Details

Time bar (total: 6.9s)

sample27.0ms

Algorithm
intervals
Results
14.0ms428×body80valid

simplify61.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0237
1596
21116
32046
43696
58396
621686
750016

prune5.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
6.2b
(- (+ (* x x) (* y y)) (* z z))
28.4b
(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-log-exp
8×add-exp-log add-cbrt-cube
7×add-cube-cbrt *-un-lft-identity
4×times-frac associate-/l*
3×pow1 expm1-log1p-u fma-neg prod-diff log1p-expm1-u difference-of-squares
2×cbrt-undiv flip3-- diff-log div-exp sum-log flip-- associate-/l/
1×+-commutative sub-neg fma-def frac-2neg flip3-+ div-sub prod-exp associate--l+ clear-num associate-/r* cbrt-unprod flip-+ div-inv
Counts
3 → 65
Calls
3 calls:
3.0ms
(+ (* x x) (* y y))
20.0ms
(- (+ (* x x) (* y y)) (* z z))
35.0ms
(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

series160.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(+ (* x x) (* y y))
46.0ms
(- (+ (* x x) (* y y)) (* z z))
86.0ms
(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

simplify46.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0365571
11599486
25002469

prune230.0ms

Filtered
74 candidates to 57 candidates (77.0%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 13.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.4b
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
10.1b
(/ (pow x 2) y)
10.5b
(/ (pow z 2) y)

rewrite349.0ms

Algorithm
rewrite-expression-head
Rules
332×*-un-lft-identity
244×times-frac
229×add-sqr-sqrt
224×prod-diff
215×add-cube-cbrt
115×distribute-rgt-in distribute-lft-in
97×unpow-prod-down
57×distribute-lft-out
33×unpow2 sqr-pow
16×associate-/l*
15×add-exp-log
10×associate-*r* div-inv
9×add-cbrt-cube
6×div-exp associate-/r*
5×pow1 difference-of-squares
4×associate-*r/
3×expm1-log1p-u associate-*l* log1p-expm1-u add-log-exp
2×cbrt-undiv pow-to-exp sub-neg frac-2neg pow-exp associate--l+ clear-num frac-sub distribute-lft-out--
1×flip3-- flip3-+ pow-prod-down prod-exp *-commutative flip-- cbrt-unprod flip-+ unswap-sqr
Counts
3 → 363
Calls
3 calls:
312.0ms
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
4.0ms
(/ (pow x 2) y)
5.0ms
(/ (pow z 2) y)

series128.0ms

Counts
3 → 9
Calls
3 calls:
72.0ms
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
31.0ms
(/ (pow x 2) y)
25.0ms
(/ (pow z 2) y)

simplify176.0ms

Algorithm
egg-herbie
Counts
372 → 372
Iterations

Useful iterations: 2 (105.0ms)

IterNodesCost
012568458
147586147
250016143

prune551.0ms

Filtered
372 candidates to 114 candidates (30.6%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ z (/ y z))
0.4b
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ z (/ y z))))
10.1b
(/ (pow x 2) y)

rewrite416.0ms

Algorithm
rewrite-expression-head
Rules
630×times-frac
613×*-un-lft-identity
443×add-sqr-sqrt
432×add-cube-cbrt
352×prod-diff
179×distribute-rgt-in distribute-lft-in
89×distribute-lft-out
38×div-inv
16×associate-/r*
15×add-exp-log
12×unpow-prod-down add-cbrt-cube
11×associate-/l*
9×associate-/r/
8×associate-*r*
6×div-exp
5×pow1
4×cbrt-undiv associate-*r/ unpow2 sqr-pow
3×expm1-log1p-u associate-*l* log1p-expm1-u add-log-exp difference-of-squares
2×sub-neg frac-2neg associate--l+ clear-num frac-sub distribute-lft-out--
1×pow-to-exp flip3-- flip3-+ pow-prod-down pow-exp prod-exp *-commutative flip-- cbrt-unprod flip-+ unswap-sqr
Counts
3 → 510
Calls
3 calls:
5.0ms
(/ z (/ y z))
347.0ms
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ z (/ y z))))
9.0ms
(/ (pow x 2) y)

series128.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(/ z (/ y z))
72.0ms
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ z (/ y z))))
25.0ms
(/ (pow x 2) y)

simplify169.0ms

Algorithm
egg-herbie
Counts
519 → 519
Iterations

Useful iterations: 1 (53.0ms)

IterNodesCost
0186415006
1500111885

prune898.0ms

Filtered
519 candidates to 185 candidates (35.6%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ z (/ y z))
0.2b
(/ (pow x (/ 2 2)) (/ y x))
0.4b
(* 0.5 (- (+ y (/ (pow x (/ 2 2)) (/ y x))) (/ z (/ y z))))

rewrite857.0ms

Algorithm
rewrite-expression-head
Rules
769×times-frac
680×*-un-lft-identity
510×add-sqr-sqrt
499×add-cube-cbrt
352×prod-diff
179×distribute-rgt-in distribute-lft-in
89×distribute-lft-out
46×div-inv
42×unpow-prod-down
26×associate-/r*
23×add-exp-log
15×add-cbrt-cube
14×sqr-pow
12×div-exp
10×associate-/r/ associate-/l*
8×associate-*r*
6×cbrt-undiv
5×pow1
4×associate-*r/
3×expm1-log1p-u associate-*l* log1p-expm1-u add-log-exp difference-of-squares
2×pow-to-exp sub-neg frac-2neg pow-exp associate--l+ clear-num frac-sub distribute-lft-out--
1×flip3-- flip3-+ pow-prod-down prod-exp *-commutative flip-- cbrt-unprod flip-+ unswap-sqr
Counts
3 → 591
Calls
3 calls:
5.0ms
(/ z (/ y z))
8.0ms
(/ (pow x (/ 2 2)) (/ y x))
786.0ms
(* 0.5 (- (+ y (/ (pow x (/ 2 2)) (/ y x))) (/ z (/ y z))))

series132.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(/ z (/ y z))
25.0ms
(/ (pow x (/ 2 2)) (/ y x))
82.0ms
(* 0.5 (- (+ y (/ (pow x (/ 2 2)) (/ y x))) (/ z (/ y z))))

simplify203.0ms

Algorithm
egg-herbie
Counts
600 → 600
Iterations

Useful iterations: 1 (57.0ms)

IterNodesCost
0224717421
1500214570

prune1.1s

Filtered
600 candidates to 224 candidates (37.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

regimes133.0ms

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 (0.0ms)

IterNodesCost
0198
1218
2218

end0.0ms

sample998.0ms

Algorithm
intervals
Results
707.0ms13842×body80valid