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

sample60.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
16.0ms	178×	body	80	nan

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4989	44
1	4989	44

prune6.0ms

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)))
0.4b	(/.f64 2/3 t)
3.2b	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
5.9b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

rewrite35.0ms

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)
13.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
8.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

series303.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
10.0ms	(/.f64 2/3 t)
173.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
72.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

simplify99.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4945	2992
1	4945	2992

prune166.0ms

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

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 t)
0.6b	(cbrt.f64 t)
2.6b	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
3.2b	(-.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)
22.0ms	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
20.0ms	(-.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))))

series453.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(cbrt.f64 t)
87.0ms	(cbrt.f64 t)
84.0ms	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
198.0ms	(-.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))))

simplify99.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4977	7318
1	4977	7318

prune291.0ms

Filtered

141 candidates to 178 candidates (-26.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

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

Merged error: 0.7b

Counts

182 → 4

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 2/3 t)
3.4b	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (log.f64 (exp.f64 (/.f64 2/3 t))))))
4.3b	(log.f64 (exp.f64 (/.f64 2/3 t)))
5.9b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
21×	`times-frac_binary64`
14×	`log-pow_binary64`
13×	`exp-prod_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`frac-sub_binary64`
7×	`flip3--_binary64` `flip--_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64`
5×	`pow1_binary64`
4×	`associate--r+_binary64` `associate-r/_binary64` `associate-/l_binary64` `frac-times_binary64`
3×	`sub-neg_binary64` `log-prod_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`
2×	`associate-/l/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64` `associate--l+_binary64` `associate-*l/_binary64`
1×	`flip3-+_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `prod-exp_binary64` `flip-+_binary64`

Counts

4 → 98

Calls

4 calls:

3.0ms	(/.f64 2/3 t)
13.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (log.f64 (exp.f64 (/.f64 2/3 t))))))
4.0ms	(log.f64 (exp.f64 (/.f64 2/3 t)))
8.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

series263.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/.f64 2/3 t)
176.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (log.f64 (exp.f64 (/.f64 2/3 t))))))
11.0ms	(log.f64 (exp.f64 (/.f64 2/3 t)))
67.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

simplify89.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4958	2278
1	4958	2278

prune143.0ms

Filtered

88 candidates to 110 candidates (-25.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	110	4	114

Merged error: 0.7b

Counts

114 → 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 y (pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (*.f64 a b))))
0.1b	(*.f64 c (+.f64 a 5/6))
1.0b	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

7.0ms	(pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b)))
7.0ms	(.f64 y (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))

series200.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b)))
99.0ms	(.f64 y (pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (*.f64 a b))))
21.0ms	(*.f64 c (+.f64 a 5/6))
32.0ms	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))

simplify113.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4880	1907
1	4880	1907

prune88.0ms

Filtered

69 candidates to 104 candidates (-50.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	1	1
Picked	0	1	1
Done	1	1	2
Total	104	4	108

Merged error: 0.5b

Counts

108 → 4

regimes106.0ms

Accuracy

0% (2.3b remaining)

Error of 2.8b against oracle of 0.5b and baseline of 2.8b

bsearch0.0ms

simplify8.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	248	56
1	248	56

end0.0ms

sample2.0s

Algorithm

intervals

Results

970.0ms	8000×	body	80	valid
475.0ms	5102×	body	80	nan

Details

analyze1.8s

sample60.0ms

simplify60.0ms

prune6.0ms

localize27.0ms

rewrite35.0ms

series303.0ms

simplify99.0ms

prune166.0ms

localize26.0ms

rewrite56.0ms

series453.0ms

simplify99.0ms

prune291.0ms

localize24.0ms

rewrite32.0ms

series263.0ms

simplify89.0ms

prune143.0ms

localize15.0ms

rewrite29.0ms

series200.0ms

simplify113.0ms

prune88.0ms

regimes106.0ms

bsearch0.0ms

simplify8.0ms

end0.0ms

sample2.0s

Profiling