Details

sample26.0ms

Algorithm

intervals

Results

9.0ms	272×	body	80	valid
5.0ms	278×	body	80	nan

simplify18.0ms

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 (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: 0.1b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (- 1.0 x) (* y (sqrt x)))
0.2b	(* y (sqrt x))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
9×	`add-sqr-sqrt`
7×	`add-log-exp`
6×	`associate-r`
5×	`add-cube-cbrt` `associate-l`
4×	`pow1` `add-exp-log` `sqrt-prod` `add-cbrt-cube` `distribute-lft-out`
2×	`associate-+l+` `sum-log` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `associate-+l-` `sub-neg` `flip3-+` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 41

Calls

2 calls:

11.0ms	(+ (- 1.0 x) (* y (sqrt x)))
5.0ms	(* y (sqrt x))

series83.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(+ (- 1.0 x) (* y (sqrt x)))
46.0ms	(* y (sqrt x))

simplify133.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	235	247
1	936	218
2	4562	208
3	5001	208

prune62.0ms

Filtered

47 candidates to 30 candidates (63.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	44	3	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	4	48

Merged error: 0.0b

Counts

48 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt x))
0.1b	(sqrt (sqrt x))
0.2b	(* y (sqrt (sqrt x)))
0.3b	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

rewrite28.0ms

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)))
14.0ms	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

series604.0ms

Counts

4 → 12

Calls

4 calls:

344.0ms	(sqrt (sqrt x))
132.0ms	(sqrt (sqrt x))
86.0ms	(* y (sqrt (sqrt x)))
41.0ms	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

simplify49.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (38.0ms)

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

prune197.0ms

Filtered

131 candidates to 75 candidates (57.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	127	4	131
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	128	7	135

Merged error: 0b

Counts

135 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- 1.0 x) (* (* y (sqrt (sqrt x))) (pow x 1/4)))
0.1b	(sqrt (sqrt x))
0.2b	(* y (sqrt (sqrt x)))
0.3b	(* (* y (sqrt (sqrt x))) (pow x 1/4))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
43×	`sqrt-prod`
32×	`-un-lft-identity` `associate-l*`
27×	`unswap-sqr`
25×	`associate-r`
19×	`add-exp-log`
17×	`add-cube-cbrt`
13×	`pow1`
11×	`add-cbrt-cube`
10×	`prod-exp`
9×	`add-log-exp`
7×	`unpow-prod-down`
6×	`distribute-lft-out`
5×	`sqr-pow`
4×	`sqrt-pow1` `pow-prod-down` `cbrt-unprod`
3×	`*-commutative` `distribute-lft-out--`
2×	`pow-to-exp` `rem-sqrt-square` `associate-+l+` `pow1/2` `pow-exp` `sum-log`
1×	`+-commutative` `associate-+l-` `sub-neg` `flip3-+` `diff-log` `flip-+`

Counts

4 → 123

Calls

4 calls:

23.0ms	(+ (- 1.0 x) (* (* y (sqrt (sqrt x))) (pow x 1/4)))
2.0ms	(sqrt (sqrt x))
6.0ms	(* y (sqrt (sqrt x)))
14.0ms	(* (* y (sqrt (sqrt x))) (pow x 1/4))

series381.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(+ (- 1.0 x) (* (* y (sqrt (sqrt x))) (pow x 1/4)))
141.0ms	(sqrt (sqrt x))
85.0ms	(* y (sqrt (sqrt x)))
85.0ms	(* (* y (sqrt (sqrt x))) (pow x 1/4))

simplify71.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	572	986
1	2498	922
2	5001	922

prune227.0ms

Filtered

135 candidates to 81 candidates (60.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	132	3	135
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	136	6	142

Merged error: 0b

Counts

142 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (* (* y (sqrt (sqrt x))) (pow x 1/4)))
0.1b	(sqrt (sqrt x))
0.2b	(* y (sqrt (sqrt x)))
0.3b	(* (* y (sqrt (sqrt x))) (pow x 1/4))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

103×	`add-sqr-sqrt`
52×	`sqrt-prod`
48×	`unswap-sqr`
29×	`associate-l`
25×	`associate-r`
23×	`*-un-lft-identity`
19×	`add-exp-log`
17×	`add-cube-cbrt`
13×	`pow1` `difference-of-squares`
11×	`unpow-prod-down` `add-cbrt-cube`
10×	`prod-exp`
9×	`sqr-pow`
6×	`add-log-exp`
4×	`sqrt-pow1` `pow-prod-down` `cbrt-unprod`
3×	`*-commutative` `distribute-lft-out--`
2×	`pow-to-exp` `rem-sqrt-square` `pow1/2` `pow-exp`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 130

Calls

4 calls:

21.0ms	(- x (* (* y (sqrt (sqrt x))) (pow x 1/4)))
2.0ms	(sqrt (sqrt x))
6.0ms	(* y (sqrt (sqrt x)))
14.0ms	(* (* y (sqrt (sqrt x))) (pow x 1/4))

series407.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- x (* (* y (sqrt (sqrt x))) (pow x 1/4)))
137.0ms	(sqrt (sqrt x))
81.0ms	(* y (sqrt (sqrt x)))
121.0ms	(* (* y (sqrt (sqrt x))) (pow x 1/4))

simplify71.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	570	1170
1	2485	1112
2	5002	1112

prune230.0ms

Filtered

142 candidates to 86 candidates (60.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	139	3	142
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	143	5	148

Merged error: 0b

Counts

148 → 5

regimes67.0ms

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

sample602.0ms

Algorithm

intervals

Results

177.0ms	8540×	body	80	valid
161.0ms	8448×	body	80	nan
0.0ms	3×	body	1280	valid
0.0ms	2×	body	640	valid