Details

sample54.0ms

Algorithm

intervals

Results

40.0ms

429×

body

valid

simplify73.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize11.0ms

Local error

Found 2 expressions with local error:

2.5b	(- (+ (* x x) (* y y)) (* z z))
25.9b	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 51

Calls

2 calls:

22.0ms	(- (+ (* x x) (* y y)) (* z z))
40.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

series139.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(- (+ (* x x) (* y y)) (* z z))
93.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

simplify45.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	299	503
1	1242	422
2	5001	407

prune181.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 11.5b

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))
7.7b	(/ (pow z 2) y)
11.6b	(/ (pow x 2) y)

rewrite206.0ms

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:

164.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
13.0ms	(+ y (/ (pow x 2) y))
8.0ms	(/ (pow z 2) y)
5.0ms	(/ (pow x 2) y)

series129.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
30.0ms	(+ y (/ (pow x 2) y))
21.0ms	(/ (pow z 2) y)
27.0ms	(/ (pow x 2) y)

simplify124.0ms

Algorithm

egg-herbie

Counts

272 → 272

Iterations

Useful iterations: 2 (88.0ms)

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

prune535.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ y (* x (/ x y))) (/ (pow z 2) y))
0.0b	(+ y (* x (/ x y)))
0.1b	(* x (/ x y))
7.7b	(/ (pow z 2) y)

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

121×	`add-sqr-sqrt`
110×	`times-frac`
106×	`*-un-lft-identity`
104×	`add-cube-cbrt`
84×	`prod-diff`
40×	`unpow-prod-down`
14×	`add-exp-log` `unpow2` `sqr-pow`
13×	`associate-r`
11×	`add-cbrt-cube` `add-log-exp`
8×	`associate-/l*`
6×	`pow1`
5×	`div-inv` `difference-of-squares`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-def` `fma-neg` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `flip3-+` `diff-log` `prod-exp` `sum-log` `frac-sub` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `associate-r/` `pow-prod-down` `pow-exp` `associate--l+` `clear-num` `-commutative` `flip--` `distribute-lft-out--`

Counts

4 → 212

Calls

4 calls:

31.0ms	(- (+ y (* x (/ x y))) (/ (pow z 2) y))
3.0ms	(+ y (* x (/ x y)))
12.0ms	(* x (/ x y))
5.0ms	(/ (pow z 2) y)

series126.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (+ y (* x (/ x y))) (/ (pow z 2) y))
31.0ms	(+ y (* x (/ x y)))
26.0ms	(* x (/ x y))
21.0ms	(/ (pow z 2) y)

simplify133.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (98.0ms)

Iter	Nodes	Cost
0	994	3551
1	3667	2455
2	5001	2446

prune521.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

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:

16.0ms	(- (+ y (* x (/ x y))) (* (fabs z) (/ (fabs z) y)))
3.0ms	(+ y (* x (/ x y)))
8.0ms	(* x (/ x y))
9.0ms	(* (fabs z) (/ (fabs z) y))

series130.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (+ y (* x (/ x y))) (* (fabs z) (/ (fabs z) y)))
30.0ms	(+ y (* x (/ x y)))
26.0ms	(* x (/ x y))
24.0ms	(* (fabs z) (/ (fabs z) y))

simplify83.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	472	768
1	2271	662
2	5001	648

prune363.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes115.0ms

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	14	7
1	14	7

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.3s

13627×

body

valid