Details

Time bar (total: 4.1s)

sample29.0ms

Algorithm
intervals
Results
15.0ms440×body80valid

simplify65.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0237
1596
21116
32046
43696
58396
621686
750016

prune7.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (fma x x (- (* y y) (* z z))) 2.0)
0.3b
(fma x x (- (* y y) (* z z)))
6.1b
(- (* y y) (* z z))
28.4b
(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
54×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
11×add-exp-log add-cbrt-cube
6×associate-/r* div-inv add-log-exp
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
2×frac-2neg clear-num
1×sub-neg flip3-- fma-neg diff-log prod-diff flip-- fma-udef associate-/l/ difference-of-squares
Counts
4 → 128
Calls
4 calls:
2.0ms
(/ (fma x x (- (* y y) (* z z))) 2.0)
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)

series259.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(/ (fma x x (- (* y y) (* z z))) 2.0)
57.0ms
(fma x x (- (* y y) (* z z)))
34.0ms
(- (* y y) (* z z))
98.0ms
(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

simplify79.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
04881385
119481287
250021284

prune444.0ms

Filtered
140 candidates to 112 candidates (80.0%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.2b

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))
9.9b
(/ (pow x 2) y)
11.1b
(/ (pow z 2) y)

rewrite191.0ms

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:
156.0ms
(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
12.0ms
(+ y (/ (pow x 2) y))
4.0ms
(/ (pow x 2) y)
5.0ms
(/ (pow z 2) y)

series121.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
36.0ms
(+ y (/ (pow x 2) y))
20.0ms
(/ (pow x 2) y)
21.0ms
(/ (pow z 2) y)

simplify124.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
09664460
132723145
250012953

prune502.0ms

Filtered
272 candidates to 118 candidates (43.4%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.7b

localize12.0ms

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))
0.2b
(* z (/ z y))
9.9b
(/ (pow x 2) y)

rewrite173.0ms

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:
142.0ms
(- (+ y (/ (pow x 2) y)) (* z (/ z y)))
12.0ms
(+ y (/ (pow x 2) y))
8.0ms
(* z (/ z y))
5.0ms
(/ (pow x 2) y)

series121.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (+ y (/ (pow x 2) y)) (* z (/ z y)))
31.0ms
(+ y (/ (pow x 2) y))
20.0ms
(* z (/ z y))
21.0ms
(/ (pow x 2) y)

simplify70.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
0460747
11930676
25001670

prune370.0ms

Filtered
140 candidates to 95 candidates (67.9%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ y (* (fabs x) (/ (fabs x) y)))
0.0b
(- (+ y (* (fabs x) (/ (fabs x) y))) (* z (/ z y)))
0.2b
(* z (/ z y))
0.2b
(* (fabs x) (/ (fabs x) 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:
2.0ms
(+ y (* (fabs x) (/ (fabs x) y)))
15.0ms
(- (+ y (* (fabs x) (/ (fabs x) y))) (* z (/ z y)))
7.0ms
(* z (/ z y))
8.0ms
(* (fabs x) (/ (fabs x) y))

series124.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ y (* (fabs x) (/ (fabs x) y)))
53.0ms
(- (+ y (* (fabs x) (/ (fabs x) y))) (* z (/ z y)))
20.0ms
(* z (/ z y))
22.0ms
(* (fabs x) (/ (fabs x) y))

simplify77.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
0476812
12298717
25001703

prune334.0ms

Filtered
120 candidates to 88 candidates (73.3%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes104.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0169
1169

end0.0ms

sample783.0ms

Algorithm
intervals
Results
478.0ms13668×body80valid