Details

analyze940.0ms

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

sample258.0ms

Algorithm

intervals

Results

72.0ms	95×	body	1280	valid
54.0ms	82×	body	1280	nan
41.0ms	82×	body	640	valid
38.0ms	78×	body	640	nan
17.0ms	44×	body	320	valid
13.0ms	36×	body	320	nan
6.0ms	25×	body	160	valid
1.0ms	10×	body	80	valid
1.0ms	4×	body	160	nan

simplify604.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (122.0ms)

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: 61.2b

Counts

2 → 1

localize29.0ms

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))))
7.1b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite41.0ms

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:

6.0ms	(*.f64 (/.f64 PI.f64 4) f)
6.0ms	(*.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)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(*.f64 (/.f64 PI.f64 4) f)
21.0ms	(*.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))))
63.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

simplify101.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4968	5311
1	4968	5311

prune271.0ms

Filtered

104 candidates to 146 candidates (-40.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	143	3	146
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	144	3	147

Merged error: 1.5b

Counts

147 → 3

localize33.0ms

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))
0.8b	(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)

rewrite33.0ms

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))
16.0ms	(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)

series711.0ms

Counts

4 → 10

Calls

4 calls:

31.0ms	(pow.f64 (*.f64 PI.f64 f) 3)
400.0ms	(.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)

simplify129.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5021	7470

prune334.0ms

Filtered

82 candidates to 111 candidates (-35.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	102	9	111
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	103	11	114

Merged error: 1.1b

Counts

114 → 11

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (*.f64 PI.f64 f) 3)
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)
0.8b	(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:

4.0ms	(pow.f64 (*.f64 PI.f64 f) 3)
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)
16.0ms	(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)

series699.0ms

Counts

4 → 10

Calls

4 calls:

35.0ms	(pow.f64 (*.f64 PI.f64 f) 3)
400.0ms	(/.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)
263.0ms	(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)

simplify122.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5042	6398

prune250.0ms

Filtered

68 candidates to 99 candidates (-45.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	100	10	110

Merged error: 1.1b

Counts

110 → 10

localize39.0ms

Local error

Found 4 expressions with local error:

0.5b	(/.f64 (sqrt.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))))
0.7b	(log.f64 (/.f64 (sqrt.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)
1.7b	(log.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64`
42×	`times-frac_binary64`
38×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
34×	`log-prod_binary64`
32×	`sqrt-prod_binary64`
11×	`add-exp-log_binary64`
8×	`pow1_binary64` `distribute-lft-out_binary64`
7×	`associate-/l*_binary64`
6×	`add-cbrt-cube_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `log-pow_binary64` `associate-/r/_binary64` `flip-+_binary64` `sqrt-div_binary64`
3×	`pow-unpow_binary64` `associate-/r*_binary64` `rem-log-exp_binary64` `unpow-prod-down_binary64` `log-div_binary64`
2×	`associate-/l/_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-exp_binary64`

Counts

4 → 122

Calls

4 calls:

18.0ms	(/.f64 (sqrt.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))))
17.0ms	(log.f64 (/.f64 (sqrt.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)
6.0ms	(log.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))

series493.0ms

Counts

4 → 10

Calls

4 calls:

160.0ms	(/.f64 (sqrt.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))))
198.0ms	(log.f64 (/.f64 (sqrt.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)
134.0ms	(log.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))

simplify145.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4992	10046
1	4992	10046

prune390.0ms

Filtered

89 candidates to 132 candidates (-48.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	130	2	132
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	132	10	142

Merged error: 1.1b

Counts

142 → 10

regimes50.0ms

Accuracy

0% (0.7b remaining)

Error of 2.3b against oracle of 1.6b and baseline of 2.3b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	70
1	41	70

end0.0ms

sample8.0s

Algorithm

intervals

Results

2.4s	3406×	body	1280	valid
1.8s	2871×	body	1280	nan
1.2s	2451×	body	640	valid
1.1s	2391×	body	640	nan
457.0ms	1218×	body	320	valid
426.0ms	1211×	body	320	nan
179.0ms	675×	body	160	valid
59.0ms	243×	body	160	nan
34.0ms	250×	body	80	valid
0.0ms	1×	body	80	overflowed

Details

analyze940.0ms

sample258.0ms

simplify604.0ms

prune9.0ms

localize29.0ms

rewrite41.0ms

series248.0ms

simplify101.0ms

prune271.0ms

localize33.0ms

rewrite33.0ms

series711.0ms

simplify129.0ms

prune334.0ms

localize32.0ms

rewrite30.0ms

series699.0ms

simplify122.0ms

prune250.0ms

localize39.0ms

rewrite48.0ms

series493.0ms

simplify145.0ms

prune390.0ms

regimes50.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample8.0s

Profiling