Details

analyze1.8s (9.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample8.7s (46.3%)

Results

5.0s	2072×	body	2048	valid
2.4s	3106×	body	1024	valid
642.0ms	1538×	body	512	valid
229.0ms	775×	body	256	valid
161.0ms	118×	body	4096	valid
139.0ms	647×	body	128	valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify94.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-neg_binary64`
430×	`div-sub_binary64`
430×	`fma-def_binary64`
335×	`times-frac_binary64`
160×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	14	14
2	24	14
3	41	14
4	67	14
5	115	14
6	212	14
7	416	14
8	699	14
9	1176	14
10	1555	14
11	1621	14
12	1652	14
13	1679	14
14	1689	14
15	1693	14
16	1693	14
17	1592	14

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

30.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.1b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 x)
✓	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	1.6b	(-.f64 x (tan.f64 x))
✓	1.6b	(-.f64 x (sin.f64 x))

series21.0ms (0.1%)

Counts

4 → 34

Calls

4 calls:

12.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
5.0ms	(-.f64 x (tan.f64 x))
2.0ms	(-.f64 x (sin.f64 x))
2.0ms	(sin.f64 x)

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`*-un-lft-identity_binary64`
60×	`add-sqr-sqrt_binary64`
32×	`add-cube-cbrt_binary64`
25×	`times-frac_binary64`
18×	`prod-diff_binary64`

Counts

4 → 123

Calls

4 calls:

7.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
3.0ms	(-.f64 x (sin.f64 x))
3.0ms	(-.f64 x (tan.f64 x))
1.0ms	(sin.f64 x)

simplify139.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

497×	`fma-neg_binary64`
313×	`cancel-sign-sub-inv_binary64`
252×	`associate-/l/_binary64`
221×	`associate-/r/_binary64`
204×	`distribute-rgt-in_binary64`

Counts

157 → 167

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	265	3109
1	618	2685
2	2075	2567
3	4500	2563
4	4985	2563
5	4872	2563

prune122.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	164	3	167
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	164	4	168

Error

0.0b

Counts

168 → 4

Alt Table

Status	Error	Program
	32.6b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
✓	30.1b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
	46.9b	(/.f64 (/.f64 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2)) (+.f64 x (sin.f64 x))) (-.f64 x (tan.f64 x)))
▶	30.1b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))

Compiler

Compiled 3417 to 1006 computations (70.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 x (tan.f64 x)))
✓	0.1b	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
✓	1.4b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
	1.6b	(-.f64 x (tan.f64 x))

series26.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

11.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
8.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
7.0ms	(/.f64 x (-.f64 x (tan.f64 x)))

rewrite208.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

727×	`*-un-lft-identity_binary64`
717×	`add-sqr-sqrt_binary64`
708×	`times-frac_binary64`
441×	`prod-diff_binary64`
421×	`add-cube-cbrt_binary64`

Counts

3 → 591

Calls

3 calls:

31.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
5.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
4.0ms	(/.f64 x (-.f64 x (tan.f64 x)))

simplify818.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

461×	`fma-neg_binary64`
412×	`unsub-neg_binary64`
312×	`fma-udef_binary64`
280×	`sub-neg_binary64`
250×	`associate-+r-_binary64`

Counts

627 → 574

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	622	41023
1	1422	27517
2	3251	20234
3	4263	20192
4	4884	20192
5	4829	20192

prune471.0ms (2.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	657	1	658
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	658	4	662

Error

0.0b

Counts

662 → 4

Alt Table

Status	Error	Program
▶	30.2b	(+.f64 (fma.f64 1 (/.f64 x (-.f64 x (tan.f64 x))) (neg.f64 (.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x)))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x)))))))) (fma.f64 (neg.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x))))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x))))) (.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x)))) (/.f64 1 (*.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x))))))))
	32.6b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
✓	30.1b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
	46.9b	(/.f64 (/.f64 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2)) (+.f64 x (sin.f64 x))) (-.f64 x (tan.f64 x)))

Compiler

Compiled 34150 to 4907 computations (85.6% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x))))
✓	1.4b	(fma.f64 1 (/.f64 x (-.f64 x (tan.f64 x))) (neg.f64 (.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x)))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x))))))))
	1.6b	(-.f64 x (tan.f64 x))
✓	32.8b	(fma.f64 (neg.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x))))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x))))) (.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x)))) (/.f64 1 (*.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x)))))))

series119.0ms (0.6%)

Counts

3 → 36

Calls

3 calls:

70.0ms

(fma.f64 (neg.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x))))) (/.f64 1 (*.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x))))) (*.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x)))) (/.f64 1 (*.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x)))))))

33.0ms

(*.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x))))

15.0ms

(fma.f64 1 (/.f64 x (-.f64 x (tan.f64 x))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x)))) (/.f64 1 (*.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x))))))))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod_binary64`
27×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
12×	`cbrt-div_binary64`
11×	`add-cube-cbrt_binary64`

Counts

3 → 78

Calls

3 calls:

9.0ms

(*.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x))))

0.0ms

(fma.f64 1 (/.f64 x (-.f64 x (tan.f64 x))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x)))) (/.f64 1 (*.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x))))))))

0.0ms

(fma.f64 (neg.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x))))) (/.f64 1 (*.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x))))) (*.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x)))) (/.f64 1 (*.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x)))))))

simplify110.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

609×	`associate-/l*_binary64`
527×	`fma-def_binary64`
281×	`cancel-sign-sub-inv_binary64`
156×	`unswap-sqr_binary64`
129×	`associate-r_binary64`

Counts

114 → 159

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	254	4234
1	620	3475
2	2021	2672
3	4925	2672

prune1.1s (5.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	768	1	769
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	768	5	773

Error

0.0b

Counts

773 → 5

Alt Table

Status	Error	Program
✓	30.2b	(+.f64 (fma.f64 1 (/.f64 x (-.f64 x (tan.f64 x))) (neg.f64 (.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x)))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x)))))))) (fma.f64 (neg.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x))))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x))))) (.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x)))) (/.f64 1 (*.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x))))))))
	32.6b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
✓	30.1b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
	46.9b	(/.f64 (/.f64 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2)) (+.f64 x (sin.f64 x))) (-.f64 x (tan.f64 x)))
▶	30.2b	(+.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))) (cbrt.f64 (-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))))) (cbrt.f64 (-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))))) (fma.f64 (neg.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x))))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x))))) (.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x)))) (/.f64 1 (*.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x))))))))

Compiler

Compiled 67335 to 14805 computations (78% saved)

localize51.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x))))
	1.4b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
	1.6b	(-.f64 x (tan.f64 x))
	32.8b	(fma.f64 (neg.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x))))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x))))) (.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x)))) (/.f64 1 (*.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x)))))))

prune3.1s (16.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	2126	1	2127
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	2127	5	2132

Error

0.0b

Counts

2132 → 5

Alt Table

Status	Error	Program
✓	30.2b	(+.f64 (fma.f64 1 (/.f64 x (-.f64 x (tan.f64 x))) (neg.f64 (.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x)))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x)))))))) (fma.f64 (neg.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x))))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x))))) (.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x)))) (/.f64 1 (*.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x))))))))
	32.6b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
✓	30.1b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
	30.2b	(+.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))) (cbrt.f64 (+.f64 (fma.f64 1 (/.f64 x (-.f64 x (tan.f64 x))) (neg.f64 (.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x)))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x)))))))) (fma.f64 (neg.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x))))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x))))) (.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x)))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x)))))))))) (cbrt.f64 (-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))))) (fma.f64 (neg.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x))))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x))))) (.f64 (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x)))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x))))))))
	46.9b	(/.f64 (/.f64 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2)) (+.f64 x (sin.f64 x))) (-.f64 x (tan.f64 x)))

Compiler

Compiled 273913 to 33762 computations (87.7% saved)

regimes1.5s (8.1%)

Accuracy

Total 0.0b remaining (54.4%)

Threshold costs 0.0b (54.4%)

Counts

341 → 3

Compiler

Compiled 28084 to 11052 computations (60.6% saved)

bsearch70.0ms (0.4%)

Steps

Iters	Range		Point
6	0.036331182474937634	0.20982857141386116	0.09493097848297538
9	-0.17251299407322018	-4.4400330144481026e-7	-0.09789578775807517

Compiler

Compiled 2 to 1 computations (50% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`+-commutative_binary64`
14×	`*-commutative_binary64`
12×	`sub-neg_binary64`
9×	`neg-sub0_binary64`
9×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	52	348
1	86	346
2	113	346
3	127	346
4	132	346
5	129	346

end186.0ms (1%)

Compiler: Compiled 716 to 218 computations (69.6% saved)

Details

analyze1.8s (9.8%)

sample8.7s (46.3%)

simplify94.0ms (0.5%)

prune2.0ms (0%)

localize7.0ms (0%)

series21.0ms (0.1%)

rewrite21.0ms (0.1%)

simplify139.0ms (0.7%)

prune122.0ms (0.6%)

localize10.0ms (0.1%)

series26.0ms (0.1%)

rewrite208.0ms (1.1%)

simplify818.0ms (4.4%)

prune471.0ms (2.5%)

localize19.0ms (0.1%)

series119.0ms (0.6%)

rewrite16.0ms (0.1%)

simplify110.0ms (0.6%)

prune1.1s (5.7%)

localize51.0ms (0.3%)

prune3.1s (16.6%)

regimes1.5s (8.1%)

bsearch70.0ms (0.4%)

simplify9.0ms (0.1%)

end186.0ms (1%)

Profiling