Details

Time bar (total: 10.4s)

sample113.0ms

Algorithm
intervals
Results
65.0ms88×body1280valid
18.0ms46×body640valid
7.0ms83×body80valid
7.0ms25×body320valid
2.0ms14×body160valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02310
13910
26710
315310
443910
5183010
6500110

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

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))
0.2b
(pow (sin ky) 2.0)
0.3b
(pow (sin kx) 2.0)
3.9b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
41×*-un-lft-identity
30×associate-*l*
26×times-frac
25×add-cube-cbrt
21×sqrt-prod
20×unpow-prod-down
11×add-exp-log
9×pow1 add-cbrt-cube hypot-def
8×distribute-lft-out sqr-pow
6×pow-unpow
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×associate-*r* unswap-sqr
2×pow-to-exp pow-pow flip3-+ pow-exp prod-exp associate-/r/ cbrt-unprod flip-+
1×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp pow-prod-down associate-*l/ *-commutative div-inv
Counts
4 → 118
Calls
4 calls:
48.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
1.0ms
(pow (sin ky) 2.0)
1.0ms
(pow (sin kx) 2.0)
17.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series442.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
107.0ms
(pow (sin ky) 2.0)
106.0ms
(pow (sin kx) 2.0)
78.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify46.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04031038
11435967
25002965

prune487.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
0.2b
(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
0.2b
(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity times-frac
13×associate-*l*
10×add-exp-log add-cbrt-cube
5×pow1
3×expm1-log1p-u associate-*r* associate-/r* log1p-expm1-u associate-/l* add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×hypot-udef frac-2neg pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 73
Calls
3 calls:
0.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
3.0ms
(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
9.0ms
(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))

series956.0ms

Counts
3 → 9
Calls
3 calls:
248.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
373.0ms
(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
335.0ms
(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))

simplify41.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
02951114
11091988
25001986

prune355.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (/ 1 (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))) (/ (sin ky) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))) (sin th))
0.3b
(/ 1 (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))
0.4b
(* (/ 1 (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))) (/ (sin ky) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))
0.4b
(/ (sin ky) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
107×add-sqr-sqrt
94×times-frac
67×*-un-lft-identity
64×add-exp-log
61×add-cube-cbrt
53×sqrt-prod
38×add-cbrt-cube
25×associate-*r* prod-exp
23×associate-*l*
19×div-exp
15×unswap-sqr
13×pow1 cbrt-unprod
12×associate-/r*
10×cbrt-undiv
6×associate-/l*
5×rec-exp 1-exp associate-*l/
4×expm1-log1p-u pow-prod-down log1p-expm1-u div-inv add-log-exp
3×pow-flip
2×frac-times frac-2neg associate-*r/ clear-num *-commutative
1×sqrt-pow1 pow1/2 inv-pow
Counts
4 → 206
Calls
4 calls:
35.0ms
(* (* (/ 1 (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))) (/ (sin ky) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))) (sin th))
3.0ms
(/ 1 (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))
28.0ms
(* (/ 1 (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))) (/ (sin ky) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))
4.0ms
(/ (sin ky) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
357.0ms
(* (* (/ 1 (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))) (/ (sin ky) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))) (sin th))
279.0ms
(/ 1 (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))
292.0ms
(* (/ 1 (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))) (/ (sin ky) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))
336.0ms
(/ (sin ky) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

simplify107.0ms

Algorithm
egg-herbie
Counts
218 → 218
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
07344689
135654030
250023684

prune698.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 8.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
0.2b
(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
0.2b
(* (* (/ (sqrt 1) 1) (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))) (sin th))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
30×add-exp-log
23×add-cbrt-cube
13×prod-exp
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac cbrt-unprod
8×pow1 div-exp
5×cbrt-undiv
4×associate-*l/
3×expm1-log1p-u associate-*r* pow-prod-down associate-/r* log1p-expm1-u associate-/l* add-log-exp
2×1-exp
1×frac-times hypot-udef frac-2neg associate-*r/ associate-*l* clear-num *-commutative div-inv
Counts
3 → 70
Calls
3 calls:
0.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
3.0ms
(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
30.0ms
(* (* (/ (sqrt 1) 1) (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))) (sin th))

series964.0ms

Counts
3 → 9
Calls
3 calls:
237.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
386.0ms
(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
342.0ms
(* (* (/ (sqrt 1) 1) (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))) (sin th))

simplify42.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
04071194
11715939
25001930

prune266.0ms

Pruning

22 alts after pruning (20 fresh and 2 done)

Merged error: 8.0b

regimes685.0ms

Accuracy

0% (0.1b remaining)

Error of 8.9b against oracle of 8.8b and baseline of 8.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02213
12213

end0.0ms

sample3.6s

Algorithm
intervals
Results
2.1s2684×body1280valid
771.0ms1906×body640valid
226.0ms767×body320valid
194.0ms2275×body80valid
72.0ms368×body160valid