Details

Time bar (total: 1.3m)

sample315.0ms

Algorithm
intervals
Results
133.0ms83×body1280valid
56.0ms62×body640valid
14.0ms25×body320valid
12.0ms70×body80valid
6.0ms16×body160valid

simplify416.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
415.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.8b

localize31.0ms

Local error

Found 4 expressions with local error:

2.7b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b
(* (sin kx) (sin kx))
0.2b
(* (sin ky) (sin ky))
0.2b
(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))

rewrite505.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
31×associate-*r*
27×*-un-lft-identity add-cube-cbrt
21×pow1
20×times-frac
13×add-cbrt-cube add-exp-log sqrt-prod
9×associate-*l*
6×sqrt-div swap-sqr sin-mult
5×unswap-sqr
4×prod-exp cbrt-unprod insert-posit16 add-log-exp
3×pow-prod-down associate-/r/ *-commutative
2×pow2 flip3-+ pow-plus frac-add pow-sqr pow-prod-up flip-+ sqr-sin
1×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-*r/ div-inv
Counts
4 → 119
Calls
4 calls:
Slowest
450.0ms
(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
30.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
11.0ms
(* (sin kx) (sin kx))
10.0ms
(* (sin ky) (sin ky))

series382.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
198.0ms
(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
118.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
33.0ms
(* (sin kx) (sin kx))
33.0ms
(* (sin ky) (sin ky))

simplify9.4s

Counts
141 → 131
Calls
141 calls:
Slowest
422.0ms
(* (* (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))
406.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
387.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
357.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
350.0ms
(* (sin th) (/ (sin ky) (sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))))

prune1.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.4b

localize57.0ms

Local error

Found 4 expressions with local error:

2.7b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
2.7b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.4b
(/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
0.3b
(* (/ (sin th) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
124×add-sqr-sqrt
120×sqrt-prod
105×times-frac
66×*-un-lft-identity add-cube-cbrt
34×associate-*r* associate-*l*
24×sqrt-div
18×add-cbrt-cube add-exp-log
16×unswap-sqr
10×sin-mult
9×associate-/r* associate-/r/
8×pow1
5×cbrt-undiv flip3-+ div-exp frac-add flip-+
4×prod-exp cbrt-unprod insert-posit16 add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 194
Calls
4 calls:
Slowest
155.0ms
(* (/ (sin th) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))
39.0ms
(/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
22.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
17.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series599.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
188.0ms
(/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
166.0ms
(* (/ (sin th) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))
130.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
115.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify26.5s

Counts
258 → 206
Calls
258 calls:
Slowest
837.0ms
(* (* (* (/ (sin th) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin th) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))) (/ (sin th) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))) (* (* (/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))) (/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))))
798.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
633.0ms
(* (* (* (/ (sin th) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))) (* (/ (sin th) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))) (* (/ (sin th) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))))
578.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))
482.0ms
(* (/ (sin th) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (* (cbrt (sin ky)) (cbrt (sin ky))) (* (cbrt (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (cbrt (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))))

prune3.4s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 11.4b

localize81.0ms

Local error

Found 4 expressions with local error:

2.7b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
2.7b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
2.7b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.4b
(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
20×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
12×sqrt-div
8×sin-mult
7×pow1
4×flip3-+ add-cbrt-cube frac-add add-exp-log flip-+ insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×cbrt-div pow1/3 div-inv
Counts
4 → 86
Calls
4 calls:
Slowest
28.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
20.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
12.0ms
(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
11.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series532.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
213.0ms
(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
111.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
109.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
99.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify9.1s

Counts
135 → 98
Calls
135 calls:
Slowest
353.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
339.0ms
(cbrt (/ (sin ky) (sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))))
337.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
336.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
331.0ms
(cbrt (sqrt (+ (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (- (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))) (* (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))

prune1.9s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 11.4b

localize61.0ms

Local error

Found 4 expressions with local error:

2.7b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
2.7b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
2.7b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.6b
(cbrt (sin ky))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-div sqrt-prod
8×*-un-lft-identity add-cube-cbrt
7×pow1
6×sin-mult
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×cbrt-prod rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 frac-add flip-+
1×pow1/3
Counts
4 → 63
Calls
4 calls:
Slowest
31.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
23.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
11.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
1.0ms
(cbrt (sin ky))

series442.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
146.0ms
(cbrt (sin ky))
106.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
96.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
94.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify6.8s

Counts
89 → 75
Calls
89 calls:
Slowest
414.0ms
(sqrt (+ (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (- (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))) (* (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
349.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
342.0ms
(sqrt (+ (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (- (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))) (* (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
318.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
316.0ms
(sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))

prune1.3s

Pruning

21 alts after pruning (19 fresh and 2 done)

Merged error: 11.4b

regimes1.2s

Accuracy

0% (1.4b remaining)

Error of 12.7b against oracle of 11.2b and baseline of 12.7b

bsearch3.0ms

end0.0ms

sample11.7s

Algorithm
intervals
Results
6.6s2706×body1280valid
3.1s1800×body640valid
766.0ms765×body320valid
691.0ms2397×body80valid
298.0ms332×body160valid