Details

sample50.0ms

Algorithm

intervals

Results

34.0ms

452×

body

valid

simplify112.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

rewrite26.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `pow3` `sqrt-prod` `*-commutative` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 105

Calls

4 calls:

6.0ms	(* (* (fabs x) (fabs x)) (fabs x))
9.0ms	(* (* (fabs x) (fabs x)) (fabs x))
6.0ms	(* (* (fabs x) (fabs x)) (fabs x))
2.0ms	(sqrt PI)

series85.0ms

Counts

4 → 10

Calls

4 calls:

32.0ms	(* (* (fabs x) (fabs x)) (fabs x))
26.0ms	(* (* (fabs x) (fabs x)) (fabs x))
27.0ms	(* (* (fabs x) (fabs x)) (fabs x))
0.0ms	(sqrt PI)

simplify83.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	170	463
1	591	328
2	2465	318
3	5001	300

prune350.0ms

Filtered

115 candidates to 60 candidates (52.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	111	4	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	4	116

Merged error: 0.1b

Counts

116 → 4

localize27.0ms

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)

rewrite44.0ms

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` `expm1-log1p-u` `pow-sqr` `log1p-expm1-u` `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 → 125

Calls

4 calls:

22.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
9.0ms	(* (* (fabs x) (fabs x)) (fabs x))
6.0ms	(* (* (fabs x) (fabs x)) (fabs x))
1.0ms	(sqrt PI)

series116.0ms

Counts

4 → 10

Calls

4 calls:

59.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
30.0ms	(* (* (fabs x) (fabs x)) (fabs x))
27.0ms	(* (* (fabs x) (fabs x)) (fabs x))
0.0ms	(sqrt PI)

simplify56.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	467	1001
1	1950	596
2	5002	540

prune460.0ms

Filtered

135 candidates to 71 candidates (52.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	134	5	139

Merged error: 0.1b

Counts

139 → 5

localize39.0ms

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)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

50×	`pow1`
16×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
13×	`pow-plus` `pow-prod-up`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`pow2` `associate-l` `pow-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr` `sqrt-prod` `*-commutative` `unswap-sqr`
2×	`pow3`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 102

Calls

4 calls:

6.0ms	(* (* (fabs x) (fabs x)) (fabs x))
6.0ms	(* (* (fabs x) (fabs x)) (fabs x))
4.0ms	(* (fabs (pow (fabs x) 3/2)) (fabs (pow (fabs x) 3/2)))
2.0ms	(sqrt PI)

series76.0ms

Counts

4 → 10

Calls

4 calls:

33.0ms	(* (* (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)

simplify166.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	237	535
1	897	410
2	4698	341
3	5001	341

prune396.0ms

Filtered

112 candidates to 56 candidates (50.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	109	3	112
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	111	6	117

Merged error: 0.1b

Counts

117 → 6

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (fabs x) (fabs x)) (fabs x))
0.2b	(* (* (fabs x) (fabs x)) (fabs x))
1.0b	(expm1 (log1p (sqrt PI)))
1.0b	(sqrt PI)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

43×	`pow1`
14×	`add-exp-log` `add-cbrt-cube`
12×	`pow-plus` `pow-prod-up`
10×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`pow2` `expm1-log1p-u` `pow-sqr` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`associate-l` `pow3` `*-commutative` `unswap-sqr`
1×	`rem-sqrt-square` `expm1-log1p` `sqrt-pow1` `pow1/2` `expm1-udef`

Counts

4 → 86

Calls

4 calls:

6.0ms	(* (* (fabs x) (fabs x)) (fabs x))
6.0ms	(* (* (fabs x) (fabs x)) (fabs x))
1.0ms	(expm1 (log1p (sqrt PI)))
2.0ms	(sqrt PI)

series57.0ms

Counts

4 → 8

Calls

4 calls:

26.0ms	(* (* (fabs x) (fabs x)) (fabs x))
30.0ms	(* (* (fabs x) (fabs x)) (fabs x))
0.0ms	(expm1 (log1p (sqrt PI)))
0.0ms	(sqrt PI)

simplify115.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (31.0ms)

Iter	Nodes	Cost
0	120	319
1	342	229
2	1006	222
3	3328	210
4	5001	210

prune312.0ms

Filtered

94 candidates to 53 candidates (56.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	3	0	3
Picked	0	1	1
Done	0	2	2
Total	95	5	100

Merged error: 0.1b

Counts

100 → 5

regimes149.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

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

962.0ms

13780×

body

valid