Details

analyze110.0ms (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)

sample2.3s (37.1%)

Results

2.2s

8256×

body

128

valid

Compiler

Compiled 93 to 79 computations (15.1% saved)

simplify123.0ms (1.9%)

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

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

0.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.4b	(+.f64 (.f64 (.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)

Compiler

Compiled 78 to 68 computations (12.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
✓	0.1b	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)
✓	0.3b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))

series592.0ms (9.4%)

Counts

4 → 60

Calls

4 calls:

380.0ms	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)
170.0ms	(+.f64 (.f64 (.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
35.0ms	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))
7.0ms	(.f64 (.f64 2 (PI.f64)) u2)

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-exp-log_binary64`
25×	`add-sqr-sqrt_binary64`
24×	`prod-exp_binary64`
16×	`*-un-lft-identity_binary64`
14×	`associate-l_binary64`

Counts

4 → 107

Calls

4 calls:

9.0ms	(+.f64 (.f64 (.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
7.0ms	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))
6.0ms	(.f64 (.f64 2 (PI.f64)) u2)
3.0ms	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)

simplify145.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

411×	`unswap-sqr_binary64`
378×	`cancel-sign-sub-inv_binary64`
371×	`fma-def_binary64`
332×	`fma-neg_binary64`
234×	`associate-l_binary64`

Counts

167 → 173

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	226	2863
1	473	2660
2	1532	2604
3	3218	2602
4	4807	2602
5	4998	2602
6	4924	2602

prune199.0ms (3.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	165	8	173
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	166	8	174

Error

Counts

174 → 8

Alt Table

Status	Error	Program
	0.6b	(.f64 (sqrt.f64 (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))) 1/2)) (sqrt.f64 (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (*.f64 u2 (PI.f64))))) 1/2)))
	0.4b	(+.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 6)) (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2))) 1/2)
	0.5b	(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))
	0.7b	(+.f64 (.f64 (exp.f64 (+.f64 (neg.f64 (log.f64 6)) (.f64 (log.f64 (.f64 -2 (log.f64 u1))) 1/2))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.6b	(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)))
	0.7b	(+.f64 (.f64 (.f64 (/.f64 1 6) (exp.f64 (.f64 (log.f64 (.f64 -2 (log.f64 u1))) 1/2))) (cos.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	(+.f64 (.f64 (cbrt.f64 (.f64 1/216 (pow.f64 (.f64 -2 (log.f64 u1)) 3/2))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)

Compiler

Compiled 4786 to 3817 computations (20.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(cos.f64 (.f64 2 (.f64 u2 (PI.f64))))
✓	0.1b	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
✓	0.3b	(*.f64 u2 (PI.f64))
✓	0.4b	(fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))) 1/2)

series197.0ms (3.1%)

Counts

4 → 56

Calls

4 calls:

167.0ms	(fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))) 1/2)
24.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
3.0ms	(cos.f64 (.f64 2 (.f64 u2 (PI.f64))))
2.0ms	(*.f64 u2 (PI.f64))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

3.0ms	(*.f64 u2 (PI.f64))
2.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
1.0ms	(cos.f64 (.f64 2 (.f64 u2 (PI.f64))))
0.0ms	(fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))) 1/2)

simplify91.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

974×	`fma-neg_binary64`
603×	`associate-l_binary64`
447×	`distribute-rgt-neg-in_binary64`
416×	`distribute-lft-neg-in_binary64`
351×	`unswap-sqr_binary64`

Counts

109 → 104

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	153	1860
1	297	1745
2	831	1685
3	2364	1653
4	4839	1653
5	5149	1653

prune123.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	104	8	112

Error

Counts

112 → 8

Alt Table

Status	Error	Program
	0.6b	(.f64 (sqrt.f64 (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))) 1/2)) (sqrt.f64 (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (*.f64 u2 (PI.f64))))) 1/2)))
	0.4b	(+.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 6)) (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2))) 1/2)
	0.5b	(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))
	0.7b	(+.f64 (.f64 (exp.f64 (+.f64 (neg.f64 (log.f64 6)) (.f64 (log.f64 (.f64 -2 (log.f64 u1))) 1/2))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.6b	(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)))
✓	0.4b	(fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))) 1/2)
	0.5b	(+.f64 (.f64 (cbrt.f64 (.f64 1/216 (pow.f64 (.f64 -2 (log.f64 u1)) 3/2))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
▶	0.4b	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) (sqrt.f64 2))) 1/2)

Compiler

Compiled 2565 to 1834 computations (28.5% 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 (PI.f64) u2)
✓	0.4b	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) (sqrt.f64 2))) 1/2)
✓	0.5b	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) (sqrt.f64 2)))

series364.0ms (5.8%)

Counts

4 → 56

Calls

4 calls:

173.0ms	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) (sqrt.f64 2))) 1/2)
165.0ms	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) (sqrt.f64 2)))
23.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
3.0ms	(*.f64 (PI.f64) u2)

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`sqrt-prod_binary64`
18×	`associate-l_binary64`
16×	`add-sqr-sqrt_binary64`
16×	`pow1_binary64`
13×	`*-un-lft-identity_binary64`

Counts

4 → 86

Calls

4 calls:

8.0ms	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) (sqrt.f64 2)))
3.0ms	(*.f64 (PI.f64) u2)
2.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
0.0ms	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) (sqrt.f64 2))) 1/2)

simplify126.0ms (2%)

Algorithm

1×	egg-herbie

Rules

793×	`fma-neg_binary64`
522×	`*-commutative_binary64`
358×	`distribute-rgt-neg-in_binary64`
328×	`distribute-lft-neg-in_binary64`
266×	`fma-def_binary64`

Counts

142 → 145

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	183	3334
1	406	3156
2	1239	3062
3	2645	3043
4	4920	3041
5	5115	3041

prune145.0ms (2.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	145	8	153

Error

Counts

153 → 8

Alt Table

Status	Error	Program
	0.6b	(.f64 (sqrt.f64 (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))) 1/2)) (sqrt.f64 (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (*.f64 u2 (PI.f64))))) 1/2)))
▶	0.4b	(+.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 6)) (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2))) 1/2)
	0.5b	(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))
	0.7b	(+.f64 (.f64 (exp.f64 (+.f64 (neg.f64 (log.f64 6)) (.f64 (log.f64 (.f64 -2 (log.f64 u1))) 1/2))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.6b	(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)))
✓	0.4b	(fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))) 1/2)
	0.5b	(+.f64 (.f64 (cbrt.f64 (.f64 1/216 (pow.f64 (.f64 -2 (log.f64 u1)) 3/2))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
✓	0.4b	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) (sqrt.f64 2))) 1/2)

Compiler

Compiled 3867 to 2398 computations (38% saved)

localize16.0ms (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 (sqrt.f64 (/.f64 1 6)) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
	0.3b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.3b	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))

series60.0ms (1%)

Counts

2 → 20

Calls

2 calls:

32.0ms	(.f64 (sqrt.f64 (/.f64 1 6)) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
28.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`pow1_binary64`
20×	`associate-l_binary64`
18×	`sqrt-prod_binary64`
17×	`add-sqr-sqrt_binary64`
15×	`pow-prod-down_binary64`

Counts

2 → 67

Calls

2 calls:

17.0ms	(.f64 (sqrt.f64 (/.f64 1 6)) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
6.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))

simplify108.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

756×	`fma-def_binary64`
520×	`fma-neg_binary64`
224×	`*-commutative_binary64`
211×	`associate-*r/_binary64`
190×	`associate-*l/_binary64`

Counts

87 → 108

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	1483
1	185	1312
2	486	1272
3	634	1240
4	842	1240
5	1725	1240
6	4095	1240
7	4988	1240
8	4834	1240

prune164.0ms (2.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	153	8	161

Error

Counts

161 → 8

Alt Table

Status	Error	Program
	0.6b	(.f64 (sqrt.f64 (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))) 1/2)) (sqrt.f64 (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (*.f64 u2 (PI.f64))))) 1/2)))
✓	0.4b	(+.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 6)) (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2))) 1/2)
	0.5b	(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))
	0.7b	(+.f64 (.f64 (exp.f64 (+.f64 (neg.f64 (log.f64 6)) (.f64 (log.f64 (.f64 -2 (log.f64 u1))) 1/2))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.6b	(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)))
✓	0.4b	(fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))) 1/2)
	0.5b	(+.f64 (.f64 (cbrt.f64 (.f64 1/216 (pow.f64 (.f64 -2 (log.f64 u1)) 3/2))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
✓	0.4b	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) (sqrt.f64 2))) 1/2)

Compiler

Compiled 4291 to 3548 computations (17.3% saved)

regimes1.1s (17.9%)

Accuracy

Total 0.3b remaining (93.6%)

Threshold costs 0.3b (93.6%)

Counts

83 → 1

Compiler

Compiled 21717 to 19517 computations (10.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
2×	`+-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	18	30
1	28	30
2	30	30
3	31	30
4	31	30

end151.0ms (2.4%)

Compiler: Compiled 217 to 192 computations (11.5% saved)

Details

analyze110.0ms (1.7%)

sample2.3s (37.1%)

simplify123.0ms (1.9%)

prune4.0ms (0.1%)

localize14.0ms (0.2%)

series592.0ms (9.4%)

rewrite29.0ms (0.5%)

simplify145.0ms (2.3%)

prune199.0ms (3.1%)

localize13.0ms (0.2%)

series197.0ms (3.1%)

rewrite8.0ms (0.1%)

simplify91.0ms (1.4%)

prune123.0ms (1.9%)

localize14.0ms (0.2%)

series364.0ms (5.8%)

rewrite18.0ms (0.3%)

simplify126.0ms (2%)

prune145.0ms (2.3%)

localize16.0ms (0.3%)

series60.0ms (1%)

rewrite27.0ms (0.4%)

simplify108.0ms (1.7%)

prune164.0ms (2.6%)

regimes1.1s (17.9%)

simplify3.0ms (0%)

end151.0ms (2.4%)

Profiling