Details

Time bar (total: 38.0s)

sample431.0ms

Algorithm
intervals
Results
199.0ms85×body1280valid
133.0ms68×body640valid
21.0ms23×body320valid
20.0ms70×body80valid
6.0ms10×body160valid

simplify475.0ms

Calls
1 calls:
Slowest
474.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.8b

localize20.0ms

Local error

Found 3 expressions with local error:

2.8b
(/ (* (sin th) (sin ky)) (hypot (sin kx) (sin ky)))
0.2b
(* (sin th) (sin ky))
0.1b
(hypot (sin kx) (sin ky))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
10×add-cbrt-cube add-exp-log
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×pow1
3×expm1-log1p-u associate-/r* times-frac associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod sin-mult
1×hypot-udef clear-num frac-2neg pow-prod-down *-commutative div-inv associate-/l* associate-/l/
Calls
3 calls:
Slowest
17.0ms
(/ (* (sin th) (sin ky)) (hypot (sin kx) (sin ky)))
10.0ms
(* (sin th) (sin ky))
0.0ms
(hypot (sin kx) (sin ky))

series677.0ms

Calls
3 calls:
Slowest
424.0ms
(/ (* (sin th) (sin ky)) (hypot (sin kx) (sin ky)))
185.0ms
(hypot (sin kx) (sin ky))
67.0ms
(* (sin th) (sin ky))

simplify1.3s

Calls
33 calls:
Slowest
369.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
195.0ms
(/ (* (* (* (sin th) (sin th)) (sin th)) (* (* (sin ky) (sin ky)) (sin ky))) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
171.0ms
(/ (* (* (* (sin th) (sin ky)) (* (sin th) (sin ky))) (* (sin th) (sin ky))) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
84.0ms
(* (* (* (sin th) (sin th)) (sin th)) (* (* (sin ky) (sin ky)) (sin ky)))
71.0ms
(- (log (* (sin th) (sin ky))) (log (hypot (sin kx) (sin ky))))

prune932.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.4b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
53×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×associate-/r*
10×add-cbrt-cube add-exp-log
6×div-inv associate-/l*
4×cbrt-undiv div-exp
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×hypot-udef associate-/r/
Calls
3 calls:
Slowest
7.0ms
(/ (sin th) (/ (hypot (sin kx) (sin ky)) (sin ky)))
4.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))
0.0ms
(hypot (sin kx) (sin ky))

series761.0ms

Calls
3 calls:
Slowest
284.0ms
(/ (sin th) (/ (hypot (sin kx) (sin ky)) (sin ky)))
270.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))
207.0ms
(hypot (sin kx) (sin ky))

simplify5.8s

Calls
132 calls:
Slowest
503.0ms
(/ (* (cbrt (sin th)) (cbrt (sin th))) (/ (* (cbrt (hypot (sin kx) (sin ky))) (cbrt (hypot (sin kx) (sin ky)))) (* (cbrt (sin ky)) (cbrt (sin ky)))))
407.0ms
(/ (* (* (sin th) (sin th)) (sin th)) (* (* (/ (hypot (sin kx) (sin ky)) (sin ky)) (/ (hypot (sin kx) (sin ky)) (sin ky))) (/ (hypot (sin kx) (sin ky)) (sin ky))))
312.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
206.0ms
(/ (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))) (* (* (sin ky) (sin ky)) (sin ky)))
205.0ms
(/ (sqrt (sin th)) (/ (* (cbrt (hypot (sin kx) (sin ky))) (cbrt (hypot (sin kx) (sin ky)))) (* (cbrt (sin ky)) (cbrt (sin ky)))))

prune1.6s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 9.4b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
17×add-exp-log
11×add-cbrt-cube
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×pow1
4×expm1-log1p-u associate-/r* associate-*r* prod-exp insert-posit16 log1p-expm1-u add-log-exp
3×rec-exp times-frac div-exp associate-*l* div-inv associate-/l*
2×cbrt-undiv clear-num frac-2neg associate-*r/ associate-/r/ un-div-inv cbrt-unprod
1×hypot-udef pow-prod-down *-commutative pow-flip inv-pow
Calls
4 calls:
Slowest
7.0ms
(/ (sin th) (* (hypot (sin kx) (sin ky)) (/ 1 (sin ky))))
5.0ms
(* (hypot (sin kx) (sin ky)) (/ 1 (sin ky)))
1.0ms
(/ 1 (sin ky))
0.0ms
(hypot (sin kx) (sin ky))

series751.0ms

Calls
4 calls:
Slowest
312.0ms
(/ (sin th) (* (hypot (sin kx) (sin ky)) (/ 1 (sin ky))))
280.0ms
(* (hypot (sin kx) (sin ky)) (/ 1 (sin ky)))
140.0ms
(hypot (sin kx) (sin ky))
19.0ms
(/ 1 (sin ky))

simplify2.4s

Calls
44 calls:
Slowest
480.0ms
(* (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))) (* (* (/ 1 (sin ky)) (/ 1 (sin ky))) (/ 1 (sin ky))))
417.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
198.0ms
(/ (* (* (sin th) (sin th)) (sin th)) (* (* (* (hypot (sin kx) (sin ky)) (/ 1 (sin ky))) (* (hypot (sin kx) (sin ky)) (/ 1 (sin ky)))) (* (hypot (sin kx) (sin ky)) (/ 1 (sin ky)))))
193.0ms
(/ (* (* (sin th) (sin th)) (sin th)) (* (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))) (* (* (/ 1 (sin ky)) (/ 1 (sin ky))) (/ 1 (sin ky)))))
125.0ms
(- (log (sin th)) (log (* (hypot (sin kx) (sin ky)) (/ 1 (sin ky)))))

prune1.3s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 9.4b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
53×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×associate-/r*
10×add-cbrt-cube add-exp-log
6×div-inv associate-/l*
4×cbrt-undiv div-exp
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×hypot-udef associate-/r/
Calls
3 calls:
Slowest
12.0ms
(/ (sin th) (/ (hypot (sin ky) (sin kx)) (sin ky)))
8.0ms
(/ (hypot (sin ky) (sin kx)) (sin ky))
0.0ms
(hypot (sin ky) (sin kx))

series774.0ms

Calls
3 calls:
Slowest
372.0ms
(/ (sin th) (/ (hypot (sin ky) (sin kx)) (sin ky)))
213.0ms
(/ (hypot (sin ky) (sin kx)) (sin ky))
189.0ms
(hypot (sin ky) (sin kx))

simplify6.2s

Calls
132 calls:
Slowest
449.0ms
(/ (* (cbrt (sin th)) (cbrt (sin th))) (/ (* (cbrt (hypot (sin ky) (sin kx))) (cbrt (hypot (sin ky) (sin kx)))) (* (cbrt (sin ky)) (cbrt (sin ky)))))
444.0ms
(/ (* (* (sin th) (sin th)) (sin th)) (* (* (/ (hypot (sin ky) (sin kx)) (sin ky)) (/ (hypot (sin ky) (sin kx)) (sin ky))) (/ (hypot (sin ky) (sin kx)) (sin ky))))
262.0ms
(- (+ (* 1/12 (* kx (pow ky 2))) kx) (* 1/6 (pow kx 3)))
237.0ms
(/ (* (cbrt (sin th)) (cbrt (sin th))) (/ 1 (* (cbrt (sin ky)) (cbrt (sin ky)))))
211.0ms
(/ (* (* (sin th) (sin th)) (sin th)) (/ (* (* (hypot (sin ky) (sin kx)) (hypot (sin ky) (sin kx))) (hypot (sin ky) (sin kx))) (* (* (sin ky) (sin ky)) (sin ky))))

prune1.6s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 9.4b

regimes1.1s

Accuracy

0% (0.2b remaining)

Error of 9.0b against oracle of 8.8b and baseline of 9.0b

bsearch2.0ms

end0.0ms

sample12.0s

Algorithm
intervals
Results
6.2s2708×body1280valid
3.0s1869×body640valid
1.0s2290×body80valid
894.0ms770×body320valid
586.0ms363×body160valid