Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 10 to 7 computations (30% saved)

sample142.0ms (1.3%)

Algorithm

1×

intervals

Results

51.0ms	112×	body	1024	valid
42.0ms	38×	body	2048	valid
11.0ms	48×	body	512	valid
3.0ms	43×	body	128	valid
2.0ms	15×	body	256	valid

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

37.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	37.2b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.0b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	3.4b	(sin.f64 (+.f64 x eps))

series12.0ms (0.1%)

Counts

2 → 48

Calls

2 calls:

7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	(sin.f64 (+.f64 x eps))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 42

Calls

2 calls:

6.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	(sin.f64 (+.f64 x eps))

simplify102.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

639×	`fma-neg_binary64`
483×	`fma-def_binary64`
351×	`cancel-sign-sub-inv_binary64`
291×	`sub-neg_binary64`
284×	`associate-+l-_binary64`

Counts

90 → 92

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	128	1256
1	297	1180
2	960	1116
3	2426	1108
4	4776	1108
5	4953	1108
6	4839	1108

prune98.0ms (0.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	3	93

Error

0.2b

Counts

93 → 3

Alt Table

Status	Error	Program
▶	20.6b	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	32.4b	(fma.f64 (.f64 (sin.f64 x) (.f64 eps eps)) -1/2 (*.f64 eps (cos.f64 x)))
	20.7b	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))

Compiler

Compiled 1645 to 493 computations (70% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))
✓	0.1b	(*.f64 (sin.f64 x) (cos.f64 eps))
✓	0.2b	(*.f64 (cos.f64 x) (sin.f64 eps))
✓	2.5b	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))

series55.0ms (0.5%)

Counts

4 → 72

Calls

4 calls:

19.0ms	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
17.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))
10.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))
9.0ms	(*.f64 (sin.f64 x) (cos.f64 eps))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
11×	`add-log-exp_binary64`
9×	`prod-diff_binary64`

Counts

4 → 87

Calls

4 calls:

7.0ms	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
7.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))
4.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))
3.0ms	(*.f64 (sin.f64 x) (cos.f64 eps))

simplify138.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

418×	`fma-neg_binary64`
276×	`distribute-rgt-in_binary64`
249×	`distribute-rgt-neg-in_binary64`
245×	`distribute-lft-in_binary64`
226×	`associate-r_binary64`

Counts

159 → 189

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	3009
1	616	2802
2	2190	2695
3	4798	2695
4	4972	2695
5	4911	2695

prune161.0ms (1.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	178	11	189
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	180	12	192

Error

0.1b

Counts

192 → 12

Alt Table

Status	Error	Program
	28.8b	(.f64 (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
	32.4b	(fma.f64 (.f64 (sin.f64 x) (.f64 eps eps)) -1/2 (*.f64 eps (cos.f64 x)))
	20.6b	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	30.2b	(exp.f64 (log.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
	20.7b	(-.f64 (expm1.f64 (log1p.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x))))) (sin.f64 x))
	21.9b	(fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (cbrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))))) (cbrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (neg.f64 (sin.f64 x)))
	42.7b	(+.f64 (fma.f64 1 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (neg.f64 (.f64 (sqrt.f64 (sin.f64 x)) (sqrt.f64 (sin.f64 x))))) (fma.f64 (neg.f64 (sqrt.f64 (sin.f64 x))) (sqrt.f64 (sin.f64 x)) (.f64 (sqrt.f64 (sin.f64 x)) (sqrt.f64 (sin.f64 x)))))
	22.0b	(-.f64 (+.f64 (log.f64 (exp.f64 (.f64 (sin.f64 x) (cos.f64 eps)))) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	5.4b	(/.f64 (.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) (fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (sin.f64 eps) (cos.f64 x) (sin.f64 x)))) (fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (sin.f64 eps) (cos.f64 x) (sin.f64 x))))
	22.1b	(/.f64 (-.f64 (.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (.f64 (sin.f64 x) (sin.f64 x))) (+.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)))
▶	1.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
	19.0b	(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) 3))

Compiler

Compiled 5005 to 1432 computations (71.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
✓	0.6b	(cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
✓	2.9b	(+.f64 (cos.f64 eps) -1)

series2.2s (20.4%)

Counts

4 → 84

Calls

4 calls:

1.2s	(.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
959.0ms	(cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
31.0ms	(.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
2.0ms	(+.f64 (cos.f64 eps) -1)

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
27×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
18×	`*-un-lft-identity_binary64`
16×	`pow1/3_binary64`

Counts

4 → 111

Calls

4 calls:

9.0ms	(.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
5.0ms	(.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
3.0ms	(+.f64 (cos.f64 eps) -1)
1.0ms	(cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))

simplify149.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

843×	`times-frac_binary64`
383×	`associate-r_binary64`
303×	`associate-l_binary64`
298×	`fma-def_binary64`
264×	`fma-neg_binary64`

Counts

195 → 224

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	356	6718
1	1004	6020
2	3611	5554
3	5304	5554

prune444.0ms (4.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	375	7	382
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	379	15	394

Error

0.0b

Counts

394 → 15

Alt Table

Status	Error	Program
	14.9b	(.f64 (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x))) 2)) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
	29.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))))
	21.9b	(fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (cbrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))))) (cbrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (neg.f64 (sin.f64 x)))
	1.9b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))))
	41.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (pow.f64 (-.f64 (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x)) 1/3))
	28.8b	(.f64 (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
	32.4b	(fma.f64 (.f64 (sin.f64 x) (.f64 eps eps)) -1/2 (*.f64 eps (cos.f64 x)))
	20.6b	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	42.7b	(+.f64 (fma.f64 1 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (neg.f64 (.f64 (sqrt.f64 (sin.f64 x)) (sqrt.f64 (sin.f64 x))))) (fma.f64 (neg.f64 (sqrt.f64 (sin.f64 x))) (sqrt.f64 (sin.f64 x)) (.f64 (sqrt.f64 (sin.f64 x)) (sqrt.f64 (sin.f64 x)))))
▶	1.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (log.f64 (.f64 (exp.f64 (cos.f64 eps)) (exp.f64 -1)))))))
	22.0b	(-.f64 (+.f64 (log.f64 (exp.f64 (.f64 (sin.f64 x) (cos.f64 eps)))) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	5.4b	(/.f64 (.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) (fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (sin.f64 eps) (cos.f64 x) (sin.f64 x)))) (fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (sin.f64 eps) (cos.f64 x) (sin.f64 x))))
	40.0b	(pow.f64 (pow.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x))) 3) 1/3)
	2.7b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x))))) 4) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x))))) 4)) (cbrt.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))))
	19.0b	(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) 3))

Compiler

Compiled 21763 to 10534 computations (51.6% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (log.f64 (.f64 (exp.f64 (cos.f64 eps)) (exp.f64 -1))))))
	0.6b	(cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
✓	2.8b	(log.f64 (*.f64 (exp.f64 (cos.f64 eps)) (exp.f64 -1)))
	2.9b	(+.f64 (cos.f64 eps) -1)

series1.7s (15.9%)

Counts

2 → 36

Calls

2 calls:

1.5s	(cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (log.f64 (.f64 (exp.f64 (cos.f64 eps)) (exp.f64 -1))))))
258.0ms	(log.f64 (*.f64 (exp.f64 (cos.f64 eps)) (exp.f64 -1)))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
5×	`pow1_binary64`
3×	`cbrt-prod_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 28

Calls

2 calls:

6.0ms	(log.f64 (*.f64 (exp.f64 (cos.f64 eps)) (exp.f64 -1)))
1.0ms	(cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (log.f64 (.f64 (exp.f64 (cos.f64 eps)) (exp.f64 -1))))))

simplify71.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

866×	`fma-neg_binary64`
516×	`fma-def_binary64`
416×	`*-commutative_binary64`
331×	`cancel-sign-sub-inv_binary64`
324×	`distribute-rgt-neg-in_binary64`

Counts

64 → 72

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	166	1442
1	421	1323
2	1276	1274
3	3567	1265
4	4998	1265

prune343.0ms (3.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	229	1	230
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	230	15	245

Error

0.0b

Counts

245 → 15

Alt Table

Status	Error	Program
	14.9b	(.f64 (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x))) 2)) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
	29.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))))
	41.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (pow.f64 (-.f64 (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x)) 1/3))
	28.8b	(.f64 (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
	32.4b	(fma.f64 (.f64 (sin.f64 x) (.f64 eps eps)) -1/2 (*.f64 eps (cos.f64 x)))
	20.6b	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	1.9b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))))
	42.7b	(+.f64 (fma.f64 1 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (neg.f64 (.f64 (sqrt.f64 (sin.f64 x)) (sqrt.f64 (sin.f64 x))))) (fma.f64 (neg.f64 (sqrt.f64 (sin.f64 x))) (sqrt.f64 (sin.f64 x)) (.f64 (sqrt.f64 (sin.f64 x)) (sqrt.f64 (sin.f64 x)))))
✓	1.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (log.f64 (.f64 (exp.f64 (cos.f64 eps)) (exp.f64 -1)))))))
	22.0b	(-.f64 (+.f64 (log.f64 (exp.f64 (.f64 (sin.f64 x) (cos.f64 eps)))) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	5.4b	(/.f64 (.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) (fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (sin.f64 eps) (cos.f64 x) (sin.f64 x)))) (fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (sin.f64 eps) (cos.f64 x) (sin.f64 x))))
	40.0b	(pow.f64 (pow.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x))) 3) 1/3)
	2.7b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x))))) 4) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x))))) 4)) (cbrt.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))))
	2.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x))))) (cbrt.f64 (cbrt.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x)))))) (cbrt.f64 (cbrt.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x))))))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (log.f64 (.f64 (exp.f64 (cos.f64 eps)) (exp.f64 -1)))))))
	19.0b	(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) 3))

Compiler

Compiled 14221 to 7052 computations (50.4% saved)

regimes843.0ms (7.8%)

Accuracy

Total 0.2b remaining (67.1%)

Threshold costs 0.2b (67.1%)

Counts

214 → 1

Compiler

Compiled 20787 to 11591 computations (44.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	18	19
2	19	19
3	17	19

end1.0ms (0%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

sample4.2s (38.7%)

Algorithm

1×

intervals

Results

1.8s	3491×	body	1024	valid
1.3s	1228×	body	2048	valid
350.0ms	1392×	body	512	valid
111.0ms	1318×	body	128	valid
97.0ms	569×	body	256	valid
5.0ms	2×	body	4096	valid

Compiler

Compiled 655 to 357 computations (45.5% saved)

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11

Details

analyze2.0ms (0%)

sample142.0ms (1.3%)

simplify11.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series12.0ms (0.1%)

rewrite12.0ms (0.1%)

simplify102.0ms (0.9%)

prune98.0ms (0.9%)

localize11.0ms (0.1%)

series55.0ms (0.5%)

rewrite25.0ms (0.2%)

simplify138.0ms (1.3%)

prune161.0ms (1.5%)

localize14.0ms (0.1%)

series2.2s (20.4%)

rewrite30.0ms (0.3%)

simplify149.0ms (1.4%)

prune444.0ms (4.1%)

localize24.0ms (0.2%)

series1.7s (15.9%)

rewrite7.0ms (0.1%)

simplify71.0ms (0.7%)

prune343.0ms (3.2%)

regimes843.0ms (7.8%)

simplify3.0ms (0%)

end1.0ms (0%)

sample4.2s (38.7%)

Profiling

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11