Details

Time bar (total: 4.4s)

sample23.0ms

Algorithm
intervals
Results
9.0ms256×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0136
1206
2226
3226

prune4.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 39.6b

Counts
2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.0b
(+ (* x x) (* y y))
36.7b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
5×add-sqr-sqrt
4×pow1 add-cube-cbrt *-un-lft-identity sum-log
3×add-exp-log flip3-+ sqrt-prod add-cbrt-cube flip-+
2×+-commutative sqrt-div
1×rem-sqrt-square associate-+l+ sqrt-pow1 pow1/2
Counts
3 → 39
Calls
3 calls:
5.0ms
(+ (+ (* x x) (* y y)) (* z z))
4.0ms
(+ (* x x) (* y y))
5.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series207.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(+ (+ (* x x) (* y y)) (* z z))
37.0ms
(+ (* x x) (* y y))
125.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify89.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
0209340
1959320
23316316
35001315

prune143.0ms

Filtered
48 candidates to 37 candidates (22.9%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New43548
Fresh000
Picked011
Done000
Total43649

Merged error: 20.8b

Counts
49 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(pow (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3)
36.7b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
46.0b
(cbrt (pow (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-prod
16×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity sqrt-prod
12×unpow-prod-down cube-prod
7×pow1
6×sqrt-div add-log-exp
5×add-exp-log add-cbrt-cube
4×cube-div flip3-+ flip-+
3×pow-unpow pow-pow
2×cube-mult cbrt-div sqrt-pow1 pow1/2 unpow3 sqr-pow
1×+-commutative pow-to-exp rem-sqrt-square pow1/3 pow-exp sum-log sqrt-pow2 rem-cbrt-cube rem-cube-cbrt
Counts
4 → 89
Calls
4 calls:
4.0ms
(+ (* x x) (* y y))
6.0ms
(pow (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3)
5.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
9.0ms
(cbrt (pow (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3))

series515.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(+ (* x x) (* y y))
227.0ms
(pow (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3)
127.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
125.0ms
(cbrt (pow (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3))

simplify48.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0338867
11444834
25002822

prune313.0ms

Filtered
101 candidates to 58 candidates (42.6%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New974101
Fresh044
Picked101
Done011
Total989107

Merged error: 20.8b

Counts
107 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.0b
(+ (* x x) (* y y))
0.1b
(pow (+ (+ (* x x) (* y y)) (* z z)) 3/2)
46.0b
(cbrt (pow (+ (+ (* x x) (* y y)) (* z z)) 3/2))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
11×add-log-exp
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
7×cbrt-prod
6×unpow-prod-down
5×pow1 add-exp-log
4×sum-log add-cbrt-cube
3×pow-unpow
2×+-commutative flip3-+ flip-+ sqr-pow
1×pow-to-exp associate-+l+ pow-pow pow1/3 pow-exp
Counts
4 → 56
Calls
4 calls:
6.0ms
(+ (+ (* x x) (* y y)) (* z z))
4.0ms
(+ (* x x) (* y y))
6.0ms
(pow (+ (+ (* x x) (* y y)) (* z z)) 3/2)
5.0ms
(cbrt (pow (+ (+ (* x x) (* y y)) (* z z)) 3/2))

series305.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(+ (+ (* x x) (* y y)) (* z z))
34.0ms
(+ (* x x) (* y y))
93.0ms
(pow (+ (+ (* x x) (* y y)) (* z z)) 3/2)
130.0ms
(cbrt (pow (+ (+ (* x x) (* y y)) (* z z)) 3/2))

simplify124.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 3 (117.0ms)

IterNodesCost
0268543
11181507
24309501
35003474

prune237.0ms

Filtered
68 candidates to 48 candidates (29.4%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New68068
Fresh077
Picked011
Done011
Total68977

Merged error: 20.8b

Counts
77 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.1b
(pow (+ (* x x) (* y y)) 3)
17.3b
(cbrt (pow (+ (* x x) (* y y)) 3))
36.7b
(sqrt (+ (cbrt (pow (+ (* x x) (* y y)) 3)) (* z z)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
6×pow1 unpow-prod-down cube-prod add-log-exp
5×add-exp-log add-cbrt-cube
4×cube-div flip3-+ flip-+
3×pow-unpow sqrt-prod
2×cube-mult cbrt-div sqrt-div unpow3 sqr-pow
1×+-commutative pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 pow1/3 pow-exp sum-log rem-cbrt-cube rem-cube-cbrt
Counts
4 → 74
Calls
4 calls:
4.0ms
(+ (* x x) (* y y))
5.0ms
(pow (+ (* x x) (* y y)) 3)
4.0ms
(cbrt (pow (+ (* x x) (* y y)) 3))
10.0ms
(sqrt (+ (cbrt (pow (+ (* x x) (* y y)) 3)) (* z z)))

series276.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (* x x) (* y y))
82.0ms
(pow (+ (* x x) (* y y)) 3)
36.0ms
(cbrt (pow (+ (* x x) (* y y)) 3))
124.0ms
(sqrt (+ (cbrt (pow (+ (* x x) (* y y)) 3)) (* z z)))

simplify51.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0303616
11581576
25002568

prune279.0ms

Filtered
86 candidates to 50 candidates (41.9%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New85186
Fresh066
Picked011
Done022
Total851095

Merged error: 20.7b

Counts
95 → 10

regimes954.0ms

Accuracy

62.6% (7.4b remaining)

Error of 25.8b against oracle of 18.4b and baseline of 38.2b

bsearch85.0ms

Steps
ItersRangePoint
8
9.555849306330013e+86
1.704051699546871e+90
2.5006745594136055e+89
10
-6.856527875648579e+102
-1.7166838907982538e+84
-6.181068723284219e+102

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0217
1217

end0.0ms

sample558.0ms

Algorithm
intervals
Results
298.0ms8000×body80valid

Profiling

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