Details

sample49.0ms

Algorithm

intervals

Results

33.0ms

441×

body

valid

simplify121.0ms

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

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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:

0.1b	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.1b	(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (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)

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

527×	`add-sqr-sqrt`
380×	`associate-l`
340×	`unswap-sqr`
216×	`associate-r`
147×	`add-exp-log` `add-cbrt-cube`
98×	`prod-exp` `cbrt-unprod`
69×	`pow1`
65×	`add-cube-cbrt` `*-un-lft-identity`
54×	`times-frac`
49×	`pow-prod-down`
30×	`*-commutative`
27×	`associate-*l/`
24×	`swap-sqr`
15×	`cbrt-undiv` `div-exp`
9×	`associate-/r` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num` `sqrt-prod` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 420

Calls

4 calls:

51.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
119.0ms	(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
26.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms	(sqrt PI)

series206.0ms

Counts

4 → 10

Calls

4 calls:

65.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
83.0ms	(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
58.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms	(sqrt PI)

simplify94.0ms

Algorithm

egg-herbie

Counts

430 → 430

Iterations

Useful iterations: 1 (45.0ms)

Iter	Nodes	Cost
0	1988	4832
1	5001	3710

prune1.6s

Filtered

430 candidates to 258 candidates (40.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	427	3	430
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	427	4	431

Merged error: 0.1b

Counts

431 → 4

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.1b	(* (/ 1.0 21.0) (pow (fabs x) 4))
0.2b	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b	(sqrt PI)

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

254×	`add-sqr-sqrt`
148×	`associate-l`
134×	`unswap-sqr`
111×	`associate-r`
83×	`add-exp-log`
75×	`add-cbrt-cube`
52×	`add-cube-cbrt` `*-un-lft-identity`
48×	`prod-exp`
45×	`times-frac`
44×	`cbrt-unprod`
36×	`pow1`
27×	`associate-*l/`
22×	`pow-prod-down`
17×	`*-commutative`
14×	`swap-sqr`
11×	`div-exp`
9×	`cbrt-undiv` `associate-/r` `associate-/l`
5×	`unpow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num` `sqrt-prod` `div-inv` `sqr-pow`
2×	`pow-to-exp` `pow-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 289

Calls

4 calls:

51.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
10.0ms	(* (/ 1.0 21.0) (pow (fabs x) 4))
25.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms	(sqrt PI)

series171.0ms

Counts

4 → 10

Calls

4 calls:

67.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
55.0ms	(* (/ 1.0 21.0) (pow (fabs x) 4))
49.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms	(sqrt PI)

simplify61.0ms

Algorithm

egg-herbie

Counts

299 → 299

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1352	2714
1	5001	2028

prune1.0s

Filtered

299 candidates to 188 candidates (37.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	298	1	299
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	299	4	303

Merged error: 0.1b

Counts

303 → 4

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (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)

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

371×	`add-sqr-sqrt`
276×	`associate-l`
243×	`unswap-sqr`
146×	`associate-r`
102×	`add-exp-log` `add-cbrt-cube`
68×	`prod-exp` `cbrt-unprod`
49×	`pow1`
45×	`add-cube-cbrt` `*-un-lft-identity`
36×	`times-frac`
34×	`pow-prod-down`
20×	`*-commutative`
18×	`associate-*l/`
16×	`swap-sqr`
10×	`cbrt-undiv` `div-exp`
6×	`associate-/r` `associate-/l`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `add-log-exp`
3×	`sqrt-prod`
2×	`expm1-log1p` `frac-2neg` `clear-num` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `expm1-udef`

Counts

4 → 299

Calls

4 calls:

119.0ms	(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
25.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms	(expm1 (log1p (sqrt PI)))
2.0ms	(sqrt PI)

series136.0ms

Counts

4 → 8

Calls

4 calls:

80.0ms	(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
56.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms	(expm1 (log1p (sqrt PI)))
0.0ms	(sqrt PI)

simplify68.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1500	3301
1	5001	2483

prune1.1s

Filtered

307 candidates to 187 candidates (39.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	307	0	307
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	307	4	311

Merged error: 0.1b

Counts

311 → 4

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 21.0) (pow (fabs x) 4))
0.2b	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b	(sqrt PI)
1.4b	(log (pow (exp (/ 1.0 5.0)) (pow (fabs x) 5)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-sqr-sqrt`
44×	`associate-l`
43×	`add-cube-cbrt` `*-un-lft-identity`
41×	`associate-r`
40×	`add-exp-log`
37×	`unswap-sqr`
36×	`times-frac`
30×	`add-cbrt-cube`
23×	`log-pow`
18×	`pow1` `associate-*l/` `prod-exp`
14×	`pow-pow` `cbrt-unprod`
13×	`exp-prod`
11×	`unpow-prod-down`
7×	`pow-unpow` `log-prod` `pow-prod-down` `*-commutative`
6×	`swap-sqr` `div-exp` `associate-/r` `associate-/l`
5×	`sqr-pow`
4×	`cbrt-undiv` `expm1-log1p-u` `rem-log-exp` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `sqrt-prod` `div-inv`
2×	`frac-2neg` `clear-num`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 199

Calls

4 calls:

12.0ms	(* (/ 1.0 21.0) (pow (fabs x) 4))
23.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms	(sqrt PI)
8.0ms	(log (pow (exp (/ 1.0 5.0)) (pow (fabs x) 5)))

series411.0ms

Counts

4 → 10

Calls

4 calls:

54.0ms	(* (/ 1.0 21.0) (pow (fabs x) 4))
49.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms	(sqrt PI)
309.0ms	(log (pow (exp (/ 1.0 5.0)) (pow (fabs x) 5)))

simplify136.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 2 (120.0ms)

Iter	Nodes	Cost
0	894	1424
1	4771	1184
2	5001	1177

prune899.0ms

Filtered

209 candidates to 143 candidates (31.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	209	0	209
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	209	4	213

Merged error: 0.1b

Counts

213 → 4

regimes213.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	37
1	41	37

end0.0ms

sample1.1s

Algorithm

intervals

Results

934.0ms

13895×

body

valid