Details

Time bar (total: 26.0s)

sample521.0ms

Algorithm
intervals
Results
334.0ms81×body1280valid
56.0ms58×body640valid
19.0ms76×body80valid
17.0ms23×body320valid
7.0ms18×body160valid

simplify534.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
533.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.5b

localize44.0ms

Local error

Found 3 expressions with local error:

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

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×*-un-lft-identity times-frac add-cube-cbrt
13×associate-*r*
10×add-cbrt-cube add-exp-log
5×pow1
3×expm1-log1p-u associate-/r* associate-*l* insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×hypot-udef clear-num frac-2neg pow-prod-down associate-*r/ *-commutative
Counts
3 → 76
Calls
3 calls:
Slowest
15.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
9.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms
(hypot (sin kx) (sin ky))

series783.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
459.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
187.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
137.0ms
(hypot (sin kx) (sin ky))

simplify3.5s

Counts
59 → 85
Calls
59 calls:
Slowest
483.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
369.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
355.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
273.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
266.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin th) (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky))))
0.2b
(/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))
0.1b
(/ (hypot (sin kx) (sin ky)) (sin ky))
0.1b
(hypot (sin kx) (sin ky))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
104×add-sqr-sqrt
92×*-un-lft-identity
90×add-cube-cbrt
44×associate-*r*
36×add-exp-log
20×add-cbrt-cube
16×associate-/r*
15×div-exp
10×div-inv
7×pow1 cbrt-undiv prod-exp
6×associate-/l*
5×unswap-sqr
4×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l* cbrt-unprod
2×clear-num frac-2neg associate-/r/
1×hypot-udef pow-prod-down associate-*r/ un-div-inv *-commutative pow-flip inv-pow
Counts
4 → 196
Calls
4 calls:
Slowest
23.0ms
(* (sin th) (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky))))
8.0ms
(/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))
6.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))
0.0ms
(hypot (sin kx) (sin ky))

series942.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
282.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))
280.0ms
(* (sin th) (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky))))
210.0ms
(/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))
171.0ms
(hypot (sin kx) (sin ky))

simplify14.1s

Counts
207 → 208
Calls
207 calls:
Slowest
678.0ms
(* (* (* (sin th) (sin th)) (sin th)) (* (* (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky))) (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))) (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))))
618.0ms
(* (* (* (sin th) (sin th)) (sin th)) (/ (* (* 1 1) 1) (/ (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))) (* (* (sin ky) (sin ky)) (sin ky)))))
601.0ms
(* (* (* (sin th) (sin th)) (sin th)) (/ (* (* 1 1) 1) (* (* (/ (hypot (sin kx) (sin ky)) (sin ky)) (/ (hypot (sin kx) (sin ky)) (sin ky))) (/ (hypot (sin kx) (sin ky)) (sin ky)))))
519.0ms
(/ (* (* 1 1) 1) (* (* (/ (hypot (sin kx) (sin ky)) (sin ky)) (/ (hypot (sin kx) (sin ky)) (sin ky))) (/ (hypot (sin kx) (sin ky)) (sin ky))))
474.0ms
(/ (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))) (* (* (sin ky) (sin ky)) (sin ky)))

prune2.9s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 8.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (hypot (sin kx) (sin ky))) (sin ky))
0.2b
(/ (/ 1 (/ (sqrt (hypot (sin kx) (sin ky))) 1)) (/ (sqrt (hypot (sin kx) (sin ky))) (sin ky)))
0.2b
(/ 1 (/ (sqrt (hypot (sin kx) (sin ky))) 1))
0.2b
(* (sin th) (/ (/ 1 (/ (sqrt (hypot (sin kx) (sin ky))) 1)) (/ (sqrt (hypot (sin kx) (sin ky))) (sin ky))))

rewrite399.0ms

Algorithm
rewrite-expression-head
Rules
11363×times-frac
4895×add-sqr-sqrt
4772×*-un-lft-identity
4745×add-cube-cbrt
2573×sqrt-prod
1567×associate-*r*
331×div-inv
167×add-exp-log
121×div-exp
80×associate-/l*
61×add-cbrt-cube
48×associate-/r/
47×associate-/r*
34×cbrt-undiv unswap-sqr
30×1-exp
21×prod-exp
15×rec-exp
7×pow1 cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*l*
1×pow-prod-down associate-*r/ *-commutative pow-flip inv-pow associate-/l/
Counts
4 → 3501
Calls
4 calls:
Slowest
113.0ms
(* (sin th) (/ (/ 1 (/ (sqrt (hypot (sin kx) (sin ky))) 1)) (/ (sqrt (hypot (sin kx) (sin ky))) (sin ky))))
26.0ms
(/ (/ 1 (/ (sqrt (hypot (sin kx) (sin ky))) 1)) (/ (sqrt (hypot (sin kx) (sin ky))) (sin ky)))
14.0ms
(/ 1 (/ (sqrt (hypot (sin kx) (sin ky))) 1))
6.0ms
(/ (sqrt (hypot (sin kx) (sin ky))) (sin ky))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
340.0ms
(* (sin th) (/ (/ 1 (/ (sqrt (hypot (sin kx) (sin ky))) 1)) (/ (sqrt (hypot (sin kx) (sin ky))) (sin ky))))
259.0ms
(/ (sqrt (hypot (sin kx) (sin ky))) (sin ky))
218.0ms
(/ 1 (/ (sqrt (hypot (sin kx) (sin ky))) 1))
213.0ms
(/ (/ 1 (/ (sqrt (hypot (sin kx) (sin ky))) 1)) (/ (sqrt (hypot (sin kx) (sin ky))) (sin ky)))