Details

Time bar (total: 4.7s)

sample26.0ms

Algorithm
intervals
Results
14.0ms434×body80valid

simplify74.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0237
1596
21116
32046
43696
58396
621686
750016

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.7b

localize15.0ms

Local error

Found 3 expressions with local error:

0.3b
(fma x x (- (* y y) (* z z)))
3.5b
(- (* y y) (* z z))
23.9b
(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

rewrite17.0ms

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

series198.0ms

Counts
3 → 9
Calls
3 calls:
58.0ms
(fma x x (- (* y y) (* z z)))
34.0ms
(- (* y y) (* z z))
105.0ms
(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

simplify62.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04661096
118811029
250011026

prune376.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ y (/ (pow x 2) y))
0.0b
(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
8.6b
(/ (pow z 2) y)
9.2b
(/ (pow x 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:
10.0ms
(+ y (/ (pow x 2) y))
24.0ms
(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
5.0ms
(/ (pow z 2) y)
6.0ms
(/ (pow x 2) y)

series143.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(+ y (/ (pow x 2) y))
52.0ms
(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
23.0ms
(/ (pow z 2) y)
28.0ms
(/ (pow x 2) y)

simplify115.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
09664460
132723145
250012950

prune495.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ y (/ (pow x (/ 2 2)) (/ y x)))
0.0b
(- (+ y (/ (pow x (/ 2 2)) (/ y x))) (/ (pow z 2) y))
0.2b
(/ (pow x (/ 2 2)) (/ y x))
8.6b
(/ (pow z 2) y)

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
287×times-frac
260×*-un-lft-identity
207×add-sqr-sqrt
195×add-cube-cbrt
112×prod-diff
91×unpow-prod-down
31×distribute-lft-out sqr-pow
22×add-exp-log
17×unpow2
16×associate-/r*
15×associate-/l*
14×div-inv
12×div-exp
11×add-cbrt-cube add-log-exp
5×difference-of-squares
4×pow1 cbrt-undiv expm1-log1p-u fma-neg log1p-expm1-u
3×pow-to-exp fma-def pow-exp
2×frac-2neg flip3-+ diff-log clear-num sum-log frac-sub flip-+ distribute-lft-out--
1×+-commutative sub-neg flip3-- associate--l+ associate-/r/ flip--
Counts
4 → 341
Calls
4 calls:
27.0ms
(+ y (/ (pow x (/ 2 2)) (/ y x)))
39.0ms
(- (+ y (/ (pow x (/ 2 2)) (/ y x))) (/ (pow z 2) y))
9.0ms
(/ (pow x (/ 2 2)) (/ y x))
5.0ms
(/ (pow z 2) y)

series124.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ y (/ (pow x (/ 2 2)) (/ y x)))
52.0ms
(- (+ y (/ (pow x (/ 2 2)) (/ y x))) (/ (pow z 2) y))
21.0ms
(/ (pow x (/ 2 2)) (/ y x))
20.0ms
(/ (pow z 2) y)

simplify84.0ms

Algorithm
egg-herbie
Counts
353 → 353
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
013645425
150014022

prune669.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ y (/ (pow x (/ 2 2)) (/ y x)))
0.0b
(- (+ y (/ (pow x (/ 2 2)) (/ y x))) (/ z (/ y z)))
0.1b
(/ z (/ y z))
0.2b
(/ (pow x (/ 2 2)) (/ y x))

rewrite120.0ms

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:
23.0ms
(+ y (/ (pow x (/ 2 2)) (/ y x)))
49.0ms
(- (+ y (/ (pow x (/ 2 2)) (/ y x))) (/ z (/ y z)))
6.0ms
(/ z (/ y z))
9.0ms
(/ (pow x (/ 2 2)) (/ y x))

series125.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ y (/ (pow x (/ 2 2)) (/ y x)))
52.0ms
(- (+ y (/ (pow x (/ 2 2)) (/ y x))) (/ z (/ y z)))
20.0ms
(/ z (/ y z))
23.0ms
(/ (pow x (/ 2 2)) (/ y x))

simplify113.0ms

Algorithm
egg-herbie
Counts
436 → 436
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
018348768
150016850

prune952.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes72.0ms

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)

IterNodesCost
0188
1198
2198

end0.0ms

sample707.0ms

Algorithm
intervals
Results
440.0ms13668×body80valid