Details

sample52.0ms

Algorithm

intervals

Results

38.0ms

418×

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: 31.3b

localize11.0ms

Local error

Found 2 expressions with local error:

4.0b	(- (+ (* x x) (* y y)) (* z z))
29.0b	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

rewrite59.0ms

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:

19.0ms	(- (+ (* x x) (* y y)) (* z z))
39.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

series145.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(- (+ (* x x) (* y y)) (* z z))
97.0ms	(/ (- (+ (* 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

prune192.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 12.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
8.6b	(/ (pow z 2) y)
11.6b	(/ (pow x 2) y)

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 243

Calls

3 calls:

158.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
4.0ms	(/ (pow z 2) y)
5.0ms	(/ (pow x 2) y)

series97.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
22.0ms	(/ (pow z 2) y)
22.0ms	(/ (pow x 2) y)

simplify120.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	957	4380
1	3231	3066
2	5002	2871

prune485.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ y (/ x (/ y x))) (/ (pow z 2) y))
0.3b	(/ x (/ y x))
8.6b	(/ (pow z 2) y)

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

214×	`*-un-lft-identity`
199×	`times-frac`
163×	`add-sqr-sqrt`
151×	`add-cube-cbrt`
112×	`prod-diff`
49×	`unpow-prod-down`
30×	`distribute-lft-out`
17×	`unpow2` `sqr-pow`
16×	`associate-/r*`
13×	`add-exp-log`
11×	`associate-/l*`
10×	`add-cbrt-cube` `div-inv`
8×	`add-log-exp`
6×	`div-exp`
5×	`difference-of-squares`
4×	`cbrt-undiv` `fma-neg`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`frac-2neg` `diff-log` `clear-num` `frac-sub` `distribute-lft-out--`
1×	`pow-to-exp` `sub-neg` `flip3--` `flip3-+` `pow-exp` `associate--l+` `sum-log` `associate-/r/` `flip--` `flip-+`

Counts

3 → 264

Calls

3 calls:

221.0ms	(- (+ y (/ x (/ y x))) (/ (pow z 2) y))
5.0ms	(/ x (/ y x))
5.0ms	(/ (pow z 2) y)

series97.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(- (+ y (/ x (/ y x))) (/ (pow z 2) y))
21.0ms	(/ x (/ y x))
23.0ms	(/ (pow z 2) y)

simplify149.0ms

Algorithm

egg-herbie

Counts

273 → 273

Iterations

Useful iterations: 2 (113.0ms)

Iter	Nodes	Cost
0	1142	4591
1	4554	3151
2	5001	3146

prune582.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ y (/ x (/ y x))) (* (fabs z) (/ (fabs z) y)))
0.2b	(* (fabs z) (/ (fabs z) y))
0.3b	(/ x (/ y x))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

85×	`times-frac`
60×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
55×	`add-cube-cbrt`
13×	`add-exp-log` `associate-r` `associate-/r*` `add-cbrt-cube`
8×	`add-log-exp`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv` `fma-neg` `div-exp` `prod-diff`
3×	`expm1-log1p-u` `associate-r/` `associate-l` `log1p-expm1-u` `associate-/l`
2×	`diff-log` `prod-exp` `frac-sub` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`
1×	`sub-neg` `flip3--` `frac-2neg` `flip3-+` `pow-prod-down` `associate--l+` `clear-num` `sum-log` `associate-/r/` `*-commutative` `flip--` `flip-+`

Counts

3 → 132

Calls

3 calls:

207.0ms	(- (+ y (/ x (/ y x))) (* (fabs z) (/ (fabs z) y)))
7.0ms	(* (fabs z) (/ (fabs z) y))
5.0ms	(/ x (/ y x))

series94.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(- (+ y (/ x (/ y x))) (* (fabs z) (/ (fabs z) y)))
23.0ms	(* (fabs z) (/ (fabs z) y))
23.0ms	(/ x (/ y x))

simplify102.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	622	1033
1	3048	919
2	5001	898

prune422.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes96.0ms

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	19	10
1	19	10

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.2s

13616×

body

valid