Details

analyze216.0ms (4.3%)

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)

sample30.0ms (0.6%)

Algorithm

1×

intervals

Results

22.0ms

256×

body

128

valid

Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify53.0ms (1.1%)

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

prune3.0ms (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

0.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	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)))))

Compiler

Compiled 84 to 60 computations (28.6% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 5 (.f64 v v))
0.2b	(/.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)))))
0.2b	(*.f64 PI.f64 t)
0.4b	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))

rewrite162.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

34×	`add-cbrt-cube_binary64`
34×	`add-exp-log_binary64`
20×	`pow1_binary64`
16×	`associate-*r/_binary64`
16×	`cbrt-unprod_binary64`

Counts

4 → 113

Calls

4 calls:

13.0ms	(/.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)))))
11.0ms	(.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))
3.0ms	(*.f64 PI.f64 t)

Compiler

Compiled 4225 to 2542 computations (39.8% saved)

series141.0ms (2.8%)

Error

0.1b

Counts

4 → 24

Calls

4 calls:

66.0ms	(/.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)))))
40.0ms	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))
7.0ms	(.f64 5 (.f64 v v))
6.0ms	(*.f64 PI.f64 t)

Compiler

Compiled 2133 to 1600 computations (25% saved)

simplify169.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

670×	`times-frac_binary64`
513×	`associate-l_binary64`
490×	`associate-/r*_binary64`
317×	`associate-/l*_binary64`
116×	`*-commutative_binary64`

Counts

137 → 107

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	372	5350
1	1060	4696
2	4751	4669
3	4933	4669
4	4972	4669

prune101.0ms (2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	102	5	107
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	5	108

Error

0.0b

Counts

108 → 5

Alt Table

Status	Error	Program
	0.3b	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))) (.f64 (/.f64 5 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (/.f64 (.f64 v v) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))))
	0.7b	(.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))) (sqrt.f64 (/.f64 1 (-.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))))
	0.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 1 (.f64 PI.f64 (.f64 (.f64 t (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6)))))))
	0.4b	(.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 5 (.f64 v v)))) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 5 (.f64 v v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))

Compiler

Compiled 3089 to 1927 computations (37.6% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 v v) 6)
0.1b	(.f64 5 (.f64 v v))
0.2b	(.f64 t (.f64 PI.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))))
0.2b	(/.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))))

rewrite137.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

33×	`add-cbrt-cube_binary64`
33×	`add-exp-log_binary64`
19×	`pow1_binary64`
18×	`associate-*r/_binary64`
15×	`cbrt-unprod_binary64`

Counts

4 → 94

Calls

4 calls:

15.0ms	(/.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))))
6.0ms	(.f64 t (.f64 PI.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))))
5.0ms	(.f64 (.f64 v v) 6)
4.0ms	(.f64 5 (.f64 v v))

Compiler

Compiled 3351 to 2003 computations (40.2% saved)

series129.0ms (2.6%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

65.0ms	(/.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))))
30.0ms	(.f64 t (.f64 PI.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))))
9.0ms	(.f64 5 (.f64 v v))
7.0ms	(.f64 (.f64 v v) 6)

Compiler

Compiled 1987 to 1459 computations (26.6% saved)

simplify115.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

604×	`times-frac_binary64`
450×	`associate-l_binary64`
403×	`associate-r_binary64`
401×	`associate-/r*_binary64`
319×	`associate-/l*_binary64`

Counts

118 → 96

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	337	4091
1	962	3587
2	4777	3578
3	5127	3578

prune93.0ms (1.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	96	5	101

Error

0.0b

Counts

101 → 5

Alt Table

Status	Error	Program
	0.3b	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))) (.f64 (/.f64 5 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (/.f64 (.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))))
▶	0.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 1 (.f64 PI.f64 (.f64 (.f64 t (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6)))))))
	0.7b	(.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 t (-.f64 PI.f64 (.f64 PI.f64 (.f64 v v))))) (sqrt.f64 (/.f64 1 (-.f64 2 (.f64 (.f64 v v) 6)))))
	0.4b	(.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 5 (.f64 v v)))) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 5 (.f64 v v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))

Compiler

Compiled 2751 to 1684 computations (38.8% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 5 (.f64 v v))
0.2b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 1 (.f64 PI.f64 (.f64 (.f64 t (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6)))))))
0.3b	(.f64 PI.f64 (.f64 (.f64 t (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))))
0.4b	(.f64 (.f64 t (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6))))

rewrite186.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

57×	`add-exp-log_binary64`
48×	`associate-*r/_binary64`
43×	`add-cbrt-cube_binary64`
32×	`prod-exp_binary64`
23×	`pow1_binary64`

Counts

4 → 119

Calls

4 calls:

17.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 1 (.f64 PI.f64 (.f64 (.f64 t (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6)))))))
10.0ms	(.f64 PI.f64 (.f64 (.f64 t (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))))
9.0ms	(.f64 (.f64 t (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6))))
4.0ms	(.f64 5 (.f64 v v))

Compiler

Compiled 4948 to 3046 computations (38.4% saved)

series187.0ms (3.7%)

Error

0.0b

Counts

4 → 30

Calls

4 calls:

70.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 1 (.f64 PI.f64 (.f64 (.f64 t (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6)))))))
40.0ms	(.f64 PI.f64 (.f64 (.f64 t (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))))
35.0ms	(.f64 (.f64 t (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6))))
7.0ms	(.f64 5 (.f64 v v))

Compiler

Compiled 2802 to 2164 computations (22.8% saved)

simplify150.0ms (3%)

Algorithm

1×	egg-herbie

Rules

612×	`associate-r_binary64`
560×	`associate-l_binary64`
557×	`associate-/r*_binary64`
393×	`associate-/l*_binary64`
167×	`*-commutative_binary64`

Counts

149 → 125

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	442	6131
1	1238	5353
2	4929	5353
3	4969	5353

prune117.0ms (2.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	125	5	130

Error

0.0b

Counts

130 → 5

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))) (.f64 (/.f64 5 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (/.f64 (.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))))
✓	0.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 1 (.f64 PI.f64 (.f64 (.f64 t (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6)))))))
	0.7b	(.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 t (-.f64 PI.f64 (.f64 PI.f64 (.f64 v v))))) (sqrt.f64 (/.f64 1 (-.f64 2 (.f64 (.f64 v v) 6)))))
	0.4b	(.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 5 (.f64 v v)))) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 5 (.f64 v v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))

Compiler

Compiled 3778 to 2419 computations (36% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 (/.f64 1 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
1.0b	(/.f64 5 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))
1.0b	(/.f64 1 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))
10.5b	(/.f64 (.f64 v v) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))

rewrite285.0ms (5.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

97×	`times-frac_binary64`
70×	`add-exp-log_binary64`
60×	`*-un-lft-identity_binary64`
60×	`add-sqr-sqrt_binary64`
60×	`add-cube-cbrt_binary64`

Counts

4 → 195

Calls

4 calls:

12.0ms	(/.f64 (/.f64 1 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
10.0ms	(/.f64 (.f64 v v) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))
5.0ms	(/.f64 1 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))
5.0ms	(/.f64 5 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))

Compiler

Compiled 10215 to 5838 computations (42.8% saved)

series169.0ms (3.4%)

Error

0.0b

Counts

4 → 30

Calls

4 calls:

58.0ms	(/.f64 (/.f64 1 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
36.0ms	(/.f64 (.f64 v v) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))
21.0ms	(/.f64 1 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))
16.0ms	(/.f64 5 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))

Compiler

Compiled 3947 to 2634 computations (33.3% saved)

simplify242.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

671×	`times-frac_binary64`
505×	`associate-/r*_binary64`
404×	`associate-/l*_binary64`
191×	`associate-*r/_binary64`
163×	`associate-*l/_binary64`

Counts

225 → 161

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	432	8957
1	1208	7963
2	4750	7963
3	4918	7963
4	4996	7963

prune116.0ms (2.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	161	5	166

Error

0.0b

Counts

166 → 5

Alt Table

Status	Error	Program
✓	0.3b	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))) (.f64 (/.f64 5 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (/.f64 (.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))))
✓	0.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 1 (.f64 PI.f64 (.f64 (.f64 t (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6)))))))
	0.7b	(.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 t (-.f64 PI.f64 (.f64 PI.f64 (.f64 v v))))) (sqrt.f64 (/.f64 1 (-.f64 2 (.f64 (.f64 v v) 6)))))
	0.4b	(.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 5 (.f64 v v)))) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 5 (.f64 v v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))

Compiler

Compiled 5003 to 2910 computations (41.8% saved)

regimes1.1s (22%)

Accuracy

Total 0.3b remaining (84.4%)

Threshold costs 0.3b (84.4%)

Compiler

Compiled 27933 to 19237 computations (31.1% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
7×	`+-commutative_binary64`
7×	`sub-neg_binary64`
5×	`distribute-rgt-neg-in_binary64`
5×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	40
1	40	40
2	58	40
3	66	40
4	70	40
5	67	40

end1.0ms (0%)

Compiler: Compiled 28 to 19 computations (32.1% saved)

sample1.0s (20.8%)

Algorithm

1×

intervals

Results

685.0ms	8000×	body	128	valid
1.0ms	17×	body	128	nan

Compiler

Compiled 234 to 158 computations (32.5% saved)

Details

analyze216.0ms (4.3%)

sample30.0ms (0.6%)

simplify53.0ms (1.1%)

prune3.0ms (0.1%)

localize15.0ms (0.3%)

rewrite162.0ms (3.2%)

series141.0ms (2.8%)

simplify169.0ms (3.4%)

prune101.0ms (2%)

localize14.0ms (0.3%)

rewrite137.0ms (2.7%)

series129.0ms (2.6%)

simplify115.0ms (2.3%)

prune93.0ms (1.9%)

localize15.0ms (0.3%)

rewrite186.0ms (3.7%)

series187.0ms (3.7%)

simplify150.0ms (3%)

prune117.0ms (2.3%)

localize18.0ms (0.3%)

rewrite285.0ms (5.7%)

series169.0ms (3.4%)

simplify242.0ms (4.8%)

prune116.0ms (2.3%)

regimes1.1s (22%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.0s (20.8%)

Profiling