Details

analyze187.0ms (5.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50.1%	13
49.9%	0%	50.1%	14

Compiler

Compiled 22 to 17 computations (22.7% saved)

sample22.0ms (0.7%)

Algorithm

1×

intervals

Results

16.0ms

256×

body

128

valid

Compiler

Compiled 44 to 34 computations (22.7% saved)

simplify177.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

889×	`associate-/r*_binary64`
839×	`neg-mul-1_binary64`
735×	`sub-neg_binary64`
637×	`neg-sub0_binary64`
568×	`associate-/l/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	31
1	42	28
2	102	28
3	247	28
4	623	28
5	883	28
6	1301	28
7	2726	28
8	3095	28
9	3370	28
10	3431	28
11	3460	28
12	3552	28
13	4935	28
14	4948	28
15	4655	28
16	4895	28
17	4843	28

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

0.0b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 4/3 (.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6))))))
	1.0b	(/.f64 4 (.f64 (.f64 (.f64 3 PI.f64) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))

Status

Error

Program

▶

0.0b

(/.f64 4/3 (*.f64 PI.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))))

1.0b

(/.f64 4 (*.f64 (*.f64 (*.f64 3 PI.f64) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))

Compiler

Compiled 99 to 74 computations (25.3% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6)))))
0.0b	(/.f64 4/3 (.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6))))))
0.0b	(.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))
0.2b	(.f64 (.f64 v v) 6)

rewrite150.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

25×	`add-cbrt-cube_binary64`
25×	`add-exp-log_binary64`
22×	`associate-*r/_binary64`
18×	`flip--_binary64`
18×	`sqrt-div_binary64`

Counts

4 → 108

Calls

4 calls:

9.0ms	(/.f64 4/3 (.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6))))))
8.0ms	(.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))
8.0ms	(.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6)))))
5.0ms	(.f64 (.f64 v v) 6)

Compiler

Compiled 3262 to 2040 computations (37.5% saved)

series71.0ms (2.1%)

Error

0.0b

Counts

4 → 21

Calls

4 calls:

21.0ms	(/.f64 4/3 (.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6))))))
15.0ms	(.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6)))))
12.0ms	(.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))
5.0ms	(.f64 (.f64 v v) 6)

Compiler

Compiled 1423 to 1211 computations (14.9% saved)

simplify150.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

425×	`distribute-rgt-in_binary64`
376×	`cancel-sign-sub-inv_binary64`
270×	`associate-r_binary64`
242×	`distribute-rgt-neg-in_binary64`
240×	`associate-l_binary64`

Counts

129 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	312	3865
1	772	3451
2	3093	3390
3	4932	3390
4	4993	3390
5	4945	3390

prune94.0ms (2.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	109	2	111

Error

Counts

111 → 2

Alt Table

Status	Error	Program
	0.0b	(/.f64 4/3 (.f64 PI.f64 (/.f64 (.f64 (-.f64 1 (pow.f64 v 6)) (sqrt.f64 (-.f64 4 (.f64 (pow.f64 v 4) 36)))) (.f64 (+.f64 1 (+.f64 (.f64 v v) (pow.f64 v 4))) (sqrt.f64 (+.f64 2 (.f64 6 (*.f64 v v))))))))
▶	0.0b	(/.f64 4/3 (.f64 PI.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 v v))) (.f64 (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))) (sqrt.f64 (-.f64 1 (*.f64 v v)))))))

Status

Error

Program

0.0b

(/.f64 4/3 (*.f64 PI.f64 (/.f64 (*.f64 (-.f64 1 (pow.f64 v 6)) (sqrt.f64 (-.f64 4 (*.f64 (pow.f64 v 4) 36)))) (*.f64 (+.f64 1 (+.f64 (*.f64 v v) (pow.f64 v 4))) (sqrt.f64 (+.f64 2 (*.f64 6 (*.f64 v v))))))))

▶

0.0b

(/.f64 4/3 (*.f64 PI.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 v v))) (*.f64 (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))) (sqrt.f64 (-.f64 1 (*.f64 v v)))))))

Compiler

Compiled 2714 to 1849 computations (31.9% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 4/3 (.f64 PI.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 v v))) (.f64 (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))) (sqrt.f64 (-.f64 1 (*.f64 v v)))))))
0.0b	(.f64 (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))) (sqrt.f64 (-.f64 1 (.f64 v v))))
0.0b	(.f64 (sqrt.f64 (-.f64 1 (.f64 v v))) (.f64 (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))) (sqrt.f64 (-.f64 1 (.f64 v v)))))
0.2b	(.f64 6 (.f64 v v))

rewrite256.0ms (7.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

120×	`sqrt-div_binary64`
60×	`flip--_binary64`
60×	`frac-times_binary64`
60×	`flip3--_binary64`
56×	`associate-*r/_binary64`

Counts

4 → 164

Calls

4 calls:

19.0ms	(/.f64 4/3 (.f64 PI.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 v v))) (.f64 (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))) (sqrt.f64 (-.f64 1 (*.f64 v v)))))))
13.0ms	(.f64 (sqrt.f64 (-.f64 1 (.f64 v v))) (.f64 (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))) (sqrt.f64 (-.f64 1 (.f64 v v)))))
12.0ms	(.f64 (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))) (sqrt.f64 (-.f64 1 (.f64 v v))))
4.0ms	(.f64 6 (.f64 v v))

Compiler

Compiled 7298 to 4501 computations (38.3% saved)

series83.0ms (2.4%)

Error

Counts

4 → 23

Calls

4 calls:

27.0ms	(/.f64 4/3 (.f64 PI.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 v v))) (.f64 (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))) (sqrt.f64 (-.f64 1 (*.f64 v v)))))))
17.0ms	(.f64 (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))) (sqrt.f64 (-.f64 1 (.f64 v v))))
13.0ms	(.f64 (sqrt.f64 (-.f64 1 (.f64 v v))) (.f64 (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))) (sqrt.f64 (-.f64 1 (.f64 v v)))))
6.0ms	(.f64 6 (.f64 v v))

Compiler

Compiled 1576 to 1336 computations (15.2% saved)

simplify182.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

486×	`associate-r_binary64`
312×	`associate-l_binary64`
296×	`cancel-sign-sub-inv_binary64`
273×	`distribute-rgt-in_binary64`
257×	`associate-/r*_binary64`

Counts

187 → 157

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	404	7182
1	913	5967
2	3307	5768
3	4807	5768
4	4966	5768

prune164.0ms (4.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	157	2	159

Error

Counts

159 → 2

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 4/3 (.f64 PI.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 v v))) (.f64 (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))) (sqrt.f64 (-.f64 1 (*.f64 v v)))))))
▶	0.0b	(/.f64 4/3 (.f64 PI.f64 (sqrt.f64 (.f64 (-.f64 1 (.f64 v v)) (.f64 (-.f64 1 (.f64 v v)) (-.f64 2 (.f64 6 (*.f64 v v))))))))

Status

Error

Program

✓

0.0b

(/.f64 4/3 (*.f64 PI.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 v v))) (*.f64 (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))) (sqrt.f64 (-.f64 1 (*.f64 v v)))))))

▶

0.0b

(/.f64 4/3 (*.f64 PI.f64 (sqrt.f64 (*.f64 (-.f64 1 (*.f64 v v)) (*.f64 (-.f64 1 (*.f64 v v)) (-.f64 2 (*.f64 6 (*.f64 v v))))))))

Compiler

Compiled 4753 to 3209 computations (32.5% saved)

localize19.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 4/3 (.f64 PI.f64 (sqrt.f64 (.f64 (-.f64 1 (.f64 v v)) (.f64 (-.f64 1 (.f64 v v)) (-.f64 2 (.f64 6 (*.f64 v v))))))))
0.0b	(.f64 (-.f64 1 (.f64 v v)) (-.f64 2 (.f64 6 (.f64 v v))))
0.0b	(.f64 (-.f64 1 (.f64 v v)) (.f64 (-.f64 1 (.f64 v v)) (-.f64 2 (.f64 6 (.f64 v v)))))
0.2b	(.f64 6 (.f64 v v))

rewrite221.0ms (6.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

60×	`flip--_binary64`
60×	`frac-times_binary64`
60×	`flip3--_binary64`
56×	`associate-*r/_binary64`
26×	`associate-/r/_binary64`

Counts

4 → 152

Calls

4 calls:

17.0ms	(/.f64 4/3 (.f64 PI.f64 (sqrt.f64 (.f64 (-.f64 1 (.f64 v v)) (.f64 (-.f64 1 (.f64 v v)) (-.f64 2 (.f64 6 (*.f64 v v))))))))
10.0ms	(.f64 (-.f64 1 (.f64 v v)) (.f64 (-.f64 1 (.f64 v v)) (-.f64 2 (.f64 6 (.f64 v v)))))
7.0ms	(.f64 (-.f64 1 (.f64 v v)) (-.f64 2 (.f64 6 (.f64 v v))))
4.0ms	(.f64 6 (.f64 v v))

Compiler

Compiled 6637 to 3904 computations (41.2% saved)

series63.0ms (1.9%)

Error

Counts

4 → 22

Calls

4 calls:

22.0ms	(/.f64 4/3 (.f64 PI.f64 (sqrt.f64 (.f64 (-.f64 1 (.f64 v v)) (.f64 (-.f64 1 (.f64 v v)) (-.f64 2 (.f64 6 (*.f64 v v))))))))
12.0ms	(.f64 (-.f64 1 (.f64 v v)) (.f64 (-.f64 1 (.f64 v v)) (-.f64 2 (.f64 6 (.f64 v v)))))
9.0ms	(.f64 (-.f64 1 (.f64 v v)) (-.f64 2 (.f64 6 (.f64 v v))))
6.0ms	(.f64 6 (.f64 v v))

Compiler

Compiled 1179 to 973 computations (17.5% saved)

simplify176.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

337×	`associate-r_binary64`
326×	`associate-l_binary64`
316×	`neg-mul-1_binary64`
261×	`cancel-sign-sub-inv_binary64`
233×	`distribute-rgt-in_binary64`

Counts

174 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	386	5903
1	914	5402
2	3394	5331
3	4682	5331
4	5110	5331

prune107.0ms (3.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	125	2	127

Error

Counts

127 → 2

Alt Table

Status	Error	Program
	0.0b	(/.f64 4/3 (.f64 PI.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 v v))) (.f64 (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))) (sqrt.f64 (-.f64 1 (*.f64 v v)))))))
	0.0b	(/.f64 4/3 (.f64 PI.f64 (sqrt.f64 (.f64 (-.f64 1 (.f64 v v)) (.f64 (-.f64 1 (.f64 v v)) (-.f64 2 (.f64 6 (*.f64 v v))))))))

Status

Error

Program

0.0b

(/.f64 4/3 (*.f64 PI.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 v v))) (*.f64 (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))) (sqrt.f64 (-.f64 1 (*.f64 v v)))))))

0.0b

(/.f64 4/3 (*.f64 PI.f64 (sqrt.f64 (*.f64 (-.f64 1 (*.f64 v v)) (*.f64 (-.f64 1 (*.f64 v v)) (-.f64 2 (*.f64 6 (*.f64 v v))))))))

Compiler

Compiled 3466 to 2294 computations (33.8% saved)

regimes475.0ms (13.9%)

Accuracy

Total 0.0b remaining (45.3%)

Threshold costs 0.0b (45.3%)

Compiler

Compiled 13130 to 9786 computations (25.5% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	41
1	34	41
2	45	41
3	51	41
4	54	41
5	52	41

end1.0ms (0%)

Compiler: Compiled 27 to 19 computations (29.6% saved)

sample775.0ms (22.8%)

Algorithm

1×

intervals

Results

538.0ms	8000×	body	128	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 102 to 73 computations (28.4% saved)

Details

analyze187.0ms (5.5%)

sample22.0ms (0.7%)

simplify177.0ms (5.2%)

prune4.0ms (0.1%)

localize9.0ms (0.3%)

rewrite150.0ms (4.4%)

series71.0ms (2.1%)

simplify150.0ms (4.4%)

prune94.0ms (2.8%)

localize13.0ms (0.4%)

rewrite256.0ms (7.5%)

series83.0ms (2.4%)

simplify182.0ms (5.3%)

prune164.0ms (4.8%)

localize19.0ms (0.5%)

rewrite221.0ms (6.5%)

series63.0ms (1.9%)

simplify176.0ms (5.2%)

prune107.0ms (3.2%)

regimes475.0ms (13.9%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample775.0ms (22.8%)

Profiling