Details

sample56.0ms

Algorithm

intervals

Results

39.0ms

428×

body

valid

simplify114.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	70	42
1	252	42
2	1059	42
3	4713	42
4	5001	42

prune5.0ms

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

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x))
0.1b	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.2b	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b	(sqrt PI)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

80×	`pow1`
79×	`add-exp-log` `add-cbrt-cube`
48×	`prod-exp` `cbrt-unprod`
27×	`associate-l` `pow-prod-down`
21×	`add-sqr-sqrt` `pow-plus` `pow-prod-up`
20×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
8×	`cbrt-undiv` `div-exp`
5×	`associate-r`
4×	`pow2` `expm1-log1p-u` `pow-sqr` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod` `*-commutative`
2×	`pow3` `associate-*l/` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 146

Calls

4 calls:

9.0ms	(* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x))
24.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
12.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms	(sqrt PI)

series146.0ms

Counts

4 → 10

Calls

4 calls:

28.0ms	(* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x))
64.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
54.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms	(sqrt PI)

simplify84.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	645	1219
1	2874	841
2	5001	803

prune456.0ms

Filtered

156 candidates to 82 candidates (52.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	153	3	156
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	153	4	157

Merged error: 0.1b

Counts

157 → 4

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x))
0.1b	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.2b	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b	(sqrt PI)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

80×	`pow1`
79×	`add-exp-log` `add-cbrt-cube`
48×	`prod-exp` `cbrt-unprod`
27×	`associate-l` `pow-prod-down`
21×	`add-sqr-sqrt` `pow-plus` `pow-prod-up`
20×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
8×	`cbrt-undiv` `div-exp`
5×	`associate-r`
4×	`pow2` `expm1-log1p-u` `pow-sqr` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod` `*-commutative`
2×	`pow3` `associate-*l/` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 146

Calls

4 calls:

9.0ms	(* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x))
27.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
13.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms	(sqrt PI)

series143.0ms

Counts

4 → 10

Calls

4 calls:

29.0ms	(* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x))
66.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
47.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms	(sqrt PI)

simplify87.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	650	1214
1	2903	802
2	5001	720

prune482.0ms

Filtered

156 candidates to 82 candidates (52.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	156	4	160

Merged error: 0.1b

Counts

160 → 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	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.2b	(* (sqrt (fabs x)) (pow (fabs x) 3))
1.0b	(sqrt PI)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-exp-log`
72×	`add-cbrt-cube`
45×	`prod-exp`
43×	`cbrt-unprod`
39×	`add-sqr-sqrt`
35×	`pow1`
32×	`associate-l`
24×	`add-cube-cbrt` `*-un-lft-identity`
21×	`pow-prod-down`
18×	`times-frac`
14×	`associate-r`
10×	`sqrt-prod`
8×	`cbrt-undiv` `div-exp` `unswap-sqr`
5×	`unpow-prod-down` `cube-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `sqr-pow`
2×	`sqrt-pow1` `pow1/2` `associate-*l/` `pow-prod-up` `div-inv`
1×	`cube-mult` `pow-to-exp` `rem-sqrt-square` `unpow3` `pow-exp`

Counts

4 → 147

Calls

4 calls:

24.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
12.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
8.0ms	(* (sqrt (fabs x)) (pow (fabs x) 3))
2.0ms	(sqrt PI)

series185.0ms

Counts

4 → 10

Calls

4 calls:

67.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
51.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
67.0ms	(* (sqrt (fabs x)) (pow (fabs x) 3))
0.0ms	(sqrt PI)

simplify96.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	715	1301
1	3163	981
2	5001	923

prune585.0ms

Filtered

157 candidates to 92 candidates (58.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	157	4	161

Merged error: 0.1b

Counts

161 → 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	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b	(expm1 (log1p (sqrt PI)))
1.0b	(sqrt PI)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-exp-log` `add-cbrt-cube`
42×	`prod-exp` `cbrt-unprod`
34×	`pow1`
26×	`associate-l`
21×	`pow-prod-down`
20×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
8×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`associate-r` `associate-l/` `-commutative` `div-inv`
1×	`rem-sqrt-square` `expm1-log1p` `sqrt-pow1` `pow1/2` `expm1-udef`

Counts

4 → 116

Calls

4 calls:

23.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
12.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms	(expm1 (log1p (sqrt PI)))
2.0ms	(sqrt PI)

series111.0ms

Counts

4 → 8

Calls

4 calls:

60.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
51.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms	(expm1 (log1p (sqrt PI)))
0.0ms	(sqrt PI)

simplify59.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	567	1033
1	2237	725
2	5001	653

prune445.0ms

Filtered

124 candidates to 77 candidates (62.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	123	5	128

Merged error: 0.1b

Counts

128 → 5

regimes242.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	37
1	45	37

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.3s

13823×

body

valid