Details

Time bar (total: 6.0s)

sample44.0ms

Algorithm
intervals
Results
30.0ms417×body80valid

simplify72.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0237
1596
21116
32046
43696
58396
621686
750016

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.4b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma x x (- (* y y) (* z z)))
2.3b
(- (* y y) (* z z))
23.7b
(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

rewrite13.0ms

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:
0.0ms
(fma x x (- (* y y) (* z z)))
3.0ms
(- (* y y) (* z z))
6.0ms
(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

series203.0ms

Counts
3 → 9
Calls
3 calls:
61.0ms
(fma x x (- (* y y) (* z z)))
36.0ms
(- (* 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

prune363.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 9.5b

localize16.0ms

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))
6.2b
(/ (pow z 2) y)
7.8b
(/ (pow x 2) y)

rewrite190.0ms

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:
152.0ms
(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
12.0ms
(+ y (/ (pow x 2) y))
4.0ms
(/ (pow z 2) y)
4.0ms
(/ (pow x 2) y)

series127.0ms

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)
23.0ms
(/ (pow x 2) y)

simplify121.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
09664460
132723145
250012950

prune519.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize256.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (+ y (/ (pow x (/ 2 2)) (/ y x))) (/ (pow z 2) y))
0.0b
(+ y (/ (pow x (/ 2 2)) (/ y x)))
0.1b
(/ (pow x (/ 2 2)) (/ y x))
6.2b
(/ (pow z 2) y)

rewrite461.0ms

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:
397.0ms
(- (+ y (/ (pow x (/ 2 2)) (/ y x))) (/ (pow z 2) y))
31.0ms
(+ y (/ (pow x (/ 2 2)) (/ y x)))
8.0ms
(/ (pow x (/ 2 2)) (/ y x))
5.0ms
(/ (pow z 2) y)

series134.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(- (+ y (/ (pow x (/ 2 2)) (/ y x))) (/ (pow z 2) y))
31.0ms
(+ y (/ (pow x (/ 2 2)) (/ y x)))
22.0ms
(/ (pow x (/ 2 2)) (/ y x))
28.0ms
(/ (pow z 2) y)

simplify86.0ms

Algorithm
egg-herbie
Counts
353 → 353
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
013645425
150014022

prune709.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite431.0ms

Algorithm
rewrite-expression-head
Rules
173×times-frac
105×*-un-lft-identity
104×add-sqr-sqrt
99×add-cube-cbrt
42×unpow-prod-down
22×add-exp-log
14×add-cbrt-cube sqr-pow
13×associate-*r* associate-/r*
11×add-log-exp
10×div-exp div-inv
7×associate-/l*
6×pow1
4×cbrt-undiv expm1-log1p-u fma-neg prod-diff log1p-expm1-u
3×fma-def associate-*r/ associate-*l* distribute-lft-out
2×pow-to-exp flip3-+ diff-log pow-exp prod-exp sum-log frac-sub cbrt-unprod flip-+ unswap-sqr
1×+-commutative sub-neg flip3-- frac-2neg pow-prod-down associate--l+ clear-num associate-/r/ *-commutative flip--
Counts
4 → 209
Calls
4 calls:
374.0ms
(- (+ y (/ (pow x (/ 2 2)) (/ y x))) (* z (/ z y)))
31.0ms
(+ y (/ (pow x (/ 2 2)) (/ y x)))
8.0ms
(/ (pow x (/ 2 2)) (/ y x))
8.0ms
(* z (/ z y))

series131.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (+ y (/ (pow x (/ 2 2)) (/ y x))) (* z (/ z y)))
39.0ms
(+ y (/ (pow x (/ 2 2)) (/ y x)))
22.0ms
(/ (pow x (/ 2 2)) (/ y x))
22.0ms
(* z (/ z y))

simplify145.0ms

Algorithm
egg-herbie
Counts
221 → 221
Iterations

Useful iterations: 2 (124.0ms)

IterNodesCost
08451511
141621304
250011289

prune510.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

regimes70.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0188
1208
2208

end0.0ms

sample1.3s

Algorithm
intervals
Results
1.0s13834×body80valid