Details

Time bar (total: 56.8s)

sample396.0ms

Algorithm
intervals
Results
171.0ms83×body1280valid
68.0ms62×body640valid
23.0ms25×body320valid
19.0ms80×body80valid
3.0ms6×body160valid

simplify644.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
643.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize42.0ms

Local error

Found 4 expressions with local error:

2.4b
(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))))))

rewrite299.0ms

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
151.0ms
(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
65.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
53.0ms
(* (sin ky) (sin ky))
24.0ms
(* (sin kx) (sin kx))

series451.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
226.0ms
(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
161.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
32.0ms
(* (sin ky) (sin ky))
32.0ms
(* (sin kx) (sin kx))

simplify5.3s

Counts
105 → 131
Calls
105 calls:
Slowest
399.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
352.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
335.0ms
(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))))))
334.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
317.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))

prune2.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.8b

localize46.0ms

Local error

Found 4 expressions with local error:

2.5b
(sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
0.3b
(* (sin ky) (* (sin th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))
0.3b
(* (sin kx) (sin kx))
0.3b
(* (sin th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
35×sqrt-prod
27×*-un-lft-identity
25×add-cube-cbrt
23×associate-*r*
22×times-frac
20×pow1
13×add-cbrt-cube add-exp-log
9×associate-*l*
6×associate-/r/
5×pow-prod-down prod-exp cbrt-unprod sin-mult unswap-sqr
4×insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 sqrt-div swap-sqr associate-*r/ *-commutative
2×flip3-+ frac-add flip-+ div-inv
1×pow2 pow-plus pow1/2 pow-sqr pow-prod-up sqr-sin pow-flip inv-pow
Counts
4 → 119
Calls
4 calls:
Slowest
77.0ms
(* (sin ky) (* (sin th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))
61.0ms
(* (sin th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
40.0ms
(sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
15.0ms
(* (sin kx) (sin kx))

series573.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
219.0ms
(* (sin th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
197.0ms
(* (sin ky) (* (sin th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))
133.0ms
(sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
24.0ms
(* (sin kx) (sin kx))

simplify6.7s

Counts
101 → 131
Calls
101 calls:
Slowest
590.0ms
(* (* (* (sin ky) (sin ky)) (sin ky)) (* (* (* (sin th) (sin th)) (sin th)) (* (* (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))))))))
545.0ms
(* (* (* (sin ky) (sin ky)) (sin ky)) (* (* (* (sin th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (* (sin th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))) (* (sin th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))))
385.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
380.0ms
(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))))))
364.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))

prune1.9s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.8b

localize70.0ms

Local error

Found 4 expressions with local error:

2.4b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
2.4b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.5b
(* (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
0.3b
(* (sin kx) (sin kx))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
56×add-sqr-sqrt
54×sqrt-div
36×pow1
34×sqrt-pow1
22×*-un-lft-identity add-cube-cbrt
21×sin-mult
18×pow1/2 swap-sqr
12×associate-*r* associate-*l*
10×flip3-+ frac-add pow-prod-up flip-+ unswap-sqr
9×frac-times
8×add-cbrt-cube add-exp-log
6×pow-prod-down pow-sqr
4×insert-posit16 add-log-exp
3×associate-*l/ associate-*r/
2×pow2 rem-sqrt-square pow-plus prod-exp *-commutative cbrt-unprod
1×rem-square-sqrt sqrt-unprod sqr-sin
Counts
4 → 153
Calls
4 calls:
Slowest
134.0ms
(* (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
23.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
23.0ms
(* (sin kx) (sin kx))
13.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series309.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
107.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
102.0ms
(* (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
81.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
19.0ms
(* (sin kx) (sin kx))

simplify12.4s

Counts
181 → 165
Calls
181 calls:
Slowest
517.0ms
(* (sqrt (sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))) (sqrt (sqrt (+ (* (- (cos (- kx kx)) (cos (+ kx kx))) 2) (* 2 (- (cos (- ky ky)) (cos (+ ky ky))))))))
421.0ms
(* (sqrt (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))))))) (sqrt (sqrt (- (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
414.0ms
(* (sqrt (sqrt (- (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (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))))))))
403.0ms
(sqrt (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)))))))
388.0ms
(* (sqrt (sqrt (+ (* (- (cos (- kx kx)) (cos (+ kx kx))) 2) (* 2 (- (cos (- ky ky)) (cos (+ ky ky))))))) (sqrt (sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))))

prune2.8s

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 11.8b

localize99.0ms

Local error

Found 4 expressions with local error:

2.4b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
2.4b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
2.4b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.4b
(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))

rewrite70.0ms

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
21.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
19.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
16.0ms
(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
12.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series509.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
209.0ms
(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
108.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
99.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
93.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify6.8s

Counts
62 → 98
Calls
62 calls:
Slowest
462.0ms
(cbrt (/ (* (cbrt (sin ky)) (cbrt (sin ky))) (sqrt 1)))
373.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
331.0ms
(cbrt (/ (sin ky) (sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))))
326.0ms
(cbrt (/ (sin ky) (sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))))
323.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))

prune1.6s

Pruning

18 alts after pruning (15 fresh and 3 done)

Merged error: 11.8b

regimes1.2s

Accuracy

0% (1.6b remaining)

Error of 12.6b against oracle of 11.0b and baseline of 12.6b

bsearch3.0ms

end0.0ms

sample11.7s

Algorithm
intervals
Results
6.7s2797×body1280valid
2.6s1773×body640valid
1.2s767×body320valid
724.0ms2324×body80valid
228.0ms339×body160valid