Details

Time bar (total: 3.5s)

sample16.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
074
174

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) (* y y))
31.6b
(sqrt (+ (* x x) (* y y)))

rewrite16.0ms

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:
7.0ms
(+ (* x x) (* y y))
8.0ms
(sqrt (+ (* x x) (* y y)))

series67.0ms

Counts
2 → 6
Calls
2 calls:
31.0ms
(+ (* x x) (* y y))
36.0ms
(sqrt (+ (* x x) (* y y)))

simplify50.0ms

Algorithm
egg-herbie
Counts
32 → 32
Iterations

Useful iterations: 3 (47.0ms)

IterNodesCost
0125177
1530163
21540163
35001162

prune74.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 9.9b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (cbrt (+ (* x x) (* y y))))
0.2b
(* (fabs (cbrt (+ (* x x) (* y y)))) (sqrt (cbrt (+ (* x x) (* y y)))))
32.5b
(cbrt (+ (* x x) (* y y)))
32.5b
(cbrt (+ (* x x) (* y y)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
14×cbrt-prod sqrt-prod
12×add-cube-cbrt *-un-lft-identity
9×associate-*r*
8×cbrt-div
7×pow1
6×add-exp-log add-cbrt-cube
4×flip3-+ sqrt-div flip-+ add-log-exp
3×pow1/3 associate-*l* unswap-sqr
2×rem-sqrt-square sqrt-pow1 associate-*r/
1×pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
4 → 74
Calls
4 calls:
15.0ms
(sqrt (cbrt (+ (* x x) (* y y))))
29.0ms
(* (fabs (cbrt (+ (* x x) (* y y)))) (sqrt (cbrt (+ (* x x) (* y y)))))
5.0ms
(cbrt (+ (* x x) (* y y)))
5.0ms
(cbrt (+ (* x x) (* y y)))

series395.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(sqrt (cbrt (+ (* x x) (* y y))))
109.0ms
(* (fabs (cbrt (+ (* x x) (* y y)))) (sqrt (cbrt (+ (* x x) (* y y)))))
93.0ms
(cbrt (+ (* x x) (* y y)))
101.0ms
(cbrt (+ (* x x) (* y y)))

simplify128.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 3 (120.0ms)

IterNodesCost
0278853
11080799
24410792
35002785

prune242.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (fabs (exp (log (cbrt (+ (* x x) (* y y)))))) (sqrt (cbrt (+ (* x x) (* y y)))))
5.2b
(exp (log (cbrt (+ (* x x) (* y y)))))
32.5b
(cbrt (+ (* x x) (* y y)))
32.5b
(cbrt (+ (* x x) (* y y)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
13×cbrt-prod add-cube-cbrt *-un-lft-identity
9×associate-*r*
8×cbrt-div sqrt-prod
7×pow1
6×add-exp-log log-prod exp-sum add-cbrt-cube
5×exp-prod
4×flip3-+ flip-+ add-log-exp
3×pow1/3 associate-*l* unswap-sqr
2×log-div exp-diff sqrt-div associate-*r/ log-pow
1×pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log
Counts
4 → 75
Calls
4 calls:
26.0ms
(* (fabs (exp (log (cbrt (+ (* x x) (* y y)))))) (sqrt (cbrt (+ (* x x) (* y y)))))
9.0ms
(exp (log (cbrt (+ (* x x) (* y y)))))
8.0ms
(cbrt (+ (* x x) (* y y)))
5.0ms
(cbrt (+ (* x x) (* y y)))

series405.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(* (fabs (exp (log (cbrt (+ (* x x) (* y y)))))) (sqrt (cbrt (+ (* x x) (* y y)))))
93.0ms
(exp (log (cbrt (+ (* x x) (* y y)))))
95.0ms
(cbrt (+ (* x x) (* y y)))
92.0ms
(cbrt (+ (* x x) (* y y)))

simplify118.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 3 (110.0ms)

IterNodesCost
0301930
11091835
24337811
35001797

prune285.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.9b

localize23.0ms

Local error

Found 4 expressions with local error:

32.5b
(cbrt (+ (* x x) (* y y)))
32.5b
(cbrt (+ (* x x) (* y y)))
32.5b
(cbrt (+ (* x x) (* y y)))
32.5b
(cbrt (+ (* x x) (* y y)))

rewrite227.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt cbrt-div *-un-lft-identity
4×pow1 add-exp-log flip3-+ pow1/3 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 52
Calls
4 calls:
5.0ms
(cbrt (+ (* x x) (* y y)))
5.0ms
(cbrt (+ (* x x) (* y y)))
5.0ms
(cbrt (+ (* x x) (* y y)))
5.0ms
(cbrt (+ (* x x) (* y y)))

series370.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(cbrt (+ (* x x) (* y y)))
93.0ms
(cbrt (+ (* x x) (* y y)))
90.0ms
(cbrt (+ (* x x) (* y y)))
94.0ms
(cbrt (+ (* x x) (* y y)))

simplify53.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0123488
1408452
21387444
35001444

prune282.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.9b

regimes255.0ms

Accuracy

56.6% (10.6b remaining)

Error of 18.1b against oracle of 7.5b and baseline of 32.0b

bsearch39.0ms

Steps
ItersRangePoint
8
3.095505661370574e+39
1.544957661845675e+42
3.219835102538229e+41
9
-8.135496072504979e+92
-3.137185362884227e+83
-3.4884190203618856e+90

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0175
1175

end0.0ms

sample329.0ms

Algorithm
intervals
Results
164.0ms8000×body80valid