Details

analyze1.7s

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

sample63.0ms

Algorithm

intervals

Results

24.0ms	256×	body	128	valid
15.0ms	165×	body	128	nan

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4882	44
1	4882	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: 2.0b

Counts

2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 z (sqrt.f64 (+.f64 t a)))
0.4b	(/.f64 2/3 t)
1.4b	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
3.3b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

rewrite49.0ms

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)
15.0ms	(-.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)

series630.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
21.0ms	(/.f64 2/3 t)
372.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
132.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

simplify92.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4947	2992
1	4947	2992

prune164.0ms

Filtered

92 candidates to 116 candidates (-26.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	114	3	117

Merged error: 0.3b

Counts

117 → 3

localize37.0ms

Local error

Found 4 expressions with local error:

3.6b	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (.f64 2/3 (-.f64 a 5/6)))))
4.4b	(.f64 t (-.f64 (.f64 a a) 25/36))
4.6b	(.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (*.f64 2/3 (-.f64 a 5/6))))))
22.2b	(/.f64 (.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (.f64 2/3 (-.f64 a 5/6)))))) (.f64 t (*.f64 t (-.f64 a 5/6))))

rewrite681.0ms

Algorithm

rewrite-expression-head

Rules

1530×	`associate-*r/_binary64`
768×	`frac-sub_binary64`
713×	`flip3--_binary64` `flip--_binary64`
528×	`frac-times_binary64`
360×	`sqrt-div_binary64`
180×	`flip3-+_binary64` `flip-+_binary64`
168×	`associate-*l/_binary64`
162×	`associate-/l/_binary64`
29×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
17×	`sub-neg_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
11×	`cbrt-unprod_binary64` `prod-exp_binary64`
10×	`associate--l+_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64` `associate--r+_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-exp_binary64`
2×	`pow-prod-down_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
1×	`associate-/r_binary64` `diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `associate-/l_binary64` `times-frac_binary64` `div-inv_binary64`

Counts

4 → 577

Calls

4 calls:

30.0ms	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (.f64 2/3 (-.f64 a 5/6)))))
8.0ms	(.f64 t (-.f64 (.f64 a a) 25/36))
55.0ms	(.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (*.f64 2/3 (-.f64 a 5/6))))))
67.0ms	(/.f64 (.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (.f64 2/3 (-.f64 a 5/6)))))) (.f64 t (*.f64 t (-.f64 a 5/6))))

series3.9s

Counts

4 → 12

Calls

4 calls:

952.0ms	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (.f64 2/3 (-.f64 a 5/6)))))
81.0ms	(.f64 t (-.f64 (.f64 a a) 25/36))
1.3s	(.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (*.f64 2/3 (-.f64 a 5/6))))))
1.6s	(/.f64 (.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (.f64 2/3 (-.f64 a 5/6)))))) (.f64 t (*.f64 t (-.f64 a 5/6))))

simplify485.0ms

Algorithm

egg-herbie

Counts

589 → 589

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5378	62096

prune5.8s

Filtered

563 candidates to 589 candidates (-4.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	588	1	589
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	589	3	592

Merged error: 0.0b

Counts

592 → 3

localize35.0ms

Local error

Found 4 expressions with local error:

1.6b	(.f64 (-.f64 b c) (-.f64 (.f64 (.f64 t (+.f64 a 5/6)) (-.f64 a (sqrt.f64 25/36))) (.f64 2/3 (-.f64 a 5/6))))
3.6b	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 (.f64 t (+.f64 a 5/6)) (-.f64 a (sqrt.f64 25/36))) (.f64 2/3 (-.f64 a 5/6)))))
4.6b	(.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 (.f64 t (+.f64 a 5/6)) (-.f64 a (sqrt.f64 25/36))) (*.f64 2/3 (-.f64 a 5/6))))))
22.2b	(/.f64 (.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 (.f64 t (+.f64 a 5/6)) (-.f64 a (sqrt.f64 25/36))) (.f64 2/3 (-.f64 a 5/6)))))) (.f64 t (*.f64 t (-.f64 a 5/6))))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

5098×	`associate-*r/_binary64`
2544×	`frac-sub_binary64`
2172×	`frac-times_binary64`
2108×	`flip3--_binary64` `flip--_binary64`
1008×	`sqrt-div_binary64`
954×	`flip3-+_binary64` `flip-+_binary64`
686×	`associate-*l/_binary64`
450×	`associate-/l/_binary64`
29×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
21×	`sub-neg_binary64`
16×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
14×	`add-sqr-sqrt_binary64` `associate--l+_binary64`
11×	`cbrt-unprod_binary64` `prod-exp_binary64`
10×	`*-un-lft-identity_binary64`
8×	`pow1_binary64` `add-cube-cbrt_binary64` `associate-l_binary64`
6×	`add-log-exp_binary64` `associate--r+_binary64` `associate-r_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
2×	`pow-prod-down_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
1×	`associate-/r_binary64` `diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `div-inv_binary64`

Counts

4 → 1500

Calls

4 calls:

26.0ms	(.f64 (-.f64 b c) (-.f64 (.f64 (.f64 t (+.f64 a 5/6)) (-.f64 a (sqrt.f64 25/36))) (.f64 2/3 (-.f64 a 5/6))))
57.0ms	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 (.f64 t (+.f64 a 5/6)) (-.f64 a (sqrt.f64 25/36))) (.f64 2/3 (-.f64 a 5/6)))))
109.0ms	(.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 (.f64 t (+.f64 a 5/6)) (-.f64 a (sqrt.f64 25/36))) (*.f64 2/3 (-.f64 a 5/6))))))
140.0ms	(/.f64 (.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 (.f64 t (+.f64 a 5/6)) (-.f64 a (sqrt.f64 25/36))) (.f64 2/3 (-.f64 a 5/6)))))) (.f64 t (*.f64 t (-.f64 a 5/6))))

series4.1s

Counts

4 → 12

Calls

4 calls:

310.0ms	(.f64 (-.f64 b c) (-.f64 (.f64 (.f64 t (+.f64 a 5/6)) (-.f64 a (sqrt.f64 25/36))) (.f64 2/3 (-.f64 a 5/6))))
968.0ms	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 (.f64 t (+.f64 a 5/6)) (-.f64 a (sqrt.f64 25/36))) (.f64 2/3 (-.f64 a 5/6)))))
1.3s	(.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 (.f64 t (+.f64 a 5/6)) (-.f64 a (sqrt.f64 25/36))) (*.f64 2/3 (-.f64 a 5/6))))))
1.6s	(/.f64 (.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 (.f64 t (+.f64 a 5/6)) (-.f64 a (sqrt.f64 25/36))) (.f64 2/3 (-.f64 a 5/6)))))) (.f64 t (*.f64 t (-.f64 a 5/6))))

simplify1.3s

Algorithm

egg-herbie

Counts

1512 → 1512

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	7054	183745

prune35.2s

Filtered

1495 candidates to 1512 candidates (-1.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	1512	0	1512
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	1512	3	1515

Merged error: 0.0b

Counts

1515 → 3

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 y (pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (*.f64 a b))))
0.0b	(pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b)))
0.1b	(*.f64 c (+.f64 a 5/6))
0.7b	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))

rewrite39.0ms

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:

8.0ms	(.f64 y (pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (*.f64 a b))))
8.0ms	(pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b)))
7.0ms	(*.f64 c (+.f64 a 5/6))
7.0ms	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))

series441.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(.f64 y (pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (*.f64 a b))))
114.0ms	(pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b)))
48.0ms	(*.f64 c (+.f64 a 5/6))
55.0ms	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))

simplify91.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4922	1907
1	4922	1907

prune89.0ms

Filtered

70 candidates to 104 candidates (-48.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	104	3	107

Merged error: 0.0b

Counts

107 → 3

regimes107.0ms

Accuracy

0% (3.1b remaining)

Error of 3.8b against oracle of 0.7b and baseline of 3.8b

bsearch0.0ms

simplify6.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	245	44
1	245	44

end0.0ms

sample1.8s

Algorithm

intervals

Results

769.0ms	8000×	body	128	valid
470.0ms	5027×	body	128	nan

Details

analyze1.7s

sample63.0ms

simplify50.0ms

prune5.0ms

localize29.0ms

rewrite49.0ms

series630.0ms

simplify92.0ms

prune164.0ms

localize37.0ms

rewrite681.0ms

series3.9s

simplify485.0ms

prune5.8s

localize35.0ms

rewrite1.3s

series4.1s

simplify1.3s

prune35.2s

localize22.0ms

rewrite39.0ms

series441.0ms

simplify91.0ms

prune89.0ms

regimes107.0ms

bsearch0.0ms

simplify6.0ms

end0.0ms

sample1.8s

Profiling