Details

analyze72.0ms (0.8%)

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 36 to 30 computations (16.7% saved)

sample313.0ms (3.6%)

Algorithm

1×

intervals

Results

31.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 59 to 51 computations (13.6% saved)

simplify194.0ms (2.2%)

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

prune3.0ms (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)
✓	0.3b	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))

series267.0ms (3%)

Counts

4 → 52

Calls

4 calls:

161.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
78.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
23.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
4.0ms	(.f64 (.f64 2 (PI.f64)) u2)

rewrite15.0ms (0.2%)

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:

5.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
4.0ms	(.f64 (.f64 2 (PI.f64)) u2)
2.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)

simplify111.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

621×	`unswap-sqr_binary64`
393×	`cancel-sign-sub-inv_binary64`
381×	`*-commutative_binary64`
263×	`fma-neg_binary64`
249×	`sub-neg_binary64`

Counts

116 → 104

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	161	2057
1	326	1932
2	949	1852
3	1807	1800
4	3478	1800
5	4916	1800
6	4917	1800

prune132.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	95	9	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	9	105

Error

Counts

105 → 9

Alt Table

Status	Error	Program
	0.6b	(.f64 (sqrt.f64 (fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)) (sqrt.f64 (fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)))
	0.7b	(fma.f64 (.f64 1/6 (exp.f64 (log.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	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))
	0.4b	(fma.f64 (exp.f64 (log.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.7b	(fma.f64 (exp.f64 (+.f64 (log.f64 1/6) (log.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.6b	(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)
	0.6b	(expm1.f64 (log1p.f64 (fma.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 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))) (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)

Compiler

Compiled 2619 to 2000 computations (23.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series76.0ms (0.9%)

Counts

3 → 32

Calls

3 calls:

29.0ms	(.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))
24.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))
23.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`sqrt-prod_binary64`
24×	`add-sqr-sqrt_binary64`
18×	`associate-l_binary64`
17×	`pow1_binary64`
13×	`*-un-lft-identity_binary64`

Counts

3 → 86

Calls

3 calls:

7.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))
6.0ms	(.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))
4.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))

simplify118.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

502×	`associate-l_binary64`
460×	`neg-sub0_binary64`
445×	`neg-mul-1_binary64`
380×	`associate-r_binary64`
355×	`distribute-rgt-neg-in_binary64`

Counts

118 → 119

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	113	1620
1	194	1566
2	496	1566
3	1396	1566
4	2549	1566
5	4114	1566
6	4381	1566
7	4851	1566

prune159.0ms (1.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	148	8	156

Error

Counts

156 → 8

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))
▶	0.4b	(fma.f64 (exp.f64 (log.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.7b	(fma.f64 (exp.f64 (+.f64 (log.f64 1/6) (log.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.5b	(fma.f64 (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.6b	(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)
	0.6b	(expm1.f64 (log1p.f64 (fma.f64 (.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	(.f64 (sqrt.f64 (fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)) (sqrt.f64 (fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)))

Compiler

Compiled 3662 to 2447 computations (33.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series408.0ms (4.7%)

Counts

2 → 20

Calls

2 calls:

383.0ms	(log.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))
25.0ms	(exp.f64 (log.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`pow1_binary64`
5×	`add-exp-log_binary64`
5×	`exp-prod_binary64`
4×	`log-pow_binary64`
3×	`*-un-lft-identity_binary64`

Counts

2 → 30

Calls

2 calls:

5.0ms	(log.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))
4.0ms	(exp.f64 (log.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))))

simplify151.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

833×	`fma-neg_binary64`
439×	`neg-sub0_binary64`
412×	`neg-mul-1_binary64`
295×	`distribute-rgt-neg-out_binary64`
294×	`distribute-lft-neg-out_binary64`

Counts

50 → 41

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	761
1	79	711
2	160	676
3	343	655
4	632	655
5	1886	655
6	2633	655
7	4077	655
8	4848	655
9	4951	655
10	4998	655
11	5000	655
12	4778	655

prune202.0ms (2.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	98	7	105

Error

Counts

105 → 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))
▶	0.5b	(fma.f64 (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.6b	(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)
	0.6b	(expm1.f64 (log1p.f64 (fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)))
	0.9b	(fma.f64 (exp.f64 (expm1.f64 (log1p.f64 (log.f64 (.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	(.f64 (sqrt.f64 (fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)) (sqrt.f64 (fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)))

Compiler

Compiled 2508 to 1978 computations (21.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series66.0ms (0.8%)

Counts

2 → 24

Calls

2 calls:

35.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))))
31.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`pow1_binary64`
19×	`pow-prod-down_binary64`
16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
13×	`add-sqr-sqrt_binary64`

Counts

2 → 57

Calls

2 calls:

22.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))))
8.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))

simplify146.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

766×	`fma-def_binary64`
638×	`neg-mul-1_binary64`
637×	`neg-sub0_binary64`
489×	`distribute-rgt-neg-out_binary64`
485×	`distribute-lft-neg-out_binary64`

Counts

81 → 91

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	89	1429
1	204	1341
2	717	1341
3	1401	1321
4	3165	1321
5	4785	1321
6	4899	1321

prune199.0ms (2.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	179	6	185

Error

Counts

185 → 6

Alt Table

Status	Error	Program
	0.3b	(fma.f64 (sqrt.f64 (.f64 1/6 (.f64 1/6 (.f64 (neg.f64 (log.f64 u1)) 2)))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.9b	(fma.f64 (exp.f64 (expm1.f64 (log1p.f64 (log.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
✓	0.5b	(fma.f64 (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.6b	(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)
	0.5b	(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	(.f64 (sqrt.f64 (fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)) (sqrt.f64 (fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)))

Compiler

Compiled 4779 to 3447 computations (27.9% saved)

regimes4.2s (47.6%)

Accuracy

Total 0.2b remaining (88.4%)

Threshold costs 0.2b (88.4%)

Counts

284 → 1

Compiler

Compiled 68123 to 59537 computations (12.6% saved)

simplify7.0ms (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)

sample1.8s (20.9%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
278.0ms	8000×	pre	128	true

Compiler

Compiled 212 to 182 computations (14.2% saved)

Details

analyze72.0ms (0.8%)

sample313.0ms (3.6%)

simplify194.0ms (2.2%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series267.0ms (3%)

rewrite15.0ms (0.2%)

simplify111.0ms (1.3%)

prune132.0ms (1.5%)

localize14.0ms (0.2%)

series76.0ms (0.9%)

rewrite21.0ms (0.2%)

simplify118.0ms (1.4%)

prune159.0ms (1.8%)

localize14.0ms (0.2%)

series408.0ms (4.7%)

rewrite10.0ms (0.1%)

simplify151.0ms (1.7%)

prune202.0ms (2.3%)

localize15.0ms (0.2%)

series66.0ms (0.8%)

rewrite34.0ms (0.4%)

simplify146.0ms (1.7%)

prune199.0ms (2.3%)

regimes4.2s (47.6%)

simplify7.0ms (0.1%)

end1.0ms (0%)

sample1.8s (20.9%)

Profiling