Details

analyze3.3s (35.3%)

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)

sample2.1s (22.1%)

Results

1.9s

8256×

body

128

valid

Compiler

Compiled 57 to 49 computations (14% saved)

simplify125.0ms (1.3%)

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

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

0.4b

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
✓	0.0b	(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)
✓	0.4b	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))

series221.0ms (2.4%)

Counts

4 → 52

Calls

4 calls:

161.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
30.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
26.0ms	(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)

simplify115.0ms (1.2%)

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

prune113.0ms (1.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	96	8	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	8	105

Error

0.0b

Counts

105 → 8

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)
▶	0.3b	(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)
	0.6b	(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 (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)
	0.4b	(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)
	0.7b	(fma.f64 (.f64 (.f64 (sqrt.f64 1/6) (sqrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))))) (.f64 (sqrt.f64 1/6) (sqrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (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)))

Compiler

Compiled 2603 to 1984 computations (23.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (neg.f64 (log.f64 u1)))
	0.2b	(.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 (0.8%)

Counts

3 → 32

Calls

3 calls:

28.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))
26.0ms	(.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))
22.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))

rewrite20.0ms (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)))

simplify119.0ms (1.3%)

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

prune168.0ms (1.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	144	3	147
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	148	7	155

Error

Counts

155 → 7

Alt Table

Status	Error	Program
▶	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)
	0.4b	(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)
	0.6b	(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 1/6 (.f64 (exp.f64 (log.f64 (sqrt.f64 (neg.f64 (log.f64 u1))))) (sqrt.f64 2))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.6b	(fma.f64 (.f64 (sqrt.f64 (.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))) (sqrt.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)))

Compiler

Compiled 3632 to 2417 computations (33.5% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (neg.f64 (log.f64 u1)))
	0.2b	(.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))

series51.0ms (0.5%)

Counts

2 → 20

Calls

2 calls:

28.0ms	(.f64 (.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1)))) (sqrt.f64 2))
22.0ms	(*.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1))))

rewrite15.0ms (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:

7.0ms	(.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))))

simplify80.0ms (0.8%)

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

prune125.0ms (1.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	122	7	129

Error

Counts

129 → 7

Alt Table

Status	Error	Program
✓	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)
▶	0.4b	(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)
	0.6b	(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 1/6 (.f64 (exp.f64 (log.f64 (sqrt.f64 (neg.f64 (log.f64 u1))))) (sqrt.f64 2))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.6b	(fma.f64 (.f64 (sqrt.f64 (.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))) (sqrt.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)))

Compiler

Compiled 3079 to 2063 computations (33% saved)

localize14.0ms (0.1%)

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))))

series59.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

31.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (sqrt.f64 (*.f64 -2 (log.f64 u1)))))
28.0ms	(.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))))

simplify87.0ms (0.9%)

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

prune146.0ms (1.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	130	3	133
Fresh	4	1	5
Picked	0	1	1
Done	0	1	1
Total	134	6	140

Error

Counts

140 → 6

Alt Table

Status	Error	Program
✓	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)
✓	0.4b	(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)
	0.2b	(fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.5b	(fma.f64 (cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 3) 1/216)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.6b	(fma.f64 (exp.f64 (+.f64 (log.f64 (sqrt.f64 1/6)) (log.f64 (.f64 (sqrt.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 1/6 (.f64 (exp.f64 (log.f64 (sqrt.f64 (neg.f64 (log.f64 u1))))) (sqrt.f64 2))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)

Compiler

Compiled 3238 to 2591 computations (20% saved)

regimes2.3s (24.2%)

Accuracy

Total 0.2b remaining (93.2%)

Threshold costs 0.2b (93.2%)

Counts

176 → 1

Compiler

Compiled 42856 to 36864 computations (14% saved)

simplify2.0ms (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

end108.0ms (1.2%)

Compiler: Compiled 150 to 134 computations (10.7% saved)

Details

analyze3.3s (35.3%)

sample2.1s (22.1%)

simplify125.0ms (1.3%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series221.0ms (2.4%)

rewrite16.0ms (0.2%)

simplify115.0ms (1.2%)

prune113.0ms (1.2%)

localize13.0ms (0.1%)

series76.0ms (0.8%)

rewrite20.0ms (0.2%)

simplify119.0ms (1.3%)

prune168.0ms (1.8%)

localize16.0ms (0.2%)

series51.0ms (0.5%)

rewrite15.0ms (0.2%)

simplify80.0ms (0.8%)

prune125.0ms (1.3%)

localize14.0ms (0.1%)

series59.0ms (0.6%)

rewrite17.0ms (0.2%)

simplify87.0ms (0.9%)

prune146.0ms (1.6%)

regimes2.3s (24.2%)

simplify2.0ms (0%)

end108.0ms (1.2%)

Profiling