Details

analyze1.8s

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

sample70.0ms

Algorithm

intervals

Results

29.0ms	256×	body	80	valid
16.0ms	169×	body	80	nan

simplify62.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4989	44
1	4989	44

prune5.0ms

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: 3.7b

Counts

2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 z (sqrt.f64 (+.f64 t a)))
0.3b	(/.f64 2/3 t)
1.9b	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
5.2b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

rewrite38.0ms

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:

7.0ms	(*.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)

series325.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
15.0ms	(/.f64 2/3 t)
185.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
75.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

simplify96.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4945	2992
1	4945	2992

prune165.0ms

Filtered

92 candidates to 116 candidates (-26.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	3	117

Merged error: 0.3b

Counts

117 → 3

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 t)
0.6b	(cbrt.f64 t)
0.7b	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
1.9b	(-.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))))

rewrite56.0ms

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:

1.0ms	(cbrt.f64 t)
1.0ms	(cbrt.f64 t)
23.0ms	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
21.0ms	(-.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))))

series494.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(cbrt.f64 t)
86.0ms	(cbrt.f64 t)
80.0ms	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
245.0ms	(-.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))))

simplify90.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4977	7318
1	4977	7318

prune320.0ms

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	0	2	2
Picked	0	1	1
Done	0	0	0
Total	177	4	181

Merged error: 0.2b

Counts

181 → 4

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 t)
0.6b	(cbrt.f64 t)
5.4b	(-.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))))
10.6b	(log.f64 (exp.f64 (cbrt.f64 t)))

rewrite33.0ms

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)
1.0ms	(cbrt.f64 t)
22.0ms	(-.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)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(cbrt.f64 t)
88.0ms	(cbrt.f64 t)
201.0ms	(-.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))))
87.0ms	(log.f64 (exp.f64 (cbrt.f64 t)))

simplify76.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5214	5241

prune223.0ms

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: 0.2b

Counts

113 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 a 5/6)
0.0b	(pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b)))
0.2b	(*.f64 c (+.f64 a 5/6))
2.1b	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))

rewrite28.0ms

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:

3.0ms	(+.f64 a 5/6)
9.0ms	(pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b)))
6.0ms	(*.f64 c (+.f64 a 5/6))
7.0ms	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))

series110.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+.f64 a 5/6)
47.0ms	(pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b)))
22.0ms	(*.f64 c (+.f64 a 5/6))
29.0ms	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))

simplify131.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	4903	1239
1	4903	1239

prune69.0ms

Filtered

56 candidates to 85 candidates (-51.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	1	1
Picked	0	1	1
Done	1	1	2
Total	85	4	89

Merged error: 0.2b

Counts

89 → 4

regimes125.0ms

Accuracy

0% (2.3b remaining)

Error of 2.7b against oracle of 0.4b and baseline of 2.7b

bsearch0.0ms

simplify8.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	248	56
1	248	56

end0.0ms

sample1.8s

Algorithm

intervals

Results

793.0ms	8000×	body	80	valid
495.0ms	5030×	body	80	nan

Details

analyze1.8s

sample70.0ms

simplify62.0ms

prune5.0ms

localize29.0ms

rewrite38.0ms

series325.0ms

simplify96.0ms

prune165.0ms

localize31.0ms

rewrite56.0ms

series494.0ms

simplify90.0ms

prune320.0ms

localize30.0ms

rewrite33.0ms

series466.0ms

simplify76.0ms

prune223.0ms

localize15.0ms

rewrite28.0ms

series110.0ms

simplify131.0ms

prune69.0ms

regimes125.0ms

bsearch0.0ms

simplify8.0ms

end0.0ms

sample1.8s

Profiling