Details

analyze244.0ms (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)

sample77.0ms (1.3%)

Algorithm

1×

intervals

Results

56.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 59 to 51 computations (13.6% saved)

simplify125.0ms (2%)

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

series539.0ms (8.8%)

Counts

4 → 52

Calls

4 calls:

465.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
36.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
34.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
3.0ms	(.f64 (.f64 2 (PI.f64)) u2)

rewrite15.0ms (0.3%)

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)
3.0ms	(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 (1.9%)

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

prune333.0ms (5.4%)

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
	0.3b	(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)
	0.6b	(expm1.f64 (log1p.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)
	0.5b	(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)
	0.7b	(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 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)

Compiler

Compiled 2503 to 1904 computations (23.9% saved)

localize13.0ms (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 u2 (PI.f64))
✓	0.4b	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)
✓	0.4b	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))))

series372.0ms (6.1%)

Counts

4 → 68

Calls

4 calls:

183.0ms	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)
165.0ms	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))))
21.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
2.0ms	(*.f64 u2 (PI.f64))

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

simplify132.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

793×	`fma-neg_binary64`
515×	`*-commutative_binary64`
379×	`distribute-rgt-neg-in_binary64`
347×	`distribute-lft-neg-in_binary64`
263×	`fma-def_binary64`

Counts

154 → 143

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	180	3395
1	401	3209
2	1225	3115
3	2639	3096
4	4926	3094
5	5120	3094

prune141.0ms (2.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	143	7	150

Error

0.0b

Counts

150 → 7

Alt Table

Status	Error	Program
▶	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)
	0.6b	(expm1.f64 (log1p.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)
	0.5b	(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)
	0.7b	(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 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)

Compiler

Compiled 3799 to 2348 computations (38.2% 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) (.f64 (sqrt.f64 1/6) (sqrt.f64 (*.f64 -2 (log.f64 u1)))))
	0.2b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.3b	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 -2 (log.f64 u1))))

series61.0ms (1%)

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))))

rewrite21.0ms (0.3%)

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:

9.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (sqrt.f64 (*.f64 -2 (log.f64 u1)))))
7.0ms	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 -2 (log.f64 u1))))

simplify86.0ms (1.4%)

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 (2.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	131	2	133
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	134	6	140

Error

Counts

140 → 6

Alt Table

Status	Error	Program
	0.2b	(fma.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) (.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 (pow.f64 (.f64 1/6 (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)
✓	0.3b	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)
▶	0.2b	(fma.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)

Compiler

Compiled 3306 to 2651 computations (19.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.1b	(sqrt.f64 (neg.f64 (log.f64 u1)))
	0.2b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.2b	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2)))

series200.0ms (3.3%)

Counts

2 → 36

Calls

2 calls:

173.0ms	(fma.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
27.0ms	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2)))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`associate-l_binary64`
12×	`sqrt-prod_binary64`
9×	`pow1_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`

Counts

2 → 42

Calls

2 calls:

7.0ms	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2)))
0.0ms	(fma.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)

simplify204.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

855×	`fma-def_binary64`
436×	`cancel-sign-sub-inv_binary64`
361×	`*-commutative_binary64`
264×	`fma-neg_binary64`
254×	`neg-mul-1_binary64`

Counts

78 → 79

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	1988
1	301	1870
2	879	1824
3	1802	1790
4	4566	1790
5	4963	1790

prune123.0ms (2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	134	6	140

Error

Counts

140 → 6

Alt Table

Status	Error	Program
	0.2b	(fma.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) (.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 (pow.f64 (.f64 1/6 (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)
✓	0.3b	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)
✓	0.2b	(fma.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)

Compiler

Compiled 3278 to 2119 computations (35.4% saved)

regimes1.3s (21.4%)

Accuracy

Total 0.2b remaining (92%)

Threshold costs 0.2b (92%)

Counts

97 → 1

Compiler

Compiled 21439 to 18801 computations (12.3% 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

end1.0ms (0%)

Compiler: Compiled 15 to 13 computations (13.3% saved)

sample1.8s (29.3%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
264.0ms	8000×	pre	128	true

Compiler

Compiled 167 to 147 computations (12% saved)

Details

analyze244.0ms (4%)

sample77.0ms (1.3%)

simplify125.0ms (2%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

series539.0ms (8.8%)

rewrite15.0ms (0.3%)

simplify115.0ms (1.9%)

prune333.0ms (5.4%)

localize13.0ms (0.2%)

series372.0ms (6.1%)

rewrite18.0ms (0.3%)

simplify132.0ms (2.2%)

prune141.0ms (2.3%)

localize13.0ms (0.2%)

series61.0ms (1%)

rewrite21.0ms (0.3%)

simplify86.0ms (1.4%)

prune146.0ms (2.4%)

localize13.0ms (0.2%)

series200.0ms (3.3%)

rewrite10.0ms (0.2%)

simplify204.0ms (3.3%)

prune123.0ms (2%)

regimes1.3s (21.4%)

simplify2.0ms (0%)

end1.0ms (0%)

sample1.8s (29.3%)

Profiling