Details

Time bar (total: 53.0s)

sample688.0ms

Algorithm
intervals
Results
526.0ms81×body1280valid
72.0ms69×body640valid
16.0ms25×body320valid
14.0ms69×body80valid
5.0ms12×body160valid

simplify246.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
245.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.3b

localize22.0ms

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))

rewrite41.0ms

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
22.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
15.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms
(hypot (sin kx) (sin ky))

series775.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
359.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
252.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
164.0ms
(hypot (sin kx) (sin ky))

simplify3.5s

Counts
59 → 85
Calls
59 calls:
Slowest
426.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
344.0ms
(* (* (* (sin th) (sin th)) (sin th)) (* (* (/ (sin ky) (hypot (sin kx) (sin ky))) (/ (sin ky) (hypot (sin kx) (sin ky)))) (/ (sin ky) (hypot (sin kx) (sin ky)))))
284.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
281.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
272.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.2b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite111.0ms

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-*l* prod-exp
23×associate-*r*
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-*r/
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u div-inv add-log-exp
3×pow-flip
2×frac-times clear-num frac-2neg associate-*l/ *-commutative
1×sqrt-pow1 pow1/2 inv-pow
Counts
4 → 210
Calls
4 calls:
Slowest
41.0ms
(* (sin th) (* (/ 1 (sqrt (hypot (sin kx) (sin ky)))) (/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))))
39.0ms
(* (/ 1 (sqrt (hypot (sin kx) (sin ky)))) (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))))
17.0ms
(/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))
10.0ms
(/ 1 (sqrt (hypot (sin kx) (sin ky))))

series875.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
295.0ms
(* (sin th) (* (/ 1 (sqrt (hypot (sin kx) (sin ky)))) (/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))))
209.0ms
(/ 1 (sqrt (hypot (sin kx) (sin ky))))
201.0ms
(/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))
169.0ms
(* (/ 1 (sqrt (hypot (sin kx) (sin ky)))) (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))))

simplify15.1s

Counts
219 → 222
Calls
219 calls:
Slowest
587.0ms
(+ (log (sin th)) (+ (- (log 1) (log (sqrt (hypot (sin kx) (sin ky))))) (log (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))))))
492.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky)))) (sqrt (hypot (sin kx) (sin ky)))))
466.0ms
(* (* (* (/ 1 (sqrt (hypot (sin kx) (sin ky)))) (/ 1 (sqrt (hypot (sin kx) (sin ky))))) (/ 1 (sqrt (hypot (sin kx) (sin ky))))) (* (* (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))) (/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))) (/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))))
447.0ms
(* (* (* (sin th) (sin th)) (sin th)) (* (/ (* (* 1 1) 1) (* (* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky)))) (sqrt (hypot (sin kx) (sin ky))))) (/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky)))) (sqrt (hypot (sin kx) (sin ky)))))))
419.0ms
(+ (log (sin th)) (+ (- 0 (log (sqrt (hypot (sin kx) (sin ky))))) (log (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))))))

prune3.3s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 7.2b

localize33.0ms

Local error

Found 3 expressions with local error:

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

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×*-un-lft-identity times-frac add-cube-cbrt
13×associate-*l*
10×add-cbrt-cube add-exp-log
5×pow1
3×expm1-log1p-u associate-/r* associate-*r* 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-*l/ *-commutative
Counts
3 → 76
Calls
3 calls:
Slowest
20.0ms
(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))
13.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms
(hypot (sin kx) (sin ky))

series708.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
339.0ms
(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))
211.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
157.0ms
(hypot (sin kx) (sin ky))

simplify3.5s

Counts
59 → 85
Calls
59 calls:
Slowest
486.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
378.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
285.0ms
(* (* (* (/ (sin ky) (hypot (sin kx) (sin ky))) (/ (sin ky) (hypot (sin kx) (sin ky)))) (/ (sin ky) (hypot (sin kx) (sin ky)))) (* (* (sin th) (sin th)) (sin th)))
284.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
267.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))

prune1.2s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 7.2b

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin ky) (/ 1 (hypot (sin kx) (sin ky))))
0.2b
(/ 1 (hypot (sin kx) (sin ky)))
0.2b
(* (* (sin ky) (/ 1 (hypot (sin kx) (sin ky)))) (sin th))
0.1b
(hypot (sin kx) (sin ky))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
28×add-sqr-sqrt
22×*-un-lft-identity
21×add-cube-cbrt
20×times-frac add-cbrt-cube
16×associate-*r*
13×prod-exp
12×pow1
7×cbrt-unprod
6×div-exp
4×expm1-log1p-u associate-*l* pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv rec-exp associate-/r* 1-exp associate-/l* unswap-sqr
2×associate-*l/ associate-*r/ un-div-inv *-commutative div-inv
1×hypot-udef clear-num frac-2neg pow-flip inv-pow
Counts
4 → 111
Calls
4 calls:
Slowest
43.0ms
(* (* (sin ky) (/ 1 (hypot (sin kx) (sin ky)))) (sin th))
13.0ms
(* (sin ky) (/ 1 (hypot (sin kx) (sin ky))))
5.0ms
(/ 1 (hypot (sin kx) (sin ky)))
0.0ms
(hypot (sin kx) (sin ky))

series898.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
303.0ms
(* (* (sin ky) (/ 1 (hypot (sin kx) (sin ky)))) (sin th))
218.0ms
(* (sin ky) (/ 1 (hypot (sin kx) (sin ky))))
203.0ms
(/ 1 (hypot (sin kx) (sin ky)))
173.0ms
(hypot (sin kx) (sin ky))

simplify6.7s

Counts
85 → 123
Calls
85 calls:
Slowest
645.0ms
(sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))
518.0ms
(* (* (* (sin ky) (sin ky)) (sin ky)) (* (* (/ 1 (hypot (sin kx) (sin ky))) (/ 1 (hypot (sin kx) (sin ky)))) (/ 1 (hypot (sin kx) (sin ky)))))
364.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
313.0ms
(* (* (* (sin ky) (sin ky)) (sin ky)) (/ (* (* 1 1) 1) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky)))))
290.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))

prune1.6s

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 7.2b

regimes907.0ms

Accuracy

0% (0.2b remaining)

Error of 9.1b against oracle of 9.0b and baseline of 9.1b

bsearch2.0ms

end0.0ms

sample11.4s

Algorithm
intervals
Results
6.6s2645×body1280valid
2.7s1864×body640valid
887.0ms791×body320valid
743.0ms2346×body80valid
280.0ms354×body160valid