Details

Time bar (total: 1.0m)

sample463.0ms

Algorithm
intervals
Results
192.0ms81×body1280valid
82.0ms67×body640valid
21.0ms75×body80valid
18.0ms19×body320valid
7.0ms14×body160valid

simplify338.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
337.0ms
(* (/ (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: 12.2b

localize57.0ms

Local error

Found 4 expressions with local error:

3.4b
(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))))))

rewrite168.0ms

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
103.0ms
(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
23.0ms
(* (sin kx) (sin kx))
22.0ms
(* (sin ky) (sin ky))
14.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series388.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
209.0ms
(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
135.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
24.0ms
(* (sin ky) (sin ky))
20.0ms
(* (sin kx) (sin kx))

simplify9.9s

Counts
141 → 131
Calls
141 calls:
Slowest
780.0ms
(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))))))
451.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
410.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
392.0ms
(* (* (* (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)))))))
374.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))

prune1.8s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 11.1b

localize39.0ms

Local error

Found 4 expressions with local error:

3.4b
(sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
0.3b
(* (sin ky) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
0.3b
(* (sin kx) (sin kx))
0.3b
(* (sin ky) (sin ky))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt
35×sqrt-prod
30×*-un-lft-identity
28×add-cube-cbrt
25×associate-*r*
22×pow1 times-frac
10×add-cbrt-cube add-exp-log
9×associate-*l*
6×swap-sqr associate-/r/ sin-mult unswap-sqr
4×insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 pow-prod-down prod-exp *-commutative cbrt-unprod
2×pow2 flip3-+ pow-plus sqrt-div frac-add pow-sqr pow-prod-up flip-+ sqr-sin div-inv
1×pow1/2 associate-*r/ pow-flip inv-pow
Counts
4 → 127
Calls
4 calls:
Slowest
94.0ms
(* (sin ky) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
31.0ms
(sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
11.0ms
(* (sin ky) (sin ky))
11.0ms
(* (sin kx) (sin kx))

series403.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
183.0ms
(* (sin ky) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
149.0ms
(sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
38.0ms
(* (sin kx) (sin kx))
33.0ms
(* (sin ky) (sin ky))

simplify8.7s

Counts
159 → 139
Calls
159 calls:
Slowest
445.0ms
(* (* (* (sin ky) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (* (sin ky) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))) (* (sin ky) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))
428.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
378.0ms
(* (sin ky) (sqrt (/ 1 (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))))
357.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
356.0ms
(* (* (* (sin ky) (sin ky)) (sin ky)) (* (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))

prune1.9s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 11.1b

localize72.0ms

Local error

Found 4 expressions with local error:

15.8b
(cbrt (* (sin kx) (sin kx)))
15.8b
(cbrt (* (sin kx) (sin kx)))
15.8b
(cbrt (* (sin kx) (sin kx)))
3.4b
(sqrt (/ 1 (+ (* (* (cbrt (* (sin kx) (sin kx))) (cbrt (* (sin kx) (sin kx)))) (cbrt (* (sin kx) (sin kx)))) (* (sin ky) (sin ky)))))

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
22×sqrt-prod sin-mult
15×add-sqr-sqrt cbrt-div
12×*-un-lft-identity
11×times-frac add-cube-cbrt
9×associate-/r/
7×frac-add
6×pow1
5×frac-times associate-*l/
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×cbrt-prod rem-sqrt-square sqrt-pow1 pow1/3 associate-*r/
1×flip3-+ pow1/2 sqrt-div flip-+ div-inv pow-flip inv-pow
Counts
4 → 71
Calls
4 calls:
Slowest
190.0ms
(sqrt (/ 1 (+ (* (* (cbrt (* (sin kx) (sin kx))) (cbrt (* (sin kx) (sin kx)))) (cbrt (* (sin kx) (sin kx)))) (* (sin ky) (sin ky)))))
10.0ms
(cbrt (* (sin kx) (sin kx)))
10.0ms
(cbrt (* (sin kx) (sin kx)))
10.0ms
(cbrt (* (sin kx) (sin kx)))

series569.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
158.0ms
(cbrt (* (sin kx) (sin kx)))
141.0ms
(cbrt (* (sin kx) (sin kx)))
137.0ms
(cbrt (* (sin kx) (sin kx)))
133.0ms
(sqrt (/ 1 (+ (* (* (cbrt (* (sin kx) (sin kx))) (cbrt (* (sin kx) (sin kx)))) (cbrt (* (sin kx) (sin kx)))) (* (sin ky) (sin ky)))))

simplify7.8s

Counts
105 → 83
Calls
105 calls:
Slowest
383.0ms
(sqrt (/ 1 (+ (* (* (* (cbrt (- (cos (- kx kx)) (cos (+ kx kx)))) (cbrt (- (cos (- kx kx)) (cos (+ kx kx))))) (cbrt (- (cos (- kx kx)) (cos (+ kx kx))))) 2) (* (* (* (cbrt 2) (cbrt 2)) (cbrt 2)) (- (cos (- ky ky)) (cos (+ ky ky)))))))
314.0ms
(sqrt (/ 1 (+ (* (* (* (cbrt (- (cos (- kx kx)) (cos (+ kx kx)))) (cbrt (- (cos (- kx kx)) (cos (+ kx kx))))) (cbrt (* (sin kx) (sin kx)))) 2) (* (* (cbrt 2) (cbrt 2)) (- (cos (- ky ky)) (cos (+ ky ky)))))))
310.0ms
(sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))
297.0ms
(sqrt (/ 1 (+ (pow (* (* (cbrt (* (sin kx) (sin kx))) (cbrt (* (sin kx) (sin kx)))) (cbrt (* (sin kx) (sin kx)))) 3) (pow (* (sin ky) (sin ky)) 3))))
294.0ms
(sqrt (/ 1 (- (* (* (* (cbrt (* (sin kx) (sin kx))) (cbrt (* (sin kx) (sin kx)))) (cbrt (* (sin kx) (sin kx)))) (* (* (cbrt (* (sin kx) (sin kx))) (cbrt (* (sin kx) (sin kx)))) (cbrt (* (sin kx) (sin kx))))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))))))

prune1.5s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 11.1b

localize36.0ms

Local error

Found 4 expressions with local error:

3.4b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
3.4b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b
(/ (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))))))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
78×sqrt-prod
54×times-frac
52×add-sqr-sqrt
50×*-un-lft-identity add-cube-cbrt
18×associate-/r* sqrt-div
8×add-cbrt-cube add-exp-log sin-mult
6×pow1 associate-/r/ associate-/l*
4×flip3-+ frac-add flip-+ insert-posit16 add-log-exp
2×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Counts
4 → 144
Calls
4 calls:
Slowest
33.0ms
(/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
23.0ms
(/ (sin th) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
20.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
12.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series531.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
171.0ms
(/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
162.0ms
(/ (sin th) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
109.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
90.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify12.1s

Counts
220 → 156
Calls
220 calls:
Slowest
731.0ms
(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))))))
520.0ms
(/ (* (* (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)))))))
487.0ms
(/ (* (* (sin th) (sin th)) (sin th)) (* (* (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)))))))
365.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
364.0ms
(/ (sin th) (sqrt (sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))))

prune2.3s

Pruning

18 alts after pruning (15 fresh and 3 done)

Merged error: 11.1b

regimes1.2s

Accuracy

0% (1.6b remaining)

Error of 12.7b against oracle of 11.1b and baseline of 12.7b

bsearch5.0ms

end0.0ms

sample11.6s

Algorithm
intervals
Results
6.1s2781×body1280valid
2.7s1839×body640valid
1.6s2301×body80valid
794.0ms725×body320valid
192.0ms354×body160valid