Details

sample21.0ms

Algorithm

intervals

Results

5.0ms	269×	body	80	valid
5.0ms	236×	body	80	nan

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	4
1	23	4
2	40	4
3	59	4
4	74	4
5	103	4
6	120	4
7	145	4
8	226	4
9	257	4
10	257	4

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 0.1b

Counts

2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

0.2b	(* y (sqrt x))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`associate-r`
4×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
3×	`pow1` `add-exp-log` `associate-l` `add-cbrt-cube`
2×	`unswap-sqr`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `add-log-exp`

Counts

1 → 22

Calls

1 calls:

5.0ms

(* y (sqrt x))

series48.0ms

Counts

1 → 3

Calls

1 calls:

48.0ms

(* y (sqrt x))

simplify90.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	147	113
1	605	100
2	2969	94
3	5002	94

prune48.0ms

Filtered

25 candidates to 16 candidates (36.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	19	6	25
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	19	7	26

Merged error: 0.0b

Counts

26 → 7

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt x))
0.1b	(sqrt (sqrt x))
0.2b	(* y (sqrt (sqrt x)))
0.4b	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

74×	`sqrt-prod`
69×	`add-sqr-sqrt`
27×	`associate-r` `unswap-sqr`
26×	`associate-l`
20×	`add-cube-cbrt` `*-un-lft-identity`
15×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
8×	`sqrt-pow1`
4×	`rem-sqrt-square` `pow1/2` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`*-commutative`

Counts

4 → 119

Calls

4 calls:

2.0ms	(sqrt (sqrt x))
2.0ms	(sqrt (sqrt x))
6.0ms	(* y (sqrt (sqrt x)))
15.0ms	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

series592.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(sqrt (sqrt x))
326.0ms	(sqrt (sqrt x))
83.0ms	(* y (sqrt (sqrt x)))
48.0ms	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

simplify46.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	360	816
1	1509	664
2	5001	628

prune189.0ms

Filtered

131 candidates to 73 candidates (44.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	128	3	131
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	131	7	138

Merged error: 0b

Counts

138 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ 1 x) -1/4)
0.1b	(sqrt (sqrt x))
0.2b	(* y (pow (/ 1 x) -1/4))
0.4b	(* (* y (pow (/ 1 x) -1/4)) (sqrt (sqrt x)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-sqr-sqrt`
54×	`unpow-prod-down`
43×	`associate-r` `unswap-sqr`
41×	`add-exp-log` `*-un-lft-identity`
37×	`times-frac` `sqrt-prod`
36×	`add-cube-cbrt` `associate-l`
19×	`prod-exp`
15×	`pow1`
12×	`pow-exp`
11×	`add-cbrt-cube`
8×	`sqr-pow`
6×	`div-exp`
4×	`sqrt-pow1` `pow-prod-down` `cbrt-unprod` `add-log-exp`
3×	`pow-to-exp` `rec-exp` `pow-unpow` `pow-pow` `1-exp` `*-commutative` `div-inv`
2×	`rem-sqrt-square` `pow1/2`
1×	`pow-flip` `inv-pow`

Counts

4 → 168

Calls

4 calls:

4.0ms	(pow (/ 1 x) -1/4)
2.0ms	(sqrt (sqrt x))
10.0ms	(* y (pow (/ 1 x) -1/4))
21.0ms	(* (* y (pow (/ 1 x) -1/4)) (sqrt (sqrt x)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(pow (/ 1 x) -1/4)
133.0ms	(sqrt (sqrt x))
62.0ms	(* y (pow (/ 1 x) -1/4))
84.0ms	(* (* y (pow (/ 1 x) -1/4)) (sqrt (sqrt x)))

simplify73.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	646	1256
1	2759	1164
2	5002	1162

prune328.0ms

Filtered

180 candidates to 109 candidates (39.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	178	2	180
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	181	6	187

Merged error: 0b

Counts

187 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt x) (cbrt x))
0.5b	(cbrt x)
0.5b	(cbrt x)
0.5b	(cbrt x)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
8×	`add-cbrt-cube`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`cbrt-unprod` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative`

Counts

4 → 76

Calls

4 calls:

6.0ms	(* (cbrt x) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series746.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(* (cbrt x) (cbrt x))
182.0ms	(cbrt x)
176.0ms	(cbrt x)
180.0ms	(cbrt x)

simplify87.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	124	311
1	521	267
2	3234	241
3	5002	238

prune257.0ms

Filtered

88 candidates to 64 candidates (27.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	88	6	94

Merged error: 0b

Counts

94 → 6

regimes78.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	4
1	9	4

end0.0ms

sample583.0ms

Algorithm

intervals

Results

176.0ms	8521×	body	80	valid
153.0ms	8318×	body	80	nan
0.0ms	1×	body	320	valid