Details

analyze74.0ms (1.3%)

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)

sample2.2s (39%)

Results

2.1s

8256×

body

128

valid

Compiler

Compiled 93 to 79 computations (15.1% saved)

simplify122.0ms (2.1%)

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)

localize12.0ms (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)))
✓	0.3b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))

series315.0ms (5.5%)

Counts

4 → 52

Calls

4 calls:

163.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
113.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
35.0ms	(.f64 1/6 (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:

4.0ms	(.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)

simplify108.0ms (1.9%)

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 (2.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	97	7	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	7	105

Error

0.0b

Counts

105 → 7

Alt Table

Status	Error	Program
	0.5b	(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)))
▶	0.3b	(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	(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 (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 (cbrt.f64 (pow.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) 3)) (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 (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)

Compiler

Compiled 2515 to 1912 computations (24% saved)

localize12.0ms (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 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))
✓	0.4b	(.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))

series75.0ms (1.3%)

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 (0.3%)

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)))

simplify115.0ms (2%)

Algorithm

1×	egg-herbie

Rules

503×	`associate-l_binary64`
460×	`neg-sub0_binary64`
445×	`neg-mul-1_binary64`
380×	`associate-r_binary64`
355×	`distribute-rgt-neg-in_binary64`

Counts

118 → 117

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

prune158.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	145	7	152

Error

0.0b

Counts

152 → 7

Alt Table

Status	Error	Program
	0.4b	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 (log.f64 u1) -2))) (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)
▶	0.4b	(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)
	0.6b	(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 (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 (cbrt.f64 (pow.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) 3)) (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)

Compiler

Compiled 3531 to 2342 computations (33.7% 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))

series51.0ms (0.9%)

Counts

2 → 20

Calls

2 calls:

27.0ms	(.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))))

rewrite15.0ms (0.3%)

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 (1.4%)

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

prune123.0ms (2.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	122	7	129

Error

Counts

129 → 7

Alt Table

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

Compiler

Compiled 3026 to 2018 computations (33.3% 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 (log.f64 u1) -2))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
✓	0.1b	(sqrt.f64 (*.f64 (log.f64 u1) -2))
	0.3b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(.f64 1/6 (sqrt.f64 (.f64 (log.f64 u1) -2)))

series245.0ms (4.2%)

Counts

3 → 48

Calls

3 calls:

185.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 (log.f64 u1) -2))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
34.0ms	(sqrt.f64 (*.f64 (log.f64 u1) -2))
25.0ms	(.f64 1/6 (sqrt.f64 (.f64 (log.f64 u1) -2)))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`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:

5.0ms	(.f64 1/6 (sqrt.f64 (.f64 (log.f64 u1) -2)))
2.0ms	(sqrt.f64 (*.f64 (log.f64 u1) -2))
0.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 (log.f64 u1) -2))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)

simplify87.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

728×	`unswap-sqr_binary64`
433×	`fma-neg_binary64`
377×	`associate-l_binary64`
345×	`associate-r_binary64`
309×	`distribute-rgt-neg-in_binary64`

Counts

92 → 92

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	128	1724
1	249	1638
2	621	1608
3	1983	1586
4	4098	1586
5	5736	1586

prune115.0ms (2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	121	6	127

Error

Counts

127 → 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)
✓	0.3b	(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)
	0.4b	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 (log.f64 u1) -2))) (cos.f64 (expm1.f64 (log1p.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 (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 (.f64 (.f64 1/6 (.f64 (fabs.f64 (cbrt.f64 (log.f64 u1))) (sqrt.f64 (neg.f64 (cbrt.f64 (log.f64 u1)))))) (sqrt.f64 2)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)

Compiler

Compiled 2681 to 2013 computations (24.9% saved)

regimes1.5s (25.9%)

Accuracy

Total 0.3b remaining (88.9%)

Threshold costs 0.3b (88.9%)

Counts

125 → 1

Compiler

Compiled 29777 to 25289 computations (15.1% saved)

simplify2.0ms (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

end127.0ms (2.2%)

Compiler: Compiled 181 to 156 computations (13.8% saved)

Details

analyze74.0ms (1.3%)

sample2.2s (39%)

simplify122.0ms (2.1%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

series315.0ms (5.5%)

rewrite13.0ms (0.2%)

simplify108.0ms (1.9%)

prune120.0ms (2.1%)

localize12.0ms (0.2%)

series75.0ms (1.3%)

rewrite19.0ms (0.3%)

simplify115.0ms (2%)

prune158.0ms (2.7%)

localize14.0ms (0.2%)

series51.0ms (0.9%)

rewrite15.0ms (0.3%)

simplify80.0ms (1.4%)

prune123.0ms (2.1%)

localize11.0ms (0.2%)

series245.0ms (4.2%)

rewrite8.0ms (0.1%)

simplify87.0ms (1.5%)

prune115.0ms (2%)

regimes1.5s (25.9%)

simplify2.0ms (0%)

end127.0ms (2.2%)

Profiling