Details

Time bar (total: 3.6s)

sample27.0ms

Algorithm
intervals
Results
14.0ms428×body80valid

simplify51.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0227
1557
21017
31827
43357
57317
618287
750017

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize9.0ms

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))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
8×add-exp-log add-sqr-sqrt add-cbrt-cube
5×add-cube-cbrt *-un-lft-identity
4×times-frac associate-/l*
3×pow1 difference-of-squares
2×cbrt-undiv flip3-- diff-log div-exp sum-log flip-- associate-/l/
1×+-commutative sub-neg frac-2neg flip3-+ div-sub prod-exp associate--l+ clear-num associate-/r* cbrt-unprod flip-+ div-inv
Counts
3 → 52
Calls
3 calls:
3.0ms
(+ (* x x) (* y y))
18.0ms
(- (+ (* x x) (* y y)) (* z z))
29.0ms
(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

series143.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(+ (* x x) (* y y))
42.0ms
(- (+ (* x x) (* y y)) (* z z))
75.0ms
(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

simplify39.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0337520
11492454
25001446

prune155.0ms

Filtered
61 candidates to 46 candidates (75.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 13.0b

localize13.0ms

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)

rewrite274.0ms

Algorithm
rewrite-expression-head
Rules
53×add-sqr-sqrt
52×times-frac
44×*-un-lft-identity
39×add-cube-cbrt
25×unpow-prod-down
16×associate-/l*
15×add-exp-log
10×associate-*r*
9×add-cbrt-cube unpow2 sqr-pow
6×div-exp associate-/r*
5×pow1 difference-of-squares
4×associate-*r/
3×distribute-rgt-in distribute-lft-in associate-*l* add-log-exp
2×cbrt-undiv pow-to-exp sub-neg frac-2neg pow-exp associate--l+ clear-num frac-sub div-inv distribute-lft-out--
1×flip3-- flip3-+ pow-prod-down prod-exp *-commutative flip-- cbrt-unprod flip-+ distribute-lft-out unswap-sqr
Counts
3 → 133
Calls
3 calls:
257.0ms
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
4.0ms
(/ (pow x 2) y)
4.0ms
(/ (pow z 2) y)

series93.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
17.0ms
(/ (pow x 2) y)
22.0ms
(/ (pow z 2) y)

simplify58.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0481830
11901743
25003737

prune331.0ms

Filtered
142 candidates to 90 candidates (63.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.0b

localize10.0ms

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)

rewrite260.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
75×add-sqr-sqrt
69×*-un-lft-identity
64×add-cube-cbrt
16×associate-/r*
15×add-exp-log
12×unpow-prod-down add-cbrt-cube
11×associate-/l*
8×associate-*r*
6×div-exp div-inv
5×pow1
4×cbrt-undiv associate-*r/ unpow2 sqr-pow
3×distribute-rgt-in distribute-lft-in associate-*l* 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 associate-/r/ *-commutative flip-- cbrt-unprod flip-+ distribute-lft-out unswap-sqr
Counts
3 → 152
Calls
3 calls:
4.0ms
(/ z (/ y z))
245.0ms
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ z (/ y z))))
4.0ms
(/ (pow x 2) y)

series89.0ms

Counts
3 → 9
Calls
3 calls:
18.0ms
(/ z (/ y z))
53.0ms
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ z (/ y z))))
18.0ms
(/ (pow x 2) y)

simplify86.0ms

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
06521026
13142928
25001927

prune376.0ms

Filtered
161 candidates to 106 candidates (65.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
88×times-frac
71×add-sqr-sqrt
57×*-un-lft-identity
55×add-cube-cbrt
20×associate-*r*
15×add-exp-log add-cbrt-cube
13×associate-/r*
7×pow1
6×associate-*l* div-inv
5×associate-*r/
4×cbrt-undiv div-exp
3×distribute-rgt-in distribute-lft-in prod-exp cbrt-unprod associate-/l* add-log-exp difference-of-squares unswap-sqr
2×sub-neg pow-prod-down associate--l+ *-commutative frac-sub
1×flip3-- frac-2neg flip3-+ clear-num associate-/r/ flip-- flip-+ distribute-lft-out--
Counts
3 → 134
Calls
3 calls:
5.0ms
(/ z (/ y z))
7.0ms
(* x (/ x y))
81.0ms
(* 0.5 (- (+ y (* x (/ x y))) (/ z (/ y z))))

series90.0ms

Counts
3 → 9
Calls
3 calls:
18.0ms
(/ z (/ y z))
21.0ms
(* x (/ x y))
52.0ms
(* 0.5 (- (+ y (* x (/ x y))) (/ z (/ y z))))

simplify89.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
0668918
13414833
25001833

prune291.0ms

Filtered
143 candidates to 97 candidates (67.8%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

regimes103.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0147
1147

end0.0ms

sample808.0ms

Algorithm
intervals
Results
492.0ms13842×body80valid