Details

analyze7.0ms

Algorithm

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
37.5%	37.5%	25.1%	2
37.5%	18.7%	43.8%	3
46.8%	9.4%	43.8%	4
51.5%	4.7%	43.8%	5
51.5%	2.3%	46.1%	6
52.7%	1.2%	46.1%	7
53.3%	0.6%	46.1%	8
53.3%	0.3%	46.4%	9
53.4%	0.1%	46.4%	10
53.5%	0.1%	46.4%	11
53.5%	0%	46.5%	12
53.5%	0%	46.5%	13
53.5%	0%	46.5%	14

sample34.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify285.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (141.0ms)

Iter	Nodes	Cost
0	5204	47

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

Merged error: 0.0b

Counts

2 → 2

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
0.1b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
0.1b	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
1.0b	(sqrt.f64 PI.f64)

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

119×	`add-exp-log_binary64_554`
76×	`prod-exp_binary64_537`
75×	`add-cbrt-cube_binary64_562`
48×	`associate-l_binary64_650`
46×	`add-sqr-sqrt_binary64_575`
44×	`cbrt-unprod_binary64_559`
40×	`times-frac_binary64_585`
36×	`pow1_binary64_532`
35×	`*-un-lft-identity_binary64_590`
33×	`add-cube-cbrt_binary64_561`
22×	`pow-prod-down_binary64_513`
15×	`associate-*l/_binary64_652` `div-exp_binary64_539`
14×	`sqrt-prod_binary64_569`
12×	`frac-add_binary64_580`
9×	`cbrt-undiv_binary64_560`
6×	`flip-+_binary64_615` `rec-exp_binary64_538` `frac-times_binary64_582` `flip3-+_binary64_588` `associate-*r/_binary64_651` `1-exp_binary64_550`
5×	`unswap-sqr_binary64_618` `associate-r_binary64_649`
4×	`add-log-exp_binary64_555`
3×	`div-inv_binary64_591` `*-commutative_binary64_658`
1×	`rem-sqrt-square_binary64_578` `distribute-rgt-in_binary64_633` `distribute-lft-in_binary64_632` `pow1/2_binary64_522` `sqrt-pow1_binary64_571`

Counts

4 → 169

Calls

4 calls:

28.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
12.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
30.0ms	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
2.0ms	(sqrt.f64 PI.f64)

series409.0ms

Counts

4 → 10

Calls

4 calls:

63.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
43.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
304.0ms	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
0.0ms	(sqrt.f64 PI.f64)

simplify161.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4900	5408
1	4900	5408

prune314.0ms

Filtered

106 candidates to 179 candidates (-68.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	175	4	179
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	177	4	181

Merged error: 0b

Counts

181 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
0.1b	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
0.1b	(.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (/.f64 1 PI.f64)))
0.1b	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt_binary64_575`
42×	`associate-r_binary64_649`
24×	`*-un-lft-identity_binary64_590`
23×	`add-cube-cbrt_binary64_561`
21×	`add-exp-log_binary64_554`
16×	`sqrt-prod_binary64_569`
14×	`unswap-sqr_binary64_618`
12×	`add-cbrt-cube_binary64_562` `unpow-prod-down_binary64_521` `associate-l_binary64_650`
11×	`times-frac_binary64_585`
10×	`prod-exp_binary64_537`
6×	`sqr-pow_binary64_622` `pow1_binary64_532`
4×	`cbrt-unprod_binary64_559` `*-commutative_binary64_658` `add-log-exp_binary64_555` `cube-prod_binary64_563`
3×	`pow-to-exp_binary64_511` `sqrt-div_binary64_570` `pow-exp_binary64_510`
2×	`flip-+_binary64_615` `frac-times_binary64_582` `associate-*l/_binary64_652` `flip3-+_binary64_588`
1×	`pow-prod-down_binary64_513` `div-inv_binary64_591` `cube-mult_binary64_565` `unpow3_binary64_530` `associate-*r/_binary64_651`

Counts

4 → 120

Calls

4 calls:

5.0ms	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
5.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
17.0ms	(.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (/.f64 1 PI.f64)))
7.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))

series464.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
62.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
286.0ms	(.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (/.f64 1 PI.f64)))
43.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))

simplify107.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5186	3518

prune196.0ms

Filtered

87 candidates to 132 candidates (-51.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	132	4	136

Merged error: 0b

Counts

136 → 4

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (sqrt.f64 PI.f64)))
0.3b	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 PI.f64))) (/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (sqrt.f64 PI.f64))))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt_binary64_575`
141×	`sqrt-prod_binary64_569`
126×	`times-frac_binary64_585`
78×	`*-un-lft-identity_binary64_590`
66×	`add-cube-cbrt_binary64_561`
31×	`associate-l_binary64_650` `associate-r_binary64_649`
28×	`unswap-sqr_binary64_618` `add-exp-log_binary64_554`
18×	`add-cbrt-cube_binary64_562`
9×	`associate-/r*_binary64_653` `div-exp_binary64_539`
8×	`prod-exp_binary64_537` `pow1_binary64_532`
5×	`cbrt-undiv_binary64_560`
4×	`cbrt-unprod_binary64_559` `add-log-exp_binary64_555`
3×	`div-inv_binary64_591` `associate-/l*_binary64_654`
2×	`rem-sqrt-square_binary64_578` `rec-exp_binary64_538` `pow1/2_binary64_522` `associate-/l/_binary64_656` `sqrt-pow1_binary64_571` `1-exp_binary64_550`
1×	`pow-prod-down_binary64_513` `flip-+_binary64_615` `frac-times_binary64_582` `-commutative_binary64_658` `frac-2neg_binary64_583` `associate-l/_binary64_652` `flip3-+_binary64_588` `clear-num_binary64_593` `associate-*r/_binary64_651`

Counts

4 → 193

Calls

4 calls:

15.0ms	(/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (sqrt.f64 PI.f64)))
33.0ms	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 PI.f64))) (/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (sqrt.f64 PI.f64))))
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

series650.0ms

Counts

4 → 8

Calls

4 calls:

359.0ms	(/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (sqrt.f64 PI.f64)))
290.0ms	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 PI.f64))) (/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (sqrt.f64 PI.f64))))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify174.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4934	12016
1	4934	12016

prune276.0ms

Filtered

107 candidates to 201 candidates (-87.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	201	4	205

Merged error: 0b

Counts

205 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
1.0b	(/.f64 1/21 (sqrt.f64 PI.f64))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64_575`
36×	`add-cube-cbrt_binary64_561` `*-un-lft-identity_binary64_590` `times-frac_binary64_585`
30×	`sqrt-prod_binary64_569`
12×	`associate-/r*_binary64_653`
8×	`add-cbrt-cube_binary64_562` `add-exp-log_binary64_554`
6×	`pow1_binary64_532` `associate-/l*_binary64_654`
4×	`add-log-exp_binary64_555`
2×	`rem-sqrt-square_binary64_578` `div-inv_binary64_591` `cbrt-undiv_binary64_560` `frac-2neg_binary64_583` `pow1/2_binary64_522` `associate-/l/_binary64_656` `sqrt-pow1_binary64_571` `clear-num_binary64_593` `div-exp_binary64_539`
1×	`flip-+_binary64_615` `flip3-+_binary64_588`

Counts

4 → 106

Calls

4 calls:

14.0ms	(/.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (sqrt.f64 PI.f64))
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)
4.0ms	(/.f64 1/21 (sqrt.f64 PI.f64))

series193.0ms

Counts

4 → 6

Calls

4 calls:

193.0ms	(/.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (sqrt.f64 PI.f64))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(/.f64 1/21 (sqrt.f64 PI.f64))

simplify72.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4924	3173
1	4924	3173

prune158.0ms

Filtered

76 candidates to 112 candidates (-47.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	112	4	116

Merged error: 0b

Counts

116 → 4

regimes31.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	50
1	36	50

end0.0ms

sample930.0ms

Algorithm

intervals

Results

726.0ms	8000×	body	80	valid
87.0ms	8001×	pre	80	true
0.0ms	1×	body	80	invalid

Details

analyze7.0ms

sample34.0ms

simplify285.0ms

prune7.0ms

localize27.0ms

rewrite81.0ms

series409.0ms

simplify161.0ms

prune314.0ms

localize19.0ms

rewrite38.0ms

series464.0ms

simplify107.0ms

prune196.0ms

localize23.0ms

rewrite61.0ms

series650.0ms

simplify174.0ms

prune276.0ms

localize19.0ms

rewrite24.0ms

series193.0ms

simplify72.0ms

prune158.0ms

regimes31.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample930.0ms

Profiling