Details

sample52.0ms

Algorithm

intervals

Results

35.0ms

452×

body

valid

simplify110.0ms

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)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 154

Calls

4 calls:

9.0ms	(* (* (fabs x) (fabs x)) (fabs x))
9.0ms	(* (* (fabs x) (fabs x)) (fabs x))
9.0ms	(* (* (fabs x) (fabs x)) (fabs x))
1.0ms	(sqrt PI)

series78.0ms

Counts

4 → 10

Calls

4 calls:

25.0ms	(* (* (fabs x) (fabs x)) (fabs x))
26.0ms	(* (* (fabs x) (fabs x)) (fabs x))
26.0ms	(* (* (fabs x) (fabs x)) (fabs x))
0.0ms	(sqrt PI)

simplify143.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 3 (129.0ms)

Iter	Nodes	Cost
0	188	690
1	747	522
2	3574	512
3	5001	470

prune536.0ms

Filtered

164 candidates to 88 candidates (53.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	160	4	164
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	161	4	165

Merged error: 0.1b

Counts

165 → 4

localize35.0ms

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)

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

198×	`add-sqr-sqrt`
140×	`associate-l`
111×	`unswap-sqr`
82×	`associate-r`
63×	`pow1`
59×	`add-exp-log` `add-cbrt-cube`
37×	`add-cube-cbrt` `*-un-lft-identity`
36×	`prod-exp` `cbrt-unprod`
21×	`pow-prod-down`
18×	`times-frac` `*-commutative`
16×	`swap-sqr`
12×	`pow-plus` `pow-prod-up`
9×	`associate-*l/`
5×	`cbrt-undiv` `div-exp`
4×	`pow2` `pow3` `pow-sqr` `add-log-exp`
3×	`associate-/r` `sqrt-prod` `associate-/l`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `div-inv`

Counts

4 → 238

Calls

4 calls:

59.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
9.0ms	(* (* (fabs x) (fabs x)) (fabs x))
9.0ms	(* (* (fabs x) (fabs x)) (fabs x))
1.0ms	(sqrt PI)

series118.0ms

Counts

4 → 10

Calls

4 calls:

57.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
34.0ms	(* (* (fabs x) (fabs x)) (fabs x))
27.0ms	(* (* (fabs x) (fabs x)) (fabs x))
0.0ms	(sqrt PI)

simplify133.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 2 (108.0ms)

Iter	Nodes	Cost
0	837	1969
1	4212	1409
2	5001	1352

prune927.0ms

Filtered

248 candidates to 139 candidates (56.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	247	1	248
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	247	5	252

Merged error: 0.1b

Counts

252 → 5

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (fabs x) (fabs x)) (fabs x))
0.2b	(* (* (fabs x) (fabs x)) (fabs x))
0.3b	(* (fabs (pow (fabs x) 3/2)) (fabs (pow (fabs x) 3/2)))
1.0b	(sqrt PI)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

50×	`pow1`
48×	`add-sqr-sqrt`
39×	`associate-l`
21×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log` `add-cbrt-cube`
15×	`associate-r` `unswap-sqr`
13×	`pow-plus` `pow-prod-up`
11×	`swap-sqr`
9×	`*-commutative`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`pow2` `pow-sqr`
4×	`pow3` `add-log-exp`
3×	`sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 132

Calls

4 calls:

16.0ms	(* (* (fabs x) (fabs x)) (fabs x))
9.0ms	(* (* (fabs x) (fabs x)) (fabs x))
4.0ms	(* (fabs (pow (fabs x) 3/2)) (fabs (pow (fabs x) 3/2)))
1.0ms	(sqrt PI)

series69.0ms

Counts

4 → 10

Calls

4 calls:

26.0ms	(* (* (fabs x) (fabs x)) (fabs x))
26.0ms	(* (* (fabs x) (fabs x)) (fabs x))
17.0ms	(* (fabs (pow (fabs x) 3/2)) (fabs (pow (fabs x) 3/2)))
0.0ms	(sqrt PI)

simplify50.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	253	668
1	1074	522
2	5001	457

prune523.0ms

Filtered

142 candidates to 72 candidates (50.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	142	5	147

Merged error: 0.1b

Counts

147 → 5

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (fabs x) (sqrt (fabs x)))
0.3b	(* (* (fabs x) (sqrt (fabs x))) (pow (sqrt (fabs x)) 3))
0.5b	(pow (sqrt (fabs x)) 3)
1.0b	(sqrt PI)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-sqr-sqrt`
35×	`sqrt-prod`
34×	`unswap-sqr`
30×	`associate-r`
29×	`pow1`
23×	`-un-lft-identity` `associate-l*`
22×	`add-cube-cbrt`
20×	`add-exp-log`
18×	`unpow-prod-down` `cube-prod`
16×	`pow-prod-up`
12×	`add-cbrt-cube`
10×	`prod-exp`
8×	`pow-pow` `sqrt-pow1` `pow1/2`
6×	`pow3` `pow-prod-down`
5×	`sqr-pow`
4×	`pow-unpow` `cbrt-unprod` `add-log-exp`
3×	`cube-mult` `pow-to-exp` `pow-exp` `*-commutative` `sqrt-pow2`
2×	`unpow3`
1×	`rem-sqrt-square` `swap-sqr` `pow-sqr` `rem-cube-cbrt`

Counts

4 → 152

Calls

4 calls:

11.0ms	(* (fabs x) (sqrt (fabs x)))
20.0ms	(* (* (fabs x) (sqrt (fabs x))) (pow (sqrt (fabs x)) 3))
3.0ms	(pow (sqrt (fabs x)) 3)
1.0ms	(sqrt PI)

series105.0ms

Counts

4 → 10

Calls

4 calls:

44.0ms	(* (fabs x) (sqrt (fabs x)))
27.0ms	(* (* (fabs x) (sqrt (fabs x))) (pow (sqrt (fabs x)) 3))
34.0ms	(pow (sqrt (fabs x)) 3)
0.0ms	(sqrt PI)

simplify104.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	403	1075
1	2224	734
2	5002	653

prune493.0ms

Filtered

162 candidates to 72 candidates (44.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	0	2	2
Picked	0	1	1
Done	1	1	2
Total	162	5	167

Merged error: 0.1b

Counts

167 → 5

regimes88.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	39
1	47	39

end0.0ms

sample1.1s

Algorithm

intervals

Results

972.0ms

13780×

body

valid