Details

Time bar (total: 2.7s)

sample28.0ms

Algorithm
intervals
Results
13.0ms256×body80valid

simplify33.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0189
1369
2689
31179
41749
51959
61979
71979

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* (* y 4.0) y))
5.3b
(- (* x x) (* (* y 4.0) y))
28.9b
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
7×add-log-exp
5×add-exp-log add-cbrt-cube
3×pow1 associate-/r* associate-/l*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg frac-2neg diff-log div-sub div-exp clear-num sum-log div-inv
Counts
3 → 55
Calls
3 calls:
3.0ms
(+ (* x x) (* (* y 4.0) y))
2.0ms
(- (* x x) (* (* y 4.0) y))
10.0ms
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series147.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(+ (* x x) (* (* y 4.0) y))
47.0ms
(- (* x x) (* (* y 4.0) y))
63.0ms
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify41.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0234680
11007622
25001620

prune143.0ms

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
(+ (* x x) (* (* y 4.0) y))
0.0b
(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
22.5b
(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
22.9b
(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
10×*-un-lft-identity
8×add-cube-cbrt associate-/r/ add-log-exp
7×times-frac
6×associate-/r*
5×cbrt-undiv flip3-+ div-exp flip-+
4×pow1 prod-exp cbrt-unprod div-inv
3×distribute-rgt-out--
2×frac-2neg clear-num associate-/l* difference-of-squares
1×+-commutative sub-neg flip3-- diff-log sum-log frac-sub flip-- distribute-lft-out-- sub-div
Counts
4 → 79
Calls
4 calls:
3.0ms
(+ (* x x) (* (* y 4.0) y))
31.0ms
(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
6.0ms
(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
10.0ms
(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

series215.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(+ (* x x) (* (* y 4.0) y))
72.0ms
(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
49.0ms
(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
56.0ms
(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

simplify52.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0396987
11942882
25001881

prune179.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

22.9b
(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
22.9b
(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
27.5b
(sqrt (+ (* x x) (* (* y 4.0) y)))
27.5b
(sqrt (+ (* x x) (* (* y 4.0) y)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-undiv times-frac div-exp prod-exp associate-/r* sqrt-prod cbrt-unprod
4×flip3-+ sqrt-div associate-/r/ flip-+ add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num div-inv associate-/l*
Counts
4 → 80
Calls
4 calls:
10.0ms
(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
10.0ms
(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
3.0ms
(sqrt (+ (* x x) (* (* y 4.0) y)))
6.0ms
(sqrt (+ (* x x) (* (* y 4.0) y)))

series224.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
58.0ms
(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
56.0ms
(sqrt (+ (* x x) (* (* y 4.0) y)))
54.0ms
(sqrt (+ (* x x) (* (* y 4.0) y)))

simplify46.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0248798
11252680
25001678

prune255.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 4 expressions with local error:

22.9b
(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
27.5b
(sqrt (+ (* x x) (* (* y 4.0) y)))
27.5b
(sqrt (+ (* x x) (* (* y 4.0) y)))
27.5b
(sqrt (+ (* x x) (* (* y 4.0) y)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity sqrt-prod
7×pow1
6×sqrt-div
4×flip3-+ flip-+ add-log-exp
3×cbrt-undiv rem-sqrt-square sqrt-pow1 times-frac pow1/2 div-exp prod-exp associate-/r* cbrt-unprod
2×associate-/r/
1×frac-2neg clear-num div-inv associate-/l*
Counts
4 → 70
Calls
4 calls:
12.0ms
(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
3.0ms
(sqrt (+ (* x x) (* (* y 4.0) y)))
4.0ms
(sqrt (+ (* x x) (* (* y 4.0) y)))
3.0ms
(sqrt (+ (* x x) (* (* y 4.0) y)))

series211.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
50.0ms
(sqrt (+ (* x x) (* (* y 4.0) y)))
53.0ms
(sqrt (+ (* x x) (* (* y 4.0) y)))
50.0ms
(sqrt (+ (* x x) (* (* y 4.0) y)))

simplify40.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0248645
11252578
25001575

prune263.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.3b

regimes145.0ms

Accuracy

62.2% (11.9b remaining)

Error of 12.2b against oracle of 0.3b and baseline of 31.8b

bsearch139.0ms

Steps
ItersRangePoint
11
5.10808278574109e+145
3.366560557353129e+171
1.2142912145306137e+146
8
3.382408398818948e-133
1.7648023804592677e-130
1.5260934382653551e-130
8
-1.475295989046636e-148
-3.994845717138672e-153
-7.276729573857139e-151
7
-6.579287999353623e+83
-2.1130938932944453e+82
-6.485144449769119e+83

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03029
13029

end0.0ms

sample360.0ms

Algorithm
intervals
Results
225.0ms8000×body80valid