Details

analyze602.0ms

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
3.1%	90.5%	6.3%	6
4.7%	85.9%	9.5%	7
21.1%	64%	14.9%	8
23.4%	58.9%	17.7%	9
27.7%	51.3%	21%	10
28.9%	48.5%	22.6%	11
31.1%	44.4%	24.5%	12
31.7%	42.9%	25.4%	13
32.7%	41%	26.3%	14

sample69.0ms

Algorithm

intervals

Results

25.0ms	50×	body	1280	valid
14.0ms	39×	body	640	valid
9.0ms	141×	body	80	valid
4.0ms	20×	body	320	valid
2.0ms	8×	body	640	invalid
2.0ms	5×	body	1280	invalid
1.0ms	7×	body	320	invalid
1.0ms	6×	body	160	valid
0.0ms	8×	body	80	invalid
0.0ms	7×	body	80	nan
0.0ms	2×	body	160	invalid

simplify91.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4959	13
1	4959	13

prune3.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 10.9b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (+.f64 x y))
0.0b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
7.0b	(pow.f64 (/.f64 x (+.f64 x y)) x)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac_binary64`
118×	`*-un-lft-identity_binary64`
90×	`unpow-prod-down_binary64`
80×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
25×	`associate-/l*_binary64`
19×	`distribute-lft-out_binary64`
16×	`add-exp-log_binary64`
12×	`associate-/r/_binary64`
7×	`associate-/r*_binary64` `add-cbrt-cube_binary64` `div-inv_binary64` `div-exp_binary64`
6×	`flip3-+_binary64` `flip-+_binary64`
5×	`sqr-pow_binary64`
4×	`pow1_binary64` `pow-exp_binary64`
3×	`pow-unpow_binary64` `add-log-exp_binary64`
2×	`pow-to-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64`

Counts

3 → 172

Calls

3 calls:

5.0ms	(/.f64 x (+.f64 x y))
11.0ms	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
7.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)

series340.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(/.f64 x (+.f64 x y))
139.0ms	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
176.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)

simplify122.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4946	4029
1	4946	4029

prune118.0ms

Filtered

131 candidates to 181 candidates (-38.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	176	5	181
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	177	5	182

Merged error: 1.0b

Counts

182 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (+.f64 x y))
0.6b	(cbrt.f64 (+.f64 x y))
0.7b	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
2.1b	(pow.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) x)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

61×	`unpow-prod-down_binary64`
53×	`cbrt-prod_binary64`
52×	`*-un-lft-identity_binary64`
43×	`times-frac_binary64`
36×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
20×	`add-exp-log_binary64`
18×	`cbrt-div_binary64`
10×	`associate-/r/_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
8×	`distribute-lft-out_binary64`
7×	`pow-exp_binary64`
6×	`pow-unpow_binary64` `pow1_binary64`
5×	`div-exp_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `prod-exp_binary64` `frac-times_binary64`
2×	`pow-to-exp_binary64` `associate-r/_binary64` `pow1/3_binary64` `pow-pow_binary64` `sqr-pow_binary64` `div-inv_binary64` `associate-l/_binary64`

Counts

4 → 122

Calls

4 calls:

3.0ms	(cbrt.f64 (+.f64 x y))
3.0ms	(cbrt.f64 (+.f64 x y))
13.0ms	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
16.0ms	(pow.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) x)

series702.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(cbrt.f64 (+.f64 x y))
120.0ms	(cbrt.f64 (+.f64 x y))
224.0ms	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
243.0ms	(pow.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) x)

simplify118.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4977	3478
1	4977	3478

prune130.0ms

Filtered

104 candidates to 134 candidates (-28.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	135	4	139

Merged error: 0.0b

Counts

139 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (+.f64 x y))
0.6b	(cbrt.f64 (+.f64 x y))
0.7b	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
2.5b	(log.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

98×	`cbrt-prod_binary64`
89×	`*-un-lft-identity_binary64`
84×	`times-frac_binary64`
61×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
48×	`log-prod_binary64` `unpow-prod-down_binary64`
14×	`distribute-lft-out_binary64`
10×	`add-exp-log_binary64`
8×	`cbrt-div_binary64`
6×	`pow1_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64` `flip-+_binary64`
3×	`pow-unpow_binary64`
2×	`rem-log-exp_binary64` `pow1/3_binary64` `div-inv_binary64` `div-exp_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `pow-pow_binary64` `log-pow_binary64` `sqr-pow_binary64` `log-div_binary64`

Counts

4 → 150

Calls

4 calls:

3.0ms	(cbrt.f64 (+.f64 x y))
3.0ms	(cbrt.f64 (+.f64 x y))
13.0ms	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
8.0ms	(log.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))))

series531.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(cbrt.f64 (+.f64 x y))
118.0ms	(cbrt.f64 (+.f64 x y))
220.0ms	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
72.0ms	(log.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))))

simplify97.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4993	4046
1	4993	4046

prune161.0ms

Filtered

130 candidates to 162 candidates (-24.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	162	4	166

Merged error: 0.0b

Counts

166 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (*.f64 (sqrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) x)) (sqrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) x))) x)
0.0b	(*.f64 (sqrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) x)) (sqrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) x)))
7.0b	(pow.f64 (/.f64 x (+.f64 x y)) x)
7.0b	(pow.f64 (/.f64 x (+.f64 x y)) x)

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

142×	`sqrt-prod_binary64`
140×	`unpow-prod-down_binary64`
122×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
97×	`times-frac_binary64`
68×	`add-cube-cbrt_binary64`
33×	`swap-sqr_binary64`
25×	`associate-r_binary64` `associate-l_binary64` `unswap-sqr_binary64`
24×	`distribute-lft-out_binary64`
17×	`add-exp-log_binary64`
16×	`sqr-pow_binary64`
13×	`pow1_binary64`
12×	`associate-/r/_binary64`
11×	`add-cbrt-cube_binary64`
7×	`div-inv_binary64`
6×	`flip3-+_binary64` `pow-unpow_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `div-exp_binary64` `pow-exp_binary64`
3×	`pow-prod-down_binary64` `associate-/r*_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
2×	`pow-to-exp_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `prod-exp_binary64`
1×	`rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `pow2_binary64` `-commutative_binary64`

Counts

4 → 218

Calls

4 calls:

22.0ms	(/.f64 (*.f64 (sqrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) x)) (sqrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) x))) x)
28.0ms	(*.f64 (sqrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) x)) (sqrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) x)))
7.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)
7.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)

series654.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/.f64 (*.f64 (sqrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) x)) (sqrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) x))) x)
179.0ms	(*.f64 (sqrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) x)) (sqrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) x)))
167.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)
177.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)

simplify136.0ms

Algorithm

egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4997	5379
1	4997	5379

prune114.0ms

Filtered

139 candidates to 230 candidates (-65.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	229	1	230
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	230	4	234

Merged error: 0.0b

Counts

234 → 4

regimes47.0ms

Accuracy

99.6% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 5.6b

bsearch74.0ms

Steps

Iters	Range		Point
9	4.4409362384920846e-07	4.047745055852596	3.9786591048773174
9	-1.9209356177674876e+20	-2261393630453033.5	-1.755158979227715e+16

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	62
1	39	62

end0.0ms

sample1.9s

Algorithm

intervals

Results

718.0ms	1433×	body	1280	valid
364.0ms	1178×	body	640	valid
249.0ms	4387×	body	80	valid
137.0ms	676×	body	320	valid
74.0ms	240×	body	640	invalid
53.0ms	119×	body	1280	invalid
42.0ms	326×	body	160	valid
40.0ms	196×	body	320	invalid
12.0ms	102×	body	160	invalid
12.0ms	167×	body	80	invalid
9.0ms	200×	body	80	nan

Details

analyze602.0ms

sample69.0ms

simplify91.0ms

prune3.0ms

localize6.0ms

rewrite34.0ms

series340.0ms

simplify122.0ms

prune118.0ms

localize17.0ms

rewrite41.0ms

series702.0ms

simplify118.0ms

prune130.0ms

localize16.0ms

rewrite34.0ms

series531.0ms

simplify97.0ms

prune161.0ms

localize9.0ms

rewrite76.0ms

series654.0ms

simplify136.0ms

prune114.0ms

regimes47.0ms

bsearch74.0ms

simplify3.0ms

end0.0ms

sample1.9s

Profiling