Details

analyze435.0ms (7.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
3.1%	3.1%	93.8%	2
3.1%	3.1%	93.8%	3
4.7%	1.6%	93.8%	4
4.7%	1.6%	93.8%	5
5.5%	0.8%	93.8%	6
5.5%	0.8%	93.8%	7
5.8%	0.4%	93.8%	8
5.8%	0.4%	93.8%	9
6%	0.2%	93.8%	10
6%	0.2%	93.8%	11
6.1%	0.1%	93.8%	12
6.1%	0.1%	93.8%	13
6.2%	0%	93.8%	14

Compiler

Compiled 30 to 26 computations (13.3% saved)

sample56.0ms (0.9%)

Algorithm

1×

intervals

Results

33.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 53 to 47 computations (11.3% saved)

simplify140.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

909×	`cube-prod_binary64`
818×	`unswap-sqr_binary64`
698×	`fabs-mul_binary64`
671×	`sqr-pow_binary64`
541×	`cube-mult_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	26
1	37	26
2	60	26
3	95	26
4	193	26
5	510	26
6	613	26
7	798	26
8	1384	26
9	1423	26
10	1454	26
11	1518	26
12	1524	26
13	1796	26
14	2019	26
15	2440	26
16	3048	26
17	3546	26
18	3979	26
19	4387	26
20	4696	26
21	4801	26

prune9.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.4b	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))

Compiler

Compiled 54 to 48 computations (11.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
0.1b	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.3b	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))

rewrite112.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

14×	`pow1_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64` `-un-lft-identity_binary64` `associate-r*_binary64`
6×	`add-log-exp_binary64`

Counts

4 → 59

Calls

4 calls:

8.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
5.0ms	(.f64 (.f64 2 PI.f64) u2)
3.0ms	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
2.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))

Compiler

Compiled 1319 to 1005 computations (23.8% saved)

series129.0ms (2.1%)

Error

0.2b

Counts

4 → 18

Calls

4 calls:

59.0ms	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
28.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
15.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
9.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 954 to 816 computations (14.5% saved)

simplify92.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

526×	`*-commutative_binary64`
408×	`sub-neg_binary64`
308×	`distribute-rgt-neg-in_binary64`
289×	`distribute-lft-neg-in_binary64`
249×	`cancel-sign-sub-inv_binary64`

Counts

77 → 42

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	168	1474
1	402	1350
2	1247	1310
3	2405	1290
4	4721	1290
5	5121	1290

prune52.0ms (0.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	35	7	42
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	36	7	43

Error

0.0b

Counts

43 → 7

Alt Table

Status	Error	Program
▶	0.3b	(+.f64 1/2 (.f64 (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))) (cos.f64 (.f64 (.f64 2 PI.f64) u2))))
	0.4b	(+.f64 1/2 (.f64 (.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
	0.6b	(+.f64 1/2 (.f64 (cbrt.f64 (pow.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) 3)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
	0.4b	(/.f64 (-.f64 1/4 (.f64 (.f64 (log.f64 u1) -1/18) (.f64 (cos.f64 (.f64 2 (.f64 u2 PI.f64))) (cos.f64 (.f64 2 (.f64 u2 PI.f64)))))) (-.f64 1/2 (.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 PI.f64)))))))
	0.5b	(exp.f64 (log.f64 (+.f64 (.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (*.f64 u2 PI.f64))))) 1/2)))
	0.5b	(cbrt.f64 (pow.f64 (+.f64 (.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (*.f64 u2 PI.f64))))) 1/2) 3))
	0.7b	(.f64 (sqrt.f64 (+.f64 (.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 PI.f64))))) 1/2)) (sqrt.f64 (+.f64 (.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (*.f64 u2 PI.f64))))) 1/2)))

Compiler

Compiled 1004 to 774 computations (22.9% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.2b	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.3b	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))

rewrite159.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

31×	`pow1_binary64`
19×	`pow-prod-down_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`sqrt-pow1_binary64`

Counts

4 → 81

Calls

4 calls:

11.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
8.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
5.0ms	(.f64 (.f64 2 PI.f64) u2)
2.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))

Compiler

Compiled 1801 to 1453 computations (19.3% saved)

series81.0ms (1.3%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

21.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
21.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
18.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
9.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 748 to 675 computations (9.8% saved)

simplify136.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

374×	`*-commutative_binary64`
343×	`associate-+l+_binary64`
275×	`distribute-rgt-in_binary64`
216×	`distribute-lft-in_binary64`
213×	`sub-neg_binary64`

Counts

93 → 58

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	128	1334
1	261	1130
2	767	1130
3	1071	1122
4	1509	1122
5	3347	1122
6	4417	1122
7	4912	1122
8	4995	1122

prune73.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	55	3	58
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	58	7	65

Error

Counts

65 → 7

Alt Table

Status	Error	Program
✓	0.3b	(+.f64 1/2 (.f64 (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))) (cos.f64 (.f64 (.f64 2 PI.f64) u2))))
	0.4b	(+.f64 1/2 (.f64 (.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
	0.6b	(+.f64 1/2 (.f64 (.f64 (sqrt.f64 1/6) (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)) 3))) (cos.f64 (.f64 (.f64 2 PI.f64) u2))))
	0.4b	(/.f64 (-.f64 1/4 (.f64 (.f64 (log.f64 u1) -1/18) (.f64 (cos.f64 (.f64 2 (.f64 u2 PI.f64))) (cos.f64 (.f64 2 (.f64 u2 PI.f64)))))) (-.f64 1/2 (.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 PI.f64)))))))
▶	0.4b	(+.f64 1/2 (.f64 (log.f64 (exp.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
	0.5b	(cbrt.f64 (pow.f64 (+.f64 (.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (*.f64 u2 PI.f64))))) 1/2) 3))
	0.8b	(+.f64 1/2 (.f64 (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 1/6) (sqrt.f64 2)))) (cos.f64 (.f64 (.f64 2 PI.f64) u2))))

Compiler

Compiled 1168 to 945 computations (19.1% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.3b	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6)
0.9b	(exp.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6))

rewrite101.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

14×	`pow1_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64`

Counts

4 → 58

Calls

4 calls:

6.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6)
5.0ms	(.f64 (.f64 2 PI.f64) u2)
2.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
2.0ms	(exp.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6))

Compiler

Compiled 1239 to 967 computations (22% saved)

series74.0ms (1.2%)

Error

Counts

4 → 12

Calls

4 calls:

20.0ms	(exp.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6))
18.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6)
16.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
11.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 672 to 602 computations (10.4% saved)

simplify120.0ms (2%)

Algorithm

1×	egg-herbie

Rules

399×	`distribute-rgt-in_binary64`
342×	`distribute-lft-in_binary64`
307×	`associate-+l+_binary64`
306×	`*-commutative_binary64`
298×	`log-prod_binary64`

Counts

70 → 40

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	110	877
1	206	789
2	624	786
3	937	781
4	1398	781
5	3528	781
6	4481	781
7	4933	781
8	4887	781

prune52.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	39	1	40
Fresh	1	4	5
Picked	0	1	1
Done	1	0	1
Total	41	6	47

Error

Counts

47 → 6

Alt Table

Status	Error	Program
	0.4b	(+.f64 1/2 (.f64 (.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
▶	0.3b	(+.f64 1/2 (.f64 (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))))))) (cos.f64 (.f64 (.f64 2 PI.f64) u2))))
	0.6b	(+.f64 1/2 (.f64 (.f64 (sqrt.f64 1/6) (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)) 3))) (cos.f64 (.f64 (.f64 2 PI.f64) u2))))
	0.4b	(/.f64 (-.f64 1/4 (.f64 (.f64 (log.f64 u1) -1/18) (.f64 (cos.f64 (.f64 2 (.f64 u2 PI.f64))) (cos.f64 (.f64 2 (.f64 u2 PI.f64)))))) (-.f64 1/2 (.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 PI.f64)))))))
✓	0.4b	(+.f64 1/2 (.f64 (log.f64 (exp.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
	0.8b	(+.f64 1/2 (.f64 (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 1/6) (sqrt.f64 2)))) (cos.f64 (.f64 (.f64 2 PI.f64) u2))))

Compiler

Compiled 900 to 721 computations (19.9% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1)))))
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.6b	(cbrt.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))))))
2.5b	(exp.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))))

rewrite109.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

11×	`add-sqr-sqrt_binary64`
10×	`pow1_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`exp-prod_binary64` `sqrt-prod_binary64`
6×	`cbrt-prod_binary64`

Counts

4 → 61

Calls

4 calls:

5.0ms	(.f64 (.f64 2 PI.f64) u2)
3.0ms	(cbrt.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))))))
2.0ms	(exp.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))))
2.0ms	(sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1)))))

Compiler

Compiled 1383 to 1081 computations (21.8% saved)

series87.0ms (1.4%)

Error

Counts

4 → 12

Calls

4 calls:

29.0ms	(cbrt.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))))))
21.0ms	(sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1)))))
19.0ms	(exp.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))))
9.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 672 to 602 computations (10.4% saved)

simplify127.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

279×	`sqr-pow_binary64`
263×	`*-commutative_binary64`
244×	`unsub-neg_binary64` `sub-neg_binary64`
212×	`associate-*l/_binary64`
205×	`associate--r+_binary64`

Counts

73 → 39

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	112	1058
1	194	988
2	535	988
3	833	952
4	1391	943
5	2976	935
6	4145	935
7	4850	935
8	4829	935

prune57.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	38	1	39
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	40	5	45

Error

Counts

45 → 5

Alt Table

Status	Error	Program
	0.4b	(+.f64 1/2 (.f64 (.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
	0.4b	(/.f64 (-.f64 1/4 (.f64 (.f64 (log.f64 u1) -1/18) (.f64 (cos.f64 (.f64 2 (.f64 u2 PI.f64))) (cos.f64 (.f64 2 (.f64 u2 PI.f64)))))) (-.f64 1/2 (.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 PI.f64)))))))
	0.4b	(+.f64 1/2 (.f64 (log.f64 (exp.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
	0.3b	(+.f64 1/2 (.f64 (log.f64 (cbrt.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))) 3))))) (cos.f64 (.f64 (.f64 2 PI.f64) u2))))
	0.8b	(+.f64 1/2 (.f64 (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 1/6) (sqrt.f64 2)))) (cos.f64 (.f64 (.f64 2 PI.f64) u2))))

Compiler

Compiled 771 to 610 computations (20.9% saved)

regimes2.2s (36.8%)

Accuracy

Total 0.2b remaining (90.9%)

Threshold costs 0.2b (90.9%)

Compiler

Compiled 34312 to 30262 computations (11.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	26
1	23	26
2	23	26

end1.0ms (0%)

Compiler: Compiled 18 to 16 computations (11.1% saved)

sample1.5s (25.5%)

Algorithm

1×

intervals

Results

809.0ms	8000×	body	128	valid
204.0ms	8000×	pre	128	true

Compiler

Compiled 176 to 152 computations (13.6% saved)

Details

analyze435.0ms (7.2%)

sample56.0ms (0.9%)

simplify140.0ms (2.3%)

prune9.0ms (0.1%)

localize14.0ms (0.2%)

rewrite112.0ms (1.9%)

series129.0ms (2.1%)

simplify92.0ms (1.5%)

prune52.0ms (0.9%)

localize18.0ms (0.3%)

rewrite159.0ms (2.6%)

series81.0ms (1.3%)

simplify136.0ms (2.3%)

prune73.0ms (1.2%)

localize19.0ms (0.3%)

rewrite101.0ms (1.7%)

series74.0ms (1.2%)

simplify120.0ms (2%)

prune52.0ms (0.9%)

localize17.0ms (0.3%)

rewrite109.0ms (1.8%)

series87.0ms (1.4%)

simplify127.0ms (2.1%)

prune57.0ms (1%)

regimes2.2s (36.8%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.5s (25.5%)

Profiling