Details

analyze3.1s (40.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
0%	6.2%	93.8%	2
0%	6.2%	93.8%	3
0%	6.2%	93.8%	4
0%	6.2%	93.8%	5
0%	6.2%	93.8%	6
0%	6.2%	93.8%	7
0%	6.2%	93.8%	8
0%	6.2%	93.8%	9
0%	6.2%	93.8%	10
0%	6.2%	93.8%	11
0%	6.2%	93.8%	12
0%	6.2%	93.8%	13
0%	6.2%	93.8%	14

Compiler

Compiled 36 to 30 computations (16.7% saved)

sample2.3s (29.1%)

Results

2.1s

8256×

body

128

valid

Compiler

Compiled 57 to 49 computations (14% saved)

simplify126.0ms (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

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)

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)
✓	0.4b	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))

series240.0ms (3.1%)

Counts

4 → 52

Calls

4 calls:

175.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
34.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
28.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
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)

simplify115.0ms (1.5%)

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

prune141.0ms (1.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	93	11	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	11	105

Error

Counts

105 → 11

Alt Table

Status	Error	Program
	0.6b	(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)
	0.7b	(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 (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)
	0.6b	(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 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) u2)) (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) u2)))) 1/2)
	0.4b	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (log.f64 (exp.f64 (.f64 (.f64 2 (PI.f64)) u2)))) 1/2)
	0.4b	(fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))) 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 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))) (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 2675 to 2052 computations (23.3% saved)

localize15.0ms (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)
✓	0.4b	(.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))

series76.0ms (1%)

Counts

3 → 32

Calls

3 calls:

27.0ms	(.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))
25.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))
23.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))

rewrite19.0ms (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)))
2.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))

simplify122.0ms (1.6%)

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

prune166.0ms (2.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	149	9	158

Error

Counts

158 → 9

Alt Table

Status	Error	Program
	0.6b	(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)
	0.7b	(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 (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 (.f64 (.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1)))) (sqrt.f64 2)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.4b	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) u2)) (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) u2)))) 1/2)
	0.4b	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (log.f64 (exp.f64 (.f64 (.f64 2 (PI.f64)) u2)))) 1/2)
	0.4b	(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 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))) (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 3611 to 2410 computations (33.3% 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)
✓	0.4b	(*.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1))))
✓	0.4b	(.f64 (.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1)))) (sqrt.f64 2))

series52.0ms (0.7%)

Counts

2 → 20

Calls

2 calls:

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

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`associate-r_binary64`
16×	`sqrt-prod_binary64`
13×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`
9×	`*-un-lft-identity_binary64`

Counts

2 → 56

Calls

2 calls:

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

simplify82.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

553×	`associate-r_binary64`
450×	`associate-*l/_binary64`
448×	`*-commutative_binary64`
381×	`neg-mul-1_binary64`
379×	`neg-sub0_binary64`

Counts

76 → 67

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	106	1064
1	193	1020
2	506	1020
3	1226	1020
4	2474	1020
5	3766	1020
6	4938	1020

prune129.0ms (1.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	122	9	131

Error

Counts

131 → 9

Alt Table

Status	Error	Program
	0.6b	(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)
	0.7b	(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 (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 (.f64 (.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1)))) (sqrt.f64 2)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.4b	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) u2)) (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) u2)))) 1/2)
	0.4b	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (log.f64 (exp.f64 (.f64 (.f64 2 (PI.f64)) u2)))) 1/2)
	0.4b	(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 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))) (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 3058 to 2056 computations (32.8% 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 (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)))))
	0.3b	(.f64 (.f64 2 (PI.f64)) u2)

series61.0ms (0.8%)

Counts

2 → 24

Calls

2 calls:

34.0ms	(.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))))

rewrite17.0ms (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))))

simplify91.0ms (1.2%)

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

prune153.0ms (2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	130	3	133
Fresh	4	2	6
Picked	0	1	1
Done	0	2	2
Total	134	8	142

Error

Counts

142 → 8

Alt Table

Status	Error	Program
	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 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.4b	(fma.f64 (sqrt.f64 (.f64 1/6 (.f64 1/6 (.f64 -2 (log.f64 u1))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.6b	(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 (.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1)))) (sqrt.f64 2)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.4b	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) u2)) (sqrt.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)
✓	0.3b	(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 3274 to 2621 computations (19.9% saved)

regimes562.0ms (7.2%)

Accuracy

Total 0.2b remaining (92.4%)

Threshold costs 0.2b (92.4%)

Counts

44 → 1

Compiler

Compiled 9986 to 8772 computations (12.2% 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

end149.0ms (1.9%)

Compiler: Compiled 194 to 172 computations (11.3% saved)

Details

analyze3.1s (40.2%)

sample2.3s (29.1%)

simplify126.0ms (1.6%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series240.0ms (3.1%)

rewrite13.0ms (0.2%)

simplify115.0ms (1.5%)

prune141.0ms (1.8%)

localize15.0ms (0.2%)

series76.0ms (1%)

rewrite19.0ms (0.2%)

simplify122.0ms (1.6%)

prune166.0ms (2.1%)

localize14.0ms (0.2%)

series52.0ms (0.7%)

rewrite14.0ms (0.2%)

simplify82.0ms (1.1%)

prune129.0ms (1.7%)

localize13.0ms (0.2%)

series61.0ms (0.8%)

rewrite17.0ms (0.2%)

simplify91.0ms (1.2%)

prune153.0ms (2%)

regimes562.0ms (7.2%)

simplify3.0ms (0%)

end149.0ms (1.9%)

Profiling