Details

analyze336.0ms

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
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
40.6%	56.9%	2.5%	9
46%	49.5%	4.4%	10
50.3%	44.9%	4.8%	11
60.3%	30.5%	9.2%	12
62.9%	25.7%	11.4%	13
65.2%	23.2%	11.7%	14

sample28.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
1.0ms	23×	body	80	invalid

simplify78.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4992	11
1	4992	11

prune9.0ms

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: 0.0b

Counts

2 → 2

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 0.25 (/.f64 (-.f64 x z) y))
0.0b	(+.f64 1.0 (*.f64 4.0 (+.f64 0.25 (/.f64 (-.f64 x z) y))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp_binary64`
4×	`*-un-lft-identity_binary64`
2×	`flip3-+_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-+r+_binary64` `sum-log_binary64`
1×	`associate-+r-_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-sub_binary64`

Counts

2 → 26

Calls

2 calls:

9.0ms	(+.f64 0.25 (/.f64 (-.f64 x z) y))
4.0ms	(+.f64 1.0 (*.f64 4.0 (+.f64 0.25 (/.f64 (-.f64 x z) y))))

series17.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(+.f64 0.25 (/.f64 (-.f64 x z) y))
11.0ms	(+.f64 1.0 (*.f64 4.0 (+.f64 0.25 (/.f64 (-.f64 x z) y))))

simplify41.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5067	378

prune38.0ms

Filtered

24 candidates to 32 candidates (-33.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	30	2	32
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	31	3	34

Merged error: 0.0b

Counts

34 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1.0 (.f64 4.0 (.f64 (sqrt.f64 (+.f64 0.25 (/.f64 (-.f64 x z) y))) (sqrt.f64 (+.f64 0.25 (/.f64 (-.f64 x z) y))))))
0.1b	(sqrt.f64 (+.f64 0.25 (/.f64 (-.f64 x z) y)))
0.1b	(sqrt.f64 (+.f64 0.25 (/.f64 (-.f64 x z) y)))
0.2b	(*.f64 (sqrt.f64 (+.f64 0.25 (/.f64 (-.f64 x z) y))) (sqrt.f64 (+.f64 0.25 (/.f64 (-.f64 x z) y))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

34×	`sqrt-prod_binary64`
32×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
21×	`pow1_binary64`
16×	`sqrt-div_binary64`
14×	`add-cube-cbrt_binary64`
11×	`swap-sqr_binary64`
10×	`pow1/2_binary64` `sqrt-pow1_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
8×	`distribute-lft-out_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-up_binary64`
4×	`unswap-sqr_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `pow-sqr_binary64`
2×	`associate-r/_binary64` `rem-sqrt-square_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 105

Calls

4 calls:

4.0ms	(+.f64 1.0 (.f64 4.0 (.f64 (sqrt.f64 (+.f64 0.25 (/.f64 (-.f64 x z) y))) (sqrt.f64 (+.f64 0.25 (/.f64 (-.f64 x z) y))))))
9.0ms	(sqrt.f64 (+.f64 0.25 (/.f64 (-.f64 x z) y)))
9.0ms	(sqrt.f64 (+.f64 0.25 (/.f64 (-.f64 x z) y)))
23.0ms	(*.f64 (sqrt.f64 (+.f64 0.25 (/.f64 (-.f64 x z) y))) (sqrt.f64 (+.f64 0.25 (/.f64 (-.f64 x z) y))))

series52.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+.f64 1.0 (.f64 4.0 (.f64 (sqrt.f64 (+.f64 0.25 (/.f64 (-.f64 x z) y))) (sqrt.f64 (+.f64 0.25 (/.f64 (-.f64 x z) y))))))
19.0ms	(sqrt.f64 (+.f64 0.25 (/.f64 (-.f64 x z) y)))
17.0ms	(sqrt.f64 (+.f64 0.25 (/.f64 (-.f64 x z) y)))
7.0ms	(*.f64 (sqrt.f64 (+.f64 0.25 (/.f64 (-.f64 x z) y))) (sqrt.f64 (+.f64 0.25 (/.f64 (-.f64 x z) y))))

simplify57.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5051	1398

prune85.0ms

Filtered

65 candidates to 117 candidates (-80.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	117	3	120

Merged error: 0.0b

Counts

120 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1.0 (.f64 4.0 (/.f64 (+.f64 (pow.f64 0.25 3) (pow.f64 (/.f64 (-.f64 x z) y) 3)) (+.f64 (.f64 0.25 0.25) (*.f64 (/.f64 (-.f64 x z) y) (-.f64 (/.f64 (-.f64 x z) y) 0.25))))))
0.2b	(*.f64 (/.f64 (-.f64 x z) y) (-.f64 (/.f64 (-.f64 x z) y) 0.25))
0.3b	(pow.f64 (/.f64 (-.f64 x z) y) 3)
22.9b	(/.f64 (+.f64 (pow.f64 0.25 3) (pow.f64 (/.f64 (-.f64 x z) y) 3)) (+.f64 (.f64 0.25 0.25) (.f64 (/.f64 (-.f64 x z) y) (-.f64 (/.f64 (-.f64 x z) y) 0.25))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

107×	`*-un-lft-identity_binary64`
75×	`add-sqr-sqrt_binary64`
74×	`times-frac_binary64`
47×	`add-cube-cbrt_binary64`
35×	`unpow-prod-down_binary64` `cube-prod_binary64`
20×	`distribute-lft-out_binary64`
19×	`associate-l_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`difference-of-squares_binary64`
10×	`distribute-lft-out--_binary64`
9×	`associate-/l*_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64`
4×	`sum-cubes_binary64` `div-inv_binary64`
3×	`flip3-+_binary64` `pow-unpow_binary64` `associate-/r*_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `rem-cube-cbrt_binary64` `prod-exp_binary64` `flip--_binary64` `frac-times_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `pow-pow_binary64` `sqr-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `cube-div_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `unpow3_binary64` `associate-l/_binary64` `sum-log_binary64` `-commutative_binary64` `cube-mult_binary64`

Counts

4 → 171

Calls

4 calls:

5.0ms	(+.f64 1.0 (.f64 4.0 (/.f64 (+.f64 (pow.f64 0.25 3) (pow.f64 (/.f64 (-.f64 x z) y) 3)) (+.f64 (.f64 0.25 0.25) (*.f64 (/.f64 (-.f64 x z) y) (-.f64 (/.f64 (-.f64 x z) y) 0.25))))))
22.0ms	(*.f64 (/.f64 (-.f64 x z) y) (-.f64 (/.f64 (-.f64 x z) y) 0.25))
8.0ms	(pow.f64 (/.f64 (-.f64 x z) y) 3)
35.0ms	(/.f64 (+.f64 (pow.f64 0.25 3) (pow.f64 (/.f64 (-.f64 x z) y) 3)) (+.f64 (.f64 0.25 0.25) (.f64 (/.f64 (-.f64 x z) y) (-.f64 (/.f64 (-.f64 x z) y) 0.25))))

series293.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(+.f64 1.0 (.f64 4.0 (/.f64 (+.f64 (pow.f64 0.25 3) (pow.f64 (/.f64 (-.f64 x z) y) 3)) (+.f64 (.f64 0.25 0.25) (*.f64 (/.f64 (-.f64 x z) y) (-.f64 (/.f64 (-.f64 x z) y) 0.25))))))
22.0ms	(*.f64 (/.f64 (-.f64 x z) y) (-.f64 (/.f64 (-.f64 x z) y) 0.25))
23.0ms	(pow.f64 (/.f64 (-.f64 x z) y) 3)
72.0ms	(/.f64 (+.f64 (pow.f64 0.25 3) (pow.f64 (/.f64 (-.f64 x z) y) 3)) (+.f64 (.f64 0.25 0.25) (.f64 (/.f64 (-.f64 x z) y) (-.f64 (/.f64 (-.f64 x z) y) 0.25))))

simplify69.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4978	4436
1	4978	4436

prune201.0ms

Filtered

107 candidates to 183 candidates (-71.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	0	0	0
Picked	0	1	1
Done	1	1	2
Total	183	3	186

Merged error: 0b

Counts

186 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 (-.f64 x z) y) (-.f64 (/.f64 (-.f64 x z) y) 0.25))
0.2b	(*.f64 (/.f64 (-.f64 x z) y) (-.f64 (/.f64 (-.f64 x z) y) 0.25))
16.4b	(.f64 (+.f64 (.f64 0.25 0.25) (.f64 (/.f64 (-.f64 x z) y) (-.f64 (/.f64 (-.f64 x z) y) 0.25))) (/.f64 (+.f64 0.25 (/.f64 (-.f64 x z) y)) (+.f64 (.f64 0.25 0.25) (*.f64 (/.f64 (-.f64 x z) y) (-.f64 (/.f64 (-.f64 x z) y) 0.25)))))
16.5b	(/.f64 (+.f64 0.25 (/.f64 (-.f64 x z) y)) (+.f64 (.f64 0.25 0.25) (.f64 (/.f64 (-.f64 x z) y) (-.f64 (/.f64 (-.f64 x z) y) 0.25))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt_binary64`
72×	`*-un-lft-identity_binary64`
59×	`times-frac_binary64`
42×	`add-cube-cbrt_binary64`
41×	`associate-l_binary64`
30×	`associate-r_binary64`
21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`pow1_binary64` `difference-of-squares_binary64`
8×	`distribute-lft-out--_binary64`
7×	`distribute-lft-out_binary64`
6×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `frac-times_binary64`
5×	`flip3-+_binary64` `associate-*r/_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `associate-/l_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `associate-l/_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `-commutative_binary64`
2×	`associate-/l/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-sub_binary64`
1×	`associate-+r-_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 171

Calls

4 calls:

23.0ms	(*.f64 (/.f64 (-.f64 x z) y) (-.f64 (/.f64 (-.f64 x z) y) 0.25))
20.0ms	(*.f64 (/.f64 (-.f64 x z) y) (-.f64 (/.f64 (-.f64 x z) y) 0.25))
22.0ms	(.f64 (+.f64 (.f64 0.25 0.25) (.f64 (/.f64 (-.f64 x z) y) (-.f64 (/.f64 (-.f64 x z) y) 0.25))) (/.f64 (+.f64 0.25 (/.f64 (-.f64 x z) y)) (+.f64 (.f64 0.25 0.25) (*.f64 (/.f64 (-.f64 x z) y) (-.f64 (/.f64 (-.f64 x z) y) 0.25)))))
15.0ms	(/.f64 (+.f64 0.25 (/.f64 (-.f64 x z) y)) (+.f64 (.f64 0.25 0.25) (.f64 (/.f64 (-.f64 x z) y) (-.f64 (/.f64 (-.f64 x z) y) 0.25))))

series116.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(*.f64 (/.f64 (-.f64 x z) y) (-.f64 (/.f64 (-.f64 x z) y) 0.25))
22.0ms	(*.f64 (/.f64 (-.f64 x z) y) (-.f64 (/.f64 (-.f64 x z) y) 0.25))
12.0ms	(.f64 (+.f64 (.f64 0.25 0.25) (.f64 (/.f64 (-.f64 x z) y) (-.f64 (/.f64 (-.f64 x z) y) 0.25))) (/.f64 (+.f64 0.25 (/.f64 (-.f64 x z) y)) (+.f64 (.f64 0.25 0.25) (*.f64 (/.f64 (-.f64 x z) y) (-.f64 (/.f64 (-.f64 x z) y) 0.25)))))
59.0ms	(/.f64 (+.f64 0.25 (/.f64 (-.f64 x z) y)) (+.f64 (.f64 0.25 0.25) (.f64 (/.f64 (-.f64 x z) y) (-.f64 (/.f64 (-.f64 x z) y) 0.25))))

simplify69.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	6451	4224

prune260.0ms

Filtered

134 candidates to 183 candidates (-36.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	183	3	186

Merged error: 0b

Counts

186 → 3

regimes127.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	11
1	24	11

end0.0ms

sample521.0ms

Algorithm

intervals

Results

296.0ms	8000×	body	80	valid
33.0ms	930×	body	80	invalid

Details

analyze336.0ms

sample28.0ms

simplify78.0ms

prune9.0ms

localize7.0ms

rewrite13.0ms

series17.0ms

simplify41.0ms

prune38.0ms

localize12.0ms

rewrite48.0ms

series52.0ms

simplify57.0ms

prune85.0ms

localize16.0ms

rewrite77.0ms

series293.0ms

simplify69.0ms

prune201.0ms

localize15.0ms

rewrite87.0ms

series116.0ms

simplify69.0ms

prune260.0ms

regimes127.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample521.0ms

Profiling