Details

Time bar (total: 9.7s)

sample133.0ms

Algorithm
intervals
Results
79.0ms97×body1280valid
21.0ms45×body640valid
8.0ms76×body80valid
8.0ms26×body320valid
3.0ms12×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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.8b

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))
0.3b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
4.3b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite72.0ms

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:
45.0ms
(* (/ (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)
20.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series431.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
108.0ms
(pow (sin kx) 2.0)
102.0ms
(pow (sin ky) 2.0)
75.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify42.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0391990
11382928
25001927

prune432.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.3b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
4.3b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
41×*-un-lft-identity
34×add-sqr-sqrt
30×associate-*r*
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-*l* 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 associate-*r/ div-exp pow-prod-down *-commutative div-inv
Counts
4 → 101
Calls
4 calls:
44.0ms
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
1.0ms
(pow (sin kx) 2.0)
1.0ms
(pow (sin ky) 2.0)
15.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series433.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
105.0ms
(pow (sin kx) 2.0)
110.0ms
(pow (sin ky) 2.0)
76.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify57.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0437948
11864870
25002870

prune388.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sin th) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.4b
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.3b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.3b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
114×sqrt-prod
94×*-un-lft-identity
66×times-frac
56×add-sqr-sqrt
54×add-cube-cbrt
22×associate-/r*
20×unpow-prod-down distribute-lft-out
12×sqrt-div
8×add-exp-log add-cbrt-cube
6×pow1 associate-/l*
4×flip3-+ associate-/r/ flip-+ add-log-exp
2×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 156
Calls
4 calls:
20.0ms
(/ (sin th) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
23.0ms
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
15.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
15.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series444.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(/ (sin th) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
146.0ms
(/ (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)))
79.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify128.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
03812366
111462160
247172153
350012153

prune616.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 10.4b

localize27.0ms

Local error

Found 4 expressions with local error:

4.3b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.9b
(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.9b
(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.9b
(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
15×cbrt-prod
9×add-sqr-sqrt
8×add-cube-cbrt unpow-prod-down distribute-lft-out
6×cbrt-div
5×pow1 sqrt-prod
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×pow1/3
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 62
Calls
4 calls:
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)))
8.0ms
(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series365.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
96.0ms
(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
102.0ms
(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
96.0ms
(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify67.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 3 (59.0ms)

IterNodesCost
0177756
1517709
21979703
35001694

prune385.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 10.4b

regimes1.3s

Accuracy

0% (1.7b remaining)

Error of 13.0b against oracle of 11.3b and baseline of 13.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02436
12436

end0.0ms

sample4.1s

Algorithm
intervals
Results
2.3s2761×body1280valid
1.0s1850×body640valid
256.0ms754×body320valid
247.0ms2310×body80valid
71.0ms325×body160valid