Details

analyze905.0ms

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

sample250.0ms

Algorithm

intervals

Results

81.0ms	118×	body	1280	valid
53.0ms	86×	body	1280	nan
33.0ms	68×	body	640	nan
32.0ms	64×	body	640	valid
15.0ms	45×	body	320	nan
12.0ms	34×	body	320	valid
7.0ms	27×	body	160	valid
2.0ms	13×	body	80	valid
1.0ms	6×	body	160	nan

simplify483.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4933	32
1	4933	32

prune11.0ms

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: 60.1b

Counts

2 → 1

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.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)))))
1.5b	(/.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))))
6.7b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite51.0ms

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:

7.0ms	(*.f64 (/.f64 PI.f64 4) f)
13.0ms	(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)))))
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))))
9.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

series131.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(*.f64 (/.f64 PI.f64 4) f)
59.0ms	(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)))))
41.0ms	(/.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))))
26.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

simplify66.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5439	4936

prune309.0ms

Filtered

110 candidates to 159 candidates (-44.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	154	5	159
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	155	5	160

Merged error: 2.2b

Counts

160 → 5

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 PI.f64 f) (*.f64 PI.f64 f))
0.5b	(.f64 (-.f64 (+.f64 (.f64 1/48 (.f64 (.f64 PI.f64 f) (.f64 PI.f64 f))) (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))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1_binary64`
28×	`add-sqr-sqrt_binary64`
25×	`add-exp-log_binary64`
23×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64` `add-cbrt-cube_binary64`
19×	`times-frac_binary64`
18×	`pow-prod-down_binary64`
14×	`associate-r_binary64`
13×	`log-prod_binary64`
10×	`cbrt-unprod_binary64` `prod-exp_binary64`
8×	`flip3-+_binary64` `flip-+_binary64` `frac-sub_binary64`
6×	`associate-l_binary64` `frac-times_binary64` `associate-*l/_binary64`
4×	`add-log-exp_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
3×	`pow-unpow_binary64` `unpow-prod-down_binary64`
2×	`flip3--_binary64` `rem-log-exp_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `swap-sqr_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `pow-pow_binary64` `log-pow_binary64` `sqr-pow_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `log-div_binary64` `pow-exp_binary64` `pow2_binary64`

Counts

4 → 121

Calls

4 calls:

7.0ms	(.f64 (.f64 PI.f64 f) (*.f64 PI.f64 f))
25.0ms	(.f64 (-.f64 (+.f64 (.f64 1/48 (.f64 (.f64 PI.f64 f) (.f64 PI.f64 f))) (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))

series40.0ms

Counts

4 → 8

Calls

4 calls:

12.0ms	(.f64 (.f64 PI.f64 f) (*.f64 PI.f64 f))
27.0ms	(.f64 (-.f64 (+.f64 (.f64 1/48 (.f64 (.f64 PI.f64 f) (.f64 PI.f64 f))) (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))

simplify60.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5059	2691

prune232.0ms

Filtered

84 candidates to 129 candidates (-53.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	117	12	129
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	118	16	134

Merged error: 1.8b

Counts

134 → 16

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (log.f64 f) PI.f64)
0.3b	(-.f64 (/.f64 (log.f64 (/.f64 4 PI.f64)) PI.f64) (/.f64 (log.f64 f) PI.f64))
1.0b	(pow.f64 PI.f64 3)
2.0b	(log.f64 (/.f64 4 PI.f64))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

49×	`times-frac_binary64`
45×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`
22×	`pow1_binary64`
17×	`log-pow_binary64`
13×	`log-prod_binary64` `distribute-lft-out--_binary64`
10×	`add-exp-log_binary64`
7×	`add-cbrt-cube_binary64`
6×	`add-log-exp_binary64`
4×	`difference-of-squares_binary64` `associate-/l*_binary64` `div-inv_binary64`
3×	`pow-unpow_binary64` `associate-/r*_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
2×	`rem-log-exp_binary64` `div-exp_binary64` `log-div_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `associate--l-_binary64` `diff-log_binary64` `distribute-rgt-out--_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `sqr-pow_binary64` `div-sub_binary64` `clear-num_binary64` `rem-cube-cbrt_binary64` `frac-2neg_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 110

Calls

4 calls:

4.0ms	(/.f64 (log.f64 f) PI.f64)
18.0ms	(-.f64 (/.f64 (log.f64 (/.f64 4 PI.f64)) PI.f64) (/.f64 (log.f64 f) PI.f64))
3.0ms	(pow.f64 PI.f64 3)
3.0ms	(log.f64 (/.f64 4 PI.f64))

series46.0ms

Counts

4 → 8

Calls

4 calls:

12.0ms	(/.f64 (log.f64 f) PI.f64)
34.0ms	(-.f64 (/.f64 (log.f64 (/.f64 4 PI.f64)) PI.f64) (/.f64 (log.f64 f) PI.f64))
0.0ms	(pow.f64 PI.f64 3)
0.0ms	(log.f64 (/.f64 4 PI.f64))

simplify48.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5168	1105

prune166.0ms

Filtered

75 candidates to 118 candidates (-57.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	112	6	118
Fresh	8	7	15
Picked	1	0	1
Done	0	0	0
Total	121	13	134

Merged error: 1.8b

Counts

134 → 13

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 PI.f64 (-.f64 (log.f64 (/.f64 4 PI.f64)) (log.f64 f)))
0.4b	(/.f64 (.f64 PI.f64 (-.f64 (log.f64 (/.f64 4 PI.f64)) (log.f64 f))) (.f64 PI.f64 PI.f64))
1.0b	(pow.f64 PI.f64 3)
2.0b	(log.f64 (/.f64 4 PI.f64))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

39×	`log-prod_binary64`
34×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
30×	`add-cube-cbrt_binary64`
28×	`times-frac_binary64`
26×	`associate--l+_binary64`
22×	`add-exp-log_binary64`
19×	`add-cbrt-cube_binary64`
14×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
12×	`pow1_binary64`
8×	`associate-r_binary64`
5×	`cbrt-unprod_binary64` `log-pow_binary64` `prod-exp_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `distribute-lft-out--_binary64` `div-inv_binary64`
3×	`pow-unpow_binary64` `associate-l_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `rem-log-exp_binary64` `flip--_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `associate-/r_binary64` `pow-pow_binary64` `sqr-pow_binary64` `unswap-sqr_binary64` `clear-num_binary64` `rem-cube-cbrt_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `associate-/l_binary64` `log-div_binary64` `pow-exp_binary64` `unpow3_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

4 → 123

Calls

4 calls:

11.0ms	(*.f64 PI.f64 (-.f64 (log.f64 (/.f64 4 PI.f64)) (log.f64 f)))
14.0ms	(/.f64 (.f64 PI.f64 (-.f64 (log.f64 (/.f64 4 PI.f64)) (log.f64 f))) (.f64 PI.f64 PI.f64))
2.0ms	(pow.f64 PI.f64 3)
3.0ms	(log.f64 (/.f64 4 PI.f64))

series55.0ms

Counts

4 → 8

Calls

4 calls:

28.0ms	(*.f64 PI.f64 (-.f64 (log.f64 (/.f64 4 PI.f64)) (log.f64 f)))
26.0ms	(/.f64 (.f64 PI.f64 (-.f64 (log.f64 (/.f64 4 PI.f64)) (log.f64 f))) (.f64 PI.f64 PI.f64))
0.0ms	(pow.f64 PI.f64 3)
0.0ms	(log.f64 (/.f64 4 PI.f64))

simplify41.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5460	1350

prune132.0ms

Filtered

77 candidates to 131 candidates (-70.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	131	13	144

Merged error: 1.8b

Counts

144 → 13

regimes72.0ms

Accuracy

0% (0.8b remaining)

Error of 2.5b against oracle of 1.7b and baseline of 2.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	31
1	41	31

end0.0ms

sample7.6s

Algorithm

intervals

Results

2.3s	3435×	body	1280	valid
1.8s	2941×	body	1280	nan
1.2s	2467×	body	640	valid
1.1s	2432×	body	640	nan
436.0ms	1255×	body	320	valid
393.0ms	1207×	body	320	nan
146.0ms	592×	body	160	valid
61.0ms	270×	body	160	nan
31.0ms	251×	body	80	valid
0.0ms	1×	body	80	overflowed

Details

analyze905.0ms

sample250.0ms

simplify483.0ms

prune11.0ms

localize30.0ms

rewrite51.0ms

series131.0ms

simplify66.0ms

prune309.0ms

localize23.0ms

rewrite43.0ms

series40.0ms

simplify60.0ms

prune232.0ms

localize24.0ms

rewrite32.0ms

series46.0ms

simplify48.0ms

prune166.0ms

localize25.0ms

rewrite35.0ms

series55.0ms

simplify41.0ms

prune132.0ms

regimes72.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample7.6s

Profiling