Details

Time bar (total: 9.8s)

sample120.0ms

Algorithm
intervals
Results
66.0ms90×body1280valid
26.0ms68×body640valid
6.0ms23×body320valid
6.0ms68×body80valid
1.0ms7×body160valid

simplify49.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02310
13910
26710
315310
443910
5183010
6500110
done500110

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.9b

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)
3.3b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite125.0ms

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:
81.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
3.0ms
(pow (sin kx) 2.0)
4.0ms
(pow (sin ky) 2.0)
33.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series441.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
100.0ms
(pow (sin kx) 2.0)
102.0ms
(pow (sin ky) 2.0)
81.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify41.0ms

Counts
130 → 130
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
04031038
11435967
25002965
done5002965

prune451.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.3b

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))

rewrite31.0ms

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)))
8.0ms
(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
20.0ms
(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))

series988.0ms

Counts
3 → 9
Calls
3 calls:
258.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
380.0ms
(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
351.0ms
(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))

simplify36.0ms

Counts
82 → 82
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
02951114
11091988
25001986
done5001986

prune345.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.3b

localize17.0ms

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

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
44×add-sqr-sqrt
34×add-cube-cbrt *-un-lft-identity
25×associate-*l*
22×unpow-prod-down
18×add-exp-log
10×add-cbrt-cube
8×sqr-pow
7×associate-/r*
6×div-exp
5×pow1
4×prod-exp unswap-sqr
3×expm1-log1p-u associate-*r* log1p-expm1-u associate-/l* add-log-exp
2×cbrt-undiv pow-to-exp pow-exp cbrt-unprod div-inv
1×hypot-udef frac-2neg pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 107
Calls
3 calls:
0.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
11.0ms
(/ (sin ky) (pow (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) 1))
27.0ms
(* (/ (sin ky) (pow (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) 1)) (sin th))

series1.0s

Counts
3 → 9
Calls
3 calls:
257.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
392.0ms
(/ (sin ky) (pow (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) 1))
358.0ms
(* (/ (sin ky) (pow (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) 1)) (sin th))

simplify50.0ms

Counts
116 → 116
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03941702
115451506
250021498
done50021498

prune465.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.3b

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
0.3b
(/ (* 1 (sin th)) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
0.3b
(* (sin ky) (/ (* 1 (sin th)) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log
17×add-cbrt-cube
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity prod-exp
7×associate-*r*
6×times-frac div-exp
5×pow1 cbrt-unprod
4×cbrt-undiv
3×expm1-log1p-u associate-*l* associate-/r* log1p-expm1-u add-log-exp
2×1-exp div-inv
1×hypot-udef frac-2neg associate-*r/ pow-prod-down clear-num *-commutative associate-/l* unswap-sqr
Counts
3 → 64
Calls
3 calls:
0.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
12.0ms
(/ (* 1 (sin th)) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
24.0ms
(* (sin ky) (/ (* 1 (sin th)) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

series978.0ms

Counts
3 → 9
Calls
3 calls:
254.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
344.0ms
(/ (* 1 (sin th)) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
379.0ms
(* (sin ky) (/ (* 1 (sin th)) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

simplify41.0ms

Counts
73 → 73
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0318977
11265805
25001804
done5001804

prune238.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 7.3b

regimes708.0ms

Accuracy

0% (0.2b remaining)

Error of 8.9b against oracle of 8.7b and baseline of 8.9b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02012
12212
22212
done2212

end0.0ms

sample3.6s

Algorithm
intervals
Results
2.0s2719×body1280valid
814.0ms1892×body640valid
210.0ms760×body320valid
202.0ms2287×body80valid
69.0ms342×body160valid