Details

Time bar (total: 53.6s)

sample513.0ms

Algorithm
intervals
Results
232.0ms82×body1280valid
87.0ms62×body640valid
28.0ms25×body320valid
23.0ms76×body80valid
6.0ms11×body160valid

simplify350.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
350.0ms
(* (/ (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: 12.5b

localize63.0ms

Local error

Found 4 expressions with local error:

4.0b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.2b
(* (sin kx) (sin kx))
0.2b
(* (sin ky) (sin ky))
0.2b
(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))

rewrite89.0ms

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
46.0ms
(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
15.0ms
(* (sin ky) (sin ky))
13.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
11.0ms
(* (sin kx) (sin kx))

series384.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
207.0ms
(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
117.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
33.0ms
(* (sin ky) (sin ky))
27.0ms
(* (sin kx) (sin kx))

simplify4.5s

Counts
115 → 128
Calls
115 calls:
Slowest
337.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
314.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
296.0ms
(sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))
285.0ms
(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))))))
251.0ms
(* (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: 11.0b

localize49.0ms

Local error

Found 4 expressions with local error:

4.0b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.2b
(* (sin kx) (sin kx))
0.2b
(* (sin ky) (sin ky))
0.2b
(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))

rewrite65.0ms

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
20.0ms
(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
16.0ms
(* (sin kx) (sin kx))
15.0ms
(* (sin ky) (sin ky))
12.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series707.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
531.0ms
(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
119.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
33.0ms
(* (sin kx) (sin kx))
25.0ms
(* (sin ky) (sin ky))

simplify4.7s

Counts
115 → 128
Calls
115 calls:
Slowest
311.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
309.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (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))))))
301.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
295.0ms
(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))))))
291.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.0b

localize46.0ms

Local error

Found 4 expressions with local error:

4.0b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.2b
(* (sin kx) (sin kx))
0.2b
(* (sin ky) (sin ky))
0.2b
(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))

rewrite92.0ms

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
30.0ms
(* (sin kx) (sin kx))
25.0ms
(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
22.0ms
(* (sin ky) (sin ky))
12.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series338.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
173.0ms
(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
115.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
30.0ms
(* (sin ky) (sin ky))
20.0ms
(* (sin kx) (sin kx))

simplify13.1s

Counts
230 → 198
Calls
230 calls:
Slowest
469.0ms
(/ (* (* 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))))
349.0ms
(/ (* (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)))))
322.0ms
(sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))
303.0ms
(/ (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)))))
302.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))

prune2.8s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 11.0b

localize68.0ms

Local error

Found 4 expressions with local error:

4.0b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b
(* (sin ky) (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
0.2b
(* (sin kx) (sin kx))
0.2b
(* (sin ky) (sin ky))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
31×associate-*r*
29×*-un-lft-identity
27×add-cube-cbrt
22×times-frac
21×pow1
17×add-exp-log
14×sqrt-prod
13×add-cbrt-cube
9×associate-*l*
7×unswap-sqr
6×sqrt-div swap-sqr prod-exp sin-mult
4×cbrt-unprod insert-posit16 add-log-exp
3×pow-prod-down associate-/r/ *-commutative
2×pow2 flip3-+ pow-plus div-exp frac-add pow-sqr pow-prod-up flip-+ sqr-sin
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ un-div-inv div-inv
Counts
4 → 124
Calls
4 calls:
Slowest
82.0ms
(* (sin ky) (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
21.0ms
(* (sin ky) (sin ky))
21.0ms
(* (sin kx) (sin kx))
12.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series406.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
216.0ms
(* (sin ky) (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
116.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
39.0ms
(* (sin ky) (sin ky))
33.0ms
(* (sin kx) (sin kx))

simplify6.0s

Counts
112 → 136
Calls
112 calls:
Slowest
434.0ms
(* (* (* (sin ky) (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 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))
356.0ms
(- (+ (* 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)))
321.0ms
(* (* (* (sin ky) (sin ky)) (sin ky)) (/ (* (* 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)))))))
307.0ms
(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))))))

prune1.9s

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 11.0b

regimes1.2s

Accuracy

0% (1.2b remaining)

Error of 12.0b against oracle of 10.7b and baseline of 12.0b

bsearch6.0ms

end0.0ms

sample12.4s

Algorithm
intervals
Results
7.2s2746×body1280valid
3.2s1841×body640valid
774.0ms2292×body80valid
672.0ms778×body320valid
291.0ms343×body160valid