Details

analyze88.0ms (1.4%)

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)

sample2.3s (36%)

Results

2.2s

8256×

body

128

valid

Compiler

Compiled 93 to 79 computations (15.1% saved)

simplify223.0ms (3.4%)

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 (0.1%)

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
✓	0.1b	(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)))
✓	0.2b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))

series205.0ms (3.1%)

Counts

4 → 52

Calls

4 calls:

150.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
29.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
23.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
3.0ms	(.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 (.f64 2 (PI.f64)) u2)
5.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
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 (1.7%)

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

prune126.0ms (1.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	94	10	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	10	105

Error

0.0b

Counts

105 → 10

Alt Table

Status	Error	Program
	0.7b	(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)
	0.8b	(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)
	0.7b	(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 (expm1.f64 (log1p.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.8b	(+.f64 1/2 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (+.f64 1/6 (fma.f64 1/9 (.f64 (pow.f64 u2 4) (pow.f64 (PI.f64) 4)) (.f64 -1/3 (.f64 (.f64 u2 u2) (pow.f64 (PI.f64) 2)))))))
	0.9b	(expm1.f64 (log1p.f64 (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))) 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 (exp.f64 (log.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)

Compiler

Compiled 2655 to 2034 computations (23.4% saved)

localize12.0ms (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)
✓	0.2b	(.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))))

series62.0ms (1%)

Counts

2 → 24

Calls

2 calls:

35.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (sqrt.f64 (*.f64 -2 (log.f64 u1)))))
27.0ms	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 -2 (log.f64 u1))))

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))))

simplify86.0ms (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

prune154.0ms (2.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	131	2	133
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	135	8	143

Error

0.0b

Counts

143 → 8

Alt Table

Status	Error	Program
	0.7b	(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)
	0.3b	(fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (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)
	0.9b	(expm1.f64 (log1p.f64 (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))) 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)
	0.5b	(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)
	0.5b	(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)

Compiler

Compiled 3427 to 2754 computations (19.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (*.f64 (log.f64 u1) -1/3))
	0.2b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.2b	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 (log.f64 u1) -1/3)))
✓	0.4b	(*.f64 (log.f64 u1) -1/3)

series73.0ms (1.1%)

Counts

3 → 36

Calls

3 calls:

28.0ms	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 (log.f64 u1) -1/3)))
23.0ms	(sqrt.f64 (*.f64 (log.f64 u1) -1/3))
22.0ms	(*.f64 (log.f64 u1) -1/3)

rewrite12.0ms (0.2%)

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:

6.0ms	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 (log.f64 u1) -1/3)))
3.0ms	(*.f64 (log.f64 u1) -1/3)
2.0ms	(sqrt.f64 (*.f64 (log.f64 u1) -1/3))

simplify96.0ms (1.5%)

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: 4 (0.0ms)

Iter	Nodes	Cost
0	98	1130
1	169	1077
2	421	1077
3	743	1077
4	1218	1075
5	2535	1075
6	4170	1075
7	4878	1075

prune150.0ms (2.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	131	8	139

Error

0.0b

Counts

139 → 8

Alt Table

Status	Error	Program
	0.7b	(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)
▶	0.3b	(fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (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)
	0.9b	(expm1.f64 (log1p.f64 (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))) 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)
	0.5b	(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)
	0.5b	(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)

Compiler

Compiled 3027 to 2331 computations (23% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(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)

series188.0ms (2.9%)

Counts

3 → 48

Calls

3 calls:

144.0ms	(fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
22.0ms	(sqrt.f64 (*.f64 (log.f64 u1) -1/18))
21.0ms	(*.f64 (log.f64 u1) -1/18)

rewrite7.0ms (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)

simplify123.0ms (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

prune135.0ms (2.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	109	4	113
Fresh	4	1	5
Picked	1	0	1
Done	0	2	2
Total	114	7	121

Error

0.0b

Counts

121 → 7

Alt Table

Status	Error	Program
	0.4b	(fma.f64 (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)))) (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)
	0.6b	(cbrt.f64 (pow.f64 (fma.f64 (sqrt.f64 (.f64 -1/18 (log.f64 u1))) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2))) 1/2) 3))
	0.2b	(fma.f64 (sqrt.f64 (log.f64 (pow.f64 u1 -1/18))) (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)
	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)
	0.9b	(.f64 (sqrt.f64 (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)) (sqrt.f64 (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)))

Compiler

Compiled 2272 to 1622 computations (28.6% saved)

regimes2.1s (32.5%)

Accuracy

Total 0.3b remaining (93.9%)

Threshold costs 0.3b (93.9%)

Counts

169 → 1

Compiler

Compiled 39175 to 34053 computations (13.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	28
1	23	28
2	22	28

end133.0ms (2%)

Compiler: Compiled 192 to 166 computations (13.5% saved)

Details

analyze88.0ms (1.4%)

sample2.3s (36%)

simplify223.0ms (3.4%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

series205.0ms (3.1%)

rewrite16.0ms (0.2%)

simplify111.0ms (1.7%)

prune126.0ms (1.9%)

localize12.0ms (0.2%)

series62.0ms (1%)

rewrite16.0ms (0.2%)

simplify86.0ms (1.3%)

prune154.0ms (2.4%)

localize11.0ms (0.2%)

series73.0ms (1.1%)

rewrite12.0ms (0.2%)

simplify96.0ms (1.5%)

prune150.0ms (2.3%)

localize9.0ms (0.1%)

series188.0ms (2.9%)

rewrite7.0ms (0.1%)

simplify123.0ms (1.9%)

prune135.0ms (2.1%)

regimes2.1s (32.5%)

simplify2.0ms (0%)

end133.0ms (2%)

Profiling