Details

analyze535.0ms

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
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

sample22.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
1.0ms	12×	body	80	invalid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	15	15
1	15	15

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: 27.3b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.0b	(+.f64 (.f64 a c) (.f64 b d))
26.7b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`times-frac_binary64`
7×	`add-log-exp_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`flip3-+_binary64` `flip-+_binary64`
3×	`associate-/r_binary64` `pow1_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64` `+-commutative_binary64` `sum-log_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

3 → 53

Calls

3 calls:

4.0ms	(+.f64 (.f64 c c) (.f64 d d))
7.0ms	(+.f64 (.f64 a c) (.f64 b d))
9.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

series51.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(+.f64 (.f64 c c) (.f64 d d))
12.0ms	(+.f64 (.f64 a c) (.f64 b d))
32.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

simplify50.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5334	951

prune102.0ms

Filtered

48 candidates to 62 candidates (-29.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	54	8	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	8	63

Merged error: 26.5b

Counts

63 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
16.2b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
29.6b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
29.6b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac_binary64`
164×	`add-sqr-sqrt_binary64`
162×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
156×	`sqrt-prod_binary64`
27×	`associate-/l*_binary64`
22×	`sqrt-div_binary64`
18×	`associate-/r/_binary64`
12×	`flip3-+_binary64` `associate-/r*_binary64` `flip-+_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`div-inv_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`associate-/l/_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 264

Calls

4 calls:

22.0ms	(/.f64 (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
10.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series93.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/.f64 (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
42.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
7.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
7.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify93.0ms

Algorithm

egg-herbie

Counts

276 → 276

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4969	8788
1	4969	8788

prune182.0ms

Filtered

150 candidates to 276 candidates (-84.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	272	4	276
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	274	10	284

Merged error: 24.0b

Counts

284 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
16.2b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
29.6b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
29.6b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt_binary64`
76×	`times-frac_binary64`
53×	`*-un-lft-identity_binary64`
47×	`add-cube-cbrt_binary64` `sqrt-prod_binary64`
28×	`add-exp-log_binary64`
24×	`associate-r_binary64` `associate-l_binary64`
18×	`add-cbrt-cube_binary64`
15×	`unswap-sqr_binary64`
10×	`sqrt-div_binary64`
9×	`div-exp_binary64`
8×	`pow1_binary64` `prod-exp_binary64`
6×	`flip3-+_binary64` `associate-/r*_binary64` `associate-/r/_binary64` `flip-+_binary64`
5×	`cbrt-undiv_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64`
3×	`associate-/l*_binary64` `div-inv_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `1-exp_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rec-exp_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 160

Calls

4 calls:

28.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
10.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series95.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
46.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
7.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
7.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify71.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4989	3794
1	4989	3794

prune152.0ms

Filtered

116 candidates to 172 candidates (-48.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	171	11	182

Merged error: 24.0b

Counts

182 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a c) (.f64 b d))
0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.3b	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
26.5b	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64` `times-frac_binary64`
17×	`add-exp-log_binary64`
15×	`associate-r_binary64`
11×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
6×	`flip3-+_binary64` `flip-+_binary64`
4×	`associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64`
3×	`associate-/r_binary64` `associate-l_binary64` `unswap-sqr_binary64` `associate-/l_binary64`
2×	`cbrt-unprod_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64` `div-inv_binary64` `+-commutative_binary64` `frac-times_binary64` `associate-*l/_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `pow-flip_binary64` `-commutative_binary64`

Counts

4 → 97

Calls

4 calls:

4.0ms	(+.f64 (.f64 a c) (.f64 b d))
5.0ms	(+.f64 (.f64 c c) (.f64 d d))
6.0ms	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
13.0ms	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))

series59.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(+.f64 (.f64 a c) (.f64 b d))
6.0ms	(+.f64 (.f64 c c) (.f64 d d))
7.0ms	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
34.0ms	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))

simplify66.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5037	1453

prune73.0ms

Filtered

71 candidates to 109 candidates (-53.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	109	11	120

Merged error: 24.0b

Counts

120 → 11

regimes462.0ms

Accuracy

0% (3.1b remaining)

Error of 26.4b against oracle of 23.2b and baseline of 26.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	25
1	17	25

end0.0ms

sample580.0ms

Algorithm

intervals

Results

351.0ms	8000×	body	80	valid
20.0ms	482×	body	80	invalid

Details

analyze535.0ms

sample22.0ms

simplify5.0ms

prune4.0ms

localize10.0ms

rewrite22.0ms

series51.0ms

simplify50.0ms

prune102.0ms

localize12.0ms

rewrite55.0ms

series93.0ms

simplify93.0ms

prune182.0ms

localize16.0ms

rewrite53.0ms

series95.0ms

simplify71.0ms

prune152.0ms

localize12.0ms

rewrite31.0ms

series59.0ms

simplify66.0ms

prune73.0ms

regimes462.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample580.0ms

Profiling