Details

Time bar (total: 9.1s)

sample127.0ms

Algorithm
intervals
Results
71.0ms91×body1280valid
23.0ms53×body640valid
10.0ms80×body80valid
6.0ms19×body320valid
3.0ms13×body160valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02310
13510
26310
313710
441710
5179810
6500210

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

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)))) (sin th))
0.2b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
3.1b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
41×*-un-lft-identity
34×add-sqr-sqrt
30×associate-*l*
26×times-frac
25×add-cube-cbrt
21×sqrt-prod
14×unpow-prod-down
11×add-exp-log
9×pow1 add-cbrt-cube
8×distribute-lft-out
6×pow-unpow
4×sqrt-div add-log-exp
3×associate-*r* unswap-sqr
2×pow-to-exp pow-pow flip3-+ pow-exp prod-exp associate-/r/ cbrt-unprod flip-+ sqr-pow
1×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp pow-prod-down associate-*l/ *-commutative div-inv
Counts
4 → 101
Calls
4 calls:
49.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
1.0ms
(pow (sin kx) 2.0)
2.0ms
(pow (sin ky) 2.0)
22.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series427.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
106.0ms
(pow (sin kx) 2.0)
101.0ms
(pow (sin ky) 2.0)
75.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify41.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0391990
11382928
25001927

prune427.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sin kx))
0.6b
(cbrt (sin kx))
0.6b
(cbrt (sin kx))
3.1b
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

rewrite17.0ms

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))
14.0ms
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

series365.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(cbrt (sin kx))
96.0ms
(cbrt (sin kx))
96.0ms
(cbrt (sin kx))
77.0ms
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

simplify76.0ms

Algorithm
egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 3 (70.0ms)

IterNodesCost
0183511
1496483
22171477
35002476

prune337.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 11.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (cbrt (sin kx)))
0.6b
(cbrt (cbrt (sin kx)))
0.6b
(cbrt (cbrt (sin kx)))
3.1b
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (* (* (cbrt (cbrt (sin kx))) (cbrt (cbrt (sin kx)))) (cbrt (cbrt (sin kx)))) 2.0)) (pow (sin ky) 2.0)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
27×cbrt-prod
12×add-sqr-sqrt
11×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 → 57
Calls
4 calls:
1.0ms
(cbrt (cbrt (sin kx)))
1.0ms
(cbrt (cbrt (sin kx)))
1.0ms
(cbrt (cbrt (sin kx)))
15.0ms
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (* (* (cbrt (cbrt (sin kx))) (cbrt (cbrt (sin kx)))) (cbrt (cbrt (sin kx)))) 2.0)) (pow (sin ky) 2.0)))

series363.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(cbrt (cbrt (sin kx)))
94.0ms
(cbrt (cbrt (sin kx)))
94.0ms
(cbrt (cbrt (sin kx)))
79.0ms
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (* (* (cbrt (cbrt (sin kx))) (cbrt (cbrt (sin kx)))) (cbrt (cbrt (sin kx)))) 2.0)) (pow (sin ky) 2.0)))

simplify76.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 3 (68.0ms)

IterNodesCost
0188820
1471777
22007771
35002770

prune448.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 11.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.1b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.1b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.1b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
46×*-un-lft-identity
30×cbrt-prod sqrt-prod
25×add-sqr-sqrt
24×times-frac
22×add-cube-cbrt
12×unpow-prod-down distribute-lft-out
8×sqrt-div
7×pow1
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×associate-/r/
1×cbrt-div pow1/3 div-inv
Counts
4 → 90
Calls
4 calls:
11.0ms
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
16.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
16.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
16.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series382.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
76.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
75.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
71.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify94.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 3 (82.0ms)

IterNodesCost
02821291
18191231
234751224
350021219

prune408.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 11.9b

regimes1.2s

Accuracy

60.1% (0.6b remaining)

Error of 11.7b against oracle of 11.1b and baseline of 12.5b

bsearch3.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04637
14637

end0.0ms

sample4.0s

Algorithm
intervals
Results
2.3s2804×body1280valid
821.0ms1800×body640valid
285.0ms2287×body80valid
240.0ms751×body320valid
80.0ms358×body160valid