Details

Time bar (total: 2.2m)

sample561.0ms

Algorithm
intervals
Results
263.0ms88×body1280valid
98.0ms62×body640valid
31.0ms79×body80valid
24.0ms21×body320valid
4.0ms6×body160valid

simplify308.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
307.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.5b

localize50.0ms

Local error

Found 4 expressions with local error:

2.0b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b
(* (sin ky) (sin ky))
0.3b
(* (sin kx) (sin kx))
0.2b
(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
28×*-un-lft-identity add-cube-cbrt
19×pow1
18×times-frac
15×sqrt-prod
10×add-cbrt-cube add-exp-log
6×associate-/r* sqrt-div swap-sqr associate-*r* associate-*l* sin-mult
4×insert-posit16 add-log-exp
3×associate-/r/ associate-/l*
2×pow2 flip3-+ pow-plus pow-prod-down frac-add prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ sqr-sin unswap-sqr
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Counts
4 → 116
Calls
4 calls:
Slowest
31.0ms
(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
23.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
20.0ms
(* (sin ky) (sin ky))
19.0ms
(* (sin kx) (sin kx))

series355.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
172.0ms
(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
134.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
29.0ms
(* (sin kx) (sin kx))
20.0ms
(* (sin ky) (sin ky))

simplify4.7s

Counts
115 → 128
Calls
115 calls:
Slowest
312.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
297.0ms
(sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))
287.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
283.0ms
(sqrt (+ (* (- (cos (- kx kx)) (cos (+ kx kx))) 2) (* 2 (- (cos (- ky ky)) (cos (+ ky ky))))))
278.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))

prune1.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 10.0b

localize44.0ms

Local error

Found 4 expressions with local error:

2.0b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b
(* (sin ky) (sin ky))
0.3b
(* (sin kx) (sin kx))
0.2b
(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
93×add-sqr-sqrt
88×*-un-lft-identity add-cube-cbrt
39×sqrt-prod
22×associate-/r*
20×pow1
19×add-exp-log
13×add-cbrt-cube
7×div-exp
6×swap-sqr associate-*r* associate-*l*
5×div-inv
4×insert-posit16 sin-mult add-log-exp
3×cbrt-undiv sqrt-div associate-/l*
2×pow2 rec-exp pow-plus 1-exp pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod sqr-sin unswap-sqr
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 flip3-+ pow1/2 frac-add associate-/r/ flip-+ pow-flip inv-pow
Counts
4 → 186
Calls
4 calls:
Slowest
26.0ms
(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
16.0ms
(* (sin kx) (sin kx))
16.0ms
(* (sin ky) (sin ky))
12.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series343.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
178.0ms
(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
112.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
32.0ms
(* (sin ky) (sin ky))
20.0ms
(* (sin kx) (sin kx))

simplify13.6s

Counts
230 → 198
Calls
230 calls:
Slowest
530.0ms
(/ (* (* 1 1) 1) (* (* (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))))
366.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (cbrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (* (cbrt (sin ky)) (cbrt (sin ky)))))
358.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
298.0ms
(/ (sqrt 1) (/ (* (cbrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (cbrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (* (cbrt (sin ky)) (cbrt (sin ky)))))
275.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))

prune2.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.0b

localize75.0ms

Local error

Found 4 expressions with local error:

2.0b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b
(* (sin ky) (sin ky))
0.3b
(* (sin kx) (sin kx))
0.3b
(/ (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ 1 (sin ky)))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
811×times-frac
382×add-sqr-sqrt
377×*-un-lft-identity add-cube-cbrt
129×sqrt-prod
48×add-exp-log
45×sqrt-div
43×associate-/r/
41×div-inv
32×div-exp sin-mult
25×associate-/l*
20×add-cbrt-cube
19×pow1
15×flip3-+ frac-add flip-+
13×associate-/r*
8×cbrt-undiv rec-exp 1-exp
6×swap-sqr associate-*r* associate-*l*
4×insert-posit16 add-log-exp
2×pow2 pow-plus pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod sqr-sin unswap-sqr
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 469
Calls
4 calls:
Slowest
73.0ms
(/ (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ 1 (sin ky)))
24.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
12.0ms
(* (sin ky) (sin ky))
11.0ms
(* (sin kx) (sin kx))

series344.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
159.0ms
(/ (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ 1 (sin ky)))
117.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
34.0ms
(* (sin kx) (sin kx))
33.0ms
(* (sin ky) (sin ky))

simplify1.4m

Counts
773 → 481
Calls
773 calls:
Slowest
1.5s
(/ (* (* (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (* (* (/ 1 (sin ky)) (/ 1 (sin ky))) (/ 1 (sin ky))))
693.0ms
(/ (/ 1 (* (cbrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (cbrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))) (/ 1 (* (cbrt (sin ky)) (cbrt (sin ky)))))
685.0ms
(/ (/ (* (* 1 1) 1) (* (* (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (* (* (/ 1 (sin ky)) (/ 1 (sin ky))) (/ 1 (sin ky))))
529.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (cbrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))) (/ 1 (* (cbrt (sin ky)) (cbrt (sin ky)))))
444.0ms
(/ (/ 1 (sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))) (/ (sqrt 1) (* (cbrt (sin ky)) (cbrt (sin ky)))))

prune6.9s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.0b

localize68.0ms

Local error

Found 4 expressions with local error:

2.0b
(sqrt (+ (* (* (cbrt (sin kx)) (cbrt (sin kx))) (* (cbrt (sin kx)) (sin kx))) (* (sin ky) (sin ky))))
0.6b
(cbrt (sin kx))
0.6b
(cbrt (sin kx))
0.6b
(cbrt (sin kx))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
5×pow1
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 52
Calls
4 calls:
Slowest
67.0ms
(sqrt (+ (* (* (cbrt (sin kx)) (cbrt (sin kx))) (* (cbrt (sin kx)) (sin kx))) (* (sin ky) (sin ky))))
1.0ms
(cbrt (sin kx))
1.0ms
(cbrt (sin kx))
1.0ms
(cbrt (sin kx))

series511.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
157.0ms
(cbrt (sin kx))
126.0ms
(cbrt (sin kx))
124.0ms
(cbrt (sin kx))
105.0ms
(sqrt (+ (* (* (cbrt (sin kx)) (cbrt (sin kx))) (* (cbrt (sin kx)) (sin kx))) (* (sin ky) (sin ky))))

simplify2.9s

Counts
28 → 64
Calls
28 calls:
Slowest
489.0ms
(sqrt (* (cbrt (+ (* (* (cbrt (sin kx)) (cbrt (sin kx))) (* (cbrt (sin kx)) (sin kx))) (* (sin ky) (sin ky)))) (cbrt (+ (* (* (cbrt (sin kx)) (cbrt (sin kx))) (* (cbrt (sin kx)) (sin kx))) (* (sin ky) (sin ky))))))
473.0ms
(sqrt (- (* (* (* (cbrt (sin kx)) (cbrt (sin kx))) (* (cbrt (sin kx)) (sin kx))) (* (* (cbrt (sin kx)) (cbrt (sin kx))) (* (cbrt (sin kx)) (sin kx)))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))
326.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
302.0ms
(- (pow kx 1/3) (+ (* 1/18 (pow (pow kx 7) 1/3)) (* 1/3240 (pow (pow kx 13) 1/3))))
274.0ms
(- (pow kx 1/3) (+ (* 1/18 (pow (pow kx 7) 1/3)) (* 1/3240 (pow (pow kx 13) 1/3))))

prune1.1s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 10.0b

regimes1.0s

Accuracy

0% (1.2b remaining)

Error of 12.1b against oracle of 10.9b and baseline of 12.1b

bsearch8.0ms

end0.0ms

sample11.7s

Algorithm
intervals
Results
6.3s2794×body1280valid
3.1s1883×body640valid
1.1s734×body320valid
704.0ms2255×body80valid
189.0ms334×body160valid