Details

analyze249.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
28.1%	71.8%	0.1%	7
42.1%	57.7%	0.1%	8
43.7%	56.2%	0.1%	9
64.4%	35.5%	0.1%	10
71.6%	28.3%	0.1%	11
72.2%	27.7%	0.1%	12
81.6%	18.2%	0.2%	13
84.9%	14.9%	0.2%	14

sample15.0ms

Algorithm

intervals

Results

8.0ms	256×	body	128	valid
0.0ms	5×	body	128	invalid

simplify152.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (145.0ms)

Iter	Nodes	Cost
0	4949	16
1	4949	16

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 0.3b

Counts

2 → 2

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 v (+.f64 t1 u))
2.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

223×	`times-frac_binary64`
181×	`add-sqr-sqrt_binary64`
174×	`*-un-lft-identity_binary64`
86×	`add-cube-cbrt_binary64`
38×	`difference-of-squares_binary64`
25×	`distribute-lft-out_binary64`
21×	`associate-/l*_binary64`
19×	`distribute-lft-out--_binary64`
18×	`associate-/r/_binary64`
10×	`associate-/r*_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `div-inv_binary64`
8×	`flip3-+_binary64` `flip-+_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
2×	`add-log-exp_binary64` `pow1_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64` `flip3--_binary64` `flip--_binary64`

Counts

2 → 182

Calls

2 calls:

6.0ms	(/.f64 v (+.f64 t1 u))
18.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

series188.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(/.f64 v (+.f64 t1 u))
126.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

simplify91.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5078	5524

prune143.0ms

Filtered

125 candidates to 188 candidates (-50.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	183	5	188
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	184	6	190

Merged error: 0.2b

Counts

190 → 6

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 v (+.f64 t1 u))
0.3b	(/.f64 1 (-.f64 -1 (/.f64 u t1)))
2.6b	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

93×	`add-sqr-sqrt_binary64`
74×	`times-frac_binary64`
71×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`
25×	`add-exp-log_binary64`
24×	`associate-r_binary64`
19×	`add-cbrt-cube_binary64`
18×	`associate-l_binary64`
14×	`difference-of-squares_binary64`
10×	`associate-/r*_binary64`
8×	`associate-/r/_binary64`
7×	`distribute-lft-out_binary64` `distribute-lft-out--_binary64` `div-exp_binary64`
6×	`pow1_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l*_binary64`
4×	`cbrt-unprod_binary64` `div-inv_binary64`
3×	`add-log-exp_binary64` `rec-exp_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `inv-pow_binary64` `un-div-inv_binary64` `pow-flip_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

3 → 148

Calls

3 calls:

5.0ms	(/.f64 v (+.f64 t1 u))
9.0ms	(/.f64 1 (-.f64 -1 (/.f64 u t1)))
29.0ms	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))

series236.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(/.f64 v (+.f64 t1 u))
50.0ms	(/.f64 1 (-.f64 -1 (/.f64 u t1)))
132.0ms	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))

simplify66.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5155	2640

prune97.0ms

Filtered

101 candidates to 157 candidates (-55.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	157	6	163

Merged error: 0.2b

Counts

163 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

9.6b	(cbrt.f64 (-.f64 -1 (/.f64 u t1)))
16.3b	(cbrt.f64 (/.f64 v (+.f64 t1 u)))
16.3b	(cbrt.f64 (/.f64 v (+.f64 t1 u)))
16.3b	(cbrt.f64 (/.f64 v (+.f64 t1 u)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-prod_binary64`
49×	`*-un-lft-identity_binary64`
37×	`times-frac_binary64`
34×	`add-sqr-sqrt_binary64`
29×	`add-cube-cbrt_binary64`
9×	`distribute-lft-out_binary64`
6×	`associate-/r/_binary64`
5×	`cbrt-div_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `pow1/3_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`difference-of-squares_binary64`
1×	`flip3--_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 97

Calls

4 calls:

7.0ms	(cbrt.f64 (-.f64 -1 (/.f64 u t1)))
5.0ms	(cbrt.f64 (/.f64 v (+.f64 t1 u)))
5.0ms	(cbrt.f64 (/.f64 v (+.f64 t1 u)))
5.0ms	(cbrt.f64 (/.f64 v (+.f64 t1 u)))

series1.1s

Counts

4 → 12

Calls

4 calls:

318.0ms	(cbrt.f64 (-.f64 -1 (/.f64 u t1)))
259.0ms	(cbrt.f64 (/.f64 v (+.f64 t1 u)))
256.0ms	(cbrt.f64 (/.f64 v (+.f64 t1 u)))
263.0ms	(cbrt.f64 (/.f64 v (+.f64 t1 u)))

simplify62.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5372	1889

prune145.0ms

Filtered

92 candidates to 109 candidates (-18.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	109	6	115

Merged error: 0.2b

Counts

115 → 6

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 v (+.f64 t1 u))
0.9b	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))))
2.7b	(/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u)))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

1354×	`times-frac_binary64`
924×	`add-sqr-sqrt_binary64`
845×	`*-un-lft-identity_binary64`
469×	`add-cube-cbrt_binary64`
182×	`difference-of-squares_binary64`
135×	`associate-/r*_binary64`
97×	`distribute-lft-out_binary64`
91×	`distribute-lft-out--_binary64`
70×	`associate-/r/_binary64`
38×	`div-inv_binary64`
32×	`flip3-+_binary64` `flip-+_binary64`
25×	`add-exp-log_binary64`
19×	`add-cbrt-cube_binary64`
13×	`div-exp_binary64`
12×	`associate-/l*_binary64`
10×	`cbrt-undiv_binary64`
4×	`pow1_binary64`
3×	`add-log-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
2×	`associate-/l/_binary64`
1×	`flip3--_binary64` `div-sub_binary64` `inv-pow_binary64` `flip--_binary64` `pow-flip_binary64`

Counts

3 → 660

Calls

3 calls:

6.0ms	(/.f64 v (+.f64 t1 u))
36.0ms	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))))
17.0ms	(/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u)))

series373.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(/.f64 v (+.f64 t1 u))
247.0ms	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))))
62.0ms	(/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u)))

simplify225.0ms

Algorithm

egg-herbie

Counts

669 → 669

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5127	23636

prune489.0ms

Filtered

364 candidates to 669 candidates (-83.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	668	1	669
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	669	6	675

Merged error: 0.2b

Counts

675 → 6

regimes70.0ms

Accuracy

25.4% (1.0b remaining)

Error of 1.2b against oracle of 0.2b and baseline of 1.5b

bsearch2.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	72	85
1	72	85

end0.0ms

sample436.0ms

Algorithm

intervals

Results

258.0ms	8000×	body	128	valid
7.0ms	236×	body	128	invalid

Details

analyze249.0ms

sample15.0ms

simplify152.0ms

prune4.0ms

localize8.0ms

rewrite49.0ms

series188.0ms

simplify91.0ms

prune143.0ms

localize9.0ms

rewrite59.0ms

series236.0ms

simplify66.0ms

prune97.0ms

localize17.0ms

rewrite39.0ms

series1.1s

simplify62.0ms

prune145.0ms

localize11.0ms

rewrite195.0ms

series373.0ms

simplify225.0ms

prune489.0ms

regimes70.0ms

bsearch2.0ms

simplify3.0ms

end0.0ms

sample436.0ms

Profiling