Details

Time bar (total: 28.0s)

sample839.0ms

Algorithm
intervals
Results
165.0ms78×body1280valid
61.0ms55×body640valid
22.0ms88×body80valid
21.0ms26×body320valid
5.0ms9×body160valid

simplify67.0ms

Calls
1 calls:
Slowest
66.0ms
(* (/ (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: 11.8b

localize31.0ms

Local error

Found 3 expressions with local error:

2.7b
(/ (* (sin th) (sin ky)) (hypot (sin kx) (sin ky)))
0.2b
(* (sin th) (sin ky))
0.0b
(hypot (sin kx) (sin ky))

rewrite15.0ms

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
9.0ms
(/ (* (sin th) (sin ky)) (hypot (sin kx) (sin ky)))
4.0ms
(* (sin th) (sin ky))
0.0ms
(hypot (sin kx) (sin ky))

series489.0ms

Calls
3 calls:
Slowest
275.0ms
(/ (* (sin th) (sin ky)) (hypot (sin kx) (sin ky)))
143.0ms
(hypot (sin kx) (sin ky))
70.0ms
(* (sin th) (sin ky))

simplify1.4s

Calls
33 calls:
Slowest
401.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
230.0ms
(/ (* (* (* (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))))
187.0ms
(/ (* (* (* (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))))
122.0ms
(* (* (* (sin th) (sin th)) (sin th)) (* (* (sin ky) (sin ky)) (sin ky)))
82.0ms
(* 1/6 (* kx (* ky th)))

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (sin ky) (hypot (sin kx) (sin ky)))
0.1b
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
0.0b
(hypot (sin kx) (sin ky))

rewrite23.0ms

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
13.0ms
(* (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))

series643.0ms

Calls
3 calls:
Slowest
282.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
215.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
146.0ms
(hypot (sin kx) (sin ky))

simplify1.9s

Calls
55 calls:
Slowest
344.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
276.0ms
(* (* (* (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)))))
261.0ms
(- (+ (* 1/6 (* kx ky)) (* 7/360 (* (pow kx 3) ky))) (* 71/720 (* kx (pow ky 3))))
164.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
148.0ms
(* (* (* (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

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.2b

localize18.0ms

Local error

Found 4 expressions with local error:

1.1b
(log1p (/ (sin ky) (hypot (sin kx) (sin ky))))
0.2b
(/ (sin ky) (hypot (sin kx) (sin ky)))
0.1b
(* (sin th) (expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky))))))
0.1b
(expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky)))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
8×add-cbrt-cube add-exp-log
6×pow1
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-*r* associate-*l* associate-/l*
1×cbrt-undiv log1p-udef expm1-log1p clear-num frac-2neg div-exp pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod div-inv expm1-udef
Calls
4 calls:
Slowest
9.0ms
(* (sin th) (expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky))))))
8.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
1.0ms
(log1p (/ (sin ky) (hypot (sin kx) (sin ky))))
0.0ms
(expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky)))))

series922.0ms

Calls
4 calls:
Slowest
302.0ms
(* (sin th) (expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky))))))
224.0ms
(log1p (/ (sin ky) (hypot (sin kx) (sin ky))))
213.0ms
(expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky)))))
182.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))

simplify1.6s

Calls
47 calls:
Slowest
272.0ms
(- (+ (* 1/6 (* kx ky)) (* 7/360 (* (pow kx 3) ky))) (* 71/720 (* kx (pow ky 3))))
252.0ms
(- (+ (* 7/60 (pow ky 4)) (* 1/6 (* kx ky))) (* 1/6 (pow ky 2)))
171.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
132.0ms
(* (* (* (sin th) (sin th)) (sin th)) (* (* (expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky))))) (expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky)))))) (expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky)))))))
66.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))

prune1.3s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 10.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (sin ky) (/ (sin th) (hypot (sin kx) (sin ky))))
0.3b
(/ (sin th) (hypot (sin kx) (sin ky)))
0.0b
(hypot (sin kx) (sin ky))

rewrite13.0ms

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
7.0ms
(* (sin ky) (/ (sin th) (hypot (sin kx) (sin ky))))
5.0ms
(/ (sin th) (hypot (sin kx) (sin ky)))
0.0ms
(hypot (sin kx) (sin ky))

series543.0ms

Calls
3 calls:
Slowest
249.0ms
(* (sin ky) (/ (sin th) (hypot (sin kx) (sin ky))))
182.0ms
(/ (sin th) (hypot (sin kx) (sin ky)))
112.0ms
(hypot (sin kx) (sin ky))

simplify2.0s

Calls
55 calls:
Slowest
410.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
240.0ms
(/ (* (* (sin th) (sin th)) (sin th)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
226.0ms
(* (* (* (sin ky) (sin ky)) (sin ky)) (* (* (/ (sin th) (hypot (sin kx) (sin ky))) (/ (sin th) (hypot (sin kx) (sin ky)))) (/ (sin th) (hypot (sin kx) (sin ky)))))
148.0ms
(* (* (* (sin ky) (sin ky)) (sin ky)) (/ (* (* (sin th) (sin th)) (sin th)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky)))))
87.0ms
(+ (log (sin ky)) (log (/ (sin th) (hypot (sin kx) (sin ky)))))

prune1.1s

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 10.2b

regimes1.3s

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample11.6s

Algorithm
intervals
Results
6.2s2725×body1280valid
2.9s1811×body640valid
758.0ms2368×body80valid
740.0ms748×body320valid
717.0ms348×body160valid