Details

Time bar (total: 11.5s)

sample152.0ms

Algorithm
intervals
Results
100.0ms126×body1280valid
26.0ms57×body640valid
5.0ms49×body80valid
5.0ms17×body320valid
1.0ms7×body160valid

simplify49.0ms

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: 4.6b

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

rewrite30.0ms

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:
15.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
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)))

series437.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
103.0ms
(pow (sin ky) 2.0)
109.0ms
(pow (sin kx) 2.0)
78.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify46.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0391990
11382928
25001927

prune422.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.4b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
72×*-un-lft-identity
50×times-frac
49×add-sqr-sqrt
41×sqrt-prod
40×add-cube-cbrt
30×associate-*r*
19×unpow-prod-down
16×distribute-lft-out
12×add-exp-log
11×add-cbrt-cube
8×pow1 associate-/r*
6×sqrt-div
4×associate-/r/ add-log-exp
3×pow-unpow flip3-+ associate-*l* flip-+ associate-/l* unswap-sqr
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv
1×pow-to-exp rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down pow-exp clear-num *-commutative sqr-pow
Counts
4 → 133
Calls
4 calls:
2.0ms
(pow (sin kx) 2.0)
10.0ms
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
16.0ms
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series455.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(pow (sin kx) 2.0)
130.0ms
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
141.0ms
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
78.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify52.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04121572
116721426
250011423

prune465.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.4b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite263.0ms

Algorithm
rewrite-expression-head
Rules
1955×sqrt-prod
1638×times-frac
1328×*-un-lft-identity
777×add-sqr-sqrt
728×add-cube-cbrt
435×associate-*r*
300×unpow-prod-down distribute-lft-out
104×sqrt-div
50×associate-/r/
39×associate-/l*
27×flip3-+ flip-+
25×div-inv
18×add-exp-log add-cbrt-cube
13×unswap-sqr
11×associate-/r*
8×pow1
6×cbrt-undiv div-exp
4×add-log-exp
3×associate-*l* prod-exp cbrt-unprod
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative associate-/l/
Counts
4 → 997
Calls
4 calls:
108.0ms
(* (sin ky) (/ (/ (sin th) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
31.0ms
(/ (/ (sin th) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (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)))

series431.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(* (sin ky) (/ (/ (sin th) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
134.0ms
(/ (/ (sin th) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
75.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
80.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify216.0ms

Algorithm
egg-herbie
Counts
1009 → 1009
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0195225612
1500122591

prune1.9s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 2.4b

localize36.0ms

Local error

Found 4 expressions with local error:

4.2b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.7b
(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.7b
(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.7b
(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite29.0ms

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:
7.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms
(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms
(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms
(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series379.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
100.0ms
(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
100.0ms
(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
100.0ms
(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify72.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 3 (62.0ms)

IterNodesCost
0177756
1517709
21979703
35001694

prune482.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 2.4b

regimes612.0ms

Accuracy

60.4% (0.7b remaining)

Error of 3.3b against oracle of 2.6b and baseline of 4.3b

bsearch3.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03938
13938

end0.0ms

sample4.8s

Algorithm
intervals
Results
3.1s3761×body1280valid
1.1s1978×body640valid
238.0ms707×body320valid
125.0ms1274×body80valid
78.0ms280×body160valid