Details

sample29.0ms

Algorithm

intervals

Results

16.0ms

401×

body

valid

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 25.1b

Counts

2 → 1

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
4.5b	(- (+ (* x x) (* y y)) (* z z))
23.2b	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt` `*-un-lft-identity`
4×	`times-frac` `associate-/l*`
3×	`pow1` `expm1-log1p-u` `fma-neg` `prod-diff` `log1p-expm1-u` `difference-of-squares`
2×	`cbrt-undiv` `flip3--` `diff-log` `div-exp` `sum-log` `flip--` `associate-/l/`
1×	`+-commutative` `sub-neg` `fma-def` `frac-2neg` `flip3-+` `div-sub` `prod-exp` `associate--l+` `clear-num` `associate-/r*` `cbrt-unprod` `flip-+` `div-inv`

Counts

3 → 65

Calls

3 calls:

4.0ms	(+ (* x x) (* y y))
6.0ms	(- (+ (* x x) (* y y)) (* z z))
9.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

series160.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* x x) (* y y))
43.0ms	(- (+ (* x x) (* y y)) (* z z))
88.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	365	571
1	1599	486
2	5002	469

prune183.0ms

Filtered

74 candidates to 57 candidates (77.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	71	3	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	3	75

Merged error: 10.5b

Counts

75 → 3

localize12.0ms

Local error

Found 2 expressions with local error:

8.4b	(/ (pow x 2) y)
9.8b	(/ (pow z 2) y)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
36×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
16×	`associate-/l*`
12×	`add-exp-log`
8×	`unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*` `add-cbrt-cube`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

2 → 102

Calls

2 calls:

5.0ms	(/ (pow x 2) y)
5.0ms	(/ (pow z 2) y)

series43.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(/ (pow x 2) y)
24.0ms	(/ (pow z 2) y)

simplify42.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	276	494
1	970	434
2	5002	427

prune248.0ms

Filtered

108 candidates to 70 candidates (64.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	107	4	111

Merged error: 0.8b

Counts

111 → 4

localize11.0ms

Local error

Found 2 expressions with local error:

0.2b	(* x (/ x y))
9.8b	(/ (pow z 2) y)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

34×	`times-frac`
32×	`add-sqr-sqrt`
27×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
12×	`add-exp-log` `unpow-prod-down`
9×	`add-cbrt-cube`
8×	`associate-/l*`
4×	`pow1` `div-exp` `unpow2` `sqr-pow`
3×	`associate-l` `associate-/r*`
2×	`cbrt-undiv` `expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
1×	`pow-to-exp` `frac-2neg` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative`

Counts

2 → 85

Calls

2 calls:

7.0ms	(* x (/ x y))
5.0ms	(/ (pow z 2) y)

series38.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(* x (/ x y))
19.0ms	(/ (pow z 2) y)

simplify49.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	296	386
1	1256	335
2	5002	332

prune181.0ms

Filtered

91 candidates to 60 candidates (65.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	92	3	95

Merged error: 0b

Counts

95 → 3

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b	(* x (/ x y))
0.2b	(* z (/ z y))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
26×	`associate-r`
20×	`times-frac`
18×	`add-cube-cbrt` `*-un-lft-identity`
12×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `associate-l`
4×	`prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`cbrt-undiv` `expm1-log1p-u` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

2 → 68

Calls

2 calls:

7.0ms	(* x (/ x y))
11.0ms	(* z (/ z y))

series39.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(* x (/ x y))
20.0ms	(* z (/ z y))

simplify48.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	303	278
1	1486	236
2	5001	236

prune133.0ms

Filtered

74 candidates to 50 candidates (67.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	74	3	77

Merged error: 0b

Counts

77 → 3

regimes51.0ms

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	15	7
1	15	7

end0.0ms

sample876.0ms

Algorithm

intervals

Results

581.0ms

13562×

body

valid