Details

Time bar (total: 5.4m)

sample734.0ms

Algorithm
intervals
Results
290.0ms92×body1280valid
123.0ms25×body320valid
85.0ms75×body80valid
82.0ms54×body640valid
34.0ms10×body160valid

simplify381.0ms

Calls
1 calls:
Slowest
381.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.8b

localize29.0ms

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))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
22×*-un-lft-identity
21×add-cube-cbrt
19×times-frac
13×associate-*r*
10×add-cbrt-cube add-exp-log
9×associate-*r/
7×associate-/l*
6×associate-/r*
5×pow1
3×expm1-log1p-u clear-num associate-*l* insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-undiv frac-2neg div-exp prod-exp un-div-inv cbrt-unprod div-inv unswap-sqr
1×hypot-udef pow-prod-down *-commutative
Calls
3 calls:
Slowest
27.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
8.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms
(hypot (sin kx) (sin ky))

series816.0ms

Calls
3 calls:
Slowest
394.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
251.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
170.0ms
(hypot (sin kx) (sin ky))

simplify3.6s

Calls
69 calls:
Slowest
516.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
329.0ms
(* (* (* (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)))))
325.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
321.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
291.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.6b

localize26.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (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))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
55×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
19×associate-/r*
10×add-cbrt-cube add-exp-log
9×associate-/r/ associate-/l*
6×div-inv
4×cbrt-undiv div-exp
3×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
1×hypot-udef
Calls
3 calls:
Slowest
20.0ms
(/ (sin th) (/ (hypot (sin kx) (sin ky)) (sin ky)))
5.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))
0.0ms
(hypot (sin kx) (sin ky))

series767.0ms

Calls
3 calls:
Slowest
313.0ms
(/ (sin th) (/ (hypot (sin kx) (sin ky)) (sin ky)))
281.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))
173.0ms
(hypot (sin kx) (sin ky))

simplify8.0s

Calls
140 calls:
Slowest
568.0ms
(/ (* (cbrt (sin th)) (cbrt (sin th))) (/ (* (cbrt (hypot (sin kx) (sin ky))) (cbrt (hypot (sin kx) (sin ky)))) (* (cbrt (sin ky)) (cbrt (sin ky)))))
438.0ms
(/ (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))) (* (* (sin ky) (sin ky)) (sin ky)))
412.0ms
(/ (* (* (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))))
397.0ms
(* (sqrt (+ (pow (sin ky) 2) (pow (sin kx) 2))) (/ 1 (sin ky)))
384.0ms
(/ (cbrt (hypot (sin kx) (sin ky))) (sqrt (sin ky)))

prune1.7s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.6b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
513×times-frac
266×*-un-lft-identity
265×add-sqr-sqrt add-cube-cbrt
96×associate-/r*
64×associate-/r/
36×add-exp-log
28×associate-/l*
24×div-inv
22×div-exp
20×add-cbrt-cube
10×cbrt-undiv clear-num
9×frac-2neg
5×pow1
4×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
2×remove-double-div
1×hypot-udef pow-flip inv-pow
Calls
4 calls:
Slowest
33.0ms
(/ (sin th) (/ 1 (/ (sin ky) (hypot (sin kx) (sin ky)))))
14.0ms
(/ 1 (/ (sin ky) (hypot (sin kx) (sin ky))))
11.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms
(hypot (sin kx) (sin ky))

series914.0ms

Calls
4 calls:
Slowest
319.0ms
(/ (sin th) (/ 1 (/ (sin ky) (hypot (sin kx) (sin ky)))))
248.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
183.0ms
(/ 1 (/ (sin ky) (hypot (sin kx) (sin ky))))
163.0ms
(hypot (sin kx) (sin ky))

simplify47.0s

Calls
543 calls:
Slowest
775.0ms
(/ (* (* (sin th) (sin th)) (sin th)) (/ (* (* 1 1) 1) (* (* (/ (sin ky) (hypot (sin kx) (sin ky))) (/ (sin ky) (hypot (sin kx) (sin ky)))) (/ (sin ky) (hypot (sin kx) (sin ky))))))
604.0ms
(/ (* (* 1 1) 1) (* (* (/ (sin ky) (hypot (sin kx) (sin ky))) (/ (sin ky) (hypot (sin kx) (sin ky)))) (/ (sin ky) (hypot (sin kx) (sin ky)))))
508.0ms
(/ (* (cbrt (sin th)) (cbrt (sin th))) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sin ky)) (cbrt (sin ky))) (sqrt (hypot (sin kx) (sin ky))))))
498.0ms
(/ 1 (/ 1 (/ (* (cbrt (sin ky)) (cbrt (sin ky))) (* (cbrt (hypot (sin kx) (sin ky))) (cbrt (hypot (sin kx) (sin ky)))))))
486.0ms
(/ (* (cbrt (sin th)) (cbrt (sin th))) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sin ky)) (* (cbrt (hypot (sin kx) (sin ky))) (cbrt (hypot (sin kx) (sin ky)))))))

prune5.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.6b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
2568×times-frac
1173×*-un-lft-identity
1171×add-sqr-sqrt add-cube-cbrt
418×associate-/r*
315×associate-/r/
126×add-exp-log
100×div-exp
86×associate-/l*
85×div-inv
34×add-cbrt-cube
30×clear-num
28×rec-exp frac-2neg 1-exp
20×cbrt-undiv
7×pow1
5×pow-flip remove-double-div
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×inv-pow
Calls
4 calls:
Slowest
56.0ms
(/ (sin th) (/ 1 (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))))
17.0ms
(/ 1 (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky))))
15.0ms
(/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))
5.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))

series921.0ms

Calls
4 calls:
Slowest
293.0ms
(/ (sin th) (/ 1 (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))))
239.0ms
(/ 1 (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky))))
229.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))
159.0ms
(/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))

simplify3.7m

Calls
1893 calls:
Slowest
998.0ms
(/ 1 (/ 1 (/ (sqrt 1) (/ (* (cbrt (hypot (sin kx) (sin ky))) (cbrt (hypot (sin kx) (sin ky)))) (* (cbrt (sin ky)) (cbrt (sin ky)))))))
943.0ms
(/ (sqrt 1) (/ 1 (/ (* (cbrt (hypot (sin kx) (sin ky))) (cbrt (hypot (sin kx) (sin ky)))) (* (cbrt (sin ky)) (cbrt (sin ky))))))
822.0ms
(/ (* (cbrt (sin th)) (cbrt (sin th))) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) (/ (* (cbrt (hypot (sin kx) (sin ky))) (cbrt (hypot (sin kx) (sin ky)))) (sqrt (sin ky))))))
817.0ms
(/ (* (cbrt (sin th)) (cbrt (sin th))) (/ (sqrt 1) (/ (sqrt 1) (/ (* (cbrt (hypot (sin kx) (sin ky))) (cbrt (hypot (sin kx) (sin ky)))) (sqrt (sin ky))))))
797.0ms
(/ (* (* 1 1) 1) (/ (* (* 1 1) 1) (* (* (/ (hypot (sin kx) (sin ky)) (sin ky)) (/ (hypot (sin kx) (sin ky)) (sin ky))) (/ (hypot (sin kx) (sin ky)) (sin ky)))))

prune16.5s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 7.6b

regimes1.0s

Accuracy

0% (0.2b remaining)

Error of 8.8b against oracle of 8.6b and baseline of 8.8b

bsearch3.0ms

end0.0ms

sample11.9s

Algorithm
intervals
Results
6.2s2808×body1280valid
2.8s1816×body640valid
1.7s754×body320valid
706.0ms2259×body80valid
239.0ms363×body160valid