Details

Time bar (total: 9.7s)

sample193.0ms

Algorithm
intervals
Results
119.0ms125×body1280valid
41.0ms57×body640valid
9.0ms22×body320valid
5.0ms43×body80valid
2.0ms9×body160valid

simplify51.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02310
13510
26310
313710
441710
5179810
6500210

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 4.5b

Counts
2 → 1

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)
4.2b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite25.0ms

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:
10.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
2.0ms
(pow (sin ky) 2.0)
2.0ms
(pow (sin kx) 2.0)
6.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series92.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
18.0ms
(pow (sin ky) 2.0)
21.0ms
(pow (sin kx) 2.0)
19.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify41.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
03631053
11249978
25001961

prune255.0ms

Filtered
70 candidates to 112 candidates (-60.0%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New10012112
Fresh000
Picked101
Done000
Total10112113

Merged error: 3.4b

Counts
113 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
0.2b
(pow (sin ky) 2.0)
0.3b
(pow (sin kx) 2.0)
4.2b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
180×times-frac
150×*-un-lft-identity
99×add-sqr-sqrt
98×add-cube-cbrt
65×sqrt-prod
32×unpow-prod-down
28×associate-/r*
26×distribute-lft-out
17×add-exp-log
9×add-cbrt-cube
8×pow1
7×div-exp
6×pow-unpow
5×div-inv
4×add-log-exp
3×cbrt-undiv associate-/l*
2×pow-to-exp rec-exp pow-pow sqrt-div 1-exp pow-exp sqr-pow
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 flip3-+ pow1/2 clear-num associate-/r/ flip-+ inv-pow
Counts
4 → 187
Calls
4 calls:
15.0ms
(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
2.0ms
(pow (sin ky) 2.0)
2.0ms
(pow (sin kx) 2.0)
7.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series90.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
17.0ms
(pow (sin ky) 2.0)
17.0ms
(pow (sin kx) 2.0)
19.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify76.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
06752618
130162355
250022204

prune253.0ms

Filtered
78 candidates to 199 candidates (-155.1%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1963199
Fresh4711
Picked101
Done000
Total20110211

Merged error: 3.4b

Counts
211 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin ky)))
0.2b
(pow (sin ky) 2.0)
0.3b
(pow (sin kx) 2.0)
4.2b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
1005×times-frac
608×*-un-lft-identity
437×add-sqr-sqrt
436×add-cube-cbrt
215×sqrt-prod
92×unpow-prod-down
86×distribute-lft-out
46×add-exp-log div-inv
32×div-exp
30×sqrt-div associate-/l*
29×associate-/r/
16×add-cbrt-cube
15×flip3-+ flip-+
13×associate-/r*
8×cbrt-undiv rec-exp 1-exp
7×pow1
6×pow-unpow
4×add-log-exp
2×pow-to-exp pow-pow pow-exp sqr-pow
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 516
Calls
4 calls:
22.0ms
(/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin ky)))
2.0ms
(pow (sin ky) 2.0)
2.0ms
(pow (sin kx) 2.0)
7.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series90.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin ky)))
18.0ms
(pow (sin ky) 2.0)
17.0ms
(pow (sin kx) 2.0)
19.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify121.0ms

Algorithm
egg-herbie
Counts
528 → 528
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
0204010452
150019382

prune735.0ms

Filtered
178 candidates to 528 candidates (-196.6%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New5280528
Fresh099
Picked011
Done000
Total52810538

Merged error: 3.4b

Counts
538 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

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))))))
0.4b
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.2b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.2b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite84.0ms

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:
46.0ms
(* (/ 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))))))
11.0ms
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series117.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* (/ 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))))))
45.0ms
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
19.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
19.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify101.0ms

Algorithm
egg-herbie
Counts
237 → 237
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
06824592
132934120
250013911

prune673.0ms

Filtered
124 candidates to 237 candidates (-91.1%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New2370237
Fresh088
Picked011
Done011
Total23710247

Merged error: 3.4b

Counts
247 → 10

regimes647.0ms

Accuracy

0% (1.4b remaining)

Error of 4.2b against oracle of 2.9b and baseline of 4.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02012
12012

end0.0ms

sample5.9s

Algorithm
intervals
Results
3.7s3741×body1280valid
1.2s2019×body640valid
290.0ms712×body320valid
152.0ms1234×body80valid
75.0ms294×body160valid

Profiling

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