Details

Time bar (total: 9.2s)

sample120.0ms

Algorithm
intervals
Results
70.0ms97×body1280valid
22.0ms54×body640valid
6.0ms23×body320valid
6.0ms67×body80valid
3.0ms15×body160valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02310
13510
26310
313710
441710
5179810
6500210

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

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)))) (sin th))
0.3b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
3.4b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite69.0ms

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:
48.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
1.0ms
(pow (sin kx) 2.0)
1.0ms
(pow (sin ky) 2.0)
15.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series427.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
103.0ms
(pow (sin kx) 2.0)
103.0ms
(pow (sin ky) 2.0)
76.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify42.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0391990
11382928
25001927

prune414.0ms

Filtered
113 candidates to 78 candidates (69.0%)
Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.3b
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.3b
(pow (sin ky) 2.0)
3.4b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite89.0ms

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:
46.0ms
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
18.0ms
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
1.0ms
(pow (sin ky) 2.0)
18.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series459.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
128.0ms
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
106.0ms
(pow (sin ky) 2.0)
80.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify57.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04121572
118101426
250021423

prune450.0ms

Filtered
145 candidates to 86 candidates (59.3%)
Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 12.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.6b
(* (/ 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))))) (sin th)))
3.4b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.4b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite157.0ms

Algorithm
rewrite-expression-head
Rules
101×sqrt-prod
87×*-un-lft-identity
66×times-frac
53×add-sqr-sqrt
51×add-cube-cbrt
45×add-exp-log
39×associate-*l*
27×add-cbrt-cube
20×prod-exp
18×unpow-prod-down distribute-lft-out
12×sqrt-div
11×pow1 div-exp associate-/r*
10×cbrt-unprod
6×cbrt-undiv
4×flip3-+ associate-/r/ flip-+ add-log-exp
3×rec-exp 1-exp pow-prod-down associate-*l/ associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 div-inv
1×frac-times frac-2neg associate-*r/ associate-*r* clear-num *-commutative
Counts
4 → 166
Calls
4 calls:
23.0ms
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
94.0ms
(* (/ 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))))) (sin th)))
15.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
18.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series461.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
162.0ms
(* (/ 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))))) (sin th)))
70.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
79.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify77.0ms

Algorithm
egg-herbie
Counts
178 → 178
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
05773069
129342568
250012299

prune626.0ms

Filtered
178 candidates to 105 candidates (59.0%)
Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 12.0b

localize19.0ms

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 kx) 2.0)
0.3b
(pow (sin ky) 2.0)
3.4b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite66.0ms

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:
44.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
1.0ms
(pow (sin kx) 2.0)
1.0ms
(pow (sin ky) 2.0)
15.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series435.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
103.0ms
(pow (sin kx) 2.0)
108.0ms
(pow (sin ky) 2.0)
77.0ms
(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

prune320.0ms

Filtered
113 candidates to 70 candidates (61.9%)
Pruning

25 alts after pruning (23 fresh and 2 done)

Merged error: 12.0b

regimes1.1s

Accuracy

0% (1.3b remaining)

Error of 12.3b against oracle of 11.0b and baseline of 12.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01510
11510

end0.0ms

sample3.7s

Algorithm
intervals
Results
2.2s2755×body1280valid
769.0ms1801×body640valid
228.0ms2337×body80valid
209.0ms753×body320valid
71.0ms354×body160valid