Details

Time bar (total: 21.6s)

sample376.0ms

Algorithm
intervals
Results
138.0ms91×body1280valid
107.0ms58×body640valid
20.0ms28×body320valid
12.0ms64×body80valid
6.0ms15×body160valid

simplify4.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
01316
12316
23516
36416
413616
531116
6101916
7422316
done500116

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.8b

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 kx) 2.0)
0.3b
(pow (sin ky) 2.0)
2.5b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite130.0ms

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:
69.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
8.0ms
(pow (sin kx) 2.0)
8.0ms
(pow (sin ky) 2.0)
40.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series606.0ms

Counts
4 → 12
Calls
4 calls:
203.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
146.0ms
(pow (sin kx) 2.0)
142.0ms
(pow (sin ky) 2.0)
115.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.0s

Counts
112 → 112
Iterations

Useful iterations: 2 (211.0ms)

IterNodesCost
01701738
13281556
27941503
324191503
done50001503

prune693.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.3b
(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
0.3b
(pow (sin ky) 2)
2.5b
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
78×*-un-lft-identity
49×add-sqr-sqrt times-frac
45×sqrt-prod
36×add-cube-cbrt
24×associate-*l*
23×unpow-prod-down
20×distribute-lft-out
11×add-exp-log
10×pow1
8×add-cbrt-cube
6×associate-/r/
5×associate-/r*
4×add-log-exp unswap-sqr
3×rem-sqrt-square pow-unpow sqrt-pow1 flip3-+ associate-*r* flip-+ div-inv associate-/l*
2×pow-flip sqrt-div div-exp inv-pow
1×cbrt-undiv pow-to-exp rec-exp pow-pow frac-2neg pow1/2 1-exp pow-prod-down associate-*l/ pow-exp prod-exp clear-num *-commutative cbrt-unprod unpow2 sqr-pow
Counts
4 → 138
Calls
4 calls:
39.0ms
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
97.0ms
(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
4.0ms
(pow (sin ky) 2)
49.0ms
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

series520.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
202.0ms
(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
40.0ms
(pow (sin ky) 2)
152.0ms
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

simplify2.4s

Counts
150 → 150
Iterations

Useful iterations: 3 (1.0s)

IterNodesCost
01912472
13702168
28652039
325342029
done50002029

prune642.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 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)))))
2.5b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.5b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite415.0ms

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:
232.0ms
(* (/ 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))))))
77.0ms
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
53.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
30.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series645.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(* (/ 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))))))
234.0ms
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
129.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
108.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.8s

Counts
237 → 237
Iterations

Useful iterations: done (2.8s)

IterNodesCost
02597250
16296550
218105634
done50005632

prune1.2s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 9.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.3b
(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
0.3b
(pow (sin ky) 2)
2.5b
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

rewrite751.0ms

Algorithm
rewrite-expression-head
Rules
78×*-un-lft-identity
49×add-sqr-sqrt times-frac
45×sqrt-prod
36×add-cube-cbrt
24×associate-*l*
23×unpow-prod-down
20×distribute-lft-out
11×add-exp-log
10×pow1
8×add-cbrt-cube
6×associate-/r/
5×associate-/r*
4×add-log-exp unswap-sqr
3×rem-sqrt-square pow-unpow sqrt-pow1 flip3-+ associate-*r* flip-+ div-inv associate-/l*
2×pow-flip sqrt-div div-exp inv-pow
1×cbrt-undiv pow-to-exp rec-exp pow-pow frac-2neg pow1/2 1-exp pow-prod-down associate-*l/ pow-exp prod-exp clear-num *-commutative cbrt-unprod unpow2 sqr-pow
Counts
4 → 138
Calls
4 calls:
67.0ms
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
585.0ms
(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
8.0ms
(pow (sin ky) 2)
81.0ms
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

series475.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
158.0ms
(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
26.0ms
(pow (sin ky) 2)
153.0ms
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

simplify2.3s

Counts
150 → 150
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
01912472
13702168
28652039
325342029
done50002029

prune599.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 9.2b

regimes24.0ms