Details

analyze931.0ms

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

sample271.0ms

Algorithm

intervals

Results

85.0ms	120×	body	1280	valid
65.0ms	102×	body	1280	nan
36.0ms	73×	body	640	valid
33.0ms	69×	body	640	nan
15.0ms	41×	body	320	valid
12.0ms	34×	body	320	nan
6.0ms	14×	body	160	nan
4.0ms	13×	body	160	valid
1.0ms	9×	body	80	valid

simplify493.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4933	32
1	4933	32

prune10.0ms

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

localize19.0ms

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))))
4.6b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite56.0ms

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:

18.0ms	(*.f64 (/.f64 PI.f64 4) f)
7.0ms	(*.f64 (/.f64 PI.f64 4) f)
15.0ms	(/.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)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(*.f64 (/.f64 PI.f64 4) f)
4.0ms	(*.f64 (/.f64 PI.f64 4) f)
31.0ms	(/.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))))
24.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

simplify58.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5052	3119

prune249.0ms

Filtered

104 candidates to 146 candidates (-40.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	145	2	147

Merged error: 1.2b

Counts

147 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 PI.f64 f)
0.3b	(/.f64 4 (*.f64 PI.f64 f))
0.4b	(.f64 (.f64 PI.f64 f) 1/12)
0.4b	(.f64 (log.f64 (-.f64 (+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (.f64 PI.f64 f) 1/12)) (.f64 (pow.f64 (.f64 PI.f64 f) 3) 1/2880))) (/.f64 -4 PI.f64))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
19×	`associate-r_binary64`
17×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
14×	`pow1_binary64`
13×	`times-frac_binary64`
8×	`associate-l_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64`
5×	`pow-prod-down_binary64`
4×	`add-log-exp_binary64`
3×	`cbrt-undiv_binary64` `unswap-sqr_binary64` `associate-/l_binary64` `div-exp_binary64` `-commutative_binary64`
2×	`div-inv_binary64`
1×	`associate-/r_binary64` `associate-r/_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 90

Calls

4 calls:

4.0ms	(*.f64 PI.f64 f)
5.0ms	(/.f64 4 (*.f64 PI.f64 f))
6.0ms	(.f64 (.f64 PI.f64 f) 1/12)
11.0ms	(.f64 (log.f64 (-.f64 (+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (.f64 PI.f64 f) 1/12)) (.f64 (pow.f64 (.f64 PI.f64 f) 3) 1/2880))) (/.f64 -4 PI.f64))

series43.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(*.f64 PI.f64 f)
4.0ms	(/.f64 4 (*.f64 PI.f64 f))
4.0ms	(.f64 (.f64 PI.f64 f) 1/12)
32.0ms	(.f64 (log.f64 (-.f64 (+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (.f64 PI.f64 f) 1/12)) (.f64 (pow.f64 (.f64 PI.f64 f) 3) 1/2880))) (/.f64 -4 PI.f64))

simplify70.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4904	1346
1	4904	1346

prune129.0ms

Filtered

67 candidates to 102 candidates (-52.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	94	8	102
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	95	9	104

Merged error: 0.8b

Counts

104 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 PI.f64 f)
0.3b	(/.f64 4 (*.f64 PI.f64 f))
0.3b	(/.f64 (.f64 (log.f64 (-.f64 (+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (.f64 PI.f64 f) 1/12)) (.f64 (pow.f64 (.f64 PI.f64 f) 3) 1/2880))) -4) PI.f64)
0.4b	(.f64 (.f64 PI.f64 f) 1/12)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64` `times-frac_binary64`
4×	`pow-prod-down_binary64` `associate-/r_binary64` `add-log-exp_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `associate-/l_binary64` `div-exp_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`unswap-sqr_binary64`

Counts

4 → 78

Calls

4 calls:

4.0ms	(*.f64 PI.f64 f)
5.0ms	(/.f64 4 (*.f64 PI.f64 f))
8.0ms	(/.f64 (.f64 (log.f64 (-.f64 (+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (.f64 PI.f64 f) 1/12)) (.f64 (pow.f64 (.f64 PI.f64 f) 3) 1/2880))) -4) PI.f64)
6.0ms	(.f64 (.f64 PI.f64 f) 1/12)

series37.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(*.f64 PI.f64 f)
5.0ms	(/.f64 4 (*.f64 PI.f64 f))
26.0ms	(/.f64 (.f64 (log.f64 (-.f64 (+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (.f64 PI.f64 f) 1/12)) (.f64 (pow.f64 (.f64 PI.f64 f) 3) 1/2880))) -4) PI.f64)
4.0ms	(.f64 (.f64 PI.f64 f) 1/12)

simplify42.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5000	974

prune105.0ms

Filtered

60 candidates to 90 candidates (-50.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	90	9	99

Merged error: 0.8b

Counts

99 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (log.f64 f) (log.f64 (/.f64 4 PI.f64)))
0.4b	(*.f64 (/.f64 4 PI.f64) (-.f64 (log.f64 f) (log.f64 (/.f64 4 PI.f64))))
1.0b	(pow.f64 PI.f64 3)
2.0b	(log.f64 (/.f64 4 PI.f64))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
35×	`log-prod_binary64`
32×	`add-cube-cbrt_binary64`
28×	`times-frac_binary64`
16×	`pow1_binary64`
13×	`associate--r+_binary64` `add-exp-log_binary64` `associate-l_binary64`
10×	`add-cbrt-cube_binary64`
9×	`log-pow_binary64` `associate--l+_binary64`
8×	`associate-r_binary64` `distribute-lft-out--_binary64`
5×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`add-log-exp_binary64` `log-div_binary64`
3×	`pow-unpow_binary64` `sub-neg_binary64` `flip3--_binary64` `associate--r-_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `div-inv_binary64` `flip--_binary64`
2×	`cbrt-unprod_binary64` `rem-log-exp_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `div-exp_binary64` `frac-times_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `sqr-pow_binary64` `rem-cube-cbrt_binary64` `pow-exp_binary64` `unpow3_binary64` `associate-l/_binary64` `-commutative_binary64` `cube-mult_binary64`

Counts

4 → 131

Calls

4 calls:

8.0ms	(-.f64 (log.f64 f) (log.f64 (/.f64 4 PI.f64)))
13.0ms	(*.f64 (/.f64 4 PI.f64) (-.f64 (log.f64 f) (log.f64 (/.f64 4 PI.f64))))
2.0ms	(pow.f64 PI.f64 3)
3.0ms	(log.f64 (/.f64 4 PI.f64))

series46.0ms

Counts

4 → 8

Calls

4 calls:

21.0ms	(-.f64 (log.f64 f) (log.f64 (/.f64 4 PI.f64)))
25.0ms	(*.f64 (/.f64 4 PI.f64) (-.f64 (log.f64 f) (log.f64 (/.f64 4 PI.f64))))
0.0ms	(pow.f64 PI.f64 3)
0.0ms	(log.f64 (/.f64 4 PI.f64))

simplify46.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4985	1380
1	4985	1380

prune171.0ms

Filtered

93 candidates to 139 candidates (-49.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	134	5	139
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	139	9	148

Merged error: 0.8b

Counts

148 → 9

regimes55.0ms

Accuracy

0% (0.6b remaining)

Error of 2.1b against oracle of 1.5b and baseline of 2.1b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	24
1	48	24

end0.0ms

sample7.8s

Algorithm

intervals

Results

2.4s	3441×	body	1280	valid
1.8s	2895×	body	1280	nan
1.2s	2430×	body	640	valid
1.1s	2374×	body	640	nan
458.0ms	1257×	body	320	valid
403.0ms	1188×	body	320	nan
167.0ms	652×	body	160	valid
58.0ms	247×	body	160	nan
28.0ms	220×	body	80	valid

Details

analyze931.0ms

sample271.0ms

simplify493.0ms

prune10.0ms

localize19.0ms

rewrite56.0ms

series63.0ms

simplify58.0ms

prune249.0ms

localize14.0ms

rewrite28.0ms

series43.0ms

simplify70.0ms

prune129.0ms

localize17.0ms

rewrite26.0ms

series37.0ms

simplify42.0ms

prune105.0ms

localize21.0ms

rewrite31.0ms

series46.0ms

simplify46.0ms

prune171.0ms

regimes55.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample7.8s

Profiling