Details

Time bar (total: 4.1s)

sample30.0ms

Algorithm
intervals
Results
16.0ms465×body80valid

simplify58.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0227
1557
21017
31827
43357
57317
618287
750017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize10.0ms

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))

rewrite51.0ms

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))
15.0ms
(- (+ (* x x) (* y y)) (* z z))
32.0ms
(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

series156.0ms

Counts
3 → 9
Calls
3 calls:
32.0ms
(+ (* x x) (* y y))
41.0ms
(- (+ (* x x) (* y y)) (* z z))
83.0ms
(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

simplify42.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0337520
11492454
25001446

prune167.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 10.8b

localize11.0ms

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)

rewrite255.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
52×times-frac
47×*-un-lft-identity
40×add-cube-cbrt
25×unpow-prod-down
16×add-exp-log associate-/l*
10×associate-*r* add-cbrt-cube
9×unpow2 sqr-pow
6×pow1 div-exp associate-/r* add-log-exp
5×difference-of-squares
4×associate-*r/
3×distribute-rgt-in distribute-lft-in associate-*l*
2×cbrt-undiv pow-to-exp sub-neg frac-2neg flip3-+ pow-exp associate--l+ clear-num frac-sub flip-+ div-inv distribute-lft-out distribute-lft-out--
1×+-commutative flip3-- pow-prod-down prod-exp sum-log *-commutative flip-- cbrt-unprod unswap-sqr
Counts
4 → 145
Calls
4 calls:
11.0ms
(+ y (/ (pow x 2) y))
231.0ms
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
4.0ms
(/ (pow z 2) y)
4.0ms
(/ (pow x 2) y)

series121.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+ y (/ (pow x 2) y))
53.0ms
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
22.0ms
(/ (pow z 2) y)
19.0ms
(/ (pow x 2) y)

simplify65.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0494902
11944815
25003809

prune373.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.8b

localize15.0ms

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)

rewrite345.0ms

Algorithm
rewrite-expression-head
Rules
103×times-frac
79×add-sqr-sqrt
72×*-un-lft-identity
65×add-cube-cbrt
16×add-exp-log associate-/r*
13×unpow-prod-down add-cbrt-cube
11×associate-/l*
10×associate-*r*
6×pow1 div-exp div-inv add-log-exp
5×unpow2 difference-of-squares sqr-pow
4×cbrt-undiv associate-*r/
3×distribute-rgt-in distribute-lft-in associate-*l*
2×sub-neg frac-2neg flip3-+ associate--l+ clear-num frac-sub flip-+ distribute-lft-out 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 → 166
Calls
4 calls:
17.0ms
(+ y (/ x (/ y x)))
4.0ms
(/ x (/ y x))
312.0ms
(* 0.5 (- (+ y (/ x (/ y x))) (/ (pow z 2) y)))
4.0ms
(/ (pow z 2) y)

series124.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(+ y (/ x (/ y x)))
24.0ms
(/ x (/ y x))
54.0ms
(* 0.5 (- (+ y (/ x (/ y x))) (/ (pow z 2) y)))
19.0ms
(/ (pow z 2) y)

simplify90.0ms

Algorithm
egg-herbie
Counts
178 → 178
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
06801113
132161013
250011012

prune437.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite305.0ms

Algorithm
rewrite-expression-head
Rules
85×times-frac
63×add-sqr-sqrt
58×*-un-lft-identity
56×add-cube-cbrt
16×add-exp-log associate-*r* add-cbrt-cube
13×associate-/r*
8×pow1
7×associate-*r/
6×associate-*l* div-inv add-log-exp
4×cbrt-undiv div-exp
3×distribute-rgt-in distribute-lft-in prod-exp cbrt-unprod 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-- distribute-lft-out
Counts
4 → 142
Calls
4 calls:
15.0ms
(+ y (/ x (/ y x)))
7.0ms
(* (fabs z) (/ (fabs z) y))
4.0ms
(/ x (/ y x))
274.0ms
(* 0.5 (- (+ y (/ x (/ y x))) (* (fabs z) (/ (fabs z) y))))

series129.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ y (/ x (/ y x)))
19.0ms
(* (fabs z) (/ (fabs z) y))
18.0ms
(/ x (/ y x))
59.0ms
(* 0.5 (- (+ y (/ x (/ y x))) (* (fabs z) (/ (fabs z) y))))

simplify90.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
06601099
13366989
25002981

prune391.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

regimes94.0ms

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
0159
1159

end0.0ms

sample748.0ms

Algorithm
intervals
Results
462.0ms13650×body80valid