Details

analyze2.0s

Algorithm

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
3.1%	96.5%	0.3%	9
4.7%	95%	0.3%	10
4.7%	95%	0.3%	11
5.1%	82.1%	12.8%	12
6.2%	74.7%	19%	13
6.4%	74.5%	19%	14

sample110.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
14.0ms	149×	body	80	nan

simplify23.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	4938	29
1	4938	29

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: 4.2b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 z (sqrt.f64 (+.f64 t a)))
0.3b	(/.f64 2/3 t)
2.9b	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
6.2b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
20×	`frac-sub_binary64`
19×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`times-frac_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`associate-*r/_binary64` `frac-times_binary64`
7×	`associate-r_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `pow1_binary64`
5×	`flip3-+_binary64` `sqrt-prod_binary64` `flip-+_binary64`
4×	`associate--r+_binary64` `associate-/l*_binary64` `sqrt-div_binary64`
3×	`sub-neg_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-exp_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `associate--l+_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `*-commutative_binary64`

Counts

4 → 104

Calls

4 calls:

8.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
3.0ms	(/.f64 2/3 t)
14.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
9.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

series100.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
2.0ms	(/.f64 2/3 t)
62.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
20.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

simplify57.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4951	1974
1	4951	1974

prune133.0ms

Filtered

92 candidates to 116 candidates (-26.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	112	4	116
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	4	117

Merged error: 0.7b

Counts

117 → 4

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 t)
0.6b	(cbrt.f64 t)
1.5b	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
2.9b	(-.f64 (.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t))) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt_binary64`
60×	`frac-sub_binary64`
58×	`times-frac_binary64`
47×	`*-un-lft-identity_binary64`
46×	`associate-r_binary64`
39×	`frac-times_binary64`
35×	`add-cube-cbrt_binary64`
31×	`cbrt-prod_binary64`
28×	`sqrt-prod_binary64`
27×	`associate-*r/_binary64`
25×	`flip3--_binary64` `add-exp-log_binary64` `flip--_binary64`
21×	`associate-*l/_binary64`
18×	`add-cbrt-cube_binary64`
10×	`unswap-sqr_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`cbrt-undiv_binary64` `associate-l_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `distribute-lft-out_binary64`
4×	`associate--r+_binary64`
3×	`sub-neg_binary64`
2×	`pow1/3_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-inv_binary64` `associate--l+_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `*-commutative_binary64`

Counts

4 → 166

Calls

4 calls:

2.0ms	(cbrt.f64 t)
2.0ms	(cbrt.f64 t)
24.0ms	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
22.0ms	(-.f64 (.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t))) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))

series127.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(cbrt.f64 t)
17.0ms	(cbrt.f64 t)
26.0ms	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
69.0ms	(-.f64 (.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t))) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))

simplify49.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	4992	4847
1	4992	4847

prune237.0ms

Filtered

141 candidates to 178 candidates (-26.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	178	4	182

Merged error: 0.7b

Counts

182 → 4

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 t)
0.6b	(cbrt.f64 t)
7.3b	(-.f64 (.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (log.f64 (exp.f64 (cbrt.f64 t))))) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
10.5b	(log.f64 (exp.f64 (cbrt.f64 t)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

60×	`frac-sub_binary64`
38×	`frac-times_binary64`
26×	`associate-*r/_binary64`
25×	`flip3--_binary64` `flip--_binary64`
20×	`associate-*l/_binary64`
9×	`flip3-+_binary64` `*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `flip-+_binary64` `cbrt-prod_binary64`
7×	`log-pow_binary64`
6×	`add-log-exp_binary64` `exp-prod_binary64`
5×	`pow1_binary64`
4×	`associate--r+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`sub-neg_binary64` `log-prod_binary64`
2×	`pow1/3_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate--l+_binary64`
1×	`diff-log_binary64` `rem-log-exp_binary64`

Counts

4 → 97

Calls

4 calls:

1.0ms	(cbrt.f64 t)
2.0ms	(cbrt.f64 t)
24.0ms	(-.f64 (.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (log.f64 (exp.f64 (cbrt.f64 t))))) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
3.0ms	(log.f64 (exp.f64 (cbrt.f64 t)))

series116.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(cbrt.f64 t)
15.0ms	(cbrt.f64 t)
65.0ms	(-.f64 (.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (log.f64 (exp.f64 (cbrt.f64 t))))) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
19.0ms	(log.f64 (exp.f64 (cbrt.f64 t)))

simplify37.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5205	3516

prune163.0ms

Filtered

100 candidates to 109 candidates (-9.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	109	4	113

Merged error: 0.7b

Counts

113 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b)))
0.0b	(+.f64 a 5/6)
0.1b	(*.f64 c (+.f64 a 5/6))
1.6b	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-r_binary64` `pow-pow_binary64` `unpow-prod-down_binary64` `associate--l+_binary64`
3×	`pow-unpow_binary64` `unpow-prod-up_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `exp-prod_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `distribute-lft-out_binary64` `associate-*r/_binary64` `flip-+_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `exp-lft-sqr_binary64` `sqr-pow_binary64` `unswap-sqr_binary64` `pow-sub_binary64` `prod-exp_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 73

Calls

4 calls:

8.0ms	(pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b)))
4.0ms	(+.f64 a 5/6)
10.0ms	(*.f64 c (+.f64 a 5/6))
8.0ms	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))

series35.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b)))
2.0ms	(+.f64 a 5/6)
6.0ms	(*.f64 c (+.f64 a 5/6))
9.0ms	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))

simplify66.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4977	833
1	4977	833

prune52.0ms

Filtered

56 candidates to 85 candidates (-51.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	85	4	89

Merged error: 0.7b

Counts

89 → 4

regimes521.0ms

Accuracy

0% (1.9b remaining)

Error of 2.7b against oracle of 0.8b and baseline of 2.7b

bsearch0.0ms

simplify6.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	247	36
1	247	36

end0.0ms

sample1.9s

Algorithm

intervals

Results

806.0ms	8000×	body	80	valid
502.0ms	4917×	body	80	nan

Details

analyze2.0s

sample110.0ms

simplify23.0ms

prune11.0ms

localize27.0ms

rewrite37.0ms

series100.0ms

simplify57.0ms

prune133.0ms

localize31.0ms

rewrite59.0ms

series127.0ms

simplify49.0ms

prune237.0ms

localize29.0ms

rewrite36.0ms

series116.0ms

simplify37.0ms

prune163.0ms

localize15.0ms

rewrite31.0ms

series35.0ms

simplify66.0ms

prune52.0ms

regimes521.0ms

bsearch0.0ms

simplify6.0ms

end0.0ms

sample1.9s

Profiling