Details

Time bar (total: 1.2m)

sample2.8s

Algorithm
intervals
Results
1.4s88×body1280valid
610.0ms76×body80valid
189.0ms55×body640valid
67.0ms30×body320valid
10.0ms7×body160valid

simplify387.0ms

Calls
1 calls:
Slowest
378.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune654.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.0b

localize124.0ms

Local error

Found 4 expressions with local error:

4.1b
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.3b
(pow (sin ky) 2)
0.3b
(pow (sin kx) 2)
0.2b
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

rewrite561.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity
30×associate-*l*
24×add-sqr-sqrt times-frac
23×add-cube-cbrt
20×sqrt-prod
14×unpow-prod-down
11×add-exp-log
9×add-cbrt-cube
8×pow1 distribute-lft-out
4×sqrt-div insert-posit16 add-log-exp
3×associate-*r*
2×pow-to-exp pow-pow flip3-+ pow-exp prod-exp associate-/r/ cbrt-unprod flip-+ unpow2
1×cbrt-undiv rem-sqrt-square pow1/2 div-exp pow-prod-down associate-*l/ *-commutative div-inv
Calls
4 calls:
Slowest
102.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
60.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
2.0ms
(pow (sin kx) 2)
2.0ms
(pow (sin ky) 2)

series1.1s

Calls
4 calls:
Slowest
588.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
458.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
26.0ms
(pow (sin ky) 2)
25.0ms
(pow (sin kx) 2)

simplify3.6s

Calls
68 calls:
Slowest
344.0ms
(* (* (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (* (sin th) (sin th)) (sin th)))
320.0ms
(/ (sin ky) (sqrt (- (* (pow (sin kx) 2) (pow (sin kx) 2)) (* (pow (sin ky) 2) (pow (sin ky) 2)))))
308.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
300.0ms
(sqrt (- (* (pow (sin kx) 2) (pow (sin kx) 2)) (* (pow (sin ky) 2) (pow (sin ky) 2))))
231.0ms
(* (/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (* (sin th) (sin th)) (sin th)))

prune2.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.4b

localize16.0ms

Local error

Found 4 expressions with local error:

4.1b
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.4b
(* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
0.3b
(* (sin ky) (* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))
0.3b
(pow (sin ky) 2)

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
17×add-exp-log
13×*-un-lft-identity
12×pow1
11×add-cbrt-cube
10×add-sqr-sqrt
9×associate-*l* add-cube-cbrt
7×prod-exp
5×unpow-prod-down sqrt-prod
4×sqrt-div associate-*r* pow-prod-down cbrt-unprod insert-posit16 add-log-exp
2×rec-exp flip3-+ associate-*l/ associate-/r/ *-commutative flip-+ distribute-lft-out
1×pow-to-exp rem-sqrt-square pow-pow pow1/2 pow-exp associate-*r/ div-inv unpow2
Calls
4 calls:
Slowest
24.0ms
(* (sin ky) (* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))
16.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
12.0ms
(* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
2.0ms
(pow (sin ky) 2)

series630.0ms

Calls
4 calls:
Slowest
283.0ms
(* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
212.0ms
(* (sin ky) (* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))
110.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
24.0ms
(pow (sin ky) 2)

simplify5.4s

Calls
48 calls:
Slowest
1.2s
(* (* (* (sin ky) (sin ky)) (sin ky)) (* (* (* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (* (sin th) (sin th)) (sin th))))
800.0ms
(* (* (* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (* (sin th) (sin th)) (sin th)))
318.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
310.0ms
(/ 1 (sqrt (- (* (pow (sin kx) 2) (pow (sin kx) 2)) (* (pow (sin ky) 2) (pow (sin ky) 2)))))
295.0ms
(sqrt (- (* (pow (sin kx) 2) (pow (sin kx) 2)) (* (pow (sin ky) 2) (pow (sin ky) 2))))

prune5.0s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 11.4b

localize36.0ms

Local error

Found 4 expressions with local error:

4.1b
(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
0.3b
(* (sin ky) (pow (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) 1))
0.3b
(* (sin ky) (sin ky))
0.3b
(* (sin kx) (sin kx))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
34×associate-*r*
25×add-sqr-sqrt unpow-prod-down
24×*-un-lft-identity add-cube-cbrt
18×times-frac
16×add-exp-log
15×pow1
12×sqrt-prod
10×add-cbrt-cube
9×associate-*l*
6×sqrt-div prod-exp sin-mult
4×insert-posit16 add-log-exp
3×pow-prod-down associate-/r/ *-commutative cbrt-unprod
2×pow2 flip3-+ pow-plus frac-add pow-exp pow-prod-up flip-+ sqr-sin
1×pow-to-exp rem-sqrt-square pow1/2 div-exp div-inv
Calls
4 calls:
Slowest
53.0ms
(* (sin ky) (pow (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) 1))
19.0ms
(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
9.0ms
(* (sin ky) (sin ky))
9.0ms
(* (sin kx) (sin kx))

series370.0ms

Calls
4 calls:
Slowest
210.0ms
(* (sin ky) (pow (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) 1))
116.0ms
(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
23.0ms
(* (sin ky) (sin ky))
21.0ms
(* (sin kx) (sin kx))

simplify6.0s

Calls
81 calls:
Slowest
579.0ms
(pow (sqrt (+ (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))) (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) 1)
517.0ms
(- (+ (* 1/12 (* kx (pow ky 2))) kx) (* 1/6 (pow kx 3)))
517.0ms
(* (* (* (sin ky) (sin ky)) (sin ky)) (* (* (pow (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) 1) (pow (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) 1)) (pow (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) 1)))
441.0ms
(sqrt (- (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))) (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx)))))
345.0ms
(sqrt (+ (* (- (cos (- ky ky)) (cos (+ ky ky))) 2) (* 2 (- (cos (- kx kx)) (cos (+ kx kx))))))

prune3.7s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 10.3b

localize59.0ms

Local error

Found 4 expressions with local error:

4.6b
(cbrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
4.6b
(cbrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
4.6b
(cbrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
0.9b
(sqrt (* (cbrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (cbrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
33×cbrt-div
22×sin-mult
15×sqrt-div
11×flip3-+ frac-add flip-+
9×cbrt-prod frac-times
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow1/3 associate-*l/ associate-*r/
1×rem-sqrt-square pow1/2 sqrt-prod
Calls
4 calls:
Slowest
24.0ms
(sqrt (* (cbrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (cbrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))
9.0ms
(cbrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
9.0ms
(cbrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
9.0ms
(cbrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))

series667.0ms

Calls
4 calls:
Slowest
217.0ms
(cbrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
151.0ms
(cbrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
150.0ms
(cbrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
148.0ms
(sqrt (* (cbrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (cbrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))

simplify11.3s

Calls
47 calls:
Slowest
935.0ms
(sqrt (* (cbrt (- (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))) (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))))) (cbrt (+ (pow (* (sin ky) (sin ky)) 3) (pow (* (sin kx) (sin kx)) 3)))))
673.0ms
(sqrt (* (cbrt (+ (* (- (cos (- ky ky)) (cos (+ ky ky))) 2) (* 2 (- (cos (- kx kx)) (cos (+ kx kx)))))) (cbrt (- (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))) (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx)))))))
664.0ms
(sqrt (* (cbrt (+ (* (- (cos (- ky ky)) (cos (+ ky ky))) 2) (* 2 (- (cos (- kx kx)) (cos (+ kx kx)))))) (cbrt (+ (* (- (cos (- ky ky)) (cos (+ ky ky))) 2) (* 2 (- (cos (- kx kx)) (cos (+ kx kx))))))))
649.0ms
(sqrt (* (cbrt (+ (pow (* (sin ky) (sin ky)) 3) (pow (* (sin kx) (sin kx)) 3))) (cbrt (+ (* (- (cos (- ky ky)) (cos (+ ky ky))) 2) (* 2 (- (cos (- kx kx)) (cos (+ kx kx))))))))
634.0ms
(sqrt (* (cbrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (cbrt (- (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))) (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx)))))))

prune2.6s

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 10.3b

regimes2.6s

Accuracy

0% (2.1b remaining)

Error of 12.2b against oracle of 10.1b and baseline of 12.2b

bsearch5.0ms

end0.0ms

sample23.0s

Algorithm
intervals
Results
15.6s2710×body1280valid
4.6s1844×body640valid
1.1s2356×body80valid
1.0s745×body320valid
344.0ms345×body160valid