Details

Time bar (total: 5.6s)

sample29.0ms

Algorithm
intervals
Results
15.0ms428×body80valid

simplify76.0ms

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: 30.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.8b
(fma x x (- (* y y) (* z z)))
5.6b
(- (* y y) (* z z))
28.4b
(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

rewrite16.0ms

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)))
4.0ms
(- (* y y) (* z z))
7.0ms
(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

series201.0ms

Counts
3 → 9
Calls
3 calls:
55.0ms
(fma x x (- (* y y) (* z z)))
43.0ms
(- (* y y) (* z z))
103.0ms
(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

simplify64.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
04661096
118811029
250011026

prune375.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 14.0b

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)

rewrite81.0ms

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:
41.0ms
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
6.0ms
(/ (pow x 2) y)
6.0ms
(/ (pow z 2) y)

series117.0ms

Counts
3 → 9
Calls
3 calls:
63.0ms
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
22.0ms
(/ (pow x 2) y)
31.0ms
(/ (pow z 2) y)

simplify425.0ms

Algorithm
egg-herbie
Counts
372 → 372
Iterations

Useful iterations: 2 (118.0ms)

IterNodesCost
012568458
147586147
250016143

prune527.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.0b

localize14.0ms

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)

rewrite109.0ms

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:
7.0ms
(/ z (/ y z))
45.0ms
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ z (/ y z))))
6.0ms
(/ (pow x 2) y)

series113.0ms

Counts
3 → 9
Calls
3 calls:
21.0ms
(/ z (/ y z))
70.0ms
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ z (/ y z))))
22.0ms
(/ (pow x 2) y)

simplify175.0ms

Algorithm
egg-herbie
Counts
519 → 519
Iterations

Useful iterations: 1 (54.0ms)

IterNodesCost
0186415006
1500111885

prune851.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

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))))

rewrite140.0ms

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:
6.0ms
(/ z (/ y z))
10.0ms
(/ (pow x (/ 2 2)) (/ y x))
63.0ms
(* 0.5 (- (+ y (/ (pow x (/ 2 2)) (/ y x))) (/ z (/ y z))))

series114.0ms

Counts
3 → 9
Calls
3 calls:
21.0ms
(/ z (/ y z))
29.0ms
(/ (pow x (/ 2 2)) (/ y x))
64.0ms
(* 0.5 (- (+ y (/ (pow x (/ 2 2)) (/ y x))) (/ z (/ y z))))

simplify194.0ms

Algorithm
egg-herbie
Counts
600 → 600
Iterations

Useful iterations: 1 (56.0ms)

IterNodesCost
0224116373
1500113992

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

regimes144.0ms

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
0189
1189

end0.0ms

sample790.0ms

Algorithm
intervals
Results
484.0ms13842×body80valid