Details

analyze1.0s

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

sample315.0ms

Algorithm

intervals

Results

77.0ms	111×	body	1280	nan
73.0ms	95×	body	1280	valid
56.0ms	92×	body	640	valid
48.0ms	90×	body	640	nan
17.0ms	44×	body	320	nan
15.0ms	35×	body	320	valid
7.0ms	24×	body	160	valid
2.0ms	5×	body	160	nan
2.0ms	10×	body	80	valid

simplify594.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5050	55

prune13.0ms

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: 61.1b

Counts

2 → 1

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 PI.f64 4) f)
0.3b	(log.f64 (/.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)))))
0.5b	(/.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))))
6.8b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt_binary64`
87×	`*-un-lft-identity_binary64`
66×	`times-frac_binary64`
37×	`add-cube-cbrt_binary64`
34×	`log-prod_binary64`
30×	`difference-of-squares_binary64`
15×	`distribute-lft-out_binary64`
14×	`add-exp-log_binary64`
13×	`associate-l_binary64`
11×	`add-cbrt-cube_binary64`
10×	`sqr-pow_binary64` `unpow-prod-down_binary64` `distribute-lft-out--_binary64`
7×	`associate-/r*_binary64` `pow1_binary64`
6×	`add-log-exp_binary64`
4×	`associate-/r/_binary64` `associate-/l*_binary64`
3×	`flip3--_binary64` `associate-r_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `log-div_binary64` `flip-+_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 147

Calls

4 calls:

6.0ms	(*.f64 (/.f64 PI.f64 4) f)
12.0ms	(log.f64 (/.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)))))
13.0ms	(/.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)))

series504.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(*.f64 (/.f64 PI.f64 4) f)
271.0ms	(log.f64 (/.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)))))
146.0ms	(/.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))))
67.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

simplify127.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5146	8480

prune506.0ms

Filtered

109 candidates to 159 candidates (-45.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	153	6	159
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	154	6	160

Merged error: 1.3b

Counts

160 → 6

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 f f) (pow.f64 PI.f64 2))
0.4b	(.f64 (-.f64 (+.f64 (.f64 1/48 (.f64 (.f64 f f) (pow.f64 PI.f64 2))) (log.f64 (/.f64 4 PI.f64))) (+.f64 (log.f64 f) (.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 PI.f64 4))))) (/.f64 -4 PI.f64))
1.6b	(pow.f64 PI.f64 4)
2.0b	(log.f64 (/.f64 4 PI.f64))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
26×	`add-exp-log_binary64`
25×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`
19×	`times-frac_binary64`
14×	`add-cbrt-cube_binary64`
13×	`log-prod_binary64`
11×	`prod-exp_binary64`
8×	`flip3-+_binary64` `pow1_binary64` `flip-+_binary64` `frac-sub_binary64`
7×	`unpow-prod-down_binary64`
6×	`associate-l_binary64` `unswap-sqr_binary64` `frac-times_binary64` `associate-*l/_binary64`
5×	`cbrt-unprod_binary64`
4×	`add-log-exp_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `sqr-pow_binary64` `pow-exp_binary64`
2×	`pow-prod-down_binary64` `flip3--_binary64` `unpow2_binary64` `rem-log-exp_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `*-commutative_binary64`
1×	`cbrt-undiv_binary64` `associate-*r/_binary64` `pow-pow_binary64` `log-pow_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `log-div_binary64` `pow2_binary64`

Counts

4 → 117

Calls

4 calls:

8.0ms	(.f64 (.f64 f f) (pow.f64 PI.f64 2))
24.0ms	(.f64 (-.f64 (+.f64 (.f64 1/48 (.f64 (.f64 f f) (pow.f64 PI.f64 2))) (log.f64 (/.f64 4 PI.f64))) (+.f64 (log.f64 f) (.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 PI.f64 4))))) (/.f64 -4 PI.f64))
2.0ms	(pow.f64 PI.f64 4)
3.0ms	(log.f64 (/.f64 4 PI.f64))

series127.0ms

Counts

4 → 8

Calls

4 calls:

31.0ms	(.f64 (.f64 f f) (pow.f64 PI.f64 2))
96.0ms	(.f64 (-.f64 (+.f64 (.f64 1/48 (.f64 (.f64 f f) (pow.f64 PI.f64 2))) (log.f64 (/.f64 4 PI.f64))) (+.f64 (log.f64 f) (.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 PI.f64 4))))) (/.f64 -4 PI.f64))
0.0ms	(pow.f64 PI.f64 4)
0.0ms	(log.f64 (/.f64 4 PI.f64))

simplify86.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5108	4873

prune786.0ms

Filtered

92 candidates to 125 candidates (-35.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	117	8	125
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	118	13	131

Merged error: 1.0b

Counts

131 → 13

localize48.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt.f64 PI.f64)
1.6b	(pow.f64 (cbrt.f64 PI.f64) 4)
1.6b	(pow.f64 (pow.f64 (cbrt.f64 PI.f64) 2) 4)
2.0b	(log.f64 (/.f64 4 PI.f64))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

23×	`unpow-prod-down_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
13×	`log-prod_binary64`
10×	`add-exp-log_binary64`
9×	`times-frac_binary64` `cbrt-prod_binary64`
6×	`pow-unpow_binary64` `pow1_binary64`
5×	`pow-exp_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`pow-to-exp_binary64` `pow-pow_binary64` `sqr-pow_binary64`
2×	`rem-log-exp_binary64` `pow1/3_binary64`
1×	`unpow2_binary64` `log-pow_binary64` `div-inv_binary64` `div-exp_binary64` `log-div_binary64`

Counts

4 → 83

Calls

4 calls:

1.0ms	(cbrt.f64 PI.f64)
3.0ms	(pow.f64 (cbrt.f64 PI.f64) 4)
5.0ms	(pow.f64 (pow.f64 (cbrt.f64 PI.f64) 2) 4)
3.0ms	(log.f64 (/.f64 4 PI.f64))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(cbrt.f64 PI.f64)
0.0ms	(pow.f64 (cbrt.f64 PI.f64) 4)
0.0ms	(pow.f64 (pow.f64 (cbrt.f64 PI.f64) 2) 4)
0.0ms	(log.f64 (/.f64 4 PI.f64))

simplify59.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5315	1149

prune551.0ms

Filtered

62 candidates to 87 candidates (-40.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	12	12
Picked	1	0	1
Done	0	0	0
Total	87	13	100

Merged error: 1.0b

Counts

100 → 13

localize61.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow.f64 (cbrt.f64 (sqrt.f64 PI.f64)) 8)
1.0b	(pow.f64 (cbrt.f64 (sqrt.f64 PI.f64)) 8)
1.6b	(pow.f64 (cbrt.f64 PI.f64) 4)
2.0b	(log.f64 (/.f64 4 PI.f64))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

24×	`unpow-prod-down_binary64`
22×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
15×	`cbrt-prod_binary64`
13×	`log-prod_binary64`
10×	`add-exp-log_binary64`
9×	`pow-unpow_binary64` `times-frac_binary64`
8×	`pow1_binary64`
6×	`pow-pow_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`pow-to-exp_binary64` `pow1/3_binary64` `sqr-pow_binary64` `pow-exp_binary64`
2×	`rem-log-exp_binary64`
1×	`log-pow_binary64` `div-inv_binary64` `div-exp_binary64` `log-div_binary64`

Counts

4 → 93

Calls

4 calls:

4.0ms	(pow.f64 (cbrt.f64 (sqrt.f64 PI.f64)) 8)
4.0ms	(pow.f64 (cbrt.f64 (sqrt.f64 PI.f64)) 8)
3.0ms	(pow.f64 (cbrt.f64 PI.f64) 4)
3.0ms	(log.f64 (/.f64 4 PI.f64))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(pow.f64 (cbrt.f64 (sqrt.f64 PI.f64)) 8)
0.0ms	(pow.f64 (cbrt.f64 (sqrt.f64 PI.f64)) 8)
0.0ms	(pow.f64 (cbrt.f64 PI.f64) 4)
0.0ms	(log.f64 (/.f64 4 PI.f64))

simplify57.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5010	1468

prune486.0ms

Filtered

67 candidates to 97 candidates (-44.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	12	12
Picked	1	0	1
Done	0	0	0
Total	97	13	110

Merged error: 1.0b

Counts

110 → 13

regimes182.0ms

Accuracy

0% (0.8b remaining)

Error of 2.1b against oracle of 1.3b and baseline of 2.1b

bsearch0.0ms

simplify6.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	153	93
1	153	93

end0.0ms

sample9.0s

Algorithm

intervals

Results

2.6s	3428×	body	1280	valid
2.2s	2968×	body	1280	nan
1.4s	2492×	body	640	valid
1.3s	2448×	body	640	nan
505.0ms	1227×	body	320	valid
471.0ms	1230×	body	320	nan
183.0ms	622×	body	160	valid
65.0ms	245×	body	160	nan
34.0ms	231×	body	80	valid
0.0ms	1×	body	80	overflowed

Details

analyze1.0s

sample315.0ms

simplify594.0ms

prune13.0ms

localize49.0ms

rewrite47.0ms

series504.0ms

simplify127.0ms

prune506.0ms

localize36.0ms

rewrite41.0ms

series127.0ms

simplify86.0ms

prune786.0ms

localize48.0ms

rewrite13.0ms

series0.0ms

simplify59.0ms

prune551.0ms

localize61.0ms

rewrite15.0ms

series0.0ms

simplify57.0ms

prune486.0ms

regimes182.0ms

bsearch0.0ms

simplify6.0ms

end0.0ms

sample9.0s

Profiling