Details

sample23.0ms

Algorithm

intervals

Results

6.0ms	276×	body	80	valid
5.0ms	290×	body	80	nan

simplify21.0ms

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

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (- 1.0 x) (* y (sqrt x)))
0.3b	(* y (sqrt x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 37

Calls

2 calls:

6.0ms	(+ (- 1.0 x) (* y (sqrt x)))
5.0ms	(* y (sqrt x))

series80.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(+ (- 1.0 x) (* y (sqrt x)))
39.0ms	(* y (sqrt x))

simplify141.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	240	231
1	957	202
2	4716	192
3	5001	192

prune88.0ms

Filtered

43 candidates to 30 candidates (69.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	36	7	43
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	36	8	44

Merged error: 0.0b

Counts

44 → 8

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

2.0ms	(sqrt (sqrt x))
2.0ms	(sqrt (sqrt x))
6.0ms	(* y (sqrt (sqrt x)))
12.0ms	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(sqrt (sqrt x))
136.0ms	(sqrt (sqrt x))
78.0ms	(* y (sqrt (sqrt x)))
40.0ms	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

simplify45.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	336	516
1	1481	454
2	5001	443

prune220.0ms

Filtered

100 candidates to 67 candidates (67.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	101	7	108

Merged error: 0b

Counts

108 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-exp-log`
38×	`add-sqr-sqrt`
29×	`unpow-prod-down`
27×	`*-un-lft-identity`
26×	`add-cube-cbrt` `associate-r`
20×	`times-frac`
19×	`prod-exp` `sqrt-prod`
12×	`pow-exp`
11×	`add-cbrt-cube`
10×	`pow1`
6×	`div-exp`
5×	`unswap-sqr`
4×	`sqrt-pow1` `associate-l` `cbrt-unprod` `add-log-exp`
3×	`pow-to-exp` `rec-exp` `pow-unpow` `pow-pow` `1-exp` `sqr-pow`
2×	`rem-sqrt-square` `pow1/2` `*-commutative` `div-inv`
1×	`pow-flip` `pow-prod-down` `inv-pow`

Counts

4 → 119

Calls

4 calls:

8.0ms	(pow (/ 1 x) -1/4)
2.0ms	(sqrt (sqrt x))
8.0ms	(* y (pow (/ 1 x) -1/4))
10.0ms	(* (* y (pow (/ 1 x) -1/4)) (sqrt (sqrt x)))

series448.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(pow (/ 1 x) -1/4)
135.0ms	(sqrt (sqrt x))
59.0ms	(* y (pow (/ 1 x) -1/4))
81.0ms	(* (* y (pow (/ 1 x) -1/4)) (sqrt (sqrt x)))

simplify75.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	573	752
1	2585	668
2	5001	665

prune283.0ms

Filtered

131 candidates to 78 candidates (59.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	131	7	138

Merged error: 0b

Counts

138 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt x))
0.2b	(* y (pow (/ 1 x) -1/8))
0.3b	(* (* (* y (pow (/ 1 x) -1/8)) (pow (/ 1 x) (/ -1/4 2))) (sqrt (sqrt x)))
0.3b	(* (* y (pow (/ 1 x) -1/8)) (pow (/ 1 x) (/ -1/4 2)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

300×	`add-exp-log`
205×	`prod-exp`
108×	`pow-exp`
54×	`div-exp`
43×	`associate-r`
38×	`add-sqr-sqrt`
29×	`unpow-prod-down`
27×	`pow-to-exp` `rec-exp` `*-un-lft-identity` `1-exp`
26×	`add-cube-cbrt`
20×	`times-frac` `add-cbrt-cube`
19×	`sqrt-prod`
10×	`cbrt-unprod`
8×	`pow1`
5×	`associate-l` `unswap-sqr`
4×	`sqrt-pow1` `add-log-exp`
3×	`*-commutative` `sqr-pow`
2×	`rem-sqrt-square` `pow1/2` `div-inv`
1×	`pow-prod-down`

Counts

4 → 194

Calls

4 calls:

2.0ms	(sqrt (sqrt x))
9.0ms	(* y (pow (/ 1 x) -1/8))
20.0ms	(* (* (* y (pow (/ 1 x) -1/8)) (pow (/ 1 x) (/ -1/4 2))) (sqrt (sqrt x)))
13.0ms	(* (* y (pow (/ 1 x) -1/8)) (pow (/ 1 x) (/ -1/4 2)))

series343.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(sqrt (sqrt x))
63.0ms	(* y (pow (/ 1 x) -1/8))
76.0ms	(* (* (* y (pow (/ 1 x) -1/8)) (pow (/ 1 x) (/ -1/4 2))) (sqrt (sqrt x)))
70.0ms	(* (* y (pow (/ 1 x) -1/8)) (pow (/ 1 x) (/ -1/4 2)))

simplify89.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	904	1581
1	3517	1286
2	5001	1218

prune337.0ms

Filtered

206 candidates to 84 candidates (40.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	204	2	206
Fresh	2	2	4
Picked	1	0	1
Done	0	2	2
Total	207	6	213

Merged error: 0b

Counts

213 → 6

regimes79.0ms

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

sample597.0ms

Algorithm

intervals

Results

172.0ms	8495×	body	80	valid
165.0ms	8634×	body	80	nan
0.0ms	2×	body	320	valid
0.0ms	1×	body	640	valid