Details

sample47.0ms

Algorithm

intervals

Results

32.0ms

452×

body

valid

simplify105.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	69	42
1	231	42
2	900	42
3	3753	42
4	5001	42

prune4.0ms

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: 0.2b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (fabs x) (fabs x)) (fabs x))
0.2b	(* (* (fabs x) (fabs x)) (fabs x))
0.2b	(* (* (fabs x) (fabs x)) (fabs x))
1.0b	(sqrt PI)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

62×	`pow1`
19×	`add-exp-log` `add-cbrt-cube`
18×	`pow-plus` `pow-prod-up`
12×	`add-sqr-sqrt`
9×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow2` `pow-sqr`
4×	`add-log-exp`
3×	`associate-l` `pow3` `sqrt-prod` `*-commutative` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 97

Calls

4 calls:

6.0ms	(* (* (fabs x) (fabs x)) (fabs x))
6.0ms	(* (* (fabs x) (fabs x)) (fabs x))
6.0ms	(* (* (fabs x) (fabs x)) (fabs x))
1.0ms	(sqrt PI)

series83.0ms

Counts

4 → 10

Calls

4 calls:

26.0ms	(* (* (fabs x) (fabs x)) (fabs x))
26.0ms	(* (* (fabs x) (fabs x)) (fabs x))
30.0ms	(* (* (fabs x) (fabs x)) (fabs x))
0.0ms	(sqrt PI)

simplify78.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	164	423
1	561	288
2	2251	278
3	5001	260

prune306.0ms

Filtered

107 candidates to 52 candidates (48.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	103	4	107
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	4	108

Merged error: 0.1b

Counts

108 → 4

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.2b	(* (* (fabs x) (fabs x)) (fabs x))
0.2b	(* (* (fabs x) (fabs x)) (fabs x))
1.0b	(sqrt PI)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

63×	`pow1`
59×	`add-exp-log` `add-cbrt-cube`
36×	`prod-exp` `cbrt-unprod`
21×	`pow-prod-down`
17×	`add-sqr-sqrt`
15×	`associate-l`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow-plus` `pow-prod-up`
9×	`times-frac`
7×	`associate-r`
5×	`cbrt-undiv` `div-exp`
4×	`pow2` `pow-sqr` `add-log-exp`
3×	`sqrt-prod` `*-commutative`
2×	`pow3` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*l/` `div-inv`

Counts

4 → 117

Calls

4 calls:

22.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
6.0ms	(* (* (fabs x) (fabs x)) (fabs x))
6.0ms	(* (* (fabs x) (fabs x)) (fabs x))
1.0ms	(sqrt PI)

series113.0ms

Counts

4 → 10

Calls

4 calls:

57.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
29.0ms	(* (* (fabs x) (fabs x)) (fabs x))
27.0ms	(* (* (fabs x) (fabs x)) (fabs x))
0.0ms	(sqrt PI)

simplify56.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	463	950
1	1992	620
2	5001	580

prune404.0ms

Filtered

127 candidates to 59 candidates (46.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	127	4	131

Merged error: 0.1b

Counts

131 → 4

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (fabs x) (sqrt (fabs x)))
0.2b	(* (fabs x) (sqrt (fabs x)))
0.3b	(* (* (fabs x) (sqrt (fabs x))) (* (fabs x) (sqrt (fabs x))))
1.0b	(sqrt PI)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

78×	`pow1`
29×	`pow-prod-up`
28×	`add-sqr-sqrt`
22×	`pow-prod-down`
20×	`add-exp-log` `add-cbrt-cube`
13×	`associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1` `pow1/2` `sqrt-prod`
10×	`prod-exp` `cbrt-unprod`
8×	`pow3`
7×	`associate-l` `pow-sqr`
4×	`add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`pow-plus`
1×	`pow2` `rem-sqrt-square` `swap-sqr`

Counts

4 → 108

Calls

4 calls:

5.0ms	(* (fabs x) (sqrt (fabs x)))
5.0ms	(* (fabs x) (sqrt (fabs x)))
10.0ms	(* (* (fabs x) (sqrt (fabs x))) (* (fabs x) (sqrt (fabs x))))
1.0ms	(sqrt PI)

series106.0ms

Counts

4 → 10

Calls

4 calls:

39.0ms	(* (fabs x) (sqrt (fabs x)))
36.0ms	(* (fabs x) (sqrt (fabs x)))
30.0ms	(* (* (fabs x) (sqrt (fabs x))) (* (fabs x) (sqrt (fabs x))))
0.0ms	(sqrt PI)

simplify154.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 3 (148.0ms)

Iter	Nodes	Cost
0	187	485
1	656	356
2	3526	318
3	5002	302

prune397.0ms

Filtered

118 candidates to 59 candidates (50.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	115	3	118
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	118	4	122

Merged error: 0.1b

Counts

122 → 4

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (fabs x) (fabs x)) (fabs x))
0.2b	(* (* (fabs x) (fabs x)) (fabs x))
0.2b	(pow (pow (fabs x) 2) (+ 1 1/2))
1.0b	(sqrt PI)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

43×	`pow1`
16×	`add-exp-log`
14×	`add-cbrt-cube`
13×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `pow-plus` `pow-prod-up`
11×	`unpow-prod-down`
10×	`add-cube-cbrt`
6×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`pow2` `pow-unpow` `pow-exp` `pow-sqr` `add-log-exp`
3×	`sqrt-prod`
2×	`pow-to-exp` `associate-l` `pow3` `*-commutative` `unswap-sqr` `sqr-pow`
1×	`unpow-prod-up` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `distribute-lft-out` `unpow2`

Counts

4 → 95

Calls

4 calls:

6.0ms	(* (* (fabs x) (fabs x)) (fabs x))
6.0ms	(* (* (fabs x) (fabs x)) (fabs x))
6.0ms	(pow (pow (fabs x) 2) (+ 1 1/2))
1.0ms	(sqrt PI)

series176.0ms

Counts

4 → 10

Calls

4 calls:

29.0ms	(* (* (fabs x) (fabs x)) (fabs x))
26.0ms	(* (* (fabs x) (fabs x)) (fabs x))
120.0ms	(pow (pow (fabs x) 2) (+ 1 1/2))
0.0ms	(sqrt PI)

simplify52.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	298	435
1	1274	317
2	5001	299

prune370.0ms

Filtered

105 candidates to 56 candidates (53.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	105	4	109

Merged error: 0.1b

Counts

109 → 4

regimes75.0ms

Accuracy

0% (0.0b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	40
1	54	40

end0.0ms

sample1.0s

Algorithm

intervals

Results

891.0ms

13780×

body

valid