Details

Time bar (total: 1.8m)

sample3.1s

Algorithm
intervals
Results
2.8s726×body10240exit
111.0ms120×body1280valid
35.0ms61×body640valid
15.0ms23×body320valid
5.0ms42×body80valid
3.0ms10×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: 5.4b

localize22.0ms

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)
0.2b
(pow (sin kx) 2.0)
5.0b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite43.0ms

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:
20.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
1.0ms
(pow (sin ky) 2.0)
2.0ms
(pow (sin kx) 2.0)
16.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series425.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
111.0ms
(pow (sin ky) 2.0)
107.0ms
(pow (sin kx) 2.0)
79.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify39.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
03291021
11106946
25002943

prune359.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin ky) 2.0)
0.2b
(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
0.2b
(pow (sin kx) 2.0)
5.0b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite57.0ms

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:
1.0ms
(pow (sin ky) 2.0)
25.0ms
(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
1.0ms
(pow (sin kx) 2.0)
19.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series416.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(pow (sin ky) 2.0)
122.0ms
(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
106.0ms
(pow (sin kx) 2.0)
78.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify71.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
06422588
128822325
250012177

prune415.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin kx) 2.0)
0.3b
(* (sqrt (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))) (sqrt (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))))
5.0b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.0b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite349.0ms

Algorithm
rewrite-expression-head
Rules
928×times-frac
822×sqrt-prod
638×add-sqr-sqrt
612×*-un-lft-identity
356×add-cube-cbrt
132×swap-sqr
94×distribute-lft-out
92×associate-*r* associate-*l*
79×unpow-prod-down
64×unswap-sqr
30×pow1
26×sqrt-pow1
18×div-inv
10×pow1/2
9×pow-prod-up
8×pow-flip sqrt-div inv-pow
7×add-exp-log
6×add-cbrt-cube
5×pow-prod-down pow-sqr
4×associate-/r/ add-log-exp
3×pow-unpow
2×rem-sqrt-square flip3-+ flip-+
1×pow2 frac-times pow-to-exp pow-pow pow-plus sqrt-unprod associate-*r/ associate-*l/ pow-exp prod-exp rem-square-sqrt *-commutative cbrt-unprod sqr-pow
Counts
4 → 467
Calls
4 calls:
2.0ms
(pow (sin kx) 2.0)
247.0ms
(* (sqrt (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))) (sqrt (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))))
19.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
16.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series388.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(pow (sin kx) 2.0)
126.0ms
(* (sqrt (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))) (sqrt (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))))
74.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
81.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify115.0ms

Algorithm
egg-herbie
Counts
479 → 479
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
0106810300
150029188

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ 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)))))
5.0b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.0b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite194.0ms

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:
119.0ms
(* (/ 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))))))
25.0ms
(/ (sin ky) (sqrt (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)))

series428.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(* (/ 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))))))
153.0ms
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
77.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
74.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify102.0ms

Algorithm
egg-herbie
Counts
237 → 237
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
06674588
132184114
250013905

prune810.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.1b

regimes531.0ms

Accuracy

85.1% (0.3b remaining)

Error of 2.3b against oracle of 1.9b and baseline of 4.2b

bsearch3.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03528
13528

end0.0ms

sample1.7m

Algorithm
intervals
Results
1.6m23597×body10240exit
3.6s3672×body1280valid
1.2s2094×body640valid
319.0ms734×body320valid
147.0ms1202×body80valid
78.0ms298×body160valid