Details

analyze1.0s (20.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
18.7%	81.2%	0.1%	7
25%	73.4%	1.7%	8
28.1%	68.7%	3.2%	9
31.2%	62.8%	6%	10
32.8%	60.1%	7.1%	11
34.3%	56.7%	9%	12
35.1%	55.2%	9.7%	13
35.9%	53.4%	10.7%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample59.0ms (1.2%)

Algorithm

1×

intervals

Results

22.0ms	79×	body	1024	valid
13.0ms	123×	body	128	valid
8.0ms	38×	body	512	valid
2.0ms	16×	body	256	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify16.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

27×	`cancel-sign-sub-inv_binary64`
22×	`sub-neg_binary64`
11×	`distribute-rgt-in_binary64` `associate-/l*_binary64`
10×	`neg-mul-1_binary64` `distribute-rgt-neg-in_binary64` `associate--r+_binary64`
8×	`+-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	24	14
2	45	14
3	73	14
4	102	14
5	129	14
6	136	14
7	171	14
8	162	14
9	168	14
10	165	14
11	140	14

prune9.0ms (0.2%)

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

0.1b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
	0.2b	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))

Compiler

Compiled 61 to 46 computations (24.6% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
0.1b	(/.f64 1 (sin.f64 B))
0.2b	(/.f64 x (tan.f64 B))

rewrite147.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

43×	`add-sqr-sqrt_binary64`
36×	`times-frac_binary64`
35×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`
14×	`cancel-sign-sub-inv_binary64`

Counts

3 → 94

Calls

3 calls:

14.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
5.0ms	(/.f64 x (tan.f64 B))
3.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 1508 to 610 computations (59.5% saved)

series115.0ms (2.4%)

Error

0.1b

Counts

3 → 21

Calls

3 calls:

49.0ms	(/.f64 x (tan.f64 B))
48.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
8.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 605 to 392 computations (35.2% saved)

simplify138.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

337×	`distribute-rgt-in_binary64`
314×	`associate-/l*_binary64`
284×	`distribute-lft-in_binary64`
198×	`times-frac_binary64`
196×	`associate-l_binary64`

Counts

115 → 54

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	165	1591
1	394	1550
2	1009	1550
3	2714	1544
4	4409	1544
5	4919	1544
6	4892	1544

prune40.0ms (0.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	47	7	54
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	48	8	56

Error

0.0b

Counts

56 → 8

Alt Table

Status	Error	Program
	30.8b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (tan.f64 B))))
	36.4b	(neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
	33.7b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 x (tan.f64 B)) 3)) (+.f64 (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6) (/.f64 (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))) (sin.f64 B))))
▶	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
	23.8b	(/.f64 (-.f64 (/.f64 (/.f64 1 (sin.f64 B)) (sin.f64 B)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6)) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
	11.1b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
✓	0.1b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
	49.1b	(*.f64 (+.f64 (sqrt.f64 (/.f64 x (tan.f64 B))) (/.f64 1 (sqrt.f64 (sin.f64 B)))) (-.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (sqrt.f64 (/.f64 x (tan.f64 B)))))

Compiler

Compiled 760 to 378 computations (50.3% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)

rewrite92.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
11×	`pow1_binary64`
9×	`pow1/3_binary64`

Counts

4 → 73

Calls

4 calls:

6.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

Compiler

Compiled 1421 to 438 computations (69.2% saved)

series81.0ms (1.7%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

19.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
19.0ms	(cbrt.f64 x)
19.0ms	(cbrt.f64 x)
16.0ms	(cbrt.f64 x)

Compiler

Compiled 646 to 443 computations (31.4% saved)

simplify106.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

850×	`log-prod_binary64`
525×	`unswap-sqr_binary64`
346×	`sqr-pow_binary64`
307×	`distribute-rgt-neg-in_binary64`
298×	`associate-l_binary64`

Counts

85 → 60

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	56	642
1	97	594
2	309	574
3	800	560
4	1864	436
5	2894	436
6	4605	436
7	4971	436

prune44.0ms (0.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	58	2	60
Fresh	0	6	6
Picked	0	1	1
Done	1	0	1
Total	59	9	68

Error

0.0b

Counts

68 → 9

Alt Table

Status	Error	Program
	30.8b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (tan.f64 B))))
	36.4b	(neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
	30.8b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 (sqrt.f64 x)) (sqrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
	33.7b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 x (tan.f64 B)) 3)) (+.f64 (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6) (/.f64 (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))) (sin.f64 B))))
✓	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
▶	0.8b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 4)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
	23.8b	(/.f64 (-.f64 (/.f64 (/.f64 1 (sin.f64 B)) (sin.f64 B)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6)) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
	11.1b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
	49.1b	(*.f64 (+.f64 (sqrt.f64 (/.f64 x (tan.f64 B))) (/.f64 1 (sqrt.f64 (sin.f64 B)))) (-.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (sqrt.f64 (/.f64 x (tan.f64 B)))))

Compiler

Compiled 889 to 454 computations (48.9% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.9b	(pow.f64 (cbrt.f64 (cbrt.f64 x)) 4)

rewrite83.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

18×	`cbrt-prod_binary64`
11×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
9×	`unpow-prod-down_binary64`
5×	`pow1_binary64` `add-exp-log_binary64`
4×	`pow1/3_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64`

Counts

4 → 57

Calls

4 calls:

3.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 x)) 4)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

Compiler

Compiled 1575 to 581 computations (63.1% saved)

series94.0ms (1.9%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

29.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 x)) 4)
19.0ms	(cbrt.f64 x)
17.0ms	(cbrt.f64 x)
17.0ms	(cbrt.f64 x)

Compiler

Compiled 876 to 581 computations (33.7% saved)

simplify87.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

387×	`associate-+l+_binary64`
336×	`log-prod_binary64`
325×	`associate-+r+_binary64`
300×	`distribute-rgt-in_binary64`
274×	`distribute-lft-in_binary64`

Counts

69 → 46

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	68	637
1	125	612
2	265	598
3	696	596
4	1508	503
5	4597	503
6	4837	503

prune41.0ms (0.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	46	9	55

Error

0.0b

Counts

55 → 9

Alt Table

Status	Error	Program
	30.8b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (tan.f64 B))))
	36.4b	(neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
	30.8b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 (sqrt.f64 x)) (sqrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
	33.7b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 x (tan.f64 B)) 3)) (+.f64 (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6) (/.f64 (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))) (sin.f64 B))))
✓	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
✓	0.8b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 4)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
	23.8b	(/.f64 (-.f64 (/.f64 (/.f64 1 (sin.f64 B)) (sin.f64 B)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6)) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
▶	11.1b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
	49.1b	(*.f64 (+.f64 (sqrt.f64 (/.f64 x (tan.f64 B))) (/.f64 1 (sqrt.f64 (sin.f64 B)))) (-.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (sqrt.f64 (/.f64 x (tan.f64 B)))))

Compiler

Compiled 929 to 465 computations (49.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (tan.f64 B) (*.f64 x (sin.f64 B)))
0.2b	(*.f64 x (sin.f64 B))
0.2b	(*.f64 (sin.f64 B) (tan.f64 B))
10.4b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))

rewrite89.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

14×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
8×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64` `associate-r_binary64`

Counts

4 → 74

Calls

4 calls:

8.0ms	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
5.0ms	(*.f64 (sin.f64 B) (tan.f64 B))
4.0ms	(*.f64 x (sin.f64 B))
4.0ms	(-.f64 (tan.f64 B) (*.f64 x (sin.f64 B)))

Compiler

Compiled 1462 to 256 computations (82.5% saved)

series155.0ms (3.2%)

Error

0.0b

Counts

4 → 31

Calls

4 calls:

71.0ms	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
37.0ms	(-.f64 (tan.f64 B) (*.f64 x (sin.f64 B)))
17.0ms	(*.f64 x (sin.f64 B))
15.0ms	(*.f64 (sin.f64 B) (tan.f64 B))

Compiler

Compiled 1124 to 638 computations (43.2% saved)

simplify92.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

659×	`times-frac_binary64`
407×	`div-sub_binary64`
360×	`associate-/l*_binary64`
341×	`associate-/r*_binary64`
224×	`*-commutative_binary64`

Counts

105 → 54

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	147	1789
1	369	1569
2	1220	1468
3	3746	1468
4	4965	1468

prune53.0ms (1.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	50	4	54
Fresh	4	2	6
Picked	0	1	1
Done	0	2	2
Total	54	9	63

Error

Counts

63 → 9

Alt Table

Status	Error	Program
	36.4b	(neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
	36.2b	(/.f64 (sqrt.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B)))) (/.f64 (sin.f64 B) (/.f64 (sqrt.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B)))) (tan.f64 B))))
	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
	0.8b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 4)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
	0.2b	(/.f64 (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x) (tan.f64 B))
	23.8b	(/.f64 (-.f64 (/.f64 (/.f64 1 (sin.f64 B)) (sin.f64 B)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6)) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
	11.1b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
	28.7b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) 3)) (.f64 (sin.f64 B) (tan.f64 B)))
	0.2b	(*.f64 (cos.f64 B) (/.f64 (-.f64 (/.f64 (/.f64 (sin.f64 B) (cos.f64 B)) (sin.f64 B)) x) (sin.f64 B)))

Compiler

Compiled 884 to 311 computations (64.8% saved)

regimes528.0ms (10.8%)

Accuracy

Total 0.1b remaining (88.4%)

Threshold costs 0.1b (88.4%)

Compiler

Compiled 7048 to 4182 computations (40.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`sub-neg_binary64` `+-commutative_binary64`
2×	`neg-mul-1_binary64` `neg-sub0_binary64` `*-commutative_binary64`
1×	`1-exp_binary64` `distribute-neg-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	14	14
2	20	14
3	24	14
4	27	14
5	28	14
6	26	14

end1.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

sample1.8s (35.9%)

Algorithm

1×

intervals

Results

639.0ms	2305×	body	1024	valid
299.0ms	3955×	body	128	valid
239.0ms	1154×	body	512	valid
81.0ms	578×	body	256	valid
17.0ms	184×	body	128	invalid
4.0ms	8×	body	2048	valid
0.0ms	1×	body	512	invalid

Compiler

Compiled 196 to 117 computations (40.3% saved)

Iter	Nodes	Cost
0	11	19
1	24	14
2	45	14
3	73	14
4	102	14
5	129	14
6	136	14
7	171	14
8	162	14
9	168	14
10	165	14
11	140	14

Iter	Nodes	Cost
0	11	19
1	24	14
2	45	14
3	73	14
4	102	14
5	129	14
6	136	14
7	171	14
8	162	14
9	168	14
10	165	14
11	140	14

Details

analyze1.0s (20.6%)

sample59.0ms (1.2%)

simplify16.0ms (0.3%)

prune9.0ms (0.2%)

localize10.0ms (0.2%)

rewrite147.0ms (3%)

series115.0ms (2.4%)

simplify138.0ms (2.8%)

prune40.0ms (0.8%)

localize13.0ms (0.3%)

rewrite92.0ms (1.9%)

series81.0ms (1.7%)

simplify106.0ms (2.2%)

prune44.0ms (0.9%)

localize19.0ms (0.4%)

rewrite83.0ms (1.7%)

series94.0ms (1.9%)

simplify87.0ms (1.8%)

prune41.0ms (0.8%)

localize9.0ms (0.2%)

rewrite89.0ms (1.8%)

series155.0ms (3.2%)

simplify92.0ms (1.9%)

prune53.0ms (1.1%)

regimes528.0ms (10.8%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.8s (35.9%)

Profiling

Iter	Nodes	Cost
0	11	19
1	24	14
2	45	14
3	73	14
4	102	14
5	129	14
6	136	14
7	171	14
8	162	14
9	168	14
10	165	14
11	140	14