Details

analyze53.0ms

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%	74.9%	25.1%	4
12.5%	62.4%	25.1%	5
31.2%	31.2%	37.6%	6
37.5%	25%	37.6%	7
40.6%	15.6%	43.8%	8
42.9%	11.7%	45.4%	9
44.1%	7.4%	48.5%	10
45.1%	5.7%	49.3%	11
45.6%	3.6%	50.8%	12
46%	2.8%	51.2%	13
46.2%	1.8%	52%	14

sample18.0ms

Algorithm

intervals

Results

11.0ms	256×	body	128	valid
0.0ms	2×	body	128	nan

simplify144.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (137.0ms)

Iter	Nodes	Cost
0	1583	18
1	1583	18

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

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 y (/.f64 1 (*.f64 x 9)))
0.2b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
0.2b	(*.f64 3 (sqrt.f64 x))
0.5b	(/.f64 1 (*.f64 x 9))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64`
19×	`add-exp-log_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
15×	`associate-r_binary64`
14×	`pow1_binary64`
10×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `prod-exp_binary64`
5×	`pow-prod-down_binary64` `cbrt-unprod_binary64`
4×	`distribute-lft-out_binary64` `associate-l_binary64` `sqrt-prod_binary64`
3×	`associate-/l*_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `div-inv_binary64`
2×	`sub-neg_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `rec-exp_binary64` `div-exp_binary64` `pow-flip_binary64` `associate--l+_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `associate-/r*_binary64` `flip3--_binary64` `difference-of-sqr-1_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 91

Calls

4 calls:

6.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
15.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
6.0ms	(*.f64 3 (sqrt.f64 x))
5.0ms	(/.f64 1 (*.f64 x 9))

series159.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
72.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
28.0ms	(*.f64 3 (sqrt.f64 x))
26.0ms	(/.f64 1 (*.f64 x 9))

simplify41.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5002	1285

prune235.0ms

Filtered

66 candidates to 103 candidates (-56.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	92	11	103
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	94	11	105

Merged error: 0.0b

Counts

105 → 11

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1/9 x) y)
0.2b	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
0.3b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))))
0.3b	(/.f64 1/9 x)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`pow1_binary64`
9×	`associate-l_binary64` `times-frac_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-*r/_binary64`
5×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `prod-exp_binary64` `sqrt-prod_binary64`
3×	`flip3-+_binary64` `associate-/r_binary64` `associate-/l_binary64` `flip-+_binary64`
2×	`unswap-sqr_binary64` `*-commutative_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 91

Calls

4 calls:

8.0ms	(+.f64 (/.f64 1/9 x) y)
13.0ms	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
14.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))))
4.0ms	(/.f64 1/9 x)

series196.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+.f64 (/.f64 1/9 x) y)
59.0ms	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
77.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))))
20.0ms	(/.f64 1/9 x)

simplify74.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4876	1561
1	4876	1561

prune91.0ms

Filtered

68 candidates to 103 candidates (-51.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	102	12	114

Merged error: 0.0b

Counts

114 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
0.3b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))) (cbrt.f64 3)))
0.3b	(.f64 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))) (cbrt.f64 3))
0.3b	(/.f64 1/9 x)

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log_binary64`
32×	`pow1_binary64`
22×	`*-un-lft-identity_binary64` `add-cbrt-cube_binary64`
21×	`add-sqr-sqrt_binary64`
19×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
17×	`add-cube-cbrt_binary64`
12×	`associate-r_binary64`
9×	`times-frac_binary64`
8×	`associate-r/_binary64` `associate-l*_binary64`
4×	`add-log-exp_binary64` `sqrt-prod_binary64` `associate-*l/_binary64`
3×	`flip3-+_binary64` `associate-/r_binary64` `distribute-lft-out_binary64` `associate-/l_binary64` `flip-+_binary64` `cbrt-prod_binary64` `*-commutative_binary64`
2×	`unswap-sqr_binary64`
1×	`cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 108

Calls

4 calls:

14.0ms	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
25.0ms	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))) (cbrt.f64 3)))
17.0ms	(.f64 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))) (cbrt.f64 3))
3.0ms	(/.f64 1/9 x)

series352.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
164.0ms	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))) (cbrt.f64 3)))
102.0ms	(.f64 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))) (cbrt.f64 3))
19.0ms	(/.f64 1/9 x)

simplify88.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4939	2153
1	4939	2153

prune124.0ms

Filtered

78 candidates to 120 candidates (-53.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	120	12	132

Merged error: 0b

Counts

132 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x)) y))) (cbrt.f64 3)))
0.3b	(.f64 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x)) y))) (cbrt.f64 3))
0.4b	(/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x))
0.4b	(/.f64 1/9 (sqrt.f64 x))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

276×	`times-frac_binary64`
158×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
144×	`sqrt-prod_binary64`
37×	`add-exp-log_binary64`
30×	`pow1_binary64`
25×	`add-cbrt-cube_binary64` `associate-/l*_binary64`
18×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
12×	`associate-/r*_binary64`
9×	`div-inv_binary64`
7×	`associate-r_binary64`
6×	`associate-*r/_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `associate-*l/_binary64`
3×	`cbrt-prod_binary64`
2×	`flip3-+_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64` `*-commutative_binary64`
1×	`associate-/l/_binary64`

Counts

4 → 267

Calls

4 calls:

68.0ms	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x)) y))) (cbrt.f64 3)))
58.0ms	(.f64 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x)) y))) (cbrt.f64 3))
12.0ms	(/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x))
5.0ms	(/.f64 1/9 (sqrt.f64 x))

series390.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x)) y))) (cbrt.f64 3)))
123.0ms	(.f64 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x)) y))) (cbrt.f64 3))
33.0ms	(/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x))
54.0ms	(/.f64 1/9 (sqrt.f64 x))

simplify151.0ms

Algorithm

egg-herbie

Counts

279 → 279

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4934	5623
1	4934	5623

prune223.0ms

Filtered

137 candidates to 279 candidates (-103.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	279	0	279
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	279	12	291

Merged error: 0b

Counts

291 → 12

regimes58.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	18
1	16	18

end0.0ms

sample483.0ms

Algorithm

intervals

Results

336.0ms	8000×	body	128	valid
6.0ms	137×	body	128	nan
3.0ms	63×	body	128	invalid

Details

analyze53.0ms

sample18.0ms

simplify144.0ms

prune4.0ms

localize9.0ms

rewrite38.0ms

series159.0ms

simplify41.0ms

prune235.0ms

localize9.0ms

rewrite46.0ms

series196.0ms

simplify74.0ms

prune91.0ms

localize12.0ms

rewrite71.0ms

series352.0ms

simplify88.0ms

prune124.0ms

localize13.0ms

rewrite183.0ms

series390.0ms

simplify151.0ms

prune223.0ms

regimes58.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample483.0ms

Profiling