Details

Time bar (total: 35.1s)

sample393.0ms

Algorithm
intervals
Results
153.0ms91×body1280valid
136.0ms60×body640valid
19.0ms24×body320valid
18.0ms74×body80valid
3.0ms7×body160valid

simplify435.0ms

Calls
1 calls:
Slowest
434.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.4b

localize23.0ms

Local error

Found 3 expressions with local error:

2.2b
(/ (* (sin th) (sin ky)) (hypot (sin kx) (sin ky)))
0.2b
(* (sin th) (sin ky))
0.1b
(hypot (sin kx) (sin ky))

rewrite20.0ms

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
13.0ms
(/ (* (sin th) (sin ky)) (hypot (sin kx) (sin ky)))
5.0ms
(* (sin th) (sin ky))
0.0ms
(hypot (sin kx) (sin ky))

series639.0ms

Calls
3 calls:
Slowest
394.0ms
(/ (* (sin th) (sin ky)) (hypot (sin kx) (sin ky)))
157.0ms
(hypot (sin kx) (sin ky))
87.0ms
(* (sin th) (sin ky))

simplify1.2s

Calls
33 calls:
Slowest
337.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
192.0ms
(/ (* (* (* (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))))
157.0ms
(/ (* (* (* (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))))
98.0ms
(* (* (* (sin th) (sin th)) (sin th)) (* (* (sin ky) (sin ky)) (sin ky)))
80.0ms
(* 1/6 (* kx (* ky th)))

prune901.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 8.6b

localize5.0ms

Local error

Found 3 expressions with local error:

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

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×times-frac
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
1×hypot-udef clear-num frac-2neg pow-prod-down associate-*r/ *-commutative
Calls
3 calls:
Slowest
6.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
4.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms
(hypot (sin kx) (sin ky))

series726.0ms

Calls
3 calls:
Slowest
367.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
212.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
148.0ms
(hypot (sin kx) (sin ky))

simplify2.1s

Calls
55 calls:
Slowest
376.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
278.0ms
(- (+ (* 1/6 (* kx ky)) (* 7/360 (* (pow kx 3) ky))) (* 71/720 (* kx (pow ky 3))))
260.0ms
(* (* (* (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)))))
189.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
164.0ms
(* (* (* (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)))))

prune1.2s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 8.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (sin th) (/ (hypot (sin kx) (sin ky)) (sin ky)))
0.2b
(/ (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
8.0ms
(/ (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))

series736.0ms

Calls
3 calls:
Slowest
300.0ms
(/ (sin th) (/ (hypot (sin kx) (sin ky)) (sin ky)))
263.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))
173.0ms
(hypot (sin kx) (sin ky))

simplify6.1s

Calls
132 calls:
Slowest
582.0ms
(/ (* (cbrt (sin th)) (cbrt (sin th))) (/ (* (cbrt (hypot (sin kx) (sin ky))) (cbrt (hypot (sin kx) (sin ky)))) (* (cbrt (sin ky)) (cbrt (sin ky)))))
454.0ms
(/ (* (* (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))))
412.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
225.0ms
(/ (* (cbrt (sin th)) (cbrt (sin th))) (/ (* (cbrt (hypot (sin kx) (sin ky))) (cbrt (hypot (sin kx) (sin ky)))) (sqrt (sin ky))))
212.0ms
(/ (* (cbrt (sin th)) (cbrt (sin th))) (/ 1 (* (cbrt (sin ky)) (cbrt (sin ky)))))

prune1.6s

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 8.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
0.4b
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
0.4b
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
0.3b
(* (cbrt (/ (sin ky) (hypot (sin kx) (sin ky)))) (cbrt (/ (sin ky) (hypot (sin kx) (sin ky)))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
65×cbrt-prod
45×times-frac
41×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×associate-*r* associate-*l*
9×pow1
7×cbrt-div pow1/3
6×add-exp-log
5×div-inv
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down pow-prod-up
1×pow2 frac-times pow-plus associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Calls
4 calls:
Slowest
7.0ms
(* (cbrt (/ (sin ky) (hypot (sin kx) (sin ky)))) (cbrt (/ (sin ky) (hypot (sin kx) (sin ky)))))
1.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
1.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
1.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))

series1.1s

Calls
4 calls:
Slowest
297.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
292.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
276.0ms
(* (cbrt (/ (sin ky) (hypot (sin kx) (sin ky)))) (cbrt (/ (sin ky) (hypot (sin kx) (sin ky)))))
250.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))

simplify2.6s

Calls
98 calls:
Slowest
324.0ms
(- (+ (* 1/9 (* (exp (* 1/3 (- (* 2 (log ky)) (* 2 (log kx))))) (pow kx 2))) (exp (* 1/3 (- (* 2 (log ky)) (* 2 (log kx)))))) (* 7/27 (* (exp (* 1/3 (- (* 2 (log ky)) (* 2 (log kx))))) (pow ky 2))))
263.0ms
(- (+ (exp (* 1/3 (- (log ky) (log kx)))) (* 1/18 (* (pow kx 2) (exp (* 1/3 (- (log ky) (log kx))))))) (* 13/108 (* (pow ky 2) (exp (* 1/3 (- (log ky) (log kx)))))))
244.0ms
(- (+ (exp (* 1/3 (- (log ky) (log kx)))) (* 1/18 (* (pow kx 2) (exp (* 1/3 (- (log ky) (log kx))))))) (* 13/108 (* (pow ky 2) (exp (* 1/3 (- (log ky) (log kx)))))))
187.0ms
(- (+ (exp (* 1/3 (- (log ky) (log kx)))) (* 1/18 (* (pow kx 2) (exp (* 1/3 (- (log ky) (log kx))))))) (* 13/108 (* (pow ky 2) (exp (* 1/3 (- (log ky) (log kx)))))))
73.0ms
(cbrt (/ (* (cbrt (sin ky)) (cbrt (sin ky))) (* (cbrt (hypot (sin kx) (sin ky))) (cbrt (hypot (sin kx) (sin ky))))))

prune2.2s

Pruning

21 alts after pruning (19 fresh and 2 done)

Merged error: 8.6b

regimes1.2s

Accuracy

0% (0.2b remaining)

Error of 8.4b against oracle of 8.2b and baseline of 8.4b

bsearch2.0ms

end0.0ms

sample11.8s

Algorithm
intervals
Results
6.4s2760×body1280valid
3.6s1853×body640valid
722.0ms2279×body80valid
714.0ms783×body320valid
199.0ms325×body160valid