Details

analyze401.0ms (5.3%)

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 30 to 26 computations (13.3% saved)

sample70.0ms (0.9%)

Algorithm

1×

intervals

Results

52.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 53 to 47 computations (11.3% saved)

simplify195.0ms (2.6%)

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 → 1

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)

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

Error

0.3b

Counts

2 → 2

Alt Table

Status	Error	Program
	0.3b	(+.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)
▶	0.3b	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)

Status

Error

Program

0.3b

(+.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)

▶

0.3b

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

Compiler

Compiled 93 to 83 computations (10.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(cos.f64 (.f64 (.f64 2 PI.f64) u2))
0.1b	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.2b	(.f64 (.f64 2 PI.f64) u2)
0.3b	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))

rewrite272.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

30×	`pow1_binary64`
26×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64`

Counts

4 → 144

Calls

4 calls:

56.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
14.0ms	(.f64 (.f64 2 PI.f64) u2)
14.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
12.0ms	(cos.f64 (.f64 (.f64 2 PI.f64) u2))

Compiler

Compiled 2497 to 1714 computations (31.4% saved)

series53.0ms (0.7%)

Error

0.2b

Counts

4 → 15

Calls

4 calls:

16.0ms	(.f64 (.f64 2 PI.f64) u2)
11.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
9.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
8.0ms	(cos.f64 (.f64 (.f64 2 PI.f64) u2))

Compiler

Compiled 684 to 595 computations (13% saved)

simplify80.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

726×	`fma-def_binary64`
426×	`distribute-rgt-in_binary64`
405×	`distribute-lft-in_binary64`
344×	`*-commutative_binary64`
221×	`cancel-sign-sub-inv_binary64`

Counts

159 → 71

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	183	1740
1	393	1615
2	1069	1558
3	2220	1556
4	5012	1556

prune57.0ms (0.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	65	6	71
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	67	6	73

Error

0.0b

Counts

73 → 6

Alt Table

Status	Error	Program
	0.7b	(fma.f64 (.f64 1/6 (exp.f64 (.f64 1/2 (log.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)
	0.3b	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (sqrt.f64 (.f64 (.f64 (*.f64 u2 u2) (pow.f64 PI.f64 2)) 4))) 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)
▶	0.2b	(fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)
	0.7b	(fma.f64 (.f64 (cbrt.f64 (.f64 (log.f64 u1) -1/18)) (cbrt.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)

Compiler

Compiled 1340 to 943 computations (29.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(cos.f64 (.f64 (.f64 2 PI.f64) u2))
0.2b	(sqrt.f64 (*.f64 (log.f64 u1) -1/18))
0.2b	(.f64 (.f64 2 PI.f64) u2)
0.4b	(*.f64 (log.f64 u1) -1/18)

rewrite179.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

37×	`pow1_binary64`
26×	`add-sqr-sqrt_binary64`
18×	`add-exp-log_binary64`
18×	`add-cube-cbrt_binary64`
16×	`pow-prod-down_binary64`

Counts

4 → 145

Calls

4 calls:

16.0ms	(.f64 (.f64 2 PI.f64) u2)
13.0ms	(*.f64 (log.f64 u1) -1/18)
12.0ms	(cos.f64 (.f64 (.f64 2 PI.f64) u2))
11.0ms	(sqrt.f64 (*.f64 (log.f64 u1) -1/18))

Compiler

Compiled 2190 to 1416 computations (35.3% saved)

series40.0ms (0.5%)

Error

0.0b

Counts

4 → 15

Calls

4 calls:

10.0ms	(sqrt.f64 (*.f64 (log.f64 u1) -1/18))
8.0ms	(*.f64 (log.f64 u1) -1/18)
7.0ms	(cos.f64 (.f64 (.f64 2 PI.f64) u2))
5.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 629 to 537 computations (14.6% saved)

simplify80.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

790×	`fma-def_binary64`
509×	`distribute-rgt-in_binary64`
367×	`*-commutative_binary64`
242×	`cancel-sign-sub-inv_binary64`
182×	`distribute-rgt-neg-in_binary64`

Counts

160 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	183	1599
1	382	1468
2	1111	1409
3	2401	1407
4	5056	1407

prune88.0ms (1.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	83	6	89
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	88	7	95

Error

0.0b

Counts

95 → 7

Alt Table

Status	Error	Program
	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 1/18) (sqrt.f64 (neg.f64 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)
	0.5b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 -1/18 (log.f64 u1)) 3/2)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)
	0.7b	(fma.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 -1/18 (log.f64 u1))) (cbrt.f64 (.f64 -1/18 (log.f64 u1)))) (cbrt.f64 (.f64 -1/18 (log.f64 u1))))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)
▶	0.2b	(fma.f64 (sqrt.f64 (log.f64 (pow.f64 u1 -1/18))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
	0.4b	(fma.f64 (sqrt.f64 (exp.f64 (log.f64 (.f64 -1/18 (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 (sqrt.f64 (.f64 (.f64 (.f64 u2 u2) (pow.f64 PI.f64 2)) 4))) 1/2)

Compiler

Compiled 1515 to 1043 computations (31.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(log.f64 (pow.f64 u1 -1/18))
0.2b	(sqrt.f64 (log.f64 (pow.f64 u1 -1/18)))
0.2b	(.f64 (.f64 2 PI.f64) u2)
2.7b	(pow.f64 u1 -1/18)

rewrite179.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

27×	`pow1_binary64`
26×	`add-cube-cbrt_binary64`
22×	`add-sqr-sqrt_binary64`
15×	`add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`

Counts

4 → 142

Calls

4 calls:

16.0ms	(.f64 (.f64 2 PI.f64) u2)
15.0ms	(pow.f64 u1 -1/18)
12.0ms	(log.f64 (pow.f64 u1 -1/18))
10.0ms	(sqrt.f64 (log.f64 (pow.f64 u1 -1/18)))

Compiler

Compiled 2002 to 1541 computations (23% saved)

series56.0ms (0.7%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

19.0ms	(sqrt.f64 (log.f64 (pow.f64 u1 -1/18)))
14.0ms	(log.f64 (pow.f64 u1 -1/18))
14.0ms	(pow.f64 u1 -1/18)
6.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 481 to 422 computations (12.3% saved)

simplify93.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

640×	`fma-def_binary64`
591×	`distribute-rgt-in_binary64`
437×	`unswap-sqr_binary64`
281×	`*-commutative_binary64`
226×	`fma-neg_binary64`

Counts

154 → 77

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	141	1216
1	279	1143
2	827	1075
3	2033	1000
4	4829	1000
5	4895	1000

prune57.0ms (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	77	7	84

Error

0.0b

Counts

84 → 7

Alt Table

Status	Error	Program
	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 1/18) (sqrt.f64 (neg.f64 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)
	0.5b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 -1/18 (log.f64 u1)) 3/2)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)
	0.7b	(fma.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 -1/18 (log.f64 u1))) (cbrt.f64 (.f64 -1/18 (log.f64 u1)))) (cbrt.f64 (.f64 -1/18 (log.f64 u1))))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)
✓	0.2b	(fma.f64 (sqrt.f64 (log.f64 (pow.f64 u1 -1/18))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
	0.4b	(fma.f64 (sqrt.f64 (exp.f64 (log.f64 (.f64 -1/18 (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 (sqrt.f64 (.f64 (.f64 (.f64 u2 u2) (pow.f64 PI.f64 2)) 4))) 1/2)

Compiler

Compiled 1130 to 859 computations (24% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(sqrt.f64 (*.f64 (log.f64 u1) -1/18))
0.2b	(.f64 (.f64 u2 u2) (pow.f64 PI.f64 2))
0.4b	(*.f64 (log.f64 u1) -1/18)
30.7b	(sqrt.f64 (.f64 (.f64 (*.f64 u2 u2) (pow.f64 PI.f64 2)) 4))

rewrite286.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

24×	`add-sqr-sqrt_binary64`
23×	`pow1_binary64`
18×	`add-cube-cbrt_binary64`
16×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64`

Counts

4 → 145

Calls

4 calls:

16.0ms	(*.f64 (log.f64 u1) -1/18)
15.0ms	(.f64 (.f64 u2 u2) (pow.f64 PI.f64 2))
15.0ms	(sqrt.f64 (.f64 (.f64 (*.f64 u2 u2) (pow.f64 PI.f64 2)) 4))
11.0ms	(sqrt.f64 (*.f64 (log.f64 u1) -1/18))

Compiler

Compiled 2517 to 1731 computations (31.2% saved)

series39.0ms (0.5%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

11.0ms	(sqrt.f64 (*.f64 (log.f64 u1) -1/18))
9.0ms	(*.f64 (log.f64 u1) -1/18)
7.0ms	(.f64 (.f64 u2 u2) (pow.f64 PI.f64 2))
5.0ms	(sqrt.f64 (.f64 (.f64 (*.f64 u2 u2) (pow.f64 PI.f64 2)) 4))

Compiler

Compiled 608 to 517 computations (15% saved)

simplify100.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

736×	`associate-l_binary64`
556×	`associate-r_binary64`
384×	`log-prod_binary64`
271×	`fma-def_binary64`
256×	`prod-exp_binary64`

Counts

157 → 86

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	147	1411
1	271	1320
2	704	1152
3	2592	1119
4	4657	1119
5	4919	1119

prune79.0ms (1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	86	7	93

Error

0.0b

Counts

93 → 7

Alt Table

Status	Error	Program
	0.4b	(fma.f64 (sqrt.f64 (exp.f64 (log.f64 (.f64 -1/18 (log.f64 u1))))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)
	0.5b	(fma.f64 (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 -1/18 (log.f64 u1))))) (cos.f64 (sqrt.f64 (.f64 (.f64 (.f64 u2 u2) (pow.f64 PI.f64 2)) 4))) 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 1/18) (sqrt.f64 (neg.f64 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)
	0.5b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 -1/18 (log.f64 u1)) 3/2)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)
	0.7b	(fma.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 -1/18 (log.f64 u1))) (cbrt.f64 (.f64 -1/18 (log.f64 u1)))) (cbrt.f64 (.f64 -1/18 (log.f64 u1))))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)
	0.2b	(fma.f64 (sqrt.f64 (log.f64 (pow.f64 u1 -1/18))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)

Compiler

Compiled 1462 to 1044 computations (28.6% saved)

regimes3.4s (44.8%)

Accuracy

Total 0.2b remaining (91.8%)

Threshold costs 0.2b (91.8%)

Compiler

Compiled 43129 to 37093 computations (14% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	21
1	16	21
2	16	21

end1.0ms (0%)

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

sample1.7s (22.8%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
210.0ms	8000×	pre	128	true

Compiler

Compiled 182 to 157 computations (13.7% saved)

Details

analyze401.0ms (5.3%)

sample70.0ms (0.9%)

simplify195.0ms (2.6%)

prune4.0ms (0.1%)

localize11.0ms (0.1%)

rewrite272.0ms (3.6%)

series53.0ms (0.7%)

simplify80.0ms (1.1%)

prune57.0ms (0.8%)

localize11.0ms (0.1%)

rewrite179.0ms (2.4%)

series40.0ms (0.5%)

simplify80.0ms (1.1%)

prune88.0ms (1.2%)

localize12.0ms (0.2%)

rewrite179.0ms (2.4%)

series56.0ms (0.7%)

simplify93.0ms (1.2%)

prune57.0ms (0.7%)

localize15.0ms (0.2%)

rewrite286.0ms (3.8%)

series39.0ms (0.5%)

simplify100.0ms (1.3%)

prune79.0ms (1%)

regimes3.4s (44.8%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.7s (22.8%)

Profiling