Details

analyze141.0ms (2.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	50%	50%	4
0%	50%	50%	5
12.5%	37.5%	50%	6
18.7%	31.2%	50%	7
28.1%	21.9%	50%	8
32.8%	17.2%	50%	9
38.2%	11.7%	50%	10
41%	9%	50%	11
43.9%	6%	50%	12
45.4%	4.6%	50%	13
46.9%	3.1%	50%	14

Compiler

Compiled 31 to 22 computations (29% saved)

sample24.0ms (0.5%)

Algorithm

1×

intervals

Results

15.0ms

256×

body

128

valid

Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify53.0ms (1%)

Algorithm

1×	egg-herbie

Rules

826×	`times-frac_binary64`
719×	`distribute-neg-frac_binary64`
509×	`associate-/r*_binary64`
353×	`associate-/l*_binary64`
343×	`div-sub_binary64`

Counts

1 → 1

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	43
1	58	43
2	179	40
3	803	40
4	3764	40
5	4802	40
6	4990	40

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))

Compiler

Compiled 84 to 60 computations (28.6% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 5 (.f64 v v))
0.3b	(*.f64 PI.f64 t)
0.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))
0.4b	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))

rewrite210.0ms (4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

34×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
20×	`pow1_binary64`
16×	`prod-exp_binary64` `cbrt-unprod_binary64` `associate-*r/_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`sqrt-div_binary64` `associate-l_binary64`

Counts

4 → 113

Calls

4 calls:

15.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))
13.0ms	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))
5.0ms	(.f64 5 (.f64 v v))
4.0ms	(*.f64 PI.f64 t)

Compiler

Compiled 4225 to 2542 computations (39.8% saved)

series167.0ms (3.2%)

Error

0.1b

Counts

4 → 24

Calls

4 calls:

74.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))
46.0ms	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))
10.0ms	(.f64 5 (.f64 v v))
9.0ms	(*.f64 PI.f64 t)

Compiler

Compiled 2077 to 1572 computations (24.3% saved)

simplify138.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

572×	`times-frac_binary64`
531×	`associate-r_binary64`
482×	`associate-l_binary64`
387×	`associate-/r*_binary64`
242×	`associate-/l*_binary64`

Counts

137 → 118

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	341	4992
1	989	4342
2	4670	4315
3	5017	4315

prune137.0ms (2.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	112	6	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	6	119

Error

Counts

119 → 6

Alt Table

Status	Error	Program
	0.5b	(/.f64 1 (/.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))) (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (-.f64 1 (.f64 v v)) (*.f64 t PI.f64)))))
	0.4b	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
	0.4b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (-.f64 1 (.f64 v v)) (.f64 t PI.f64))))
	0.6b	(.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (-.f64 1 (.f64 v v)) (.f64 t PI.f64))) (sqrt.f64 (/.f64 1 (-.f64 2 (.f64 (.f64 v v) 6)))))
	0.8b	(-.f64 (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 t PI.f64)) (.f64 3/4 (/.f64 (.f64 v v) (.f64 (.f64 t PI.f64) (sqrt.f64 1/2))))) (.f64 4 (.f64 (/.f64 (sqrt.f64 1/2) (.f64 t PI.f64)) (*.f64 v v))))
▶	0.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 t (.f64 PI.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))) (-.f64 1 (.f64 v v))))

Compiler

Compiled 3445 to 2134 computations (38.1% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 5 (.f64 v v))
0.2b	(.f64 (.f64 v v) 6)
0.2b	(.f64 t (.f64 PI.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))))
0.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 t (.f64 PI.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))) (-.f64 1 (.f64 v v))))

rewrite167.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

33×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
19×	`pow1_binary64`
18×	`associate-*r/_binary64`
15×	`prod-exp_binary64` `cbrt-unprod_binary64`
11×	`add-sqr-sqrt_binary64`

Counts

4 → 94

Calls

4 calls:

14.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 t (.f64 PI.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))) (-.f64 1 (.f64 v v))))
7.0ms	(.f64 t (.f64 PI.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))))
6.0ms	(.f64 (.f64 v v) 6)
6.0ms	(.f64 5 (.f64 v v))

Compiler

Compiled 3351 to 2003 computations (40.2% saved)

series152.0ms (2.9%)

Error

Counts

4 → 24

Calls

4 calls:

74.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 t (.f64 PI.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))) (-.f64 1 (.f64 v v))))
34.0ms	(.f64 t (.f64 PI.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))))
10.0ms	(.f64 (.f64 v v) 6)
8.0ms	(.f64 5 (.f64 v v))

Compiler

Compiled 1931 to 1426 computations (26.2% saved)

simplify111.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

494×	`times-frac_binary64`
431×	`cancel-sign-sub-inv_binary64`
400×	`associate-l_binary64`
370×	`associate-r_binary64`
318×	`associate-/r*_binary64`

Counts

118 → 95

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	298	3661
1	870	3155
2	4200	3144
3	5459	3144

prune102.0ms (2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	95	6	101

Error

Counts

101 → 6

Alt Table

Status	Error	Program
	0.5b	(/.f64 1 (/.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))) (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (-.f64 1 (.f64 v v)) (*.f64 t PI.f64)))))
▶	0.4b	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
	0.4b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (-.f64 1 (.f64 v v)) (.f64 t PI.f64))))
	0.6b	(.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (-.f64 1 (.f64 v v)) (.f64 t PI.f64))) (sqrt.f64 (/.f64 1 (-.f64 2 (.f64 (.f64 v v) 6)))))
	0.8b	(-.f64 (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 t PI.f64)) (.f64 3/4 (/.f64 (.f64 v v) (.f64 (.f64 t PI.f64) (sqrt.f64 1/2))))) (.f64 4 (.f64 (/.f64 (sqrt.f64 1/2) (.f64 t PI.f64)) (*.f64 v v))))
✓	0.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 t (.f64 PI.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))) (-.f64 1 (.f64 v v))))

Compiler

Compiled 2715 to 1674 computations (38.3% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 v v) 6)
0.3b	(*.f64 PI.f64 t)
0.4b	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
1.0b	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))

rewrite245.0ms (4.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

78×	`times-frac_binary64`
51×	`add-sqr-sqrt_binary64`
48×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
34×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
30×	`sqrt-prod_binary64`

Counts

4 → 156

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
8.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))
6.0ms	(.f64 (.f64 v v) 6)
3.0ms	(*.f64 PI.f64 t)

Compiler

Compiled 5895 to 3482 computations (40.9% saved)

series131.0ms (2.5%)

Error

Counts

4 → 21

Calls

4 calls:

72.0ms	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
19.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))
9.0ms	(*.f64 PI.f64 t)
8.0ms	(.f64 (.f64 v v) 6)

Compiler

Compiled 1724 to 1304 computations (24.4% saved)

simplify221.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

395×	`times-frac_binary64`
358×	`associate-/r*_binary64`
357×	`associate-/l*_binary64`
288×	`associate-l_binary64`
245×	`associate-r_binary64`

Counts

177 → 127

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	360	7184
1	1007	6466
2	4303	6466
3	4989	6466
4	4977	6466

prune126.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	128	5	133

Error

Counts

133 → 5

Alt Table

Status	Error	Program
	0.4b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (-.f64 1 (.f64 v v)) (.f64 t PI.f64))))
	0.6b	(.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (-.f64 1 (.f64 v v)) (.f64 t PI.f64))) (sqrt.f64 (/.f64 1 (-.f64 2 (.f64 (.f64 v v) 6)))))
	0.8b	(/.f64 (-.f64 (+.f64 (sqrt.f64 1/2) (.f64 3/4 (/.f64 (.f64 v v) (sqrt.f64 1/2)))) (.f64 5 (.f64 (sqrt.f64 1/2) (.f64 v v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))
✓	0.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 t (.f64 PI.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))) (-.f64 1 (.f64 v v))))
▶	0.4b	(/.f64 (/.f64 (+.f64 -1 (.f64 (.f64 v v) 5)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (.f64 t (.f64 PI.f64 (-.f64 -1 (neg.f64 (*.f64 v v))))))

Compiler

Compiled 3789 to 2342 computations (38.2% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 v v) 6)
0.3b	(.f64 t (.f64 PI.f64 (-.f64 -1 (neg.f64 (*.f64 v v)))))
0.4b	(/.f64 (/.f64 (+.f64 -1 (.f64 (.f64 v v) 5)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (.f64 t (.f64 PI.f64 (-.f64 -1 (neg.f64 (*.f64 v v))))))
1.0b	(/.f64 (+.f64 -1 (.f64 (.f64 v v) 5)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))

rewrite291.0ms (5.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

78×	`times-frac_binary64`
52×	`add-sqr-sqrt_binary64`
51×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
37×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
36×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64`

Counts

4 → 192

Calls

4 calls:

18.0ms	(/.f64 (/.f64 (+.f64 -1 (.f64 (.f64 v v) 5)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (.f64 t (.f64 PI.f64 (-.f64 -1 (neg.f64 (*.f64 v v))))))
11.0ms	(.f64 t (.f64 PI.f64 (-.f64 -1 (neg.f64 (*.f64 v v)))))
8.0ms	(/.f64 (+.f64 -1 (.f64 (.f64 v v) 5)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))
6.0ms	(.f64 (.f64 v v) 6)

Compiler

Compiled 7332 to 4282 computations (41.6% saved)

series163.0ms (3.1%)

Error

Counts

4 → 27

Calls

4 calls:

72.0ms	(/.f64 (/.f64 (+.f64 -1 (.f64 (.f64 v v) 5)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (.f64 t (.f64 PI.f64 (-.f64 -1 (neg.f64 (*.f64 v v))))))
32.0ms	(.f64 t (.f64 PI.f64 (-.f64 -1 (neg.f64 (*.f64 v v)))))
21.0ms	(/.f64 (+.f64 -1 (.f64 (.f64 v v) 5)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))
9.0ms	(.f64 (.f64 v v) 6)

Compiler

Compiled 2105 to 1585 computations (24.7% saved)

simplify203.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

393×	`div-sub_binary64`
382×	`associate-l_binary64`
367×	`associate-r_binary64`
298×	`associate-/r*_binary64`
252×	`times-frac_binary64`

Counts

219 → 197

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	434	8092
1	1070	7273
2	4137	7273
3	5285	7273

prune146.0ms (2.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	197	5	202

Error

Counts

202 → 5

Alt Table

Status	Error	Program
	0.4b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (-.f64 1 (.f64 v v)) (.f64 t PI.f64))))
	0.6b	(.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (-.f64 1 (.f64 v v)) (.f64 t PI.f64))) (sqrt.f64 (/.f64 1 (-.f64 2 (.f64 (.f64 v v) 6)))))
	0.8b	(/.f64 (-.f64 (+.f64 (sqrt.f64 1/2) (.f64 3/4 (/.f64 (.f64 v v) (sqrt.f64 1/2)))) (.f64 5 (.f64 (sqrt.f64 1/2) (.f64 v v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))
	0.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 t (.f64 PI.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))) (-.f64 1 (.f64 v v))))
	0.4b	(/.f64 (/.f64 (+.f64 -1 (.f64 (.f64 v v) 5)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (.f64 t (.f64 PI.f64 (-.f64 -1 (neg.f64 (*.f64 v v))))))

Compiler

Compiled 4589 to 2866 computations (37.5% saved)

regimes1.3s (25.5%)

Accuracy

Total 0.2b remaining (85.7%)

Threshold costs 0.2b (85.7%)

Compiler

Compiled 31123 to 21728 computations (30.2% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

21×	`cancel-sign-sub-inv_binary64`
20×	`distribute-rgt-neg-in_binary64`
13×	`distribute-lft-neg-out_binary64`
12×	`distribute-lft-neg-in_binary64`
11×	`neg-mul-1_binary64` `neg-sub0_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	45
1	40	43
2	60	43
3	81	43
4	101	43
5	114	43
6	119	43
7	121	43
8	113	43

end1.0ms (0%)

Compiler: Compiled 30 to 21 computations (30% saved)

sample886.0ms (17%)

Algorithm

1×

intervals

Results

505.0ms	8000×	body	128	valid
1.0ms	10×	body	128	nan

Compiler

Compiled 212 to 149 computations (29.7% saved)

Details

analyze141.0ms (2.7%)

sample24.0ms (0.5%)

simplify53.0ms (1%)

prune4.0ms (0.1%)

localize15.0ms (0.3%)

rewrite210.0ms (4%)

series167.0ms (3.2%)

simplify138.0ms (2.6%)

prune137.0ms (2.6%)

localize16.0ms (0.3%)

rewrite167.0ms (3.2%)

series152.0ms (2.9%)

simplify111.0ms (2.1%)

prune102.0ms (2%)

localize14.0ms (0.3%)

rewrite245.0ms (4.7%)

series131.0ms (2.5%)

simplify221.0ms (4.2%)

prune126.0ms (2.4%)

localize15.0ms (0.3%)

rewrite291.0ms (5.6%)

series163.0ms (3.1%)

simplify203.0ms (3.9%)

prune146.0ms (2.8%)

regimes1.3s (25.5%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample886.0ms (17%)

Profiling