Details

Time bar (total: 8.8s)

sample120.0ms

Algorithm
intervals
Results
70.0ms93×body1280valid
20.0ms51×body640valid
7.0ms77×body80valid
5.0ms18×body320valid
4.0ms17×body160valid

simplify51.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02310
13510
26310
313710
441710
5179810
6500210

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.2b
(pow (sin ky) 2.0)
0.3b
(pow (sin kx) 2.0)
2.6b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
46×*-un-lft-identity
27×add-sqr-sqrt
26×add-cube-cbrt
25×sqrt-prod
24×times-frac
16×unpow-prod-down
10×distribute-lft-out
8×add-exp-log associate-/r*
7×pow1
6×pow-unpow add-cbrt-cube
4×sqrt-div add-log-exp
3×associate-/l*
2×pow-to-exp pow-pow flip3-+ pow-exp associate-/r/ flip-+ sqr-pow
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 100
Calls
4 calls:
19.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
1.0ms
(pow (sin ky) 2.0)
1.0ms
(pow (sin kx) 2.0)
15.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series416.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
104.0ms
(pow (sin ky) 2.0)
109.0ms
(pow (sin kx) 2.0)
77.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify39.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
03291021
11106946
25002943

prune382.0ms

Filtered
112 candidates to 70 candidates (62.5%)
Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (sin kx))
0.7b
(cbrt (sin kx))
0.7b
(cbrt (sin kx))
2.6b
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 48
Calls
4 calls:
1.0ms
(cbrt (sin kx))
1.0ms
(cbrt (sin kx))
1.0ms
(cbrt (sin kx))
13.0ms
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

series375.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(cbrt (sin kx))
99.0ms
(cbrt (sin kx))
97.0ms
(cbrt (sin kx))
78.0ms
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

simplify86.0ms

Algorithm
egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 3 (74.0ms)

IterNodesCost
0183511
1496483
22171477
35002476

prune332.0ms

Filtered
60 candidates to 46 candidates (76.7%)
Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 9.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin kx) 2.0)
0.3b
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
2.6b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.6b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
62×sqrt-prod
56×*-un-lft-identity
34×add-sqr-sqrt
33×times-frac
32×add-cube-cbrt
15×unpow-prod-down
12×distribute-lft-out
11×associate-/r*
8×sqrt-div
7×pow1 add-exp-log
6×add-cbrt-cube
4×add-log-exp
3×pow-unpow flip3-+ flip-+ associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×cbrt-undiv pow-to-exp pow-pow frac-2neg div-exp pow-exp clear-num div-inv sqr-pow
Counts
4 → 112
Calls
4 calls:
1.0ms
(pow (sin kx) 2.0)
21.0ms
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
18.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
16.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series403.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(pow (sin kx) 2.0)
144.0ms
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
76.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
77.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify141.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
03411434
110861322
244471318
350011318

prune483.0ms

Filtered
124 candidates to 75 candidates (60.5%)
Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 9.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sin ky) (sqrt (* (fabs (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
2.6b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0b
(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0b
(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity
17×add-sqr-sqrt
16×add-cube-cbrt
12×times-frac
10×cbrt-prod
9×sqrt-prod
6×add-exp-log unpow-prod-down cbrt-div sqrt-div add-cbrt-cube distribute-lft-out
5×pow1
4×flip3-+ associate-/r* flip-+ add-log-exp
3×associate-/l*
2×pow1/3 associate-*r/ associate-/r/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 80
Calls
4 calls:
14.0ms
(/ (sin ky) (sqrt (* (fabs (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
15.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0ms
(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0ms
(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series476.0ms

Counts
4 → 12
Calls
4 calls:
199.0ms
(/ (sin ky) (sqrt (* (fabs (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
79.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
100.0ms
(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
98.0ms
(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify43.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
03571551
112501450
250011446

prune462.0ms

Filtered
92 candidates to 72 candidates (78.3%)
Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 9.5b

regimes981.0ms

Accuracy

55.2% (0.7b remaining)

Error of 11.8b against oracle of 11.1b and baseline of 12.7b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04547
14547

end0.0ms

sample3.7s

Algorithm
intervals
Results
2.2s2739×body1280valid
795.0ms1832×body640valid
225.0ms785×body320valid
224.0ms2354×body80valid
53.0ms290×body160valid