Details

analyze4.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
6.2%	0%	93.8%	1

Compiler

Compiled 36 to 30 computations (16.7% saved)

sample3.5s (33.8%)

Results

3.2s

8256×

body

128

valid

Compiler

Compiled 93 to 79 computations (15.1% saved)

simplify236.0ms (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 → 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

0.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.4b	(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)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(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))))

series406.0ms (3.9%)

Counts

4 → 52

Calls

4 calls:

276.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
64.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
59.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
5.0ms	(.f64 (.f64 2 (PI.f64)) u2)

rewrite16.0ms (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:

6.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
5.0ms	(.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)

simplify205.0ms (2%)

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

prune271.0ms (2.6%)

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
	0.5b	(fma.f64 (.f64 1/6 (cbrt.f64 (.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 (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 (expm1.f64 (log1p.f64 (.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 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.7b	(.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 (.f64 (sqrt.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))) (sqrt.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 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))) (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.5b	(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)
	0.6b	(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)

Compiler

Compiled 2647 to 2020 computations (23.7% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series122.0ms (1.2%)

Counts

2 → 24

Calls

2 calls:

64.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (sqrt.f64 (*.f64 -2 (log.f64 u1)))))
57.0ms	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 -2 (log.f64 u1))))

rewrite161.0ms (1.6%)

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:

139.0ms	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 -2 (log.f64 u1))))
16.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (sqrt.f64 (*.f64 -2 (log.f64 u1)))))

simplify144.0ms (1.4%)

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 → 88

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

prune300.0ms (2.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	129	4	133
Fresh	5	3	8
Picked	0	1	1
Done	0	0	0
Total	134	8	142

Error

Counts

142 → 8

Alt Table

Status	Error	Program
	0.5b	(fma.f64 (expm1.f64 (log1p.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 (.f64 (sqrt.f64 1/6) (.f64 (.f64 (sqrt.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)
	0.5b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6) 3)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.5b	(fma.f64 (.f64 1/6 (cbrt.f64 (.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 (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)
	0.3b	(fma.f64 (.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 (log.f64 u1) -1/3))) (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)

Compiler

Compiled 3447 to 2770 computations (19.6% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(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)
✓	0.1b	(sqrt.f64 (neg.f64 (log.f64 u1)))
	0.3b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.3b	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2)))

series423.0ms (4.1%)

Counts

3 → 44

Calls

3 calls:

322.0ms

(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)

55.0ms

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

46.0ms

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

rewrite29.0ms (0.3%)

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:

19.0ms

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

4.0ms

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

1.0ms

(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)

simplify196.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

861×	`fma-def_binary64`
436×	`cancel-sign-sub-inv_binary64`
362×	`*-commutative_binary64`
264×	`fma-neg_binary64`
255×	`neg-mul-1_binary64`

Counts

110 → 106

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	148	2321
1	320	2199
2	899	2153
3	1827	2119
4	4597	2119
5	4990	2119

prune319.0ms (3.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	134	8	142

Error

Counts

142 → 8

Alt Table

Status	Error	Program
	0.5b	(fma.f64 (expm1.f64 (log1p.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 (.f64 (sqrt.f64 1/6) (.f64 (.f64 (sqrt.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)
	0.5b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6) 3)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.5b	(fma.f64 (.f64 1/6 (cbrt.f64 (.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 (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)
▶	0.3b	(fma.f64 (.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 (log.f64 u1) -1/3))) (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)

Compiler

Compiled 3474 to 2287 computations (34.2% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(sqrt.f64 (*.f64 (log.f64 u1) -1/3))
	0.3b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.3b	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 (log.f64 u1) -1/3)))
✓	0.4b	(*.f64 (log.f64 u1) -1/3)

series145.0ms (1.4%)

Counts

3 → 36

Calls

3 calls:

61.0ms	(sqrt.f64 (*.f64 (log.f64 u1) -1/3))
54.0ms	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 (log.f64 u1) -1/3)))
30.0ms	(*.f64 (log.f64 u1) -1/3)

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`pow1_binary64`
14×	`add-sqr-sqrt_binary64`
10×	`associate-l_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`

Counts

3 → 63

Calls

3 calls:

12.0ms	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 (log.f64 u1) -1/3)))
6.0ms	(*.f64 (log.f64 u1) -1/3)
4.0ms	(sqrt.f64 (*.f64 (log.f64 u1) -1/3))

simplify162.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

631×	`fma-def_binary64`
341×	`div-sub_binary64`
316×	`neg-mul-1_binary64`
315×	`neg-sub0_binary64`
269×	`associate-l_binary64`

Counts

99 → 103

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	98	1126
1	169	1073
2	421	1073
3	743	1073
4	1218	1073
5	2535	1073
6	4170	1073
7	4878	1073

prune421.0ms (4.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	131	8	139

Error

Counts

139 → 8

Alt Table

Status	Error	Program
	0.5b	(fma.f64 (expm1.f64 (log1p.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 (.f64 (sqrt.f64 1/6) (.f64 (.f64 (sqrt.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)
	0.5b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6) 3)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.5b	(fma.f64 (.f64 1/6 (cbrt.f64 (.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 (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)
✓	0.3b	(fma.f64 (.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 (log.f64 u1) -1/3))) (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)

Compiler

Compiled 2910 to 2228 computations (23.4% saved)

regimes2.9s (27.7%)

Accuracy

Total 0.2b remaining (91.9%)

Threshold costs 0.2b (91.9%)

Counts

126 → 1

Compiler

Compiled 28346 to 24615 computations (13.2% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	21
1	17	21
2	17	21

end290.0ms (2.8%)

Compiler: Compiled 205 to 179 computations (12.7% saved)

Details

analyze4.0ms (0%)

sample3.5s (33.8%)

simplify236.0ms (2.3%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series406.0ms (3.9%)

rewrite16.0ms (0.2%)

simplify205.0ms (2%)

prune271.0ms (2.6%)

localize28.0ms (0.3%)

series122.0ms (1.2%)

rewrite161.0ms (1.6%)

simplify144.0ms (1.4%)

prune300.0ms (2.9%)

localize27.0ms (0.3%)

series423.0ms (4.1%)

rewrite29.0ms (0.3%)

simplify196.0ms (1.9%)

prune319.0ms (3.1%)

localize25.0ms (0.2%)

series145.0ms (1.4%)

rewrite27.0ms (0.3%)

simplify162.0ms (1.6%)

prune421.0ms (4.1%)

regimes2.9s (27.7%)

simplify5.0ms (0%)

end290.0ms (2.8%)

Profiling