Details

analyze1.2s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.6%	98.2%	0.2%	10
3.1%	90.4%	6.5%	11
9.2%	84.4%	6.5%	12
13%	80.6%	6.5%	13
24.8%	68.7%	6.5%	14

sample37.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
3.0ms	78×	body	80	nan
1.0ms	27×	body	80	invalid

simplify42.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	805	14
1	805	14

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 25.5b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 z z) (.f64 t a))
4.0b	(.f64 (.f64 x y) z)
9.8b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
25.6b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
9×	`sqrt-prod_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `times-frac_binary64`
4×	`sqrt-div_binary64`
3×	`pow-prod-down_binary64` `flip3--_binary64` `associate-r_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64`
2×	`associate-/r/_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 75

Calls

4 calls:

4.0ms	(-.f64 (.f64 z z) (.f64 t a))
6.0ms	(.f64 (.f64 x y) z)
10.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(-.f64 (.f64 z z) (.f64 t a))
6.0ms	(.f64 (.f64 x y) z)
36.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
14.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify40.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5307	972

prune80.0ms

Filtered

61 candidates to 87 candidates (-42.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	79	8	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	8	88

Merged error: 2.8b

Counts

88 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 z z) (.f64 t a))
5.1b	(.f64 (/.f64 (.f64 x y) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 z (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
25.6b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
25.6b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod_binary64`
42×	`add-sqr-sqrt_binary64`
39×	`times-frac_binary64`
33×	`associate-r_binary64`
29×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
25×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`associate-l_binary64`
12×	`sqrt-div_binary64`
8×	`pow1_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`associate-/r/_binary64` `unswap-sqr_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-r/_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 117

Calls

4 calls:

4.0ms	(-.f64 (.f64 z z) (.f64 t a))
27.0ms	(.f64 (/.f64 (.f64 x y) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 z (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(-.f64 (.f64 z z) (.f64 t a))
38.0ms	(.f64 (/.f64 (.f64 x y) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 z (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
15.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
15.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify71.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4945	2244
1	4945	2244

prune75.0ms

Filtered

85 candidates to 129 candidates (-51.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	125	4	129
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	128	9	137

Merged error: 2.3b

Counts

137 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

5.3b	(.f64 (/.f64 x (sqrt.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))) (.f64 (/.f64 z (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 y (sqrt.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))))
25.6b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
25.6b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
25.6b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

63×	`sqrt-prod_binary64`
45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
42×	`associate-l_binary64`
36×	`times-frac_binary64`
35×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`cbrt-unprod_binary64` `prod-exp_binary64`
13×	`cbrt-undiv_binary64` `div-exp_binary64`
12×	`pow1_binary64` `sqrt-div_binary64`
5×	`associate-*r/_binary64` `frac-times_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64`
3×	`pow-prod-down_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `associate-*l/_binary64`
2×	`associate-/r/_binary64`
1×	`associate-r_binary64` `div-inv_binary64` `*-commutative_binary64`

Counts

4 → 125

Calls

4 calls:

35.0ms	(.f64 (/.f64 x (sqrt.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))) (.f64 (/.f64 z (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 y (sqrt.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
5.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series78.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(.f64 (/.f64 x (sqrt.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))) (.f64 (/.f64 z (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 y (sqrt.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))))
14.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
18.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
14.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify49.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5062	2745

prune75.0ms

Filtered

93 candidates to 137 candidates (-47.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	137	9	146

Merged error: 2.3b

Counts

146 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

25.6b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
26.4b	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
26.4b	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
26.4b	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64` `cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`cbrt-div_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`pow1/3_binary64` `sqrt-prod_binary64`
2×	`sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 54

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series80.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
21.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
23.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
22.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify51.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	6146	790

prune41.0ms

Filtered

60 candidates to 66 candidates (-10.0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	66	9	75

Merged error: 2.3b

Counts

75 → 9

regimes663.0ms

Accuracy

83.3% (3.4b remaining)

Error of 6.4b against oracle of 3.1b and baseline of 23.2b

bsearch47.0ms

Steps

Iters	Range		Point
7	1.4136769293514078e+87	2.2764467290927134e+89	1.3605314306565522e+89
10	-1.999953504749926e+109	-1.8162223194733415e+99	-1.9767596707461871e+99

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	71	40
1	71	40

end0.0ms

sample917.0ms

Algorithm

intervals

Results

418.0ms	8000×	body	80	valid
104.0ms	2212×	body	80	nan
43.0ms	838×	body	80	invalid

Details

analyze1.2s

sample37.0ms

simplify42.0ms

prune3.0ms

localize10.0ms

rewrite27.0ms

series65.0ms

simplify40.0ms

prune80.0ms

localize15.0ms

rewrite46.0ms

series76.0ms

simplify71.0ms

prune75.0ms

localize19.0ms

rewrite55.0ms

series78.0ms

simplify49.0ms

prune75.0ms

localize22.0ms

rewrite19.0ms

series80.0ms

simplify51.0ms

prune41.0ms

regimes663.0ms

bsearch47.0ms

simplify2.0ms

end0.0ms

sample917.0ms

Profiling