Details

Time bar (total: 9.1s)

sample118.0ms

Algorithm
intervals
Results
67.0ms91×body1280valid
22.0ms58×body640valid
6.0ms73×body80valid
4.0ms17×body320valid
3.0ms17×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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.6b

localize16.0ms

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

rewrite118.0ms

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:
77.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
3.0ms
(pow (sin ky) 2.0)
4.0ms
(pow (sin kx) 2.0)
30.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series455.0ms

Counts
4 → 12
Calls
4 calls:
164.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
104.0ms
(pow (sin ky) 2.0)
105.0ms
(pow (sin kx) 2.0)
82.0ms
(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

prune404.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.6b

localize20.0ms

Local error

Found 4 expressions with local error:

2.6b
(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
15.4b
(cbrt (pow (sin kx) 2.0))
15.4b
(cbrt (pow (sin kx) 2.0))
15.4b
(cbrt (pow (sin kx) 2.0))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
12×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
9×unpow-prod-down
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×pow1/3 sqrt-prod sqr-pow
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 60
Calls
4 calls:
78.0ms
(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
2.0ms
(cbrt (pow (sin kx) 2.0))
2.0ms
(cbrt (pow (sin kx) 2.0))
3.0ms
(cbrt (pow (sin kx) 2.0))

series687.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
200.0ms
(cbrt (pow (sin kx) 2.0))
198.0ms
(cbrt (pow (sin kx) 2.0))
203.0ms
(cbrt (pow (sin kx) 2.0))

simplify58.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (51.0ms)

IterNodesCost
0204682
1478640
21705640
35001634

prune344.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 9.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
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)))
2.6b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite97.0ms

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:
17.0ms
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
25.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
27.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
25.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series422.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
85.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
85.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
79.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify97.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 3 (86.0ms)

IterNodesCost
02821291
18191231
234751224
350021219

prune454.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 9.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sin ky))
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)))
2.6b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
15×sqrt-prod
11×add-sqr-sqrt
8×add-cube-cbrt
7×pow1
6×unpow-prod-down sqrt-div distribute-lft-out
4×add-exp-log add-cbrt-cube add-log-exp
3×cbrt-prod rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×pow1/3
Counts
4 → 62
Calls
4 calls:
1.0ms
(cbrt (sin ky))
26.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
24.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
28.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series343.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(cbrt (sin ky))
84.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
78.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
84.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify55.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 3 (49.0ms)

IterNodesCost
0171583
1424554
21478552
35002551

prune325.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 9.6b

regimes1.1s

Accuracy

0% (1.6b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01931
11931

end0.0ms

sample3.7s

Algorithm
intervals
Results
2.1s2729×body1280valid
742.0ms1817×body640valid
211.0ms785×body320valid
202.0ms2306×body80valid
75.0ms363×body160valid