Details

Time bar (total: 54.1s)

sample765.0ms

Algorithm
intervals
Results
427.0ms81×body1280valid
122.0ms66×body640valid
37.0ms9×body160valid
24.0ms87×body80valid
12.0ms13×body320valid

simplify391.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
390.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.6b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite71.0ms

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
46.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
20.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
1.0ms
(hypot (sin kx) (sin ky))

series911.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
417.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
336.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
158.0ms
(hypot (sin kx) (sin ky))

simplify3.5s

Counts
59 → 85
Calls
59 calls:
Slowest
517.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
319.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
305.0ms
(* (* (* (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)))))
297.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
266.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))
0.2b
(/ (hypot (sin kx) (sin ky)) (sin ky))
0.1b
(* (sin th) (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky))))
0.1b
(hypot (sin kx) (sin ky))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
104×add-sqr-sqrt
92×*-un-lft-identity
90×add-cube-cbrt
44×associate-*r*
36×add-exp-log
20×add-cbrt-cube
16×associate-/r*
15×div-exp
10×div-inv
7×pow1 cbrt-undiv prod-exp
6×associate-/l*
5×unswap-sqr
4×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l* cbrt-unprod
2×clear-num frac-2neg associate-/r/
1×hypot-udef pow-prod-down associate-*r/ un-div-inv *-commutative pow-flip inv-pow
Counts
4 → 196
Calls
4 calls:
Slowest
46.0ms
(* (sin th) (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky))))
7.0ms
(/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))
6.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))
0.0ms
(hypot (sin kx) (sin ky))

series944.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
287.0ms
(* (sin th) (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky))))
248.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))
236.0ms
(/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))
173.0ms
(hypot (sin kx) (sin ky))

simplify14.1s

Counts
207 → 208
Calls
207 calls:
Slowest
705.0ms
(* (* (* (sin th) (sin th)) (sin th)) (/ (* (* 1 1) 1) (* (* (/ (hypot (sin kx) (sin ky)) (sin ky)) (/ (hypot (sin kx) (sin ky)) (sin ky))) (/ (hypot (sin kx) (sin ky)) (sin ky)))))
625.0ms
(* (* (* (sin th) (sin th)) (sin th)) (* (* (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky))) (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))) (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))))
522.0ms
(/ (* (* 1 1) 1) (* (* (/ (hypot (sin kx) (sin ky)) (sin ky)) (/ (hypot (sin kx) (sin ky)) (sin ky))) (/ (hypot (sin kx) (sin ky)) (sin ky))))
473.0ms
(- 0 (- (log (hypot (sin kx) (sin ky))) (log (sin ky))))
404.0ms
(/ (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))) (* (* (sin ky) (sin ky)) (sin ky)))

prune2.7s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 8.5b

localize34.0ms

Local error

Found 3 expressions with local error:

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

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
53×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×associate-/r*
10×add-cbrt-cube add-exp-log
6×div-inv associate-/l*
4×cbrt-undiv div-exp
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×hypot-udef associate-/r/
Counts
3 → 114
Calls
3 calls:
Slowest
21.0ms
(/ (sin th) (/ (hypot (sin kx) (sin ky)) (sin ky)))
10.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))
6.0ms
(hypot (sin kx) (sin ky))

series751.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
335.0ms
(/ (sin th) (/ (hypot (sin kx) (sin ky)) (sin ky)))
249.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))
168.0ms
(hypot (sin kx) (sin ky))

simplify7.7s

Counts
132 → 123
Calls
132 calls:
Slowest
502.0ms
(/ (* (cbrt (sin th)) (cbrt (sin th))) (/ (* (cbrt (hypot (sin kx) (sin ky))) (cbrt (hypot (sin kx) (sin ky)))) (* (cbrt (sin ky)) (cbrt (sin ky)))))
454.0ms
(/ (* (* (sin th) (sin th)) (sin th)) (* (* (/ (hypot (sin kx) (sin ky)) (sin ky)) (/ (hypot (sin kx) (sin ky)) (sin ky))) (/ (hypot (sin kx) (sin ky)) (sin ky))))
406.0ms
(* (sqrt (+ (pow (sin ky) 2) (pow (sin kx) 2))) (/ 1 (sin ky)))
399.0ms
(* (sqrt (+ (pow (sin ky) 2) (pow (sin kx) 2))) (/ 1 (sin ky)))
368.0ms
(/ (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))) (* (* (sin ky) (sin ky)) (sin ky)))

prune1.7s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 8.5b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b
(expm1 (log1p (hypot (sin kx) (sin ky))))
0.2b
(log1p (hypot (sin kx) (sin ky)))
0.1b
(/ (sin ky) (expm1 (log1p (hypot (sin kx) (sin ky)))))
0.1b
(* (sin th) (/ (sin ky) (expm1 (log1p (hypot (sin kx) (sin ky))))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
20×*-un-lft-identity add-cube-cbrt
19×times-frac
13×associate-*r*
11×add-cbrt-cube add-exp-log
6×pow1
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-*l* associate-/l*
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×log1p-udef expm1-log1p clear-num frac-2neg pow-prod-down log1p-expm1 associate-*r/ *-commutative expm1-udef
Counts
4 → 89
Calls
4 calls:
Slowest
16.0ms
(/ (sin ky) (expm1 (log1p (hypot (sin kx) (sin ky)))))
13.0ms
(* (sin th) (/ (sin ky) (expm1 (log1p (hypot (sin kx) (sin ky))))))
1.0ms
(log1p (hypot (sin kx) (sin ky)))
0.0ms
(expm1 (log1p (hypot (sin kx) (sin ky))))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
351.0ms
(* (sin th) (/ (sin ky) (expm1 (log1p (hypot (sin kx) (sin ky))))))
303.0ms
(/ (sin ky) (expm1 (log1p (hypot (sin kx) (sin ky)))))
175.0ms
(log1p (hypot (sin kx) (sin ky)))
175.0ms
(expm1 (log1p (hypot (sin kx) (sin ky))))

simplify4.2s

Counts
64 → 101
Calls
64 calls:
Slowest
435.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (expm1 (log1p (hypot (sin kx) (sin ky)))) (expm1 (log1p (hypot (sin kx) (sin ky))))) (expm1 (log1p (hypot (sin kx) (sin ky))))))
315.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
311.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
306.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
298.0ms
(- ky (+ (* 1/2 (pow kx 2)) (* 1/2 (pow ky 2))))

prune1.4s

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 8.5b

regimes1.1s

Accuracy

0% (0.2b remaining)

Error of 8.7b against oracle of 8.6b and baseline of 8.7b

bsearch2.0ms

end0.0ms

sample11.3s

Algorithm
intervals
Results
6.7s2685×body1280valid
2.4s1834×body640valid
1.1s2370×body80valid
648.0ms720×body320valid
197.0ms391×body160valid