Details

sample34.0ms

Algorithm

intervals

Results

19.0ms

457×

body

valid

simplify76.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

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

prune8.0ms

Filtered

1 candidates to 1 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: 29.5b

Counts

2 → 2

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
4.0b	(- (+ (* x x) (* y y)) (* z z))
27.5b	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

rewrite24.0ms

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:

5.0ms	(+ (* x x) (* y y))
7.0ms	(- (+ (* x x) (* y y)) (* z z))
11.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

series171.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* x x) (* y y))
46.0ms	(- (+ (* x x) (* y y)) (* z z))
94.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

simplify57.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (45.0ms)

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

prune206.0ms

Filtered

74 candidates to 57 candidates (77.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	70	4	74
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	72	4	76

Merged error: 10.2b

Counts

76 → 4

localize15.0ms

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))
9.2b	(/ (pow z 2) y)
9.5b	(/ (pow x 2) y)

rewrite64.0ms

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:

26.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
12.0ms	(+ y (/ (pow x 2) y))
6.0ms	(/ (pow z 2) y)
6.0ms	(/ (pow x 2) y)

series132.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
31.0ms	(+ y (/ (pow x 2) y))
21.0ms	(/ (pow z 2) y)
28.0ms	(/ (pow x 2) y)

simplify134.0ms

Algorithm

egg-herbie

Counts

272 → 272

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	966	4460
1	3272	3145
2	5001	2950

prune461.0ms

Filtered

272 candidates to 118 candidates (43.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	266	6	272
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	269	7	276

Merged error: 1.0b

Counts

276 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ y (/ (pow x 2) y)) (* z (/ z y)))
0.0b	(+ y (/ (pow x 2) y))
0.1b	(* z (/ z y))
9.5b	(/ (pow x 2) y)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
34×	`times-frac`
32×	`add-cube-cbrt`
14×	`add-exp-log`
13×	`associate-r`
12×	`unpow-prod-down`
11×	`add-cbrt-cube` `add-log-exp`
8×	`associate-/l*`
6×	`pow1`
4×	`expm1-log1p-u` `fma-neg` `div-exp` `prod-diff` `log1p-expm1-u` `unpow2` `sqr-pow`
3×	`fma-def` `associate-r/` `associate-l` `associate-/r` `distribute-lft-out`
2×	`cbrt-undiv` `flip3-+` `diff-log` `prod-exp` `sum-log` `frac-sub` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `pow-prod-down` `pow-exp` `associate--l+` `clear-num` `*-commutative` `flip--`

Counts

4 → 128

Calls

4 calls:

15.0ms	(- (+ y (/ (pow x 2) y)) (* z (/ z y)))
14.0ms	(+ y (/ (pow x 2) y))
8.0ms	(* z (/ z y))
6.0ms	(/ (pow x 2) y)

series143.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (+ y (/ (pow x 2) y)) (* z (/ z y)))
41.0ms	(+ y (/ (pow x 2) y))
24.0ms	(* z (/ z y))
24.0ms	(/ (pow x 2) y)

simplify74.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	460	747
1	1930	676
2	5001	670

prune336.0ms

Filtered

140 candidates to 95 candidates (67.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	141	6	147

Merged error: 0.0b

Counts

147 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ y (* x (/ x y))) (* z (/ z y)))
0.0b	(+ y (* x (/ x y)))
0.1b	(* z (/ z y))
0.2b	(* x (/ x y))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`associate-r`
23×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
14×	`add-exp-log` `add-cbrt-cube`
11×	`add-log-exp`
8×	`pow1`
6×	`associate-l`
4×	`expm1-log1p-u` `associate-*r/` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `fma-neg` `prod-diff`
2×	`cbrt-undiv` `flip3-+` `diff-log` `div-exp` `pow-prod-down` `sum-log` `*-commutative` `frac-sub` `flip-+` `div-inv`
1×	`+-commutative` `sub-neg` `flip3--` `associate--l+` `flip--`

Counts

4 → 108

Calls

4 calls:

6.0ms	(- (+ y (* x (/ x y))) (* z (/ z y)))
3.0ms	(+ y (* x (/ x y)))
8.0ms	(* z (/ z y))
9.0ms	(* x (/ x y))

series134.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (+ y (* x (/ x y))) (* z (/ z y)))
37.0ms	(+ y (* x (/ x y)))
24.0ms	(* z (/ z y))
23.0ms	(* x (/ x y))

simplify78.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	471	621
1	2270	544
2	5002	536

prune255.0ms

Filtered

120 candidates to 85 candidates (70.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	119	7	126

Merged error: 0b

Counts

126 → 7

regimes131.0ms

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	15	7
1	15	7

end0.0ms

sample892.0ms

Algorithm

intervals

Results

599.0ms

13747×

body

valid