))
accuracy	24.716384156183093	(-.f64 (sin.f64 #s(approx (+ x eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))) (sin.f64 x))
accuracy	0.0	(cos.f64 x)
accuracy	0.01171875	(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
accuracy	0.0234375	(*.f64 (sin.f64 x) eps)
accuracy	0.10923034194264722	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
accuracy	0.0	(cos.f64 x)
accuracy	0.01171875	(*.f64 (cos.f64 x) eps)
accuracy	0.41837736329545205	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
accuracy	0.0	(sin.f64 eps)
accuracy	1.2274887458227144	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
accuracy	0.0	(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))
accuracy	0.0	(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))
accuracy	0.00390625	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
accuracy	0.00390625	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))

Samples

65.0ms	161×	1	valid
41.0ms	93×	0	valid
2.0ms	2×	5	exit

Compiler

Compiled 171 to 34 computations (80.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 80.0ms

ival-add: 28.0ms (35.1% of total)

adjust: 14.0ms (17.6% of total)

ival-mult: 14.0ms (17.6% of total)

ival-sin: 8.0ms (10% of total)

ival-div: 5.0ms (6.3% of total)

ival-cos: 4.0ms (5% of total)

ival-sub: 3.0ms (3.8% of total)

ival-neg: 2.0ms (2.5% of total)

exact: 1.0ms (1.3% of total)

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

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

series71.0ms (0.6%)

Memory

-31.1MiB live, 25.3MiB allocated; 7ms collecting garbage

Counts

20 → 99

Calls

Call 1

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

Outputs
(* -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 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* eps x)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
(+ eps x)
(+ (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))))))))
(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 (/ eps x))
(/ (+ (* -1 eps) (* -1 x)) 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))
(cos x)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (sin x))
x
(* x (+ 1 (/ eps x)))
(sin (+ eps x))
(cos (* -1/2 (+ eps (* 2 x))))
-1
(- (* -1 (/ eps x)) 1)
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(sin (- eps (* -1 x)))
(cos (* -1/2 (- eps (* -2 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 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin 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))))))))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* 1/2 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 (- (* -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)))
(* eps (+ 1 (/ x eps)))
(sin (* 1/2 eps))
(* -1 (* eps (+ (/ 1 eps) (/ 1 x))))
(* -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)))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(sin (- x (* -1 eps)))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))

Calls

6 calls:

Time	Variable		Point	Expression
49.0ms	eps	@	inf	((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* (neg x) (- (/ (neg eps) x) 1)) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (- (/ (neg eps) x) 1))
6.0ms	eps	@	0	((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* (neg x) (- (/ (neg eps) x) 1)) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (- (/ (neg eps) x) 1))
4.0ms	x	@	inf	((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* (neg x) (- (/ (neg eps) x) 1)) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (- (/ (neg eps) x) 1))
4.0ms	eps	@	-inf	((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* (neg x) (- (/ (neg eps) x) 1)) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (- (/ (neg eps) x) 1))
3.0ms	x	@	0	((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* (neg x) (- (/ (neg eps) x) 1)) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (- (/ (neg eps) x) 1))

simplify146.0ms (1.3%)

Memory

43.9MiB live, 88.4MiB allocated; 7ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	346	1161
1	1288	1116
2	4548	1091
0	8805	993

Stop Event

1×	iter limit
1×	node limit

Counts

99 → 97

Calls

Call 1

Inputs
(* -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 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* eps x)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
(+ eps x)
(+ (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))))))))
(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 (/ eps x))
(/ (+ (* -1 eps) (* -1 x)) 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))
(cos x)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (sin x))
x
(* x (+ 1 (/ eps x)))
(sin (+ eps x))
(cos (* -1/2 (+ eps (* 2 x))))
-1
(- (* -1 (/ eps x)) 1)
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(sin (- eps (* -1 x)))
(cos (* -1/2 (- eps (* -2 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 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin 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))))))))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* 1/2 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 (- (* -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)))
(* eps (+ 1 (/ x eps)))
(sin (* 1/2 eps))
(* -1 (* eps (+ (/ 1 eps) (/ 1 x))))
(* -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)))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(sin (- x (* -1 eps)))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))

Outputs
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1 x) (* -1/2 eps))
(-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (.f64 #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 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) 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)))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64) (.f64 (.f64 x x) (fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #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 (* eps (pow x 2))))
(fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.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 (fma.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/24 binary64) eps)) x) x (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (.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 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ eps (* -1/2 (* (pow eps 2) x)))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps)
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) 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 (* -1/2 (* eps x)))
(fma.f64 (*.f64 x eps) #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 x eps) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(* eps x)
(*.f64 x eps)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x)
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x)
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/120 binary64) eps)) x) x (.f64 #s(literal -1/6 binary64) eps)) (.f64 x eps))
(+ eps x)
(+.f64 x 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 (sin.f64 eps) #s(literal -1/2 binary64))) x (cos.f64 eps)) x (sin.f64 eps))
(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 (.f64 #s(literal -1/6 binary64) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #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)))
(* -1 (/ eps x))
(/.f64 (neg.f64 eps) x)
(/ (+ (* -1 eps) (* -1 x)) x)
(/.f64 (neg.f64 (+.f64 x eps)) x)
(* -1 x)
(neg.f64 x)
(* x (- (* -1/2 (/ eps x)) 1))
(.f64 (-.f64 (.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 x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(cos x)
(cos.f64 x)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
(* eps (sin x))
(*.f64 (sin.f64 x) eps)
x
(* x (+ 1 (/ eps x)))
(fma.f64 (/.f64 eps x) x x)
(sin (+ eps x))
(sin.f64 (+.f64 x eps))
(cos (* -1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
-1
#s(literal -1 binary64)
(- (* -1 (/ eps x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 eps x))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(*.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 x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(*.f64 (neg.f64 x) (-.f64 #s(literal -1 binary64) (/.f64 eps x)))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 x eps))
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps 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) #s(literal -1/6 binary64)) eps (*.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 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 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)) (-.f64 (.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)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) 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) #s(literal -1/6 binary64)) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) 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)) (-.f64 (.f64 (.f64 #s(literal 1/120 binary64) 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)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 eps eps) #s(literal 1/120 binary64)) eps) eps) #s(literal 1/6 binary64)) eps)
(sin x)
(sin.f64 x)
(+ (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 #s(literal -1/2 binary64) (sin.f64 x)) 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) #s(literal -1/6 binary64)) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps (sin.f64 x))
(cos (* -1 x))
(cos.f64 x)
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) eps) (cos.f64 x) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) 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 (fma.f64 #s(literal -1/8 binary64) (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/48 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 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 (-.f64 (.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))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) eps) eps) #s(literal 1/48 binary64)) (.f64 #s(literal 1/2 binary64) eps))
(* eps (- (* -1 (/ x eps)) 1/2))
(*.f64 (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64)) eps)
(* 2 (sin (* 1/2 eps)))
(.f64 #s(literal -2 binary64) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(.f64 (.f64 (*.f64 (sin.f64 x) eps) eps) #s(literal -1/2 binary64))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) eps)
(* -1/2 (* eps (sin x)))
(.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)
(* eps (+ 1 (/ x eps)))
(fma.f64 (/.f64 x eps) eps eps)
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(* -1 (* eps (+ (/ 1 eps) (/ 1 x))))
(-.f64 #s(literal -1 binary64) (/.f64 eps x))
(* -1 (* eps (+ 1/2 (/ x eps))))
(*.f64 (fma.f64 (/.f64 x eps) #s(literal -1 binary64) #s(literal -1/2 binary64)) 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 x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (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)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64)))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 x eps))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

rewrite202.0ms (1.7%)

Memory

3.4MiB live, 145.4MiB allocated; 29ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	175
0	61	167
1	211	167
2	1628	167
0	8793	167

Stop Event

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

Counts

20 → 479

Calls

Call 1

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

Outputs
(*.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (fabs.f64 eps)) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (fabs.f64 eps)))
(*.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (neg.f64 eps)) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (neg.f64 eps)))
(*.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (-.f64 eps #s(literal 0 binary64))))
(*.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps))
(.f64 (/.f64 (.f64 eps eps) (fabs.f64 eps)) (/.f64 eps (fabs.f64 eps)))
(.f64 (/.f64 eps (fabs.f64 eps)) (/.f64 (.f64 eps eps) (fabs.f64 eps)))
(*.f64 (/.f64 eps (neg.f64 eps)) (neg.f64 eps))
(*.f64 (/.f64 eps eps) eps)
(*.f64 (neg.f64 eps) (/.f64 eps (neg.f64 eps)))
(*.f64 eps (/.f64 eps (-.f64 eps #s(literal 0 binary64))))
(*.f64 eps (/.f64 eps eps))
(pow.f64 eps #s(literal 1 binary64))
(/.f64 (+.f64 (pow.f64 (/.f64 #s(literal 0 binary64) (.f64 eps eps)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 0 binary64) (.f64 eps eps)) (/.f64 #s(literal 0 binary64) (.f64 eps eps)) (-.f64 (.f64 eps eps) (.f64 (/.f64 #s(literal 0 binary64) (.f64 eps eps)) eps))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (*.f64 eps eps)))) (neg.f64 eps))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (neg.f64 eps)) (pow.f64 (neg.f64 eps) #s(literal 3 binary64))) (.f64 eps eps))
(/.f64 (+.f64 #s(literal 0 binary64) (.f64 (.f64 eps eps) (neg.f64 (neg.f64 (*.f64 eps eps))))) (pow.f64 eps #s(literal 3 binary64)))
(/.f64 (fma.f64 #s(literal 0 binary64) (neg.f64 (.f64 eps eps)) (.f64 (.f64 eps eps) (pow.f64 (neg.f64 eps) #s(literal 3 binary64)))) (.f64 (.f64 eps eps) (neg.f64 (.f64 eps eps))))
(/.f64 (fma.f64 #s(literal 0 binary64) (neg.f64 eps) (.f64 (.f64 eps eps) (neg.f64 (*.f64 eps eps)))) (pow.f64 (neg.f64 eps) #s(literal 3 binary64)))
(/.f64 (fma.f64 #s(literal 0 binary64) (-.f64 eps #s(literal 0 binary64)) (pow.f64 eps #s(literal 4 binary64))) (.f64 (.f64 eps eps) (-.f64 eps #s(literal 0 binary64))))
(/.f64 (fma.f64 #s(literal 0 binary64) (.f64 eps eps) (.f64 (*.f64 eps eps) (pow.f64 eps #s(literal 3 binary64)))) (pow.f64 eps #s(literal 4 binary64)))
(/.f64 (neg.f64 (neg.f64 (*.f64 eps eps))) eps)
(/.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 (-.f64 eps #s(literal 0 binary64))))
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 eps))
(/.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64)))
(/.f64 (*.f64 eps eps) eps)
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (neg.f64 (neg.f64 (*.f64 eps eps))))
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eval92.0ms (0.8%)

Memory: -3.2MiB live, 131.2MiB allocated; 13ms collecting garbage
Compiler: Compiled 18 051 to 2 508 computations (86.1% saved)

prune19.0ms (0.2%)

Memory

-10.8MiB live, 45.3MiB allocated; 8ms collecting garbage

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	572	12	584
Fresh	1	0	1
Picked	3	2	5
Done	1	0	1
Total	577	14	591

Accuracy

100.0%

Counts

591 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.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 (/ (+ 0 eps) 2)) (*.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))))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
✓	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64))) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
▶	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
▶	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
▶	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
✓	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
▶	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (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)))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)))

Compiler

Compiled 612 to 433 computations (29.2% saved)

simplify84.0ms (0.7%)

Memory

20.3MiB live, 111.5MiB allocated; 7ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(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)
cost-diff	0	#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (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))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (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)))
cost-diff	3	(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))
cost-diff	0	(fma.f64 (-.f64 (.f64 #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 (-.f64 (.f64 #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 (-.f64 (.f64 #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 (-.f64 (.f64 #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 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))
cost-diff	0	#s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))
cost-diff	0	(.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
cost-diff	0	#s(approx (cos x) #s(literal 1 binary64))
cost-diff	0	(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
cost-diff	0	#s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
cost-diff	0	(.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.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 (/ (+ 0 eps) 2)) (.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))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	405
0	86	399
1	168	399
2	530	399
3	2265	392
4	6190	392
0	8046	382

Stop Event

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

Calls

Call 1

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

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

localize192.0ms (1.7%)

Memory

-13.3MiB live, 276.2MiB allocated; 21ms collecting garbage

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.109375	(.f64 (.f64 eps eps) x)
accuracy	0.140625	(*.f64 eps (+.f64 x eps))
accuracy	0.140625	(.f64 #s(literal 1/12 binary64) (.f64 (*.f64 eps eps) x))
accuracy	0.791055975077261	#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (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))
accuracy	0.01171875	(.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
accuracy	0.20703125	(.f64 #s(literal 1/24 binary64) (.f64 x x))
accuracy	0.41837736329545205	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
accuracy	0.577726193809382	#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
accuracy	0.0	(*.f64 #s(literal -1/2 binary64) x)
accuracy	0.01171875	(.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps)
accuracy	0.41837736329545205	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
accuracy	0.8015056502427331	#s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))
accuracy	0.01171875	(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)
accuracy	0.41837736329545205	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
accuracy	1.2467520755945196	#s(approx (cos x) #s(literal 1 binary64))
accuracy	0.0	#s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
accuracy	0.00390625	(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
accuracy	0.00390625	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.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	0.00390625	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))

Samples

120.0ms	161×	1	valid
30.0ms	95×	0	valid

Compiler

Compiled 258 to 52 computations (79.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 115.0ms

ival-mult: 35.0ms (30.5% of total)

ival-add: 27.0ms (23.5% of total)

adjust: 26.0ms (22.7% of total)

const: 9.0ms (7.8% of total)

ival-sin: 7.0ms (6.1% of total)

ival-cos: 5.0ms (4.4% of total)

ival-div: 3.0ms (2.6% of total)

ival-sub: 3.0ms (2.6% of total)

exact: 1.0ms (0.9% of total)

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

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

series33.0ms (0.3%)

Memory

-2.7MiB live, 43.2MiB allocated; 5ms collecting garbage

Counts

26 → 105

Calls

Call 1

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

Outputs
(* -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 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* -1/2 (pow eps 2))
(+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))
(+ 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)))))))
(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 x)
(* 1/24 (pow x 2))
(* 1/12 (* (pow eps 2) x))
(pow eps 2)
(+ (* eps x) (pow eps 2))
(* (pow 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))
(cos x)
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))))
(* (pow x 2) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* 1/12 (* (pow eps 2) (pow x 3)))
(* (pow x 3) (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))))
(* (pow x 3) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))))
(* (pow x 3) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ eps (pow x 3))))))
(cos (* -1/2 (+ eps (* 2 x))))
(* eps x)
(* x (+ eps (/ (pow 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 (/ (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/12 (pow eps 2))))
(* -1 (* (pow x 3) (+ (* -1/12 (pow eps 2)) (* 1/2 (/ eps x)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))) x)) (* -1/12 (pow eps 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)) x)) (* -1/12 (pow eps 2)))))
(cos (* -1/2 (- eps (* -2 x))))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) 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)))))))))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* eps (+ eps x))
(* eps (- (* -1 (/ x eps)) 1/2))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2)))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))
(* -1/48 (pow eps 3))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* (pow eps 2) (+ 1 (/ x 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))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	x	@	-inf	((/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* -1/2 x) x) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) x) eps) (cos (/ (+ (* 2 x) eps) -2)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (* -1/2 x) (* 1/24 (* x x)) (* 1/12 (* (* eps eps) x)) (* eps (+ x eps)) (* (* eps eps) x))
8.0ms	eps	@	inf	((/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* -1/2 x) x) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) x) eps) (cos (/ (+ (* 2 x) eps) -2)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (* -1/2 x) (* 1/24 (* x x)) (* 1/12 (* (* eps eps) x)) (* eps (+ x eps)) (* (* eps eps) x))
4.0ms	x	@	inf	((/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* -1/2 x) x) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) x) eps) (cos (/ (+ (* 2 x) eps) -2)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (* -1/2 x) (* 1/24 (* x x)) (* 1/12 (* (* eps eps) x)) (* eps (+ x eps)) (* (* eps eps) x))
4.0ms	eps	@	-inf	((/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* -1/2 x) x) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) x) eps) (cos (/ (+ (* 2 x) eps) -2)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (* -1/2 x) (* 1/24 (* x x)) (* 1/12 (* (* eps eps) x)) (* eps (+ x eps)) (* (* eps eps) x))
3.0ms	eps	@	0	((/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* -1/2 x) x) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) x) eps) (cos (/ (+ (* 2 x) eps) -2)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (* -1/2 x) (* 1/24 (* x x)) (* 1/12 (* (* eps eps) x)) (* eps (+ x eps)) (* (* eps eps) x))

simplify182.0ms (1.6%)

Memory

-11.2MiB live, 259.5MiB allocated; 53ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	377	1359
1	1339	1289
2	4847	1275
0	8370	1182

Stop Event

1×	iter limit
1×	node limit

Counts

105 → 104

Calls

Call 1

Inputs
(* -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 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* -1/2 (pow eps 2))
(+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))
(+ 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)))))))
(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 x)
(* 1/24 (pow x 2))
(* 1/12 (* (pow eps 2) x))
(pow eps 2)
(+ (* eps x) (pow eps 2))
(* (pow 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))
(cos x)
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))))
(* (pow x 2) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* 1/12 (* (pow eps 2) (pow x 3)))
(* (pow x 3) (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))))
(* (pow x 3) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))))
(* (pow x 3) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ eps (pow x 3))))))
(cos (* -1/2 (+ eps (* 2 x))))
(* eps x)
(* x (+ eps (/ (pow 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 (/ (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/12 (pow eps 2))))
(* -1 (* (pow x 3) (+ (* -1/12 (pow eps 2)) (* 1/2 (/ eps x)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))) x)) (* -1/12 (pow eps 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)) x)) (* -1/12 (pow eps 2)))))
(cos (* -1/2 (- eps (* -2 x))))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) 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)))))))))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* eps (+ eps x))
(* eps (- (* -1 (/ x eps)) 1/2))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2)))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))
(* -1/48 (pow eps 3))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* (pow eps 2) (+ 1 (/ x 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))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))

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

rewrite284.0ms (2.5%)

Memory

1.4MiB live, 290.3MiB allocated; 62ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	346
0	86	340
1	314	340
2	2718	332
0	8625	330

Stop Event

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

Counts

26 → 475

Calls

Call 1

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

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

eval80.0ms (0.7%)

Memory: 34.7MiB live, 121.0MiB allocated; 16ms collecting garbage
Compiler: Compiled 26 457 to 3 005 computations (88.6% saved)

prune21.0ms (0.2%)

Memory

-14.2MiB live, 39.7MiB allocated; 11ms collecting garbage

Pruning

15 alts after pruning (11 fresh and 4 done)

	Pruned	Kept	Total
New	562	5	567
Fresh	1	6	7
Picked	2	3	5
Done	1	1	2
Total	566	15	581

Accuracy

100.0%

Counts

581 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
	99.9%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.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))))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
✓	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64))) eps))
▶	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
✓	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
✓	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
▶	4.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) #s(approx (+ ( (* -1/2 x) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
✓	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 #s(approx (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x x)) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x)) eps)) x eps)))
▶	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 #s(approx (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) (.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x x)) #s(literal 1/2 binary64)) eps) eps)) x eps)))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 #s(approx (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) (.f64 (.f64 (.f64 (.f64 eps x) eps) x) #s(literal 1/12 binary64))) x eps)))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)))

Compiler

Compiled 776 to 519 computations (33.1% saved)

simplify103.0ms (0.9%)

Memory

-1.7MiB live, 131.1MiB allocated; 20ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	607
0	106	601
1	215	601
2	684	601
3	2759	589
4	6106	589
0	8359	560

Stop Event

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

Calls

Call 1

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

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

localize343.0ms (3%)

Memory

-4.8MiB live, 482.5MiB allocated; 77ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.12109375	(.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x)
accuracy	0.328125	(.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x)
accuracy	0.41837736329545205	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
accuracy	0.5111032282682962	#s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
accuracy	0.10923034194264722	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 #s(approx (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) (.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x x)) #s(literal 1/2 binary64)) eps) eps)) x eps)))
accuracy	0.20703125	(.f64 #s(literal 1/12 binary64) (.f64 x x))
accuracy	0.791055975077261	#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 #s(approx (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) (.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x x)) #s(literal 1/2 binary64)) eps) eps)) x eps))
accuracy	33.15879109548855	#s(approx (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) (.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x x)) #s(literal 1/2 binary64)) eps) eps))
accuracy	0.0	(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64))) eps)
accuracy	0.0	(*.f64 #s(literal -1/2 binary64) x)
accuracy	0.10923034194264722	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64))) eps))
accuracy	0.80150573750389	#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)))
accuracy	0.01171875	(.f64 #s(approx (cos x) #s(approx (+ ( (* -1/2 x) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps)
accuracy	0.41837736329545205	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) #s(approx (+ ( (* -1/2 x) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
accuracy	0.8015056502427331	#s(approx (cos x) #s(approx (+ (* (* -1/2 x) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))
accuracy	62.17349630250877	#s(approx (+ (* (* -1/2 x) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))
accuracy	0.0	#s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
accuracy	0.00390625	(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
accuracy	0.00390625	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
accuracy	0.00390625	(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

Samples

158.0ms	161×	1	valid
141.0ms	95×	0	valid

Compiler

Compiled 329 to 66 computations (79.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 236.0ms

ival-mult: 116.0ms (49.1% of total)

const: 38.0ms (16.1% of total)

adjust: 35.0ms (14.8% of total)

ival-add: 25.0ms (10.6% of total)

ival-sin: 7.0ms (3% of total)

ival-cos: 6.0ms (2.5% of total)

ival-sub: 5.0ms (2.1% of total)

ival-div: 3.0ms (1.3% of total)

exact: 1.0ms (0.4% of total)

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

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

series22.0ms (0.2%)

Memory

34.7MiB live, 34.7MiB allocated; 0ms collecting garbage

Counts

27 → 123

Calls

Call 1

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

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 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
-1/2
(- (* 1/12 (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))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* -1/2 eps))
(+ (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 x)
(* -1/2 (pow eps 2))
(+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))
(* 1/12 (pow x 2))
(* 1/24 x)
(* x (+ 1/24 (* -1/720 (pow x 2))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(cos x)
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- 1/12 (* 1/2 (/ 1 (pow x 2)))))
(* 1/12 (* (pow eps 2) (pow x 3)))
(* (pow x 3) (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))))
(* (pow x 3) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))))
(* (pow x 3) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ eps (pow x 3))))))
(* -1/720 (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)))))
(cos (+ x (* 1/2 eps)))
(cos (* -1/2 (+ eps (* 2 x))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))))
(* (pow x 2) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))))
(* -1/720 (pow x 3))
(* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(* -1 (* (pow x 3) (+ (* -1/12 (pow eps 2)) (* 1/2 (/ eps x)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))) x)) (* -1/12 (pow eps 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)) x)) (* -1/12 (pow eps 2)))))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (* -1/2 (- eps (* -2 x))))
(* (pow x 2) (+ (* -1 (/ (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/12 (pow eps 2))))
(* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))
(* 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)))))))))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2))))
(* 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 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2)))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))
(* 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))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))))
(cos (- x (* -1/2 eps)))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	x	@	inf	((* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* -1/2 x) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 x) (+ x eps)) 1) (- (* 1/12 (* x x)) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) x) eps) (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (cos (+ (* 1/2 eps) x)) (cos (/ (+ (* 2 x) eps) -2)) (* -1/2 x) (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) (* 1/12 (* x x)) (* (+ (* -1/720 (* x x)) 1/24) x) (* (* (+ (* -1/720 (* x x)) 1/24) x) x))
4.0ms	x	@	-inf	((* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* -1/2 x) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 x) (+ x eps)) 1) (- (* 1/12 (* x x)) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) x) eps) (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (cos (+ (* 1/2 eps) x)) (cos (/ (+ (* 2 x) eps) -2)) (* -1/2 x) (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) (* 1/12 (* x x)) (* (+ (* -1/720 (* x x)) 1/24) x) (* (* (+ (* -1/720 (* x x)) 1/24) x) x))
3.0ms	eps	@	-inf	((* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* -1/2 x) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 x) (+ x eps)) 1) (- (* 1/12 (* x x)) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) x) eps) (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (cos (+ (* 1/2 eps) x)) (cos (/ (+ (* 2 x) eps) -2)) (* -1/2 x) (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) (* 1/12 (* x x)) (* (+ (* -1/720 (* x x)) 1/24) x) (* (* (+ (* -1/720 (* x x)) 1/24) x) x))
3.0ms	eps	@	inf	((* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* -1/2 x) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 x) (+ x eps)) 1) (- (* 1/12 (* x x)) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) x) eps) (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (cos (+ (* 1/2 eps) x)) (cos (/ (+ (* 2 x) eps) -2)) (* -1/2 x) (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) (* 1/12 (* x x)) (* (+ (* -1/720 (* x x)) 1/24) x) (* (* (+ (* -1/720 (* x x)) 1/24) x) x))
3.0ms	x	@	0	((* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* -1/2 x) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 x) (+ x eps)) 1) (- (* 1/12 (* x x)) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) x) eps) (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (cos (+ (* 1/2 eps) x)) (cos (/ (+ (* 2 x) eps) -2)) (* -1/2 x) (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) (* 1/12 (* x x)) (* (+ (* -1/720 (* x x)) 1/24) x) (* (* (+ (* -1/720 (* x x)) 1/24) x) x))

simplify230.0ms (2%)

Memory

-36.6MiB live, 150.9MiB allocated; 29ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	437	1633
1	1538	1552
2	5423	1543
0	8321	1422

Stop Event

1×	iter limit
1×	node limit

Counts

123 → 122

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 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
-1/2
(- (* 1/12 (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))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* -1/2 eps))
(+ (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 x)
(* -1/2 (pow eps 2))
(+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))
(* 1/12 (pow x 2))
(* 1/24 x)
(* x (+ 1/24 (* -1/720 (pow x 2))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(cos x)
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- 1/12 (* 1/2 (/ 1 (pow x 2)))))
(* 1/12 (* (pow eps 2) (pow x 3)))
(* (pow x 3) (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))))
(* (pow x 3) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))))
(* (pow x 3) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ eps (pow x 3))))))
(* -1/720 (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)))))
(cos (+ x (* 1/2 eps)))
(cos (* -1/2 (+ eps (* 2 x))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))))
(* (pow x 2) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))))
(* -1/720 (pow x 3))
(* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(* -1 (* (pow x 3) (+ (* -1/12 (pow eps 2)) (* 1/2 (/ eps x)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))) x)) (* -1/12 (pow eps 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)) x)) (* -1/12 (pow eps 2)))))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (* -1/2 (- eps (* -2 x))))
(* (pow x 2) (+ (* -1 (/ (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/12 (pow eps 2))))
(* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))
(* 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)))))))))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2))))
(* 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 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2)))
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))
(* 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))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))))
(cos (- x (* -1/2 eps)))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))

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

rewrite182.0ms (1.6%)

Memory

27.5MiB live, 116.5MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	512
0	106	506
1	410	506
2	3583	498
0	8365	483

Stop Event

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

Counts

27 → 251

Calls

Call 1

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

Outputs
(.f64 (.f64 #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)))
(.f64 #s(approx (cos (/ (+ ( 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) (.f64 #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))
(.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)))
(+.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)))
#s(approx (sin (/ (+ 0 eps) 2)) (.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 (-.f64 (.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1/4 binary64)) eps) (-.f64 (.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 (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)) (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 (-.f64 (.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1/4 binary64))) (-.f64 (.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 (-.f64 (.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1/4 binary64)) (neg.f64 (.f64 eps eps))) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (neg.f64 eps)))
(/.f64 (.f64 (-.f64 (.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 (-.f64 (.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)) (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 (neg.f64 (.f64 eps eps)) (-.f64 (.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1/4 binary64))) (.f64 (neg.f64 eps) (-.f64 (.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)) (-.f64 (.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1/4 binary64))) (.f64 (.f64 eps eps) (-.f64 (.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 #s(literal 1/2 binary64) eps))
(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 #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))))
(fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 #s(literal 1/2 binary64) eps))
(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))
(+.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 #s(literal 1/2 binary64) eps))
(+.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 #s(literal 1/2 binary64) eps))
(+.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) eps))
(+.f64 (.f64 #s(literal 1/2 binary64) eps) (.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)) (.f64 #s(approx (cos x) #s(approx (+ ( (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))) eps))
(.f64 #s(approx (cos x) #s(approx (+ ( (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))) eps)
(.f64 eps #s(approx (cos x) #s(approx (+ ( (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (cos x) #s(approx (+ (* (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)))) (neg.f64 eps))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(approx (cos x) #s(approx (+ ( (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)))) (*.f64 eps eps))
(/.f64 (.f64 #s(approx (cos x) #s(approx (+ ( (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))
(/.f64 (.f64 #s(approx (cos x) #s(approx (+ ( (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))
(fma.f64 #s(approx (cos x) #s(approx (+ (* (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))) eps (.f64 #s(literal 0 binary64) #s(approx (cos x) #s(approx (+ ( (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)))))
(fma.f64 #s(approx (cos x) #s(approx (+ (* (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))) eps (.f64 #s(approx (cos x) #s(approx (+ ( (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))) #s(literal 0 binary64)))
(fma.f64 #s(approx (cos x) #s(approx (+ (* (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))) #s(literal 0 binary64) (.f64 #s(approx (cos x) #s(approx (+ ( (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))) eps))
(fma.f64 eps #s(approx (cos x) #s(approx (+ (* (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))) (.f64 #s(literal 0 binary64) #s(approx (cos x) #s(approx (+ ( (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)))))
(fma.f64 eps #s(approx (cos x) #s(approx (+ (* (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))) (.f64 #s(approx (cos x) #s(approx (+ ( (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) #s(approx (cos x) #s(approx (+ (* (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))) (.f64 #s(approx (cos x) #s(approx (+ ( (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))) eps))
(+.f64 (.f64 #s(literal 0 binary64) #s(approx (cos x) #s(approx (+ ( (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)))) (.f64 #s(approx (cos x) #s(approx (+ ( (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))) eps))
(+.f64 (.f64 #s(approx (cos x) #s(approx (+ ( (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))) #s(literal 0 binary64)) (.f64 #s(approx (cos x) #s(approx (+ ( (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))) eps))
(+.f64 (.f64 #s(approx (cos x) #s(approx (+ ( (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))) eps) (.f64 #s(literal 0 binary64) #s(approx (cos x) #s(approx (+ ( (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)))))
(+.f64 (.f64 #s(approx (cos x) #s(approx (+ ( (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))) eps) (.f64 #s(approx (cos x) #s(approx (+ ( (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))) #s(literal 0 binary64)))
#s(approx (cos x) #s(approx (+ (* (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)))
#s(approx (+ (* (* -1/2 x) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64))) eps)
(.f64 eps #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64))))
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(-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))
(cos.f64 (neg.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))
(cos.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(cos.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(+.f64 (.f64 (cos.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (-.f64 (.f64 #s(literal 1/2 binary64) eps) x))) (cos.f64 (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/2 binary64) eps) x)))) (.f64 (sin.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (-.f64 (.f64 #s(literal 1/2 binary64) eps) x))) (sin.f64 (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/2 binary64) eps) x)))))
(+.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 (neg.f64 eps) #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 (neg.f64 eps) #s(literal 1/2 binary64)))))
(+.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal -1/2 binary64) eps))) (.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 x))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
(+.f64 (.f64 (sin.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 0 binary64)) (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 1 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (.f64 #s(literal 0 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(+.f64 (.f64 (sin.f64 x) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (PI.f64)))) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
(+.f64 (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 0 binary64)) (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 1 binary64)))
(+.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (PI.f64))) (sin.f64 x)))
#s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 x #s(literal -1/2 binary64))
#s(approx (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) (.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x x)) #s(literal 1/2 binary64)) eps) eps))
(.f64 (fabs.f64 (.f64 #s(literal 1/12 binary64) (neg.f64 x))) x)
(.f64 (fabs.f64 (.f64 #s(literal 1/12 binary64) x)) x)
(.f64 (.f64 #s(literal 1/12 binary64) (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 #s(literal 1/12 binary64) x) x)
(.f64 (neg.f64 x) (.f64 (neg.f64 x) #s(literal 1/12 binary64)))
(.f64 #s(literal 1/12 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(.f64 x (fabs.f64 (.f64 (neg.f64 x) #s(literal 1/12 binary64))))
(.f64 x (fabs.f64 (.f64 #s(literal 1/12 binary64) x)))
(.f64 x (.f64 #s(literal 1/12 binary64) x))
(fabs.f64 (neg.f64 (.f64 #s(literal 1/12 binary64) (.f64 x x))))
(fabs.f64 (.f64 #s(literal 1/12 binary64) (.f64 x x)))
(.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x)
(.f64 x (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/576 binary64)) x) (-.f64 (.f64 #s(literal -1/720 binary64) (.f64 x x)) #s(literal 1/24 binary64)))
(/.f64 (.f64 (fma.f64 #s(literal -1/373248000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) x) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (*.f64 x x) #s(literal -1/17280 binary64)))))
(/.f64 (.f64 x (-.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/576 binary64))) (-.f64 (.f64 #s(literal -1/720 binary64) (.f64 x x)) #s(literal 1/24 binary64)))
(/.f64 (.f64 x (fma.f64 #s(literal -1/373248000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64))) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (*.f64 x x) #s(literal -1/17280 binary64)))))
(fma.f64 (.f64 #s(literal -1/720 binary64) (.f64 x x)) x (*.f64 #s(literal 1/24 binary64) x))
(fma.f64 #s(literal 1/24 binary64) x (.f64 (.f64 #s(literal -1/720 binary64) (*.f64 x x)) x))
(fma.f64 x (.f64 #s(literal -1/720 binary64) (.f64 x x)) (*.f64 x #s(literal 1/24 binary64)))
(fma.f64 x #s(literal 1/24 binary64) (.f64 x (.f64 #s(literal -1/720 binary64) (*.f64 x x))))
(+.f64 (.f64 (.f64 #s(literal -1/720 binary64) (.f64 x x)) x) (.f64 #s(literal 1/24 binary64) x))
(+.f64 (.f64 #s(literal 1/24 binary64) x) (.f64 (.f64 #s(literal -1/720 binary64) (.f64 x x)) x))
(+.f64 (.f64 x (.f64 #s(literal -1/720 binary64) (.f64 x x))) (.f64 x #s(literal 1/24 binary64)))
(+.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x (.f64 #s(literal -1/720 binary64) (.f64 x x))))
(.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x)
(.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x))
(.f64 (.f64 x x) (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)))
(.f64 x (.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/576 binary64)) (.f64 x x)) (-.f64 (.f64 #s(literal -1/720 binary64) (*.f64 x x)) #s(literal 1/24 binary64)))
(/.f64 (.f64 (fma.f64 #s(literal -1/373248000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) (.f64 x x)) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal -1/17280 binary64)))))

eval126.0ms (1.1%)

Memory: -2.1MiB live, 54.9MiB allocated; 73ms collecting garbage
Compiler: Compiled 15 494 to 1 793 computations (88.4% saved)

prune27.0ms (0.2%)

Memory

-23.1MiB live, 26.1MiB allocated; 5ms collecting garbage

Pruning

16 alts after pruning (7 fresh and 9 done)

	Pruned	Kept	Total
New	354	4	358
Fresh	3	3	6
Picked	0	5	5
Done	0	4	4
Total	357	16	373

Accuracy

100.0%

Counts

373 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
	99.9%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ ( 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
	57.0%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)))) (neg.f64 eps)))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
✓	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
✓	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64))) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (fma.f64 (.f64 #s(literal -1/720 binary64) (.f64 x x)) x (.f64 #s(literal 1/24 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
✓	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
✓	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
✓	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
✓	4.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) #s(approx (+ ( (* -1/2 x) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
✓	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 #s(approx (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) (.f64 (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x)) eps)) x eps)))
✓	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 #s(approx (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) (.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x x)) #s(literal 1/2 binary64)) eps) eps)) x eps)))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 #s(approx (+ (* (* eps (+ x eps)) -1/2) (* (* 1/12 (* (* eps eps) x)) x)) (.f64 (.f64 (.f64 (.f64 eps x) eps) x) #s(literal 1/12 binary64))) x eps)))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)))

Compiler

Compiled 1 339 to 522 computations (61% saved)

regimes22.0ms (0.2%)

Memory

19.5MiB live, 19.5MiB allocated; 0ms collecting garbage

Counts

28 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes20.0ms (0.2%)

Memory

18.1MiB live, 18.1MiB allocated; 0ms collecting garbage

Counts

26 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes28.0ms (0.2%)

Memory

-30.7MiB live, 15.8MiB allocated; 2ms collecting garbage

Counts

21 → 1

Calls

Call 1

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

Calls

3 calls:

16.0ms	eps
5.0ms	x
5.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes15.0ms (0.1%)

Memory

14.4MiB live, 14.4MiB allocated; 0ms collecting garbage

Counts

19 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes14.0ms (0.1%)

Memory

13.3MiB live, 13.3MiB allocated; 0ms collecting garbage

Counts

17 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.3%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.3%	1	`x`
99.3%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes31.0ms (0.3%)

Memory

-33.4MiB live, 13.2MiB allocated; 2ms collecting garbage

Counts

16 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

22.0ms	x
4.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	eps

Results

Accuracy	Segments	Branch
98.8%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.8%	1	`x`
98.8%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes11.0ms (0.1%)

Memory

12.0MiB live, 12.0MiB allocated; 0ms collecting garbage

Counts

13 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes7.0ms (0.1%)

Memory

8.4MiB live, 8.4MiB allocated; 0ms collecting garbage

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes5.0ms (0%)

Memory

7.0MiB live, 7.0MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes5.0ms (0%)

Memory

6.7MiB live, 6.7MiB allocated; 0ms collecting garbage

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps 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
98.6%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.6%	1	`x`
98.6%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory

6.0MiB live, 6.0MiB allocated; 0ms collecting garbage

Accuracy

Total -59.7b remaining (-4861.6%)

Threshold costs -59.7b (-4861.6%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (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
98.1%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.1%	1	`x`
98.1%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify106.0ms (0.9%)

Memory

-28.3MiB live, 66.2MiB allocated; 8ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	88	240
1	122	240
2	209	240
3	505	240
4	1130	240
5	1871	240
6	2609	240
7	3825	240
8	5658	240

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations962.0ms (8.3%)

Memory

37.4MiB live, 634.4MiB allocated; 161ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	346	1161
1	1288	1116
2	4548	1091
0	8805	993
0	437	1633
1	1538	1552
2	5423	1543
0	8321	1422
0	107	303
1	366	303
2	1224	296
3	4149	296
4	7986	296
0	8046	267
0	377	1359
1	1339	1289
2	4847	1275
0	8370	1182
0	6	16
0	10	16
1	51	16
2	365	16
3	4452	16
0	8177	16

Stop Event

1×	fuel
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
1×	iter limit
1×	node limit

Compiler

Compiled 244 to 90 computations (63.1% saved)

preprocess88.0ms (0.8%)

Memory: 6.9MiB live, 104.2MiB allocated; 10ms collecting garbage
Compiler: Compiled 532 to 218 computations (59% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze63.0ms (0.5%)

sample6.8s (58.9%)

explain116.0ms (1%)

preprocess45.0ms (0.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0%)

localize32.0ms (0.3%)

series4.0ms (0%)

simplify166.0ms (1.4%)

rewrite196.0ms (1.7%)

eval53.0ms (0.5%)

prune6.0ms (0.1%)

simplify172.0ms (1.5%)

localize136.0ms (1.2%)

series71.0ms (0.6%)

simplify146.0ms (1.3%)

rewrite202.0ms (1.7%)

eval92.0ms (0.8%)

prune19.0ms (0.2%)

simplify84.0ms (0.7%)

localize192.0ms (1.7%)

series33.0ms (0.3%)

simplify182.0ms (1.6%)

rewrite284.0ms (2.5%)

eval80.0ms (0.7%)

prune21.0ms (0.2%)

simplify103.0ms (0.9%)

localize343.0ms (3%)

series22.0ms (0.2%)

simplify230.0ms (2%)

rewrite182.0ms (1.6%)

eval126.0ms (1.1%)

prune27.0ms (0.2%)

regimes22.0ms (0.2%)

regimes20.0ms (0.2%)

regimes28.0ms (0.2%)

regimes15.0ms (0.1%)

regimes14.0ms (0.1%)

regimes31.0ms (0.3%)

regimes11.0ms (0.1%)

regimes7.0ms (0.1%)

regimes5.0ms (0%)

regimes5.0ms (0%)

regimes4.0ms (0%)

simplify106.0ms (0.9%)

derivations962.0ms (8.3%)

preprocess88.0ms (0.8%)

end0.0ms (0%)

Profiling