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

sample31.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
3.0ms	73×	body	80	nan
1.0ms	23×	body	80	invalid

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

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: 24.6b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 z z) (.f64 t a))
6.0b	(.f64 (.f64 x y) z)
8.1b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
23.5b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite29.0ms

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)
10.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
8.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(-.f64 (.f64 z z) (.f64 t a))
8.0ms	(.f64 (.f64 x y) z)
38.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
16.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify39.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5307	972

prune125.0ms

Filtered

61 candidates to 87 candidates (-42.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	76	11	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	76	12	88

Merged error: 4.3b

Counts

88 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
1.0b	(-.f64 (.f64 z z) (.f64 t a))
4.2b	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
23.5b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite31.0ms

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))))
4.0ms	(-.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)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
9.0ms	(-.f64 (.f64 z z) (.f64 t a))
38.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
18.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify54.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5256	1640

prune198.0ms

Filtered

81 candidates to 123 candidates (-51.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	1	9	10
Picked	1	0	1
Done	1	0	1
Total	123	12	135

Merged error: 4.0b

Counts

135 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 z z) (.f64 t a))
1.7b	(.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)))))
23.5b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite34.0ms

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)))

series87.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(-.f64 (.f64 z z) (.f64 t a))
40.0ms	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
23.0ms	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
16.0ms	(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

prune111.0ms

Filtered

71 candidates to 103 candidates (-45.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	104	11	115

Merged error: 4.0b

Counts

115 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 z z) (.f64 t a))
1.7b	(.f64 x (.f64 (.f64 y (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
6.6b	(.f64 (.f64 y (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 z) (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
23.5b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-exp-log_binary64`
43×	`associate-r_binary64`
40×	`add-cbrt-cube_binary64`
36×	`times-frac_binary64`
32×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64` `cbrt-unprod_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64`
28×	`pow1_binary64`
21×	`sqrt-prod_binary64`
18×	`cbrt-prod_binary64`
16×	`pow-prod-down_binary64`
6×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
4×	`associate-l_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `associate-*r/_binary64` `flip--_binary64`
2×	`associate-/r/_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 → 124

Calls

4 calls:

4.0ms	(-.f64 (.f64 z z) (.f64 t a))
18.0ms	(.f64 x (.f64 (.f64 y (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
21.0ms	(.f64 (.f64 y (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 z) (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series98.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(-.f64 (.f64 z z) (.f64 t a))
45.0ms	(.f64 x (.f64 (.f64 y (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
28.0ms	(.f64 (.f64 y (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 z) (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
16.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify70.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4903	1919
1	4903	1919

prune77.0ms

Filtered

80 candidates to 136 candidates (-70.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	135	12	147

Merged error: 4.0b

Counts

147 → 12

regimes781.0ms

Accuracy

80.4% (3.9b remaining)

Error of 7.3b against oracle of 3.4b and baseline of 23.1b

bsearch33.0ms

Steps

Iters	Range		Point
7	9.412867195948032e+140	6.560810260066545e+142	9.594770076281723e+140
4	-1.3318014264147303e+60	-8.937591876171522e+59	-1.3181126064523061e+60

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	75	36
1	75	36

end0.0ms

sample874.0ms

Algorithm

intervals

Results

392.0ms	8000×	body	80	valid
99.0ms	2171×	body	80	nan
49.0ms	907×	body	80	invalid

Details

analyze1.1s

sample31.0ms

simplify38.0ms

prune4.0ms

localize10.0ms

rewrite29.0ms

series70.0ms

simplify39.0ms

prune125.0ms

localize10.0ms

rewrite31.0ms

series77.0ms

simplify54.0ms

prune198.0ms

localize10.0ms

rewrite34.0ms

series87.0ms

simplify49.0ms

prune111.0ms

localize14.0ms

rewrite53.0ms

series98.0ms

simplify70.0ms

prune77.0ms

regimes781.0ms

bsearch33.0ms

simplify3.0ms

end0.0ms

sample874.0ms

Profiling