Details

analyze108.0ms (1.7%)

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 36 to 30 computations (16.7% saved)

sample2.0s (31.4%)

Results

1.8s

8256×

body

128

valid

Compiler

Compiled 93 to 79 computations (15.1% saved)

simplify125.0ms (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 (0.1%)

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)

localize11.0ms (0.2%)

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

series633.0ms (10.2%)

Counts

4 → 52

Calls

4 calls:

249.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
204.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
177.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
3.0ms	(.f64 (.f64 2 (PI.f64)) u2)

rewrite13.0ms (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)

simplify106.0ms (1.7%)

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

prune120.0ms (1.9%)

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
	0.5b	(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)
	0.5b	(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	(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 (expm1.f64 (log1p.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.3b	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)
	0.8b	(fma.f64 (.f64 1/6 (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.6b	(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)
	0.5b	(fma.f64 (.f64 1/6 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 3))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
▶	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)

Compiler

Compiled 2591 to 1980 computations (23.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series176.0ms (2.8%)

Counts

2 → 24

Calls

2 calls:

151.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (sqrt.f64 (*.f64 -2 (log.f64 u1)))))
26.0ms	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 -2 (log.f64 u1))))

rewrite16.0ms (0.3%)

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))))

simplify81.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

572×	`fma-neg_binary64`
311×	`*-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

prune143.0ms (2.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	130	3	133
Fresh	6	2	8
Picked	0	1	1
Done	0	0	0
Total	136	6	142

Error

0.0b

Counts

142 → 6

Alt Table

Status	Error	Program
	0.7b	(fma.f64 (.f64 (sqrt.f64 1/6) (expm1.f64 (log1p.f64 (.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 (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 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)
▶	0.2b	(fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (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 (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)

Compiler

Compiled 3341 to 2680 computations (19.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
✓	0.1b	(sqrt.f64 (*.f64 (log.f64 u1) -1/18))
	0.2b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(*.f64 (log.f64 u1) -1/18)

series179.0ms (2.9%)

Counts

3 → 48

Calls

3 calls:

132.0ms	(fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
25.0ms	(*.f64 (log.f64 u1) -1/18)
21.0ms	(sqrt.f64 (*.f64 (log.f64 u1) -1/18))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 44

Calls

3 calls:

3.0ms	(*.f64 (log.f64 u1) -1/18)
2.0ms	(sqrt.f64 (*.f64 (log.f64 u1) -1/18))
0.0ms	(fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)

simplify120.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

416×	`fma-neg_binary64`
390×	`associate-l_binary64`
350×	`associate-r_binary64`
312×	`distribute-rgt-neg-in_binary64`
302×	`distribute-lft-neg-in_binary64`

Counts

92 → 85

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	124	1434
1	230	1354
2	607	1326
3	1966	1314
4	4165	1314
5	4837	1308
6	4995	1308
7	4891	1308

prune116.0ms (1.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	113	6	119

Error

0.0b

Counts

119 → 6

Alt Table

Status	Error	Program
	0.7b	(fma.f64 (.f64 (sqrt.f64 1/6) (expm1.f64 (log1p.f64 (.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 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)
▶	0.2b	(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
✓	0.2b	(fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (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 (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)

Compiler

Compiled 2322 to 1670 computations (28.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2))))
✓	0.1b	(sqrt.f64 (neg.f64 (log.f64 u1)))
✓	0.2b	(*.f64 (PI.f64) u2)
✓	0.2b	(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2)))) 1/2)

series161.0ms (2.6%)

Counts

4 → 36

Calls

4 calls:

132.0ms	(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
21.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
5.0ms	(.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2))))
2.0ms	(*.f64 (PI.f64) u2)

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
16×	`sqrt-prod_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
11×	`pow1_binary64`

Counts

4 → 78

Calls

4 calls:

6.0ms	(.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2))))
3.0ms	(*.f64 (PI.f64) u2)
2.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
0.0ms	(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2)))) 1/2)

simplify125.0ms (2%)

Algorithm

1×	egg-herbie

Rules

596×	`fma-neg_binary64`
403×	`*-commutative_binary64`
397×	`distribute-rgt-neg-in_binary64`
360×	`distribute-lft-neg-in_binary64`
321×	`fma-def_binary64`

Counts

114 → 132

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	197	2246
1	373	2103
2	1119	2049
3	2382	2011
4	4819	2011
5	4946	2011
6	4978	2011

prune131.0ms (2.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	130	2	132
Fresh	3	0	3
Picked	0	1	1
Done	0	2	2
Total	133	5	138

Error

Counts

138 → 5

Alt Table

Status	Error	Program
	1.2b	(fma.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (neg.f64 (log.f64 u1)))) (cbrt.f64 (sqrt.f64 (neg.f64 (log.f64 u1))))) (cbrt.f64 (sqrt.f64 (neg.f64 (log.f64 u1))))) (.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
✓	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)
✓	0.2b	(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
✓	0.2b	(fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.6b	(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (exp.f64 (+.f64 (log.f64 (sqrt.f64 1/18)) (log.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2)))))) 1/2)

Compiler

Compiled 3003 to 1819 computations (39.4% saved)

regimes1.7s (28.1%)

Accuracy

Total 0.2b remaining (94.9%)

Threshold costs 0.2b (94.9%)

Counts

143 → 1

Compiler

Compiled 32896 to 29109 computations (11.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	21
1	16	21
2	16	21

end96.0ms (1.5%)

Compiler: Compiled 133 to 109 computations (18% saved)

Details

analyze108.0ms (1.7%)

sample2.0s (31.4%)

simplify125.0ms (2%)

prune3.0ms (0.1%)

localize11.0ms (0.2%)

series633.0ms (10.2%)

rewrite13.0ms (0.2%)

simplify106.0ms (1.7%)

prune120.0ms (1.9%)

localize13.0ms (0.2%)

series176.0ms (2.8%)

rewrite16.0ms (0.3%)

simplify81.0ms (1.3%)

prune143.0ms (2.3%)

localize10.0ms (0.2%)

series179.0ms (2.9%)

rewrite6.0ms (0.1%)

simplify120.0ms (1.9%)

prune116.0ms (1.9%)

localize13.0ms (0.2%)

series161.0ms (2.6%)

rewrite13.0ms (0.2%)

simplify125.0ms (2%)

prune131.0ms (2.1%)

regimes1.7s (28.1%)

simplify2.0ms (0%)

end96.0ms (1.5%)

Profiling