Details

Time bar (total: 3.0s)

sample15.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
2.0ms80×body80nan

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
073
173

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.8b

localize4.0ms

Local error

Found 1 expressions with local error:

21.3b
(sqrt (+ (* x x) y))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt
3×sqrt-prod
2×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
1×add-exp-log expm1-log1p-u rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ hypot-def log1p-expm1-u add-log-exp
Counts
1 → 18
Calls
1 calls:
9.0ms
(sqrt (+ (* x x) y))

series38.0ms

Counts
1 → 3
Calls
1 calls:
38.0ms
(sqrt (+ (* x x) y))

simplify141.0ms

Algorithm
egg-herbie
Counts
21 → 21
Iterations

Useful iterations: 3 (34.0ms)

IterNodesCost
0126102
137895
2114792
3456790
4500190

prune67.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize6.0ms

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))))
21.3b
(sqrt (+ (* x x) y))
21.3b
(sqrt (+ (* x x) y))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod
56×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×expm1-log1p-u frac-times rem-sqrt-square log1p-expm1-u add-log-exp
2×associate-*r/ associate-*l/ hypot-def
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 144
Calls
4 calls:
10.0ms
(sqrt (sqrt (+ (* x x) y)))
59.0ms
(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
11.0ms
(sqrt (+ (* x x) y))
9.0ms
(sqrt (+ (* x x) y))

series177.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(sqrt (sqrt (+ (* x x) y)))
36.0ms
(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
39.0ms
(sqrt (+ (* x x) y))
36.0ms
(sqrt (+ (* x x) y))

simplify48.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0279927
11130856
25001822

prune455.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

21.3b
(sqrt (+ (* x x) y))
22.1b
(cbrt (+ (* x x) y))
22.1b
(cbrt (+ (* x x) y))
22.1b
(cbrt (+ (* x x) y))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×cbrt-prod
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div
5×pow1
4×add-exp-log expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
Counts
4 → 63
Calls
4 calls:
12.0ms
(sqrt (+ (* x x) y))
5.0ms
(cbrt (+ (* x x) y))
5.0ms
(cbrt (+ (* x x) y))
6.0ms
(cbrt (+ (* x x) y))

series245.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(sqrt (+ (* x x) y))
70.0ms
(cbrt (+ (* x x) y))
71.0ms
(cbrt (+ (* x x) y))
68.0ms
(cbrt (+ (* x x) y))

simplify51.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (45.0ms)

IterNodesCost
0171420
1484392
21501380
35001378

prune687.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
3×fma-def add-log-exp
2×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
1×pow1 add-exp-log +-commutative expm1-log1p-u flip3-+ sum-log add-cbrt-cube flip-+ log1p-expm1-u
Counts
1 → 16
Calls
1 calls:
6.0ms
(+ x (* 1/2 (/ y x)))

series20.0ms

Counts
1 → 3
Calls
1 calls:
20.0ms
(+ x (* 1/2 (/ y x)))

simplify114.0ms

Algorithm
egg-herbie
Counts
19 → 19
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
08884
132270
2125370
3455270
4500170

prune46.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes244.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 21.3b

bsearch45.0ms

Steps
ItersRangePoint
7
2.7734301821360193e+115
2.559947004859794e+117
2.0526915538089415e+117
7
-6.601498896219609e+155
-5.9312350862110166e+153
-1.3572182934668635e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0239
1309
2329
3329

end0.0ms

sample390.0ms

Algorithm
intervals
Results
168.0ms8000×body80valid
50.0ms2676×body80nan