Details

analyze1.1s

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	75%	25%	3
0%	62.5%	37.5%	4
0%	56.2%	43.8%	5
3.1%	46.9%	50%	6
3.1%	45.3%	51.6%	7
3.1%	44.5%	52.4%	8
3.5%	44.1%	52.4%	9
3.7%	43.9%	52.4%	10
3.8%	43.8%	52.4%	11
3.8%	43.8%	52.4%	12
3.8%	43.8%	52.4%	13
3.8%	43.7%	52.4%	14

sample231.0ms

Algorithm

intervals

Results

68.0ms	124×	body	1024	valid
61.0ms	115×	body	1024	nan
24.0ms	62×	body	512	valid
23.0ms	61×	body	512	nan
21.0ms	17×	body	2048	valid
11.0ms	37×	body	256	valid
7.0ms	30×	body	256	nan
2.0ms	16×	body	128	valid

simplify234.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4831	55
1	4831	55

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

Merged error: 62.2b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 PI.f64 4) f)
0.3b	(*.f64 (/.f64 PI.f64 4) f)
1.2b	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
5.3b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-sqr-sqrt_binary64`
61×	`*-un-lft-identity_binary64`
48×	`times-frac_binary64`
33×	`add-cube-cbrt_binary64`
26×	`associate-l_binary64`
18×	`difference-of-squares_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64` `distribute-lft-out_binary64`
7×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `distribute-lft-out--_binary64`
4×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l*_binary64`
3×	`cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`

Counts

4 → 134

Calls

4 calls:

7.0ms	(*.f64 (/.f64 PI.f64 4) f)
7.0ms	(*.f64 (/.f64 PI.f64 4) f)
14.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
8.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

series612.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(*.f64 (/.f64 PI.f64 4) f)
41.0ms	(*.f64 (/.f64 PI.f64 4) f)
445.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
90.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

simplify75.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5328	5639

prune308.0ms

Filtered

104 candidates to 146 candidates (-40.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	145	2	147

Merged error: 1.6b

Counts

147 → 2

localize82.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow.f64 PI.f64 3)
1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 PI.f64 4)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
12×	`pow-unpow_binary64` `unpow-prod-down_binary64`
8×	`pow1_binary64` `add-exp-log_binary64`
5×	`add-cbrt-cube_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `pow-pow_binary64` `sqr-pow_binary64` `pow-exp_binary64`
3×	`cube-prod_binary64`
1×	`rem-cube-cbrt_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 74

Calls

4 calls:

3.0ms	(pow.f64 PI.f64 3)
3.0ms	(pow.f64 PI.f64 4)
3.0ms	(pow.f64 PI.f64 4)
3.0ms	(pow.f64 PI.f64 4)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(pow.f64 PI.f64 3)
0.0ms	(pow.f64 PI.f64 4)
0.0ms	(pow.f64 PI.f64 4)
0.0ms	(pow.f64 PI.f64 4)

simplify43.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5295	1148

prune551.0ms

Filtered

46 candidates to 78 candidates (-69.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	78	2	80

Merged error: 1.6b

Counts

80 → 2

localize95.0ms

Local error

Found 4 expressions with local error:

1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 (cbrt.f64 PI.f64) 4)
2.0b	(pow.f64 (cbrt.f64 PI.f64) 8)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

18×	`unpow-prod-down_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
12×	`pow-unpow_binary64`
8×	`pow1_binary64` `add-exp-log_binary64`
6×	`pow-pow_binary64` `cbrt-prod_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `sqr-pow_binary64` `add-cbrt-cube_binary64` `pow-exp_binary64`
2×	`pow1/3_binary64`

Counts

4 → 76

Calls

4 calls:

3.0ms	(pow.f64 PI.f64 4)
2.0ms	(pow.f64 PI.f64 4)
3.0ms	(pow.f64 (cbrt.f64 PI.f64) 4)
4.0ms	(pow.f64 (cbrt.f64 PI.f64) 8)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(pow.f64 PI.f64 4)
0.0ms	(pow.f64 PI.f64 4)
0.0ms	(pow.f64 (cbrt.f64 PI.f64) 4)
0.0ms	(pow.f64 (cbrt.f64 PI.f64) 8)

simplify42.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5147	1240

prune696.0ms

Filtered

53 candidates to 80 candidates (-50.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	80	2	82

Merged error: 1.6b

Counts

82 → 2

localize98.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt.f64 PI.f64)
1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 (cbrt.f64 PI.f64) 4)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `unpow-prod-down_binary64`
9×	`pow-unpow_binary64`
8×	`pow1_binary64`
7×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `pow-pow_binary64` `add-cbrt-cube_binary64`
3×	`pow-to-exp_binary64` `sqr-pow_binary64` `sqrt-prod_binary64` `cbrt-prod_binary64` `pow-exp_binary64`
1×	`pow1/2_binary64` `pow1/3_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 68

Calls

4 calls:

2.0ms	(sqrt.f64 PI.f64)
2.0ms	(pow.f64 PI.f64 4)
2.0ms	(pow.f64 PI.f64 4)
4.0ms	(pow.f64 (cbrt.f64 PI.f64) 4)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(sqrt.f64 PI.f64)
0.0ms	(pow.f64 PI.f64 4)
0.0ms	(pow.f64 PI.f64 4)
0.0ms	(pow.f64 (cbrt.f64 PI.f64) 4)

simplify53.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4885	578
1	4885	578

prune546.0ms

Filtered

44 candidates to 72 candidates (-63.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	72	2	74

Merged error: 1.6b

Counts

74 → 2

regimes31.0ms

Accuracy

0% (0.5b remaining)

Error of 2.5b against oracle of 2.0b and baseline of 2.5b

bsearch0.0ms

simplify8.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	319	319
1	319	319

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.1s	3811×	body	1024	valid
1.9s	3985×	body	1024	nan
772.0ms	2011×	body	512	valid
694.0ms	1954×	body	512	nan
608.0ms	534×	body	2048	valid
271.0ms	1004×	body	256	valid
231.0ms	959×	body	256	nan
90.0ms	640×	body	128	valid
1.0ms	1×	body	2048	nan
0.0ms	1×	body	128	nan

Details

analyze1.1s

sample231.0ms

simplify234.0ms

prune8.0ms

localize26.0ms

rewrite57.0ms

series612.0ms

simplify75.0ms

prune308.0ms

localize82.0ms

rewrite37.0ms

series0.0ms

simplify43.0ms

prune551.0ms

localize95.0ms

rewrite41.0ms

series0.0ms

simplify42.0ms

prune696.0ms

localize98.0ms

rewrite37.0ms

series0.0ms

simplify53.0ms

prune546.0ms

regimes31.0ms

bsearch0.0ms

simplify8.0ms

end0.0ms

sample6.9s

Profiling