Details

sample32.0ms

Algorithm

intervals

Results

18.0ms

436×

body

valid

simplify69.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	23	7
1	59	6
2	111	6
3	204	6
4	369	6
5	839	6
6	2168	6
7	5001	6

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 30.4b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (- (* y y) (* z z)))
5.0b	(- (* y y) (* z z))
28.2b	(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
45×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
13×	`associate-/l*`
8×	`add-exp-log` `add-cbrt-cube`
5×	`div-inv` `add-log-exp`
3×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r*` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `clear-num` `flip--` `fma-udef` `associate-/l/` `difference-of-squares`

Counts

3 → 99

Calls

3 calls:

1.0ms	(fma x x (- (* y y) (* z z)))
4.0ms	(- (* y y) (* z z))
7.0ms	(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

series197.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(fma x x (- (* y y) (* z z)))
35.0ms	(- (* y y) (* z z))
105.0ms	(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

simplify64.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	466	1096
1	1881	1029
2	5001	1026

prune376.0ms

Filtered

108 candidates to 87 candidates (80.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	99	9	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	9	109

Merged error: 11.2b

Counts

109 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
0.0b	(+ y (/ (pow x 2) y))
7.4b	(/ (pow x 2) y)
9.7b	(/ (pow z 2) y)

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

193×	`*-un-lft-identity`
148×	`times-frac`
140×	`add-sqr-sqrt`
128×	`add-cube-cbrt`
112×	`prod-diff`
61×	`unpow-prod-down`
31×	`distribute-lft-out`
21×	`unpow2` `sqr-pow`
16×	`associate-/l*`
14×	`add-exp-log`
11×	`add-log-exp`
8×	`add-cbrt-cube`
6×	`div-exp` `associate-/r*` `div-inv`
5×	`difference-of-squares`
4×	`pow1` `expm1-log1p-u` `fma-neg` `log1p-expm1-u`
3×	`fma-def`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `flip3-+` `diff-log` `pow-exp` `clear-num` `sum-log` `frac-sub` `flip-+` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `flip3--` `associate--l+` `flip--`

Counts

4 → 260

Calls

4 calls:

24.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
13.0ms	(+ y (/ (pow x 2) y))
5.0ms	(/ (pow x 2) y)
5.0ms	(/ (pow z 2) y)

series128.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
31.0ms	(+ y (/ (pow x 2) y))
27.0ms	(/ (pow x 2) y)
23.0ms	(/ (pow z 2) y)

simplify137.0ms

Algorithm

egg-herbie

Counts

272 → 272

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	966	4460
1	3272	3145
2	5001	2953

prune514.0ms

Filtered

272 candidates to 118 candidates (43.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	265	7	272
Fresh	8	0	8
Picked	1	0	1
Done	0	0	0
Total	274	7	281

Merged error: 1.5b

Counts

281 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ y (/ (pow x 2) y)) (/ z (/ y z)))
0.0b	(+ y (/ (pow x 2) y))
0.2b	(/ z (/ y z))
7.4b	(/ (pow x 2) y)

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

366×	`times-frac`
346×	`*-un-lft-identity`
258×	`add-sqr-sqrt`
249×	`add-cube-cbrt`
176×	`prod-diff`
47×	`distribute-lft-out`
22×	`div-inv`
16×	`associate-/r*`
14×	`add-exp-log`
12×	`unpow-prod-down`
11×	`add-cbrt-cube` `associate-/l*` `add-log-exp`
6×	`div-exp`
5×	`associate-/r/`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `fma-neg` `log1p-expm1-u` `unpow2` `sqr-pow`
3×	`fma-def` `difference-of-squares`
2×	`frac-2neg` `flip3-+` `diff-log` `clear-num` `sum-log` `frac-sub` `flip-+` `distribute-lft-out--`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `pow-exp` `associate--l+` `flip--`

Counts

4 → 343

Calls

4 calls:

33.0ms	(- (+ y (/ (pow x 2) y)) (/ z (/ y z)))
10.0ms	(+ y (/ (pow x 2) y))
6.0ms	(/ z (/ y z))
5.0ms	(/ (pow x 2) y)

series127.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (+ y (/ (pow x 2) y)) (/ z (/ y z)))
30.0ms	(+ y (/ (pow x 2) y))
21.0ms	(/ z (/ y z))
29.0ms	(/ (pow x 2) y)

simplify98.0ms

Algorithm

egg-herbie

Counts

355 → 355

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	1460	7695
1	5001	5654

prune699.0ms

Filtered

355 candidates to 162 candidates (45.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	350	5	355
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	356	6	362

Merged error: 0.0b

Counts

362 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ y (/ (pow x (/ 2 2)) (/ y x))) (/ z (/ y z)))
0.0b	(+ y (/ (pow x (/ 2 2)) (/ y x)))
0.2b	(/ z (/ y z))
0.2b	(/ (pow x (/ 2 2)) (/ y x))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

505×	`times-frac`
413×	`*-un-lft-identity`
325×	`add-sqr-sqrt`
316×	`add-cube-cbrt`
176×	`prod-diff`
47×	`distribute-lft-out`
42×	`unpow-prod-down`
30×	`div-inv`
26×	`associate-/r*`
22×	`add-exp-log`
14×	`add-cbrt-cube` `sqr-pow`
12×	`div-exp`
11×	`add-log-exp`
10×	`associate-/l*`
6×	`cbrt-undiv` `associate-/r/`
4×	`pow1` `expm1-log1p-u` `fma-neg` `log1p-expm1-u`
3×	`fma-def` `difference-of-squares`
2×	`pow-to-exp` `frac-2neg` `flip3-+` `diff-log` `pow-exp` `clear-num` `sum-log` `frac-sub` `flip-+` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `flip3--` `associate--l+` `flip--`

Counts

4 → 424

Calls

4 calls:

47.0ms	(- (+ y (/ (pow x (/ 2 2)) (/ y x))) (/ z (/ y z)))
23.0ms	(+ y (/ (pow x (/ 2 2)) (/ y x)))
6.0ms	(/ z (/ y z))
9.0ms	(/ (pow x (/ 2 2)) (/ y x))

series131.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (+ y (/ (pow x (/ 2 2)) (/ y x))) (/ z (/ y z)))
31.0ms	(+ y (/ (pow x (/ 2 2)) (/ y x)))
22.0ms	(/ z (/ y z))
31.0ms	(/ (pow x (/ 2 2)) (/ y x))

simplify127.0ms

Algorithm

egg-herbie

Counts

436 → 436

Iterations

Useful iterations: 1 (49.0ms)

Iter	Nodes	Cost
0	1834	8768
1	5001	6850

prune976.0ms

Filtered

436 candidates to 227 candidates (52.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	432	4	436
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	437	5	442

Merged error: 0b

Counts

442 → 5

regimes80.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	18	9
1	18	9

end0.0ms

sample771.0ms

Algorithm

intervals

Results

478.0ms

13768×

body

valid