Details

Time bar (total: 13.8s)

sample139.0ms

Algorithm
intervals
Results
78.0ms83×body1280valid
26.0ms53×body640valid
9.0ms27×body320valid
8.0ms82×body80valid
2.0ms11×body160valid

simplify52.0ms

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: 12.6b

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))))
0.2b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
2.2b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite77.0ms

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:
35.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.0ms
(pow (sin kx) 2.0)
4.0ms
(pow (sin ky) 2.0)
31.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series400.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
100.0ms
(pow (sin kx) 2.0)
100.0ms
(pow (sin ky) 2.0)
74.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify138.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
03291022
11104946
24889943
35002943

prune636.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (sin kx))
0.7b
(cbrt (sin kx))
0.7b
(cbrt (sin kx))
2.2b
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

rewrite35.0ms

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:
4.0ms
(cbrt (sin kx))
1.0ms
(cbrt (sin kx))
1.0ms
(cbrt (sin kx))
28.0ms
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

series355.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(cbrt (sin kx))
98.0ms
(cbrt (sin kx))
92.0ms
(cbrt (sin kx))
68.0ms
(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
0183512
1496483
22171477
35002476

prune634.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 11.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.3b
(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
2.2b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.2b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite274.0ms

Algorithm
rewrite-expression-head
Rules
185×sqrt-prod
163×add-sqr-sqrt
144×times-frac
132×*-un-lft-identity
72×add-cube-cbrt
39×associate-*r* associate-*l*
28×add-exp-log unswap-sqr
24×unpow-prod-down distribute-lft-out
18×add-cbrt-cube
16×sqrt-div
11×associate-/r*
9×div-exp
8×pow1 prod-exp
6×associate-/r/
5×cbrt-undiv flip3-+ flip-+
4×cbrt-unprod add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 225
Calls
4 calls:
36.0ms
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
170.0ms
(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
28.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
26.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series396.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
113.0ms
(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
74.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
69.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify92.0ms

Algorithm
egg-herbie
Counts
237 → 237
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06674588
132144114
250013905

prune1.8s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 11.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (sin kx))
0.7b
(cbrt (sin kx))
0.7b
(cbrt (sin kx))
2.2b
(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)))

rewrite48.0ms

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))
43.0ms
(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)))

series486.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(cbrt (sin kx))
226.0ms
(cbrt (sin kx))
99.0ms
(cbrt (sin kx))
69.0ms
(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)))

simplify78.0ms

Algorithm
egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 3 (71.0ms)

IterNodesCost
0185700
1497663
22175657
35002656

prune713.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 11.6b

regimes3.0s

Accuracy

0% (1.6b remaining)

Error of 12.5b against oracle of 10.9b and baseline of 12.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02427
12427

end0.0ms

sample4.2s

Algorithm
intervals
Results
2.5s2738×body1280valid
955.0ms1873×body640valid
254.0ms747×body320valid
245.0ms2294×body80valid
88.0ms348×body160valid