Details

analyze272.0ms (2.7%)

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)

sample285.0ms (2.9%)

Algorithm

1×

intervals

Results

266.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 53 to 47 computations (11.3% saved)

simplify138.0ms (1.4%)

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 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	24
1	38	24
2	63	24
3	101	24
4	203	24
5	528	24
6	667	24
7	856	24
8	1442	24
9	1481	24
10	1512	24
11	1576	24
12	1582	24
13	1854	24
14	2077	24
15	2498	24
16	3106	24
17	3604	24
18	4037	24
19	4445	24
20	4754	24
21	4859	24

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)

Compiler

Compiled 70 to 60 computations (14.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
✓	0.1b	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
✓	0.3b	(.f64 (.f64 2 PI.f64) u2)
✓	0.4b	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`pow1_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`associate-r_binary64`

Counts

4 → 64

Calls

4 calls:

18.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
5.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
4.0ms	(.f64 (.f64 2 PI.f64) u2)
0.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)

series1.2s (11.7%)

Counts

4 → 52

Calls

4 calls:

482.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
469.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
209.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
11.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify123.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

765×	`fma-def_binary64`
424×	`*-commutative_binary64`
391×	`unswap-sqr_binary64`
345×	`distribute-rgt-neg-in_binary64`
327×	`cancel-sign-sub-inv_binary64`

Counts

116 → 190

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	153	2049
1	322	1936
2	915	1852
3	1718	1796
4	3438	1796
5	4798	1796
6	4916	1796

prune107.0ms (1.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	183	7	190
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	184	7	191

Error

0.0b

Counts

191 → 7

Alt Table

Status	Error	Program
	0.6b	(cbrt.f64 (pow.f64 (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 PI.f64)))) 1/2) 3))
	0.3b	(fma.f64 (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 -2 (log.f64 u1))))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)
	0.5b	(fma.f64 (cbrt.f64 (.f64 (.f64 (.f64 1/6 1/6) 1/6) (.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 (.f64 -2 (log.f64 u1)))) (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
	1.2b	(fma.f64 (.f64 (.f64 (cbrt.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))) (cbrt.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cbrt.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
▶	0.3b	(fma.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
	0.5b	(fma.f64 (.f64 (.f64 1/6 (sqrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))))) (sqrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
	0.3b	(fma.f64 (.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)

Compiler

Compiled 2456 to 1865 computations (24.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
	0.1b	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
	0.3b	(.f64 (.f64 2 PI.f64) u2)
✓	0.4b	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6)

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`associate-l_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 31

Calls

2 calls:

6.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6)
0.0ms	(fma.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)

series665.0ms (6.7%)

Counts

2 → 36

Calls

2 calls:

438.0ms	(fma.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
226.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6)

simplify185.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

459×	`fma-neg_binary64`
437×	`associate-l_binary64`
430×	`unswap-sqr_binary64`
411×	`associate-r_binary64`
331×	`distribute-rgt-neg-in_binary64`

Counts

67 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	114	1486
1	242	1417
2	653	1383
3	2134	1363
4	4128	1363
5	5132	1363

prune109.0ms (1.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	200	1	201
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	201	7	208

Error

0.0b

Counts

208 → 7

Alt Table

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

Compiler

Compiled 2616 to 1982 computations (24.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`pow1_binary64`
15×	`pow-prod-down_binary64`
12×	`associate-l_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`sqrt-pow1_binary64`

Counts

2 → 56

Calls

2 calls:

8.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (sqrt.f64 (*.f64 -2 (log.f64 u1)))))
6.0ms	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 -2 (log.f64 u1))))

series483.0ms (4.8%)

Counts

2 → 24

Calls

2 calls:

255.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (sqrt.f64 (*.f64 -2 (log.f64 u1)))))
228.0ms	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 -2 (log.f64 u1))))

simplify96.0ms (1%)

Algorithm

1×	egg-herbie

Rules

572×	`fma-neg_binary64`
313×	`*-commutative_binary64`
240×	`neg-mul-1_binary64`
239×	`associate-*r/_binary64`
218×	`associate-*l/_binary64`

Counts

80 → 145

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	1130
1	170	1084
2	470	1084
3	633	1076
4	841	1076
5	1846	1076
6	3632	1076
7	4942	1076

prune134.0ms (1.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	302	1	303
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	305	5	310

Error

Counts

310 → 5

Alt Table

Status	Error	Program
✓	0.3b	(fma.f64 (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 -2 (log.f64 u1))))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)
	0.5b	(fma.f64 (cbrt.f64 (.f64 (.f64 (.f64 1/6 1/6) 1/6) (.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 (.f64 -2 (log.f64 u1)))) (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
▶	0.3b	(fma.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
✓	0.3b	(fma.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
	0.5b	(fma.f64 (.f64 (.f64 1/6 (sqrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))))) (sqrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)

Compiler

Compiled 3250 to 2598 computations (20.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
✓	0.2b	(sqrt.f64 (neg.f64 (log.f64 u1)))
✓	0.3b	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2)))
	0.3b	(.f64 (.f64 2 PI.f64) u2)

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`sqrt-prod_binary64`
15×	`associate-l_binary64`
13×	`pow1_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`

Counts

3 → 66

Calls

3 calls:

7.0ms

(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (*.f64 1/6 (sqrt.f64 2)))

2.0ms

(sqrt.f64 (neg.f64 (log.f64 u1)))

0.0ms

(fma.f64 (*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (*.f64 1/6 (sqrt.f64 2))) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2)) 1/2)

series938.0ms (9.4%)

Counts

3 → 44

Calls

3 calls:

508.0ms

(fma.f64 (*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (*.f64 1/6 (sqrt.f64 2))) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2)) 1/2)

229.0ms

(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (*.f64 1/6 (sqrt.f64 2)))

201.0ms

(sqrt.f64 (neg.f64 (log.f64 u1)))

simplify143.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

436×	`cancel-sign-sub-inv_binary64`
362×	`*-commutative_binary64`
345×	`unswap-sqr_binary64`
303×	`sub-neg_binary64`
266×	`fma-neg_binary64`

Counts

110 → 197

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	147	2213
1	320	2127
2	893	2081
3	1839	2051
4	3900	2051
5	4921	2051

prune132.0ms (1.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	385	0	385
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	385	5	390

Error

Counts

390 → 5

Alt Table

Status	Error	Program
✓	0.3b	(fma.f64 (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 -2 (log.f64 u1))))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)
	0.5b	(fma.f64 (cbrt.f64 (.f64 (.f64 (.f64 1/6 1/6) 1/6) (.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 (.f64 -2 (log.f64 u1)))) (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
✓	0.3b	(fma.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
✓	0.3b	(fma.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
	0.5b	(fma.f64 (.f64 (.f64 1/6 (sqrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))))) (sqrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)

Compiler

Compiled 3244 to 2091 computations (35.5% saved)

regimes1.8s (18.3%)

Accuracy

Total 0.2b remaining (84%)

Threshold costs 0.2b (84%)

Compiler

Compiled 28138 to 24360 computations (13.4% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	22
1	21	22
2	19	22

end1.0ms (0%)

Compiler: Compiled 16 to 14 computations (12.5% saved)

sample3.1s (30.6%)

Algorithm

1×

intervals

Results

1.9s	8000×	body	128	valid
359.0ms	8000×	pre	128	true

Compiler

Compiled 164 to 142 computations (13.4% saved)

Details

analyze272.0ms (2.7%)

sample285.0ms (2.9%)

simplify138.0ms (1.4%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite29.0ms (0.3%)

series1.2s (11.7%)

simplify123.0ms (1.2%)

prune107.0ms (1.1%)

localize11.0ms (0.1%)

rewrite8.0ms (0.1%)

series665.0ms (6.7%)

simplify185.0ms (1.9%)

prune109.0ms (1.1%)

localize13.0ms (0.1%)

rewrite16.0ms (0.2%)

series483.0ms (4.8%)

simplify96.0ms (1%)

prune134.0ms (1.3%)

localize15.0ms (0.2%)

rewrite12.0ms (0.1%)

series938.0ms (9.4%)

simplify143.0ms (1.4%)

prune132.0ms (1.3%)

regimes1.8s (18.3%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample3.1s (30.6%)

Profiling