Details

Time bar (total: 53.1s)

sample1.4s

Algorithm
intervals
Results
338.0ms72×body1280valid
98.0ms81×body80valid
98.0ms66×body640valid
24.0ms21×body320valid
10.0ms16×body160valid

simplify402.0ms

Calls
1 calls:
Slowest
401.0ms
(* (/ (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: 8.8b

localize21.0ms

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))

rewrite85.0ms

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
Calls
3 calls:
Slowest
61.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
21.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms
(hypot (sin kx) (sin ky))

series704.0ms

Calls
3 calls:
Slowest
410.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
170.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
124.0ms
(hypot (sin kx) (sin ky))

simplify3.4s

Calls
59 calls:
Slowest
431.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
370.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
326.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
299.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
271.0ms
(* (* (* (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)))))

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.7b

localize27.0ms

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))

rewrite24.0ms

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
Calls
3 calls:
Slowest
15.0ms
(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))
8.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms
(hypot (sin kx) (sin ky))

series775.0ms

Calls
3 calls:
Slowest
361.0ms
(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))
274.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
139.0ms
(hypot (sin kx) (sin ky))

simplify3.5s

Calls
59 calls:
Slowest
449.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
382.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
374.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
312.0ms
(* (* (* (/ (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)))
294.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.7b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
104×add-sqr-sqrt
92×*-un-lft-identity
90×add-cube-cbrt
44×associate-*l*
36×add-exp-log
20×add-cbrt-cube
16×associate-/r*
15×div-exp
10×div-inv
7×pow1 cbrt-undiv prod-exp
6×associate-/l*
5×unswap-sqr
4×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* cbrt-unprod
2×clear-num frac-2neg associate-/r/
1×hypot-udef pow-prod-down associate-*l/ *-commutative pow-flip inv-pow
Calls
4 calls:
Slowest
34.0ms
(* (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky))) (sin th))
10.0ms
(/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))
10.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))
0.0ms
(hypot (sin kx) (sin ky))

series897.0ms

Calls
4 calls:
Slowest
284.0ms
(* (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky))) (sin th))
247.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))
187.0ms
(hypot (sin kx) (sin ky))
180.0ms
(/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))

simplify15.6s

Calls
205 calls:
Slowest
756.0ms
(* (/ (* (* 1 1) 1) (* (* (/ (hypot (sin kx) (sin ky)) (sin ky)) (/ (hypot (sin kx) (sin ky)) (sin ky))) (/ (hypot (sin kx) (sin ky)) (sin ky)))) (* (* (sin th) (sin th)) (sin th)))
707.0ms
(* (* (* (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky))) (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))) (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))) (* (* (sin th) (sin th)) (sin th)))
503.0ms
(/ (* (* 1 1) 1) (* (* (/ (hypot (sin kx) (sin ky)) (sin ky)) (/ (hypot (sin kx) (sin ky)) (sin ky))) (/ (hypot (sin kx) (sin ky)) (sin ky))))
475.0ms
(/ (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))) (* (* (sin ky) (sin ky)) (sin ky)))
460.0ms
(* (sqrt (+ (pow (sin ky) 2) (pow (sin kx) 2))) (/ 1 (sin ky)))

prune2.8s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 8.7b

localize41.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky))))
0.2b
(* (/ (sin ky) (* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky))))) (sin th))
0.2b
(/ (sin ky) (* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky)))))
0.1b
(sqrt (hypot (sin kx) (sin ky)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
22×pow1
21×sqrt-prod
20×add-cbrt-cube add-exp-log
18×*-un-lft-identity add-cube-cbrt
13×associate-*l*
9×sqrt-pow1 pow1/2 associate-*r*
8×swap-sqr
7×times-frac
6×prod-exp cbrt-unprod unswap-sqr
5×pow-prod-up
4×expm1-log1p-u cbrt-undiv div-exp pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×pow-sqr associate-/l*
2×*-commutative div-inv
1×pow2 rem-sqrt-square clear-num associate-/r* rem-square-sqrt frac-2neg pow-plus sqrt-unprod associate-*l/
Calls
4 calls:
Slowest
62.0ms
(* (/ (sin ky) (* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky))))) (sin th))
20.0ms
(/ (sin ky) (* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky)))))
9.0ms
(* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky))))
1.0ms
(sqrt (hypot (sin kx) (sin ky)))

series1.4s

Calls
4 calls:
Slowest
570.0ms
(* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky))))
366.0ms
(* (/ (sin ky) (* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky))))) (sin th))
241.0ms
(/ (sin ky) (* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky)))))
182.0ms
(sqrt (hypot (sin kx) (sin ky)))

simplify5.5s

Calls
112 calls:
Slowest
431.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky)))) (* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky))))) (* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky))))))
343.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky)))) (sqrt (hypot (sin kx) (sin ky)))) (* (* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky)))) (sqrt (hypot (sin kx) (sin ky))))))
335.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
325.0ms
(* (/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky)))) (sqrt (hypot (sin kx) (sin ky)))) (* (* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky)))) (sqrt (hypot (sin kx) (sin ky)))))) (* (* (sin th) (sin th)) (sin th)))
325.0ms
(* (/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky)))) (* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky))))) (* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky)))))) (* (* (sin th) (sin th)) (sin th)))

prune1.7s

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 8.7b

regimes1.0s

Accuracy

0% (0.2b remaining)

Error of 9.1b against oracle of 8.9b and baseline of 9.1b

bsearch3.0ms

end0.0ms

sample11.5s

Algorithm
intervals
Results
6.0s2680×body1280valid
3.3s1863×body640valid
826.0ms777×body320valid
748.0ms2321×body80valid
379.0ms359×body160valid