Details

Time bar (total: 4.6s)

sample29.0ms

Algorithm
intervals
Results
16.0ms465×body80valid

simplify55.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0237
1596
21116
32046
43696
58396
621686
750016

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
3.6b
(- (+ (* x x) (* y y)) (* z z))
28.2b
(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

rewrite59.0ms

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))

series146.0ms

Counts
3 → 9
Calls
3 calls:
25.0ms
(+ (* x x) (* y y))
43.0ms
(- (+ (* x x) (* y y)) (* z z))
78.0ms
(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

simplify39.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0365571
11599486
25002469

prune184.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 10.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ y (/ (pow x 2) y))
0.2b
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
10.0b
(/ (pow z 2) y)
10.3b
(/ (pow x 2) y)

rewrite334.0ms

Algorithm
rewrite-expression-head
Rules
336×*-un-lft-identity
244×times-frac
231×add-sqr-sqrt
224×prod-diff
217×add-cube-cbrt
115×distribute-rgt-in distribute-lft-in
97×unpow-prod-down
58×distribute-lft-out
33×unpow2 sqr-pow
16×add-exp-log associate-/l*
10×associate-*r* add-cbrt-cube div-inv
6×pow1 div-exp associate-/r* add-log-exp
5×difference-of-squares
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×fma-def associate-*l*
2×cbrt-undiv pow-to-exp sub-neg frac-2neg flip3-+ pow-exp associate--l+ clear-num frac-sub flip-+ distribute-lft-out--
1×+-commutative flip3-- pow-prod-down prod-exp sum-log *-commutative flip-- cbrt-unprod unswap-sqr
Counts
4 → 380
Calls
4 calls:
12.0ms
(+ y (/ (pow x 2) y))
288.0ms
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
4.0ms
(/ (pow z 2) y)
5.0ms
(/ (pow x 2) y)

series123.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ y (/ (pow x 2) y))
51.0ms
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
18.0ms
(/ (pow z 2) y)
24.0ms
(/ (pow x 2) y)

simplify156.0ms

Algorithm
egg-herbie
Counts
392 → 392
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
012698538
148036226
250016222

prune481.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ y (/ x (/ y x)))
0.2b
(/ x (/ y x))
0.2b
(* 0.5 (- (+ y (/ x (/ y x))) (/ (pow z 2) y)))
10.0b
(/ (pow z 2) y)

rewrite434.0ms

Algorithm
rewrite-expression-head
Rules
361×*-un-lft-identity
295×times-frac
256×add-sqr-sqrt
242×add-cube-cbrt
224×prod-diff
115×distribute-rgt-in distribute-lft-in
85×unpow-prod-down
58×distribute-lft-out
29×unpow2 sqr-pow
16×add-exp-log associate-/r*
14×div-inv
13×add-cbrt-cube
11×associate-/l*
10×associate-*r*
6×pow1 div-exp add-log-exp
5×difference-of-squares
4×cbrt-undiv expm1-log1p-u associate-*r/ log1p-expm1-u
3×fma-def associate-*l*
2×sub-neg frac-2neg flip3-+ associate--l+ clear-num frac-sub flip-+ distribute-lft-out--
1×+-commutative pow-to-exp flip3-- pow-prod-down pow-exp prod-exp sum-log associate-/r/ *-commutative flip-- cbrt-unprod unswap-sqr
Counts
4 → 401
Calls
4 calls:
19.0ms
(+ y (/ x (/ y x)))
5.0ms
(/ x (/ y x))
378.0ms
(* 0.5 (- (+ y (/ x (/ y x))) (/ (pow z 2) y)))
4.0ms
(/ (pow z 2) y)

series121.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+ y (/ x (/ y x)))
17.0ms
(/ x (/ y x))
58.0ms
(* 0.5 (- (+ y (/ x (/ y x))) (/ (pow z 2) y)))
19.0ms
(/ (pow z 2) y)

simplify94.0ms

Algorithm
egg-herbie
Counts
413 → 413
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
014548749
150016247

prune542.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ y (/ x (/ y x)))
0.2b
(* z (/ z y))
0.2b
(/ x (/ y x))
0.2b
(* 0.5 (- (+ y (/ x (/ y x))) (* z (/ z y))))

rewrite359.0ms

Algorithm
rewrite-expression-head
Rules
85×times-frac
66×add-sqr-sqrt
65×*-un-lft-identity
59×add-cube-cbrt
16×add-exp-log associate-*r* add-cbrt-cube
13×associate-/r*
8×pow1 prod-diff
7×distribute-rgt-in distribute-lft-in associate-*r/
6×associate-*l* div-inv add-log-exp
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×fma-def prod-exp cbrt-unprod distribute-lft-out associate-/l* unswap-sqr
2×sub-neg flip3-+ pow-prod-down associate--l+ *-commutative frac-sub flip-+
1×+-commutative flip3-- frac-2neg clear-num sum-log associate-/r/ flip--
Counts
4 → 161
Calls
4 calls:
18.0ms
(+ y (/ x (/ y x)))
7.0ms
(* z (/ z y))
5.0ms
(/ x (/ y x))
323.0ms
(* 0.5 (- (+ y (/ x (/ y x))) (* z (/ z y))))

series120.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(+ y (/ x (/ y x)))
23.0ms
(* z (/ z y))
18.0ms
(/ x (/ y x))
52.0ms
(* 0.5 (- (+ y (/ x (/ y x))) (* z (/ z y))))

simplify91.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
06971138
135211017
250011016

prune359.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

regimes69.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0147
1147

end0.0ms

sample752.0ms

Algorithm
intervals
Results
474.0ms13650×body80valid