Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
81.2%	18.7%	0%	5
90.6%	9.4%	0%	6
95.3%	4.7%	0%	7
97.6%	2.3%	0%	8
98.8%	1.2%	0%	9
99.4%	0.6%	0%	10
99.7%	0.3%	0%	11
99.8%	0.1%	0%	12
99.9%	0.1%	0%	13
99.9%	0%	0%	14

sample23.0ms

Algorithm

intervals

Results

10.0ms	65×	body	640	valid
3.0ms	134×	body	80	valid
3.0ms	38×	body	320	valid
1.0ms	19×	body	160	valid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	497	9
1	497	9

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 17.7b

Counts

2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

3.0b	(-.f64 (/.f64 1.0 (+.f64 x 1.0)) (/.f64 1.0 x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
16×	`times-frac_binary64`
8×	`distribute-lft-out--_binary64`
5×	`add-cube-cbrt_binary64`
4×	`difference-of-squares_binary64`
3×	`add-log-exp_binary64` `distribute-lft-out_binary64`
2×	`div-inv_binary64`
1×	`sub-neg_binary64` `pow1_binary64` `flip3--_binary64` `diff-log_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

1 → 24

Calls

1 calls:

19.0ms

(-.f64 (/.f64 1.0 (+.f64 x 1.0)) (/.f64 1.0 x))

series5.0ms

Counts

1 → 3

Calls

1 calls:

5.0ms

(-.f64 (/.f64 1.0 (+.f64 x 1.0)) (/.f64 1.0 x))

simplify38.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4937	382
1	4937	382

prune34.0ms

Filtered

22 candidates to 27 candidates (-22.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	26	1	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	2	28

Merged error: 0.5b

Counts

28 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 1.0 (pow.f64 x 4))
0.6b	(/.f64 (-.f64 (/.f64 1.0 x) 1.0) (*.f64 x x))
10.1b	(-.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) (*.f64 x x)) (/.f64 1.0 (pow.f64 x 4)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
39×	`times-frac_binary64`
27×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
14×	`unpow-prod-down_binary64`
13×	`add-exp-log_binary64`
12×	`difference-of-squares_binary64`
10×	`add-cbrt-cube_binary64`
9×	`associate-/l*_binary64`
8×	`associate-/r*_binary64`
6×	`sqr-pow_binary64`
5×	`add-log-exp_binary64` `div-exp_binary64`
3×	`pow1_binary64` `cbrt-undiv_binary64` `distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate--l-_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `frac-sub_binary64` `pow-exp_binary64`

Counts

3 → 97

Calls

3 calls:

7.0ms	(/.f64 1.0 (pow.f64 x 4))
12.0ms	(/.f64 (-.f64 (/.f64 1.0 x) 1.0) (*.f64 x x))
27.0ms	(-.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) (*.f64 x x)) (/.f64 1.0 (pow.f64 x 4)))

series24.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(/.f64 1.0 (pow.f64 x 4))
12.0ms	(/.f64 (-.f64 (/.f64 1.0 x) 1.0) (*.f64 x x))
6.0ms	(-.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) (*.f64 x x)) (/.f64 1.0 (pow.f64 x 4)))

simplify54.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5003	1390

prune108.0ms

Filtered

72 candidates to 106 candidates (-47.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	102	4	106
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	102	6	108

Merged error: 0.0b

Counts

108 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1.0 (pow.f64 x 4))
0.1b	(/.f64 (-.f64 (/.f64 1.0 x) 1.0) x)
0.1b	(/.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) x) x)
10.1b	(-.f64 (/.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) x) x) (/.f64 1.0 (pow.f64 x 4)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

216×	`add-sqr-sqrt_binary64` `times-frac_binary64`
132×	`*-un-lft-identity_binary64`
94×	`add-cube-cbrt_binary64`
44×	`difference-of-squares_binary64`
31×	`associate-/l*_binary64`
18×	`distribute-lft-out--_binary64`
16×	`add-exp-log_binary64`
15×	`unpow-prod-down_binary64`
13×	`associate-/r*_binary64` `add-cbrt-cube_binary64`
7×	`sqr-pow_binary64` `div-inv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-undiv_binary64` `div-sub_binary64`
4×	`pow1_binary64`
3×	`associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`flip3--_binary64` `flip--_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate--l-_binary64` `diff-log_binary64` `frac-sub_binary64` `pow-exp_binary64`

Counts

4 → 221

Calls

4 calls:

5.0ms	(/.f64 1.0 (pow.f64 x 4))
11.0ms	(/.f64 (-.f64 (/.f64 1.0 x) 1.0) x)
15.0ms	(/.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) x) x)
91.0ms	(-.f64 (/.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) x) x) (/.f64 1.0 (pow.f64 x 4)))

series36.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/.f64 1.0 (pow.f64 x 4))
13.0ms	(/.f64 (-.f64 (/.f64 1.0 x) 1.0) x)
12.0ms	(/.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) x) x)
6.0ms	(-.f64 (/.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) x) x) (/.f64 1.0 (pow.f64 x 4)))

simplify78.0ms

Algorithm

egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4950	3517
1	4950	3517

prune245.0ms

Filtered

154 candidates to 233 candidates (-51.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	230	3	233
Fresh	3	0	3
Picked	0	1	1
Done	0	2	2
Total	233	6	239

Merged error: 0.0b

Counts

239 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

10.1b	(-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) x)) (cbrt.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) x))) (/.f64 (cbrt.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) x)) x)) (/.f64 1.0 (pow.f64 x 4)))
16.3b	(cbrt.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) x))
16.3b	(cbrt.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) x))
16.3b	(cbrt.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) x))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt_binary64`
66×	`cbrt-prod_binary64`
63×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
34×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64`
11×	`cbrt-div_binary64`
9×	`distribute-lft-out--_binary64`
7×	`frac-sub_binary64`
6×	`add-log-exp_binary64`
5×	`frac-times_binary64` `associate-*l/_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-*r/_binary64` `pow1/3_binary64` `div-inv_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64`

Counts

4 → 111

Calls

4 calls:

47.0ms	(-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) x)) (cbrt.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) x))) (/.f64 (cbrt.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) x)) x)) (/.f64 1.0 (pow.f64 x 4)))
9.0ms	(cbrt.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) x))
9.0ms	(cbrt.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) x))
9.0ms	(cbrt.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) x))

series45.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) x)) (cbrt.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) x))) (/.f64 (cbrt.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) x)) x)) (/.f64 1.0 (pow.f64 x 4)))
12.0ms	(cbrt.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) x))
12.0ms	(cbrt.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) x))
14.0ms	(cbrt.f64 (/.f64 (-.f64 (/.f64 1.0 x) 1.0) x))

simplify71.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4950	2350
1	4950	2350

prune228.0ms

Filtered

103 candidates to 123 candidates (-19.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	2	0	2
Picked	1	0	1
Done	2	1	3
Total	127	2	129

Merged error: 0b

Counts

129 → 2

regimes65.0ms

Accuracy

95% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 13.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	49
1	53	49

end0.0ms

sample476.0ms

Algorithm

intervals

Results

167.0ms	1858×	body	640	valid
101.0ms	4281×	body	80	valid
88.0ms	1262×	body	320	valid
27.0ms	599×	body	160	valid
0.0ms	2×	body	80	invalid

Details

analyze4.0ms

sample23.0ms

simplify39.0ms

prune4.0ms

localize5.0ms

rewrite21.0ms

series5.0ms

simplify38.0ms

prune34.0ms

localize10.0ms

rewrite50.0ms

series24.0ms

simplify54.0ms

prune108.0ms

localize10.0ms

rewrite135.0ms

series36.0ms

simplify78.0ms

prune245.0ms

localize17.0ms

rewrite83.0ms

series45.0ms

simplify71.0ms

prune228.0ms

regimes65.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample476.0ms

Profiling