Details

analyze1.1s

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

sample33.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
3.0ms	77×	body	80	nan
1.0ms	23×	body	80	invalid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	805	14
1	805	14

prune4.0ms

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: 26.4b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 z z) (.f64 t a))
4.3b	(.f64 (.f64 x y) z)
9.3b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
25.8b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite31.0ms

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))
5.0ms	(.f64 (.f64 x y) z)
14.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(-.f64 (.f64 z z) (.f64 t a))
6.0ms	(.f64 (.f64 x y) z)
32.0ms	(/.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)))

simplify41.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5307	972

prune116.0ms

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: 2.7b

Counts

88 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
0.2b	(-.f64 (.f64 z z) (.f64 t a))
2.2b	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
25.8b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

7.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
5.0ms	(-.f64 (.f64 z z) (.f64 t a))
12.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
11.0ms	(-.f64 (.f64 z z) (.f64 t a))
32.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
14.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify57.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5256	1640

prune110.0ms

Filtered

81 candidates to 123 candidates (-51.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	124	7	131

Merged error: 2.7b

Counts

131 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 z z) (.f64 t a))
1.2b	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
1.8b	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
25.8b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

4.0ms	(-.f64 (.f64 z z) (.f64 t a))
11.0ms	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
12.0ms	(.f64 y (/.f64 z (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:

7.0ms	(-.f64 (.f64 z z) (.f64 t a))
32.0ms	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
22.0ms	(.f64 y (/.f64 z (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

103 → 103

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4973	1238
1	4973	1238

prune92.0ms

Filtered

72 candidates to 103 candidates (-43.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	103	7	110

Merged error: 2.7b

Counts

110 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(/.f64 (.f64 x y) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
5.3b	(.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))))))
25.8b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
25.8b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

63×	`sqrt-prod_binary64`
48×	`add-sqr-sqrt_binary64` `times-frac_binary64`
35×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
33×	`associate-r_binary64`
30×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`sqrt-div_binary64`
15×	`associate-l_binary64`
9×	`associate-/r*_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
8×	`pow1_binary64`
6×	`associate-/r/_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
3×	`div-inv_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `frac-times_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 141

Calls

4 calls:

12.0ms	(/.f64 (.f64 x y) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
26.0ms	(.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)))

series111.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/.f64 (.f64 x y) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
33.0ms	(.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))))))
16.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
24.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify84.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4955	2668
1	4955	2668

prune98.0ms

Filtered

101 candidates to 153 candidates (-51.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	153	7	160

Merged error: 2.7b

Counts

160 → 7

regimes747.0ms

Accuracy

85.2% (2.8b remaining)

Error of 6.2b against oracle of 3.4b and baseline of 22.3b

bsearch43.0ms

Steps

Iters	Range		Point
8	1.7424911013383455e+59	8.675904123350865e+61	7.14742597666009e+61
6	-2.184584455914151e+142	-2.3414016191794142e+141	-2.0295156182980508e+142

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	71	29
1	71	29

end0.0ms

sample919.0ms

Algorithm

intervals

Results

408.0ms	8000×	body	80	valid
107.0ms	2218×	body	80	nan
42.0ms	858×	body	80	invalid

Details

analyze1.1s

sample33.0ms

simplify39.0ms

prune4.0ms

localize11.0ms

rewrite31.0ms

series60.0ms

simplify41.0ms

prune116.0ms

localize12.0ms

rewrite32.0ms

series67.0ms

simplify57.0ms

prune110.0ms

localize10.0ms

rewrite35.0ms

series76.0ms

simplify49.0ms

prune92.0ms

localize13.0ms

rewrite55.0ms

series111.0ms

simplify84.0ms

prune98.0ms

regimes747.0ms

bsearch43.0ms

simplify2.0ms

end0.0ms

sample919.0ms

Profiling