Details

analyze906.0ms

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

sample253.0ms

Algorithm

intervals

Results

69.0ms	95×	body	1280	valid
50.0ms	81×	body	1280	nan
42.0ms	91×	body	640	nan
38.0ms	79×	body	640	valid
16.0ms	44×	body	320	valid
13.0ms	39×	body	320	nan
8.0ms	31×	body	160	valid
2.0ms	8×	body	160	nan
1.0ms	7×	body	80	valid

simplify613.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	4749	55
1	4749	55

prune9.0ms

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: 60.9b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 PI.f64 4) f)
0.2b	(*.f64 (/.f64 PI.f64 4) f)
0.8b	(/.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))))
7.3b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite42.0ms

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)))

series257.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(*.f64 (/.f64 PI.f64 4) f)
23.0ms	(*.f64 (/.f64 PI.f64 4) f)
144.0ms	(/.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))))
66.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

simplify104.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4968	5311
1	4968	5311

prune287.0ms

Filtered

104 candidates to 146 candidates (-40.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	142	4	146
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	143	4	147

Merged error: 1.9b

Counts

147 → 4

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (*.f64 PI.f64 f) 3)
0.4b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (+.f64 (.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 PI.f64 5))) (.f64 (*.f64 PI.f64 f) 1/2))))) (/.f64 -4 PI.f64))
0.7b	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (+.f64 (.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 PI.f64 5))) (.f64 (.f64 PI.f64 f) 1/2)))))
1.0b	(pow.f64 PI.f64 5)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`
22×	`times-frac_binary64`
18×	`log-prod_binary64`
16×	`add-exp-log_binary64`
13×	`associate-r_binary64`
12×	`pow1_binary64` `add-cbrt-cube_binary64`
6×	`pow-unpow_binary64`
4×	`add-log-exp_binary64` `associate-l_binary64` `unpow-prod-down_binary64`
3×	`cbrt-unprod_binary64` `distribute-lft-out_binary64` `pow-pow_binary64` `prod-exp_binary64` `pow-exp_binary64`
2×	`pow-to-exp_binary64` `pow-prod-down_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `rem-cube-cbrt_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`flip3-+_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `cube-prod_binary64` `log-div_binary64` `flip-+_binary64` `unpow3_binary64` `-commutative_binary64` `cube-mult_binary64`

Counts

4 → 101

Calls

4 calls:

4.0ms	(pow.f64 (*.f64 PI.f64 f) 3)
7.0ms	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (+.f64 (.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 PI.f64 5))) (.f64 (*.f64 PI.f64 f) 1/2))))) (/.f64 -4 PI.f64))
17.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (+.f64 (.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 PI.f64 5))) (.f64 (.f64 PI.f64 f) 1/2)))))
2.0ms	(pow.f64 PI.f64 5)

series730.0ms

Counts

4 → 10

Calls

4 calls:

36.0ms	(pow.f64 (*.f64 PI.f64 f) 3)
413.0ms	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (+.f64 (.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 PI.f64 5))) (.f64 (*.f64 PI.f64 f) 1/2))))) (/.f64 -4 PI.f64))
281.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (+.f64 (.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 PI.f64 5))) (.f64 (.f64 PI.f64 f) 1/2)))))
0.0ms	(pow.f64 PI.f64 5)

simplify128.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5021	7470

prune335.0ms

Filtered

82 candidates to 111 candidates (-35.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	100	11	111
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	101	14	115

Merged error: 1.4b

Counts

115 → 14

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (+.f64 (.f64 1/61440 (.f64 (pow.f64 PI.f64 5) (pow.f64 f 5))) (.f64 (*.f64 PI.f64 f) 1/2))))) -4) PI.f64)
0.3b	(pow.f64 (*.f64 PI.f64 f) 3)
0.7b	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (+.f64 (.f64 1/61440 (.f64 (pow.f64 PI.f64 5) (pow.f64 f 5))) (.f64 (.f64 PI.f64 f) 1/2)))))
1.0b	(pow.f64 PI.f64 5)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
18×	`log-prod_binary64`
17×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
16×	`add-exp-log_binary64`
15×	`times-frac_binary64`
12×	`add-cbrt-cube_binary64`
9×	`pow1_binary64`
6×	`pow-unpow_binary64`
4×	`add-log-exp_binary64` `unpow-prod-down_binary64`
3×	`associate-/r*_binary64` `distribute-lft-out_binary64` `pow-pow_binary64` `div-exp_binary64` `pow-exp_binary64`
2×	`pow-to-exp_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `rem-cube-cbrt_binary64` `prod-exp_binary64` `div-inv_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `cube-prod_binary64` `associate-/l*_binary64` `log-div_binary64` `flip-+_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 89

Calls

4 calls:

5.0ms	(/.f64 (.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (+.f64 (.f64 1/61440 (.f64 (pow.f64 PI.f64 5) (pow.f64 f 5))) (.f64 (*.f64 PI.f64 f) 1/2))))) -4) PI.f64)
4.0ms	(pow.f64 (*.f64 PI.f64 f) 3)
17.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (+.f64 (.f64 1/61440 (.f64 (pow.f64 PI.f64 5) (pow.f64 f 5))) (.f64 (.f64 PI.f64 f) 1/2)))))
2.0ms	(pow.f64 PI.f64 5)

series711.0ms

Counts

4 → 10

Calls

4 calls:

408.0ms	(/.f64 (.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (+.f64 (.f64 1/61440 (.f64 (pow.f64 PI.f64 5) (pow.f64 f 5))) (.f64 (*.f64 PI.f64 f) 1/2))))) -4) PI.f64)
31.0ms	(pow.f64 (*.f64 PI.f64 f) 3)
270.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (+.f64 (.f64 1/61440 (.f64 (pow.f64 PI.f64 5) (pow.f64 f 5))) (.f64 (.f64 PI.f64 f) 1/2)))))
0.0ms	(pow.f64 PI.f64 5)

simplify119.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5042	6398

prune262.0ms

Filtered

68 candidates to 99 candidates (-45.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	100	13	113

Merged error: 1.4b

Counts

113 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (*.f64 PI.f64 f) 4)
0.3b	(/.f64 (.f64 (-.f64 (+.f64 (.f64 (pow.f64 (.f64 PI.f64 f) 2) 1/48) (log.f64 (/.f64 4 PI.f64))) (+.f64 (log.f64 f) (.f64 7/23040 (pow.f64 (*.f64 PI.f64 f) 4)))) -4) PI.f64)
0.3b	(pow.f64 (*.f64 PI.f64 f) 2)
2.0b	(log.f64 (/.f64 4 PI.f64))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
13×	`log-prod_binary64`
12×	`times-frac_binary64`
11×	`pow1_binary64`
9×	`add-cbrt-cube_binary64`
6×	`associate-/l/_binary64` `pow-unpow_binary64` `associate-*l/_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `pow-pow_binary64` `flip-+_binary64` `frac-sub_binary64` `pow-exp_binary64`
3×	`associate-/r*_binary64` `prod-exp_binary64` `div-exp_binary64`
2×	`pow-to-exp_binary64` `pow-prod-down_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `div-inv_binary64`
1×	`flip3--_binary64` `cbrt-unprod_binary64` `unpow2_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `log-div_binary64` `flip--_binary64`

Counts

4 → 86

Calls

4 calls:

4.0ms	(pow.f64 (*.f64 PI.f64 f) 4)
15.0ms	(/.f64 (.f64 (-.f64 (+.f64 (.f64 (pow.f64 (.f64 PI.f64 f) 2) 1/48) (log.f64 (/.f64 4 PI.f64))) (+.f64 (log.f64 f) (.f64 7/23040 (pow.f64 (*.f64 PI.f64 f) 4)))) -4) PI.f64)
4.0ms	(pow.f64 (*.f64 PI.f64 f) 2)
3.0ms	(log.f64 (/.f64 4 PI.f64))

series155.0ms

Counts

4 → 10

Calls

4 calls:

33.0ms	(pow.f64 (*.f64 PI.f64 f) 4)
94.0ms	(/.f64 (.f64 (-.f64 (+.f64 (.f64 (pow.f64 (.f64 PI.f64 f) 2) 1/48) (log.f64 (/.f64 4 PI.f64))) (+.f64 (log.f64 f) (.f64 7/23040 (pow.f64 (*.f64 PI.f64 f) 4)))) -4) PI.f64)
27.0ms	(pow.f64 (*.f64 PI.f64 f) 2)
0.0ms	(log.f64 (/.f64 4 PI.f64))

simplify60.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5934	2265

prune128.0ms

Filtered

67 candidates to 96 candidates (-43.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	89	7	96
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	96	13	109

Merged error: 1.4b

Counts

109 → 13

regimes65.0ms

Accuracy

0% (0.7b remaining)

Error of 2.2b against oracle of 1.5b and baseline of 2.2b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	100
1	45	100

end0.0ms

sample7.7s

Algorithm

intervals

Results

2.3s	3416×	body	1280	valid
1.8s	2982×	body	1280	nan
1.2s	2485×	body	640	valid
1.1s	2375×	body	640	nan
449.0ms	1257×	body	320	valid
408.0ms	1231×	body	320	nan
158.0ms	629×	body	160	valid
55.0ms	247×	body	160	nan
30.0ms	213×	body	80	valid

Details

analyze906.0ms

sample253.0ms

simplify613.0ms

prune9.0ms

localize27.0ms

rewrite42.0ms

series257.0ms

simplify104.0ms

prune287.0ms

localize32.0ms

rewrite34.0ms

series730.0ms

simplify128.0ms

prune335.0ms

localize33.0ms

rewrite30.0ms

series711.0ms

simplify119.0ms

prune262.0ms

localize18.0ms

rewrite29.0ms

series155.0ms

simplify60.0ms

prune128.0ms

regimes65.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample7.7s

Profiling