Details

Time bar (total: 45.5s)

sample442.0ms

Algorithm
intervals
Results
203.0ms81×body1280valid
71.0ms58×body640valid
41.0ms18×body160valid
23.0ms76×body80valid
17.0ms23×body320valid

simplify348.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
346.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.3b

localize58.0ms

Local error

Found 4 expressions with local error:

1.9b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b
(* (sin kx) (sin kx))
0.3b
(* (sin ky) (sin ky))
0.2b
(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))

rewrite141.0ms

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
60.0ms
(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
31.0ms
(* (sin ky) (sin ky))
26.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
21.0ms
(* (sin kx) (sin kx))

series408.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
223.0ms
(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
123.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
38.0ms
(* (sin kx) (sin kx))
25.0ms
(* (sin ky) (sin ky))

simplify5.2s

Counts
105 → 131
Calls
105 calls:
Slowest
412.0ms
(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))))))
383.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
351.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
343.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
316.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))

prune2.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.9b

localize77.0ms

Local error

Found 4 expressions with local error:

1.9b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
1.9b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
1.9b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.4b
(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))

rewrite60.0ms

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
20.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
16.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
11.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
11.0ms
(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))

series596.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
247.0ms
(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
128.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
122.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
99.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify6.5s

Counts
62 → 98
Calls
62 calls:
Slowest
369.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
338.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
336.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
335.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
328.0ms
(cbrt (/ (sin ky) (sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))))

prune2.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.9b

localize88.0ms

Local error

Found 4 expressions with local error:

1.9b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
1.9b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
1.9b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.6b
(cbrt (sin ky))

rewrite43.0ms

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
18.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
11.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
11.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
2.0ms
(cbrt (sin ky))

series540.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
152.0ms
(cbrt (sin ky))
130.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
130.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
128.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify4.9s

Counts
39 → 75
Calls
39 calls:
Slowest
399.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
357.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
353.0ms
(sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))
353.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
324.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))

prune2.1s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 8.9b

localize58.0ms

Local error

Found 4 expressions with local error:

1.9b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
1.9b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
1.9b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.6b
(cbrt (sin ky))

rewrite35.0ms

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
11.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
11.0ms
(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))

series459.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
126.0ms
(cbrt (sin ky))
124.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
118.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
90.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify4.6s

Counts
39 → 75
Calls
39 calls:
Slowest
347.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
331.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
330.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
310.0ms
(- (pow ky 1/3) (+ (* 1/3240 (pow (pow ky 13) 1/3)) (* 1/18 (pow (pow ky 7) 1/3))))
304.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))

prune1.5s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 8.9b

regimes1.3s

Accuracy

0% (1.4b remaining)

Error of 12.4b against oracle of 11.0b and baseline of 12.4b

bsearch5.0ms

end0.0ms

sample12.1s

Algorithm
intervals
Results
6.8s2737×body1280valid
2.5s1854×body640valid
1.5s752×body320valid
762.0ms2310×body80valid
297.0ms347×body160valid