Details

Time bar (total: 2.0s)

sample16.0ms

Algorithm
intervals
Results
4.0ms256×body80valid
1.0ms82×body80nan

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
063
163

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.6b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) y)
18.3b
(sqrt (+ (* x x) y))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt add-log-exp
3×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
2×add-exp-log flip3-+ sqrt-div add-cbrt-cube flip-+
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
2 → 26
Calls
2 calls:
8.0ms
(+ (* x x) y)
10.0ms
(sqrt (+ (* x x) y))

series59.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(+ (* x x) y)
42.0ms
(sqrt (+ (* x x) y))

simplify51.0ms

Algorithm
egg-herbie
Counts
32 → 32
Iterations

Useful iterations: 3 (47.0ms)

IterNodesCost
0141152
1475139
21515138
35002136

prune73.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (sqrt (+ (* x x) y)))
0.5b
(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
18.3b
(sqrt (+ (* x x) y))
18.3b
(sqrt (+ (* x x) y))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod
54×add-sqr-sqrt
38×sqrt-pow1
32×sqrt-div
31×pow1
20×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×flip3-+ associate-*r* associate-*l* pow-prod-up flip-+ unswap-sqr
6×add-exp-log add-cbrt-cube
5×pow-prod-down pow-sqr
4×frac-times rem-sqrt-square add-log-exp
2×associate-*r/ associate-*l/
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 134
Calls
4 calls:
11.0ms
(sqrt (sqrt (+ (* x x) y)))
64.0ms
(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
10.0ms
(sqrt (+ (* x x) y))
12.0ms
(sqrt (+ (* x x) y))

series184.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(sqrt (sqrt (+ (* x x) y)))
37.0ms
(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
41.0ms
(sqrt (+ (* x x) y))
38.0ms
(sqrt (+ (* x x) y))

simplify47.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0264901
11062835
25001816

prune258.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(* 1/2 (/ y x))
0.0b
(+ x (* 1/2 (/ y x)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×associate-*r*
10×add-cube-cbrt *-un-lft-identity times-frac
7×add-exp-log add-cbrt-cube
4×pow1 add-log-exp
3×associate-*l*
2×prod-exp cbrt-unprod unswap-sqr
1×cbrt-undiv +-commutative flip3-+ associate-*r/ div-exp pow-prod-down sum-log *-commutative flip-+ div-inv
Counts
2 → 43
Calls
2 calls:
17.0ms
(* 1/2 (/ y x))
6.0ms
(+ x (* 1/2 (/ y x)))

series37.0ms

Counts
2 → 6
Calls
2 calls:
16.0ms
(* 1/2 (/ y x))
21.0ms
(+ x (* 1/2 (/ y x)))

simplify103.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0223199
1960187
24238187
35003187

prune83.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(* 1/2 (/ y x))
0.0b
(+ x (* 1/2 (/ y x)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×associate-*r*
10×add-cube-cbrt *-un-lft-identity times-frac
7×add-exp-log add-cbrt-cube
4×pow1 add-log-exp
3×associate-*l*
2×prod-exp cbrt-unprod unswap-sqr
1×cbrt-undiv +-commutative flip3-+ associate-*r/ div-exp pow-prod-down sum-log *-commutative flip-+ div-inv
Counts
2 → 43
Calls
2 calls:
14.0ms
(* 1/2 (/ y x))
6.0ms
(+ x (* 1/2 (/ y x)))

series36.0ms

Counts
2 → 6
Calls
2 calls:
16.0ms
(* 1/2 (/ y x))
21.0ms
(+ x (* 1/2 (/ y x)))

simplify102.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0223199
1960187
24238187
35003187

prune84.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0.0b

regimes163.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 21.0b

bsearch40.0ms

Steps
ItersRangePoint
7
7.569922578618304e+138
1.3358441697394925e+141
7.483080572797597e+140
9
-8.37881605524702e+155
-1.6181289332921645e+150
-1.3467905082205938e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02210
12910
23110
33110

end0.0ms

sample423.0ms

Algorithm
intervals
Results
140.0ms8000×body80valid
48.0ms2726×body80nan