Details

Time bar (total: 39.1s)

sample522.0ms

Algorithm
intervals
Results
249.0ms96×body1280valid
79.0ms60×body640valid
25.0ms26×body320valid
24.0ms67×body80valid
5.0ms7×body160valid

simplify347.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
346.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.2b

localize32.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
0.2b
(/ (sin ky) (hypot (sin kx) (sin ky)))
0.1b
(hypot (sin kx) (sin ky))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×*-un-lft-identity times-frac add-cube-cbrt
13×associate-*r*
10×add-cbrt-cube add-exp-log
5×pow1
3×expm1-log1p-u associate-/r* associate-*l* insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×hypot-udef clear-num frac-2neg pow-prod-down associate-*r/ *-commutative
Counts
3 → 76
Calls
3 calls:
Slowest
39.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
16.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms
(hypot (sin kx) (sin ky))

series799.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
364.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
243.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
191.0ms
(hypot (sin kx) (sin ky))

simplify3.9s

Counts
59 → 85
Calls
59 calls:
Slowest
617.0ms
(* (* (* (sin th) (sin th)) (sin th)) (* (* (/ (sin ky) (hypot (sin kx) (sin ky))) (/ (sin ky) (hypot (sin kx) (sin ky)))) (/ (sin ky) (hypot (sin kx) (sin ky)))))
452.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
340.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
282.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
259.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))

prune1.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.1b

localize40.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
0.2b
(/ (sin ky) (hypot (sin ky) (sin kx)))
0.1b
(hypot (sin ky) (sin kx))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×*-un-lft-identity times-frac add-cube-cbrt
13×associate-*r*
10×add-cbrt-cube add-exp-log
5×pow1
3×expm1-log1p-u associate-/r* associate-*l* insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×hypot-udef clear-num frac-2neg pow-prod-down associate-*r/ *-commutative
Counts
3 → 76
Calls
3 calls:
Slowest
25.0ms
(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
15.0ms
(/ (sin ky) (hypot (sin ky) (sin kx)))
0.0ms
(hypot (sin ky) (sin kx))

series712.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
326.0ms
(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
244.0ms
(/ (sin ky) (hypot (sin ky) (sin kx)))
142.0ms
(hypot (sin ky) (sin kx))

simplify3.5s

Counts
59 → 85
Calls
59 calls:
Slowest
460.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin ky) (sin kx)) (hypot (sin ky) (sin kx))) (hypot (sin ky) (sin kx))))
361.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
358.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
300.0ms
(* (* (* (sin th) (sin th)) (sin th)) (* (* (/ (sin ky) (hypot (sin ky) (sin kx))) (/ (sin ky) (hypot (sin ky) (sin kx)))) (/ (sin ky) (hypot (sin ky) (sin kx)))))
247.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))

prune1.1s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 8.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
0.4b
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
0.4b
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
0.3b
(* (cbrt (/ (sin ky) (hypot (sin kx) (sin ky)))) (cbrt (/ (sin ky) (hypot (sin kx) (sin ky)))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
103×cbrt-prod
81×add-sqr-sqrt
69×times-frac
57×*-un-lft-identity add-cube-cbrt
16×swap-sqr associate-*r* associate-*l*
11×pow1
9×pow1/3 unswap-sqr
7×cbrt-div div-inv
6×add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times pow-plus associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Counts
4 → 156
Calls
4 calls:
Slowest
18.0ms
(* (cbrt (/ (sin ky) (hypot (sin kx) (sin ky)))) (cbrt (/ (sin ky) (hypot (sin kx) (sin ky)))))
2.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
2.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
1.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
322.0ms
(* (cbrt (/ (sin ky) (hypot (sin kx) (sin ky)))) (cbrt (/ (sin ky) (hypot (sin kx) (sin ky)))))
304.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
288.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
286.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))

simplify5.6s

Counts
152 → 168
Calls
152 calls:
Slowest
449.0ms
(- (+ (exp (* 1/3 (- (log ky) (log kx)))) (* 1/18 (* (pow kx 2) (exp (* 1/3 (- (log ky) (log kx))))))) (* 13/108 (* (pow ky 2) (exp (* 1/3 (- (log ky) (log kx)))))))
391.0ms
(- (+ (exp (* 1/3 (- (log ky) (log kx)))) (* 1/18 (* (pow kx 2) (exp (* 1/3 (- (log ky) (log kx))))))) (* 13/108 (* (pow ky 2) (exp (* 1/3 (- (log ky) (log kx)))))))
384.0ms
(- (+ (exp (* 1/3 (- (log ky) (log kx)))) (* 1/18 (* (pow kx 2) (exp (* 1/3 (- (log ky) (log kx))))))) (* 13/108 (* (pow ky 2) (exp (* 1/3 (- (log ky) (log kx)))))))
364.0ms
(- (+ (* 1/9 (* (exp (* 1/3 (- (* 2 (log ky)) (* 2 (log kx))))) (pow kx 2))) (exp (* 1/3 (- (* 2 (log ky)) (* 2 (log kx)))))) (* 7/27 (* (exp (* 1/3 (- (* 2 (log ky)) (* 2 (log kx))))) (pow ky 2))))
245.0ms
(pow (* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky)) 1/3)

prune2.7s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 8.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (sin ky))
0.7b
(cbrt (sin ky))
0.7b
(cbrt (sin ky))
0.6b
(cbrt (hypot (sin kx) (sin ky)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube pow1/3 add-exp-log insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 56
Calls
4 calls:
Slowest
8.0ms
(cbrt (hypot (sin kx) (sin ky)))
1.0ms
(cbrt (sin ky))
1.0ms
(cbrt (sin ky))
1.0ms
(cbrt (sin ky))

series639.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
199.0ms
(cbrt (hypot (sin kx) (sin ky)))
174.0ms
(cbrt (sin ky))
133.0ms
(cbrt (sin ky))
133.0ms
(cbrt (sin ky))

simplify1.7s

Counts
24 → 68
Calls
24 calls:
Slowest
379.0ms
(- (+ (* 1/6 (* (pow kx 2) (pow (/ 1 (pow ky 5)) 1/3))) (pow ky 1/3)) (* 1/18 (pow (pow ky 7) 1/3)))
280.0ms
(- (pow ky 1/3) (+ (* 1/3240 (pow (pow ky 13) 1/3)) (* 1/18 (pow (pow ky 7) 1/3))))
266.0ms
(- (pow ky 1/3) (+ (* 1/3240 (pow (pow ky 13) 1/3)) (* 1/18 (pow (pow ky 7) 1/3))))
257.0ms
(- (pow ky 1/3) (+ (* 1/3240 (pow (pow ky 13) 1/3)) (* 1/18 (pow (pow ky 7) 1/3))))
202.0ms
(pow (sqrt (+ (pow (sin ky) 2) (pow (sin kx) 2))) 1/3)

prune1.2s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 8.1b

regimes1.2s

Accuracy

0% (0.1b remaining)

Error of 8.7b against oracle of 8.5b and baseline of 8.7b

bsearch2.0ms

end0.0ms

sample12.5s

Algorithm
intervals
Results
7.5s2750×body1280valid
2.8s1854×body640valid
860.0ms2308×body80valid
669.0ms742×body320valid
309.0ms346×body160valid