Details

analyze140.0ms (1.8%)

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)

sample219.0ms (2.9%)

Algorithm

1×

intervals

Results

42.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 59 to 51 computations (13.6% saved)

simplify121.0ms (1.6%)

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

0.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.5b	(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)

localize10.0ms (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)
✓	0.5b	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))

series670.0ms (8.9%)

Counts

4 → 52

Calls

4 calls:

340.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
297.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
29.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
4.0ms	(.f64 (.f64 2 (PI.f64)) u2)

rewrite14.0ms (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:

4.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
4.0ms	(.f64 (.f64 2 (PI.f64)) u2)
3.0ms	(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)

simplify106.0ms (1.4%)

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

prune115.0ms (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

0.0b

Counts

105 → 9

Alt Table

Status	Error	Program
	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)
▶	0.4b	(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)
	0.8b	(exp.f64 (log.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)
	1.2b	(fma.f64 (.f64 (.f64 1/6 (.f64 (cbrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cbrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cbrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.4b	(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)
	0.9b	(.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)))
	0.6b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) 3)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.5b	(log1p.f64 (expm1.f64 (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))) 1/2)))

Compiler

Compiled 2647 to 2020 computations (23.7% saved)

localize12.0ms (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)
✓	0.5b	(.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))
✓	0.5b	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))

series73.0ms (1%)

Counts

3 → 32

Calls

3 calls:

29.0ms	(.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))
23.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))
20.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))

rewrite20.0ms (0.3%)

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)))
3.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))

simplify113.0ms (1.5%)

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

prune162.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	144	3	147
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	148	8	156

Error

Counts

156 → 8

Alt Table

Status	Error	Program
▶	0.4b	(fma.f64 (.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)) 1/6) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.4b	(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)
	0.4b	(fma.f64 (.f64 (.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1)))) (sqrt.f64 2)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.9b	(.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)))
	0.8b	(exp.f64 (log.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	(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)
	0.4b	(fma.f64 (.f64 1/6 (.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)

Compiler

Compiled 3672 to 2457 computations (33.1% saved)

localize12.0ms (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)
✓	0.5b	(.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)) 1/6)
	0.5b	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))

series27.0ms (0.4%)

Counts

1 → 12

Calls

1 calls:

27.0ms

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

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
3×	`associate-r_binary64`
3×	`cbrt-unprod_binary64`

Counts

1 → 20

Calls

1 calls:

7.0ms

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

simplify78.0ms (1%)

Algorithm

1×	egg-herbie

Rules

591×	`sub-neg_binary64`
570×	`associate-l_binary64`
389×	`associate-r_binary64`
385×	`*-commutative_binary64`
367×	`neg-sub0_binary64`

Counts

32 → 33

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	62	540
1	120	510
2	403	510
3	1274	510
4	2332	510
5	3542	510
6	4637	510
7	5280	510

prune157.0ms (2.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	149	6	155

Error

Counts

155 → 6

Alt Table

Status	Error	Program
	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)
	0.4b	(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)
	0.4b	(fma.f64 (.f64 (.f64 1/6 (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)
	0.4b	(fma.f64 (.f64 1/6 (.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
▶	0.3b	(fma.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) 1/6)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)

Compiler

Compiled 3564 to 2365 computations (33.6% saved)

localize12.0ms (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 (sqrt.f64 2) 1/6)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.1b	(sqrt.f64 (neg.f64 (log.f64 u1)))
✓	0.2b	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) 1/6))
	0.3b	(.f64 (.f64 2 (PI.f64)) u2)

series199.0ms (2.6%)

Counts

2 → 36

Calls

2 calls:

173.0ms	(fma.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) 1/6)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
26.0ms	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) 1/6))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`associate-l_binary64`
12×	`sqrt-prod_binary64`
9×	`pow1_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`

Counts

2 → 42

Calls

2 calls:

7.0ms	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) 1/6))
0.0ms	(fma.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) 1/6)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)

simplify187.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

855×	`fma-def_binary64`
436×	`cancel-sign-sub-inv_binary64`
365×	`*-commutative_binary64`
264×	`fma-neg_binary64`
262×	`unsub-neg_binary64`

Counts

78 → 79

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	1990
1	304	1872
2	884	1826
3	1818	1792
4	4606	1792
5	5052	1792

prune149.0ms (2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	134	6	140

Error

Counts

140 → 6

Alt Table

Status	Error	Program
	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)
	0.4b	(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)
	0.4b	(fma.f64 (.f64 (.f64 1/6 (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)
	0.4b	(fma.f64 (.f64 1/6 (.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
✓	0.3b	(fma.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) 1/6)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)

Compiler

Compiled 3310 to 2145 computations (35.2% saved)

regimes3.3s (43.2%)

Accuracy

Total 0.2b remaining (89.9%)

Threshold costs 0.2b (89.9%)

Counts

237 → 1

Compiler

Compiled 55147 to 47386 computations (14.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	28
1	25	28
2	27	28
3	28	28
4	28	28

end1.0ms (0%)

Compiler: Compiled 19 to 17 computations (10.5% saved)

sample1.7s (22.2%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
233.0ms	8000×	pre	128	true

Compiler

Compiled 203 to 177 computations (12.8% saved)

Details

analyze140.0ms (1.8%)

sample219.0ms (2.9%)

simplify121.0ms (1.6%)

prune3.0ms (0%)

localize10.0ms (0.1%)

series670.0ms (8.9%)

rewrite14.0ms (0.2%)

simplify106.0ms (1.4%)

prune115.0ms (1.5%)

localize12.0ms (0.2%)

series73.0ms (1%)

rewrite20.0ms (0.3%)

simplify113.0ms (1.5%)

prune162.0ms (2.1%)

localize12.0ms (0.2%)

series27.0ms (0.4%)

rewrite8.0ms (0.1%)

simplify78.0ms (1%)

prune157.0ms (2.1%)

localize12.0ms (0.2%)

series199.0ms (2.6%)

rewrite9.0ms (0.1%)

simplify187.0ms (2.5%)

prune149.0ms (2%)

regimes3.3s (43.2%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.7s (22.2%)

Profiling