Details

Time bar (total: 9.9s)

sample20.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
4.0ms256×pre80true

simplify70.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0236
1526
21176
32406
44786
59476
618446
750016

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 20.8b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(* (- x y) (+ x y))
20.9b
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
10×add-exp-log add-cbrt-cube
8×frac-times flip3-+ flip-+ associate-/l/
7×add-cube-cbrt
6×flip3-- flip--
5×pow1 associate-*l* add-log-exp
4×associate-*r/ associate-*r* associate-*l/
3×expm1-log1p-u times-frac associate-/r* log1p-expm1-u
2×cbrt-undiv div-exp prod-exp associate-/r/ cbrt-unprod
1×+-commutative distribute-rgt-in fma-def frac-2neg distribute-lft-in pow-prod-down clear-num sum-log *-commutative div-inv distribute-lft-out associate-/l* distribute-lft-out-- difference-of-squares unswap-sqr
Counts
3 → 80
Calls
3 calls:
8.0ms
(+ (* x x) (* y y))
8.0ms
(* (- x y) (+ x y))
12.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series129.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (* x x) (* y y))
43.0ms
(* (- x y) (+ x y))
59.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify65.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
0435575
12499504
25001494

prune206.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (hypot x y) (+ x y))
0.0b
(/ (- x y) (/ (hypot x y) (+ x y)))
0.0b
(/ (/ (- x y) (/ (hypot x y) (+ x y))) (sqrt (+ (* x x) (* y y))))
20.1b
(sqrt (+ (* x x) (* y y)))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
1794×times-frac
1230×*-un-lft-identity
977×add-sqr-sqrt
686×add-cube-cbrt
291×sqrt-prod
145×distribute-lft-out-- difference-of-squares
127×distribute-lft-out
103×associate-/l*
94×associate-/r/
51×div-inv
44×flip3-+ flip-+
28×associate-/r*
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×frac-2neg div-sub clear-num associate-/l/
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip-- hypot-def
Counts
4 → 879
Calls
4 calls:
5.0ms
(/ (hypot x y) (+ x y))
12.0ms
(/ (- x y) (/ (hypot x y) (+ x y)))
39.0ms
(/ (/ (- x y) (/ (hypot x y) (+ x y))) (sqrt (+ (* x x) (* y y))))
4.0ms
(sqrt (+ (* x x) (* y y)))

series333.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(/ (hypot x y) (+ x y))
84.0ms
(/ (- x y) (/ (hypot x y) (+ x y)))
121.0ms
(/ (/ (- x y) (/ (hypot x y) (+ x y))) (sqrt (+ (* x x) (* y y))))
42.0ms
(sqrt (+ (* x x) (* y y)))

simplify181.0ms

Algorithm
egg-herbie
Counts
891 → 891
Iterations

Useful iterations: 1 (44.0ms)

IterNodesCost
0227216142
1500114529

prune1.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot x y)
0.0b
(/ (/ (- x y) (hypot x y)) (/ (hypot x y) (+ x y)))
0.0b
(/ (hypot x y) (+ x y))
0.0b
(/ (- x y) (hypot x y))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
894×times-frac
604×*-un-lft-identity
476×add-sqr-sqrt
354×add-cube-cbrt
64×distribute-lft-out
61×distribute-lft-out-- difference-of-squares
43×associate-/r/
42×div-inv
27×associate-/l*
25×associate-/r*
21×flip3-+ flip-+
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg div-sub clear-num associate-/l/
1×hypot-udef flip3-- flip--
Counts
4 → 487
Calls
4 calls:
1.0ms
(hypot x y)
18.0ms
(/ (/ (- x y) (hypot x y)) (/ (hypot x y) (+ x y)))
5.0ms
(/ (hypot x y) (+ x y))
6.0ms
(/ (- x y) (hypot x y))

series310.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(hypot x y)
89.0ms
(/ (/ (- x y) (hypot x y)) (/ (hypot x y) (+ x y)))
87.0ms
(/ (hypot x y) (+ x y))
90.0ms
(/ (- x y) (hypot x y))

simplify101.0ms

Algorithm
egg-herbie
Counts
499 → 499
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
018347484
150017310

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- x y) (hypot x y))
0.0b
(cbrt (/ (/ (- x y) (hypot x y)) (/ (hypot x y) (+ x y))))
0.0b
(cbrt (/ (/ (- x y) (hypot x y)) (/ (hypot x y) (+ x y))))
0.0b
(cbrt (/ (/ (- x y) (hypot x y)) (/ (hypot x y) (+ x y))))

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
2535×times-frac
1633×*-un-lft-identity
1291×add-sqr-sqrt
1041×cbrt-prod
959×add-cube-cbrt
171×distribute-lft-out
166×distribute-lft-out-- difference-of-squares
117×associate-/r/
115×div-inv
57×flip3-+ flip-+
6×add-exp-log add-cbrt-cube
5×associate-/l*
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-div pow1/3 associate-/r*
2×associate-/l/
1×cbrt-undiv flip3-- frac-2neg div-sub div-exp clear-num flip--
Counts
4 → 1114
Calls
4 calls:
12.0ms
(/ (- x y) (hypot x y))
27.0ms
(cbrt (/ (/ (- x y) (hypot x y)) (/ (hypot x y) (+ x y))))
27.0ms
(cbrt (/ (/ (- x y) (hypot x y)) (/ (hypot x y) (+ x y))))
31.0ms
(cbrt (/ (/ (- x y) (hypot x y)) (/ (hypot x y) (+ x y))))

series735.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(/ (- x y) (hypot x y))
226.0ms
(cbrt (/ (/ (- x y) (hypot x y)) (/ (hypot x y) (+ x y))))
203.0ms
(cbrt (/ (/ (- x y) (hypot x y)) (/ (hypot x y) (+ x y))))
217.0ms
(cbrt (/ (/ (- x y) (hypot x y)) (/ (hypot x y) (+ x y))))

simplify227.0ms

Algorithm
egg-herbie
Counts
1126 → 1126
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
0207222784
1500122560

prune3.6s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes70.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
097
197

end0.0ms

sample492.0ms

Algorithm
intervals
Results
228.0ms8000×body80valid
113.0ms8000×pre80true