Details

Time bar (total: 28.9s)Debug log

sample407.0ms

Algorithm
intervals
Results
213.0ms91×body1280valid
59.0ms54×body640valid
24.0ms77×body80valid
16.0ms22×body320valid
6.0ms12×body160valid

simplify14.0ms

Calls
1 calls:
Slowest
13.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.5b

localize55.0ms

Local error

Found 4 expressions with local error:

2.2b
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.3b
(pow (sin ky) 2)
0.2b
(pow (sin kx) 2)
0.2b
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity
30×associate-*l*
24×times-frac
24×add-sqr-sqrt
23×add-cube-cbrt
20×sqrt-prod
14×unpow-prod-down
11×add-exp-log
9×add-cbrt-cube
8×distribute-lft-out
8×pow1
4×add-log-exp
4×sqrt-div
3×associate-*r*
2×unpow2
2×flip-+
2×cbrt-unprod
2×associate-/r/
2×prod-exp
2×pow-exp
2×flip3-+
2×pow-pow
2×pow-to-exp
1×div-inv
1×*-commutative
1×associate-*l/
1×pow-prod-down
1×div-exp
1×pow1/2
1×rem-sqrt-square
1×cbrt-undiv
Calls
4 calls:
Slowest
26.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
14.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
2.0ms
(pow (sin kx) 2)
2.0ms
(pow (sin ky) 2)

series371.0ms

Calls
4 calls:
Slowest
200.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
121.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
25.0ms
(pow (sin kx) 2)
25.0ms
(pow (sin ky) 2)

simplify1.7s

Calls
68 calls:
Slowest
409.0ms
(* (/ (* (* (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)))
194.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
163.0ms
(sqrt (- (* (pow (sin kx) 2) (pow (sin kx) 2)) (* (pow (sin ky) 2) (pow (sin ky) 2))))
162.0ms
(* (* (* (/ (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)))
161.0ms
(/ (sin ky) (sqrt (- (* (pow (sin kx) 2) (pow (sin kx) 2)) (* (pow (sin ky) 2) (pow (sin ky) 2)))))

prune1.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.7b

localize24.0ms

Local error

Found 4 expressions with local error:

2.2b
(sqrt (+ (* (* (cbrt (sin kx)) (sin kx)) (pow (cbrt (sin kx)) 2)) (pow (sin ky) 2)))
0.6b
(cbrt (sin kx))
0.6b
(cbrt (sin kx))
0.5b
(pow (cbrt (sin kx)) 2)

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×add-cube-cbrt
9×*-un-lft-identity
9×cbrt-prod
6×unpow-prod-down
5×add-exp-log
5×pow1
4×add-log-exp
4×add-cbrt-cube
3×sqrt-prod
3×pow1/3
2×sqrt-div
2×pow-pow
1×unpow2
1×flip-+
1×pow-exp
1×pow1/2
1×flip3-+
1×rem-sqrt-square
1×pow-to-exp
Calls
4 calls:
Slowest
15.0ms
(sqrt (+ (* (* (cbrt (sin kx)) (sin kx)) (pow (cbrt (sin kx)) 2)) (pow (sin ky) 2)))
2.0ms
(pow (cbrt (sin kx)) 2)
1.0ms
(cbrt (sin kx))
1.0ms
(cbrt (sin kx))

series536.0ms

Calls
4 calls:
Slowest
160.0ms
(pow (cbrt (sin kx)) 2)
149.0ms
(cbrt (sin kx))
134.0ms
(cbrt (sin kx))
93.0ms
(sqrt (+ (* (* (cbrt (sin kx)) (sin kx)) (pow (cbrt (sin kx)) 2)) (pow (sin ky) 2)))

simplify1.1s

Calls
33 calls:
Slowest
310.0ms
(sqrt (+ (pow (* (* (cbrt (sin kx)) (sin kx)) (pow (cbrt (sin kx)) 2)) 3) (pow (pow (sin ky) 2) 3)))
232.0ms
(sqrt (- (* (* (* (cbrt (sin kx)) (sin kx)) (pow (cbrt (sin kx)) 2)) (* (* (cbrt (sin kx)) (sin kx)) (pow (cbrt (sin kx)) 2))) (* (pow (sin ky) 2) (pow (sin ky) 2))))
145.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
72.0ms
(- (pow kx 1/3) (+ (* 1/18 (pow (pow kx 7) 1/3)) (* 1/3240 (pow (pow kx 13) 1/3))))
64.0ms
(- (pow kx 1/3) (+ (* 1/18 (pow (pow kx 7) 1/3)) (* 1/3240 (pow (pow kx 13) 1/3))))

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.7b

localize29.0ms

Local error

Found 4 expressions with local error:

2.2b
(sqrt (+ (* (* (cbrt (sin kx)) (sin kx)) (* (pow (cbrt (* (cbrt (sin kx)) (cbrt (sin kx)))) 2) (pow (cbrt (cbrt (sin kx))) 2))) (pow (sin ky) 2)))
0.6b
(cbrt (sin kx))
0.6b
(cbrt (sin kx))
0.6b
(cbrt (sin kx))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
9×cbrt-prod
8×add-cube-cbrt
8×*-un-lft-identity
4×add-log-exp
4×add-exp-log
4×add-cbrt-cube
4×pow1
3×sqrt-prod
3×pow1/3
2×sqrt-div
1×flip-+
1×pow1/2
1×flip3-+
1×rem-sqrt-square
Calls
4 calls:
Slowest
39.0ms
(sqrt (+ (* (* (cbrt (sin kx)) (sin kx)) (* (pow (cbrt (* (cbrt (sin kx)) (cbrt (sin kx)))) 2) (pow (cbrt (cbrt (sin kx))) 2))) (pow (sin ky) 2)))
1.0ms
(cbrt (sin kx))
0.0ms
(cbrt (sin kx))
0.0ms
(cbrt (sin kx))

series539.0ms

Calls
4 calls:
Slowest
179.0ms
(cbrt (sin kx))
142.0ms
(cbrt (sin kx))
135.0ms
(cbrt (sin kx))
82.0ms
(sqrt (+ (* (* (cbrt (sin kx)) (sin kx)) (* (pow (cbrt (* (cbrt (sin kx)) (cbrt (sin kx)))) 2) (pow (cbrt (cbrt (sin kx))) 2))) (pow (sin ky) 2)))

simplify1.9s

Calls
27 calls:
Slowest
603.0ms
(sqrt (- (* (* (* (cbrt (sin kx)) (sin kx)) (* (pow (cbrt (* (cbrt (sin kx)) (cbrt (sin kx)))) 2) (pow (cbrt (cbrt (sin kx))) 2))) (* (* (cbrt (sin kx)) (sin kx)) (* (pow (cbrt (* (cbrt (sin kx)) (cbrt (sin kx)))) 2) (pow (cbrt (cbrt (sin kx))) 2)))) (* (pow (sin ky) 2) (pow (sin ky) 2))))
262.0ms
(sqrt (* (cbrt (+ (* (* (cbrt (sin kx)) (sin kx)) (* (pow (cbrt (* (cbrt (sin kx)) (cbrt (sin kx)))) 2) (pow (cbrt (cbrt (sin kx))) 2))) (pow (sin ky) 2))) (cbrt (+ (* (* (cbrt (sin kx)) (sin kx)) (* (pow (cbrt (* (cbrt (sin kx)) (cbrt (sin kx)))) 2) (pow (cbrt (cbrt (sin kx))) 2))) (pow (sin ky) 2)))))
258.0ms
(sqrt (+ (* (* (cbrt (sin kx)) (sin kx)) (* (pow (cbrt (* (cbrt (sin kx)) (cbrt (sin kx)))) 2) (pow (cbrt (cbrt (sin kx))) 2))) (pow (sin ky) 2)))
254.0ms
(sqrt (sqrt (+ (* (* (cbrt (sin kx)) (sin kx)) (* (pow (cbrt (* (cbrt (sin kx)) (cbrt (sin kx)))) 2) (pow (cbrt (cbrt (sin kx))) 2))) (pow (sin ky) 2))))
148.0ms
(sqrt (+ (pow (* (* (cbrt (sin kx)) (sin kx)) (* (pow (cbrt (* (cbrt (sin kx)) (cbrt (sin kx)))) 2) (pow (cbrt (cbrt (sin kx))) 2))) 3) (pow (pow (sin ky) 2) 3)))

prune1.2s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 8.7b

localize21.0ms

Local error

Found 4 expressions with local error:

2.2b
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.3b
(* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
0.3b
(pow (sin ky) 2)
0.3b
(* (sin ky) (* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
17×add-exp-log
13×*-un-lft-identity
12×pow1
11×add-cbrt-cube
10×add-sqr-sqrt
9×add-cube-cbrt
9×associate-*l*
7×prod-exp
5×sqrt-prod
5×unpow-prod-down
4×add-log-exp
4×cbrt-unprod
4×pow-prod-down
4×associate-*r*
4×sqrt-div
2×distribute-lft-out
2×flip-+
2×*-commutative
2×associate-/r/
2×associate-*l/
2×flip3-+
2×rec-exp
1×unpow2
1×div-inv
1×associate-*r/
1×pow-exp
1×pow1/2
1×pow-pow
1×rem-sqrt-square
1×pow-to-exp
Calls
4 calls:
Slowest
10.0ms
(* (sin ky) (* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))
7.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
5.0ms
(* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
1.0ms
(pow (sin ky) 2)

series369.0ms

Calls
4 calls:
Slowest
139.0ms
(* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
138.0ms
(* (sin ky) (* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))
77.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
15.0ms
(pow (sin ky) 2)

simplify2.4s

Calls
48 calls:
Slowest
371.0ms
(* (* (* (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))))
369.0ms
(* (* (* (sin ky) (sin ky)) (sin ky)) (* (* (* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))) (* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))))
350.0ms
(* (* (* (/ 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)))
172.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
148.0ms
(+ (log (sin ky)) (log (* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))))

prune1.1s

Pruning

21 alts after pruning (19 fresh and 2 done)

Merged error: 8.7b

regimes1.9s

Accuracy

0% (1.5b remaining)

Error of 12.4b against oracle of 10.9b and baseline of 12.4b

bsearch5.0ms

end0.0ms

sample12.3s

Algorithm
intervals
Results
7.3s2745×body1280valid
2.9s1836×body640valid
925.0ms765×body320valid
679.0ms2308×body80valid
253.0ms346×body160valid