Details

Time bar (total: 41.6s)

sample533.0ms

Algorithm
intervals
Results
176.0ms82×body1280valid
93.0ms62×body640valid
77.0ms25×body320valid
29.0ms76×body80valid
7.0ms11×body160valid

simplify304.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
303.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.4b

localize44.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (sin ky) (hypot (sin kx) (sin ky)))
0.2b
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
0.0b
(hypot (sin kx) (sin ky))

rewrite58.0ms

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
36.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
17.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms
(hypot (sin kx) (sin ky))

series776.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
350.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
259.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
166.0ms
(hypot (sin kx) (sin ky))

simplify3.5s

Counts
59 → 85
Calls
59 calls:
Slowest
440.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
334.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
329.0ms
(* (* (* (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)))))
307.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
275.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.3b

localize23.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (sin ky) (hypot (sin kx) (sin ky)))
0.2b
(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))
0.0b
(hypot (sin kx) (sin ky))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×*-un-lft-identity times-frac add-cube-cbrt
13×associate-*l*
10×add-cbrt-cube add-exp-log
5×pow1
3×expm1-log1p-u associate-/r* associate-*r* 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-*l/ *-commutative
Counts
3 → 76
Calls
3 calls:
Slowest
17.0ms
(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))
12.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms
(hypot (sin kx) (sin ky))

series682.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
288.0ms
(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))
201.0ms
(hypot (sin kx) (sin ky))
192.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))

simplify4.0s

Counts
59 → 85
Calls
59 calls:
Slowest
654.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
446.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
387.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
345.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
321.0ms
(* (* (* (/ (sin ky) (hypot (sin kx) (sin ky))) (/ (sin ky) (hypot (sin kx) (sin ky)))) (/ (sin ky) (hypot (sin kx) (sin ky)))) (* (* (sin th) (sin th)) (sin th)))

prune1.1s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 8.3b

localize65.0ms

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

rewrite34.0ms

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
14.0ms
(* (cbrt (/ (sin ky) (hypot (sin kx) (sin ky)))) (cbrt (/ (sin ky) (hypot (sin kx) (sin ky)))))
10.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
3.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
3.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
357.0ms
(* (cbrt (/ (sin ky) (hypot (sin kx) (sin ky)))) (cbrt (/ (sin ky) (hypot (sin kx) (sin ky)))))
328.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
311.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
310.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))

simplify5.3s

Counts
152 → 168
Calls
152 calls:
Slowest
443.0ms
(- (+ (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)))))))
387.0ms
(- (+ (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)))))))
349.0ms
(- (+ (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)))))))
340.0ms
(- (+ (* 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))))
268.0ms
(pow (* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky)) 1/3)

prune2.8s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 8.3b

localize65.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sin ky))
0.6b
(cbrt (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))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
32×cbrt-prod
20×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×times-frac
4×expm1-log1p-u pow1 add-cbrt-cube pow1/3 add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-div div-inv
Counts
4 → 78
Calls
4 calls:
Slowest
1.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
1.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
1.0ms
(cbrt (sin ky))
1.0ms
(cbrt (hypot (sin kx) (sin ky)))

series945.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
301.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
300.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
198.0ms
(cbrt (hypot (sin kx) (sin ky)))
144.0ms
(cbrt (sin ky))

simplify3.3s

Counts
46 → 90
Calls
46 calls:
Slowest
379.0ms
(- (+ (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)))))))
370.0ms
(- (+ (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)))))))
362.0ms
(- (+ (* 1/6 (* (pow kx 2) (pow (/ 1 (pow ky 5)) 1/3))) (pow ky 1/3)) (* 1/18 (pow (pow ky 7) 1/3)))
315.0ms
(- (pow ky 1/3) (+ (* 1/3240 (pow (pow ky 13) 1/3)) (* 1/18 (pow (pow ky 7) 1/3))))
235.0ms
(pow (* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky)) 1/3)

prune1.6s

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 8.3b

regimes1.3s

Accuracy

0% (0.2b remaining)

Error of 8.4b against oracle of 8.3b and baseline of 8.4b

bsearch1.0ms

end0.0ms

sample12.5s

Algorithm
intervals
Results
6.9s2746×body1280valid
3.1s1841×body640valid
1.3s778×body320valid
690.0ms2292×body80valid
242.0ms343×body160valid