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

sample245.0ms

Algorithm

intervals

Results

83.0ms	111×	body	1280	valid
50.0ms	79×	body	1280	nan
34.0ms	68×	body	640	valid
30.0ms	64×	body	640	nan
16.0ms	43×	body	320	valid
10.0ms	30×	body	320	nan
7.0ms	29×	body	160	valid
1.0ms	3×	body	160	nan
1.0ms	5×	body	80	valid

simplify468.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4933	32
1	4933	32

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: 62.1b

Counts

2 → 1

localize29.0ms

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)))))
0.8b	(/.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)))

rewrite52.0ms

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)))

series113.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(*.f64 (/.f64 PI.f64 4) f)
49.0ms	(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)))))
37.0ms	(/.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))))
23.0ms	(-.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 (36.0ms)

Iter	Nodes	Cost
0	5439	4936

prune256.0ms

Filtered

110 candidates to 159 candidates (-44.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	155	4	159
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	156	4	160

Merged error: 1.5b

Counts

160 → 4

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 PI.f64 f) (*.f64 PI.f64 f))
0.4b	(.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))
3.0ms	(pow.f64 PI.f64 4)
3.0ms	(log.f64 (/.f64 4 PI.f64))

series30.0ms

Counts

4 → 8

Calls

4 calls:

6.0ms	(.f64 (.f64 PI.f64 f) (*.f64 PI.f64 f))
24.0ms	(.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))

simplify63.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5059	2691

prune170.0ms

Filtered

84 candidates to 129 candidates (-53.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	119	10	129
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	121	12	133

Merged error: 1.3b

Counts

133 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1_binary64`
27×	`add-exp-log_binary64`
21×	`add-cbrt-cube_binary64`
18×	`pow-prod-down_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
13×	`log-prod_binary64`
12×	`times-frac_binary64`
10×	`prod-exp_binary64`
9×	`cbrt-unprod_binary64`
6×	`associate-/l/_binary64` `associate-*l/_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `pow-prod-up_binary64` `pow-sqr_binary64` `flip-+_binary64` `frac-sub_binary64`
3×	`pow-unpow_binary64` `associate-/r*_binary64` `div-exp_binary64`
2×	`cbrt-undiv_binary64` `rem-log-exp_binary64` `pow-pow_binary64` `pow-plus_binary64` `div-inv_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `flip3--_binary64` `swap-sqr_binary64` `associate-r_binary64` `log-pow_binary64` `sqr-pow_binary64` `associate-l_binary64` `clear-num_binary64` `unpow-prod-down_binary64` `frac-2neg_binary64` `associate-/l_binary64` `log-div_binary64` `flip--_binary64` `pow2_binary64` `-commutative_binary64`

Counts

4 → 102

Calls

4 calls:

7.0ms	(.f64 (.f64 PI.f64 f) (*.f64 PI.f64 f))
4.0ms	(pow.f64 (*.f64 PI.f64 f) 4)
14.0ms	(/.f64 (.f64 (-.f64 (+.f64 (log.f64 (/.f64 4 PI.f64)) (.f64 1/48 (.f64 (.f64 PI.f64 f) (.f64 PI.f64 f)))) (+.f64 (log.f64 f) (.f64 7/23040 (pow.f64 (*.f64 PI.f64 f) 4)))) -4) PI.f64)
3.0ms	(log.f64 (/.f64 4 PI.f64))

series35.0ms

Counts

4 → 10

Calls

4 calls:

6.0ms	(.f64 (.f64 PI.f64 f) (*.f64 PI.f64 f))
7.0ms	(pow.f64 (*.f64 PI.f64 f) 4)
23.0ms	(/.f64 (.f64 (-.f64 (+.f64 (log.f64 (/.f64 4 PI.f64)) (.f64 1/48 (.f64 (.f64 PI.f64 f) (.f64 PI.f64 f)))) (+.f64 (log.f64 f) (.f64 7/23040 (pow.f64 (*.f64 PI.f64 f) 4)))) -4) PI.f64)
0.0ms	(log.f64 (/.f64 4 PI.f64))

simplify36.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5559	1403

prune119.0ms

Filtered

67 candidates to 112 candidates (-67.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	108	4	112
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	112	12	124

Merged error: 1.3b

Counts

124 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 PI.f64 f) (*.f64 PI.f64 f))
0.3b	(/.f64 (.f64 (-.f64 (+.f64 (log.f64 (/.f64 4 PI.f64)) (.f64 1/48 (.f64 (.f64 PI.f64 f) (.f64 PI.f64 f)))) (+.f64 (log.f64 f) (.f64 7/23040 (exp.f64 (.f64 4 (log.f64 (.f64 PI.f64 f))))))) -4) PI.f64)
1.8b	(exp.f64 (.f64 4 (log.f64 (.f64 PI.f64 f))))
2.0b	(log.f64 (/.f64 4 PI.f64))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

44×	`pow1_binary64`
24×	`add-exp-log_binary64`
21×	`add-cbrt-cube_binary64`
17×	`pow-prod-down_binary64`
15×	`log-prod_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
12×	`times-frac_binary64`
9×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`associate-/l/_binary64` `add-log-exp_binary64` `associate-*l/_binary64`
4×	`flip3-+_binary64` `pow-prod-up_binary64` `pow-sqr_binary64` `flip-+_binary64` `frac-sub_binary64`
3×	`associate-/r*_binary64` `div-exp_binary64`
2×	`cbrt-undiv_binary64` `rem-log-exp_binary64` `pow-plus_binary64` `exp-sum_binary64` `div-inv_binary64`
1×	`flip3--_binary64` `swap-sqr_binary64` `associate-r_binary64` `log-pow_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `rem-exp-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `log-div_binary64` `flip--_binary64` `exp-to-pow_binary64` `pow2_binary64` `exp-prod_binary64` `-commutative_binary64`

Counts

4 → 97

Calls

4 calls:

7.0ms	(.f64 (.f64 PI.f64 f) (*.f64 PI.f64 f))
13.0ms	(/.f64 (.f64 (-.f64 (+.f64 (log.f64 (/.f64 4 PI.f64)) (.f64 1/48 (.f64 (.f64 PI.f64 f) (.f64 PI.f64 f)))) (+.f64 (log.f64 f) (.f64 7/23040 (exp.f64 (.f64 4 (log.f64 (.f64 PI.f64 f))))))) -4) PI.f64)
3.0ms	(exp.f64 (.f64 4 (log.f64 (.f64 PI.f64 f))))
3.0ms	(log.f64 (/.f64 4 PI.f64))

series35.0ms

Counts

4 → 10

Calls

4 calls:

6.0ms	(.f64 (.f64 PI.f64 f) (*.f64 PI.f64 f))
22.0ms	(/.f64 (.f64 (-.f64 (+.f64 (log.f64 (/.f64 4 PI.f64)) (.f64 1/48 (.f64 (.f64 PI.f64 f) (.f64 PI.f64 f)))) (+.f64 (log.f64 f) (.f64 7/23040 (exp.f64 (.f64 4 (log.f64 (.f64 PI.f64 f))))))) -4) PI.f64)
7.0ms	(exp.f64 (.f64 4 (log.f64 (.f64 PI.f64 f))))
0.0ms	(log.f64 (/.f64 4 PI.f64))

simplify32.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5184	1444

prune82.0ms

Filtered

65 candidates to 107 candidates (-64.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	107	12	119

Merged error: 1.3b

Counts

119 → 12

regimes76.0ms

Accuracy

0% (0.7b remaining)

Error of 2.3b against oracle of 1.5b and baseline of 2.3b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	107	37
1	107	37

end0.0ms

sample7.9s

Algorithm

intervals

Results

2.3s	3373×	body	1280	valid
1.8s	2822×	body	1280	nan
1.2s	2505×	body	640	valid
1.1s	2437×	body	640	nan
452.0ms	1222×	body	320	valid
431.0ms	1251×	body	320	nan
172.0ms	667×	body	160	valid
56.0ms	244×	body	160	nan
30.0ms	233×	body	80	valid
0.0ms	1×	body	80	overflowed

Details

analyze1.1s

sample245.0ms

simplify468.0ms

prune9.0ms

localize29.0ms

rewrite52.0ms

series113.0ms

simplify66.0ms

prune256.0ms

localize25.0ms

rewrite43.0ms

series30.0ms

simplify63.0ms

prune170.0ms

localize21.0ms

rewrite32.0ms

series35.0ms

simplify36.0ms

prune119.0ms

localize24.0ms

rewrite31.0ms

series35.0ms

simplify32.0ms

prune82.0ms

regimes76.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample7.9s

Profiling