Details

Time bar (total: 43.7s)

sample1.1s

Algorithm
intervals
Results
879.0ms83×body1280valid
94.0ms62×body640valid
27.0ms80×body80valid
25.0ms25×body320valid
6.0ms6×body160valid

simplify292.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
292.0ms
(* (/ (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: 10.1b

localize45.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
0.1b
(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0b
(hypot (sin kx) (sin ky))

rewrite32.0ms

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
21.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
8.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms
(hypot (sin kx) (sin ky))

series755.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
353.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
233.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
169.0ms
(hypot (sin kx) (sin ky))

simplify3.4s

Counts
59 → 85
Calls
59 calls:
Slowest
504.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
348.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
309.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
293.0ms
(* (* (* (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)))))
260.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))

prune1.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.0b

localize32.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))
0.1b
(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0b
(hypot (sin kx) (sin ky))

rewrite32.0ms

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
15.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
15.0ms
(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))
0.0ms
(hypot (sin kx) (sin ky))

series765.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
327.0ms
(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))
243.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
194.0ms
(hypot (sin kx) (sin ky))

simplify3.4s

Counts
59 → 85
Calls
59 calls:
Slowest
474.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
331.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
312.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
295.0ms
(* (* (* (/ (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)))
238.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin ky) (/ 1 (hypot (sin kx) (sin ky))))
0.2b
(/ 1 (hypot (sin kx) (sin ky)))
0.2b
(* (* (sin ky) (/ 1 (hypot (sin kx) (sin ky)))) (sin th))
0.0b
(hypot (sin kx) (sin ky))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
28×add-sqr-sqrt
22×*-un-lft-identity
21×add-cube-cbrt
20×times-frac add-cbrt-cube
16×associate-*r*
13×prod-exp
12×pow1
7×cbrt-unprod
6×div-exp
4×expm1-log1p-u associate-*l* pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv rec-exp associate-/r* 1-exp associate-/l* unswap-sqr
2×associate-*l/ associate-*r/ un-div-inv *-commutative div-inv
1×hypot-udef clear-num frac-2neg pow-flip inv-pow
Counts
4 → 111
Calls
4 calls:
Slowest
64.0ms
(* (* (sin ky) (/ 1 (hypot (sin kx) (sin ky)))) (sin th))
26.0ms
(* (sin ky) (/ 1 (hypot (sin kx) (sin ky))))
9.0ms
(/ 1 (hypot (sin kx) (sin ky)))
0.0ms
(hypot (sin kx) (sin ky))

series871.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
327.0ms
(* (* (sin ky) (/ 1 (hypot (sin kx) (sin ky)))) (sin th))
213.0ms
(* (sin ky) (/ 1 (hypot (sin kx) (sin ky))))
200.0ms
(/ 1 (hypot (sin kx) (sin ky)))
131.0ms
(hypot (sin kx) (sin ky))

simplify5.9s

Counts
85 → 123
Calls
85 calls:
Slowest
438.0ms
(* (* (* (sin ky) (sin ky)) (sin ky)) (* (* (/ 1 (hypot (sin kx) (sin ky))) (/ 1 (hypot (sin kx) (sin ky)))) (/ 1 (hypot (sin kx) (sin ky)))))
347.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
332.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
274.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
264.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))

prune1.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin ky) (* (/ 1 (hypot (sin kx) (sin ky))) (sin th)))
0.3b
(* (/ 1 (hypot (sin kx) (sin ky))) (sin th))
0.2b
(/ 1 (hypot (sin kx) (sin ky)))
0.0b
(hypot (sin kx) (sin ky))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
28×add-sqr-sqrt
22×*-un-lft-identity
21×add-cube-cbrt
20×times-frac add-cbrt-cube
16×associate-*l*
13×prod-exp
12×pow1
7×cbrt-unprod
6×div-exp
4×expm1-log1p-u associate-*r* pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv rec-exp associate-/r* 1-exp associate-/l* unswap-sqr
2×associate-*l/ *-commutative div-inv
1×hypot-udef clear-num frac-2neg associate-*r/ pow-flip inv-pow
Counts
4 → 109
Calls
4 calls:
Slowest
50.0ms
(* (sin ky) (* (/ 1 (hypot (sin kx) (sin ky))) (sin th)))
13.0ms
(* (/ 1 (hypot (sin kx) (sin ky))) (sin th))
4.0ms
(/ 1 (hypot (sin kx) (sin ky)))
0.0ms
(hypot (sin kx) (sin ky))

series963.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
285.0ms
(* (sin ky) (* (/ 1 (hypot (sin kx) (sin ky))) (sin th)))
285.0ms
(* (/ 1 (hypot (sin kx) (sin ky))) (sin th))
213.0ms
(/ 1 (hypot (sin kx) (sin ky)))
179.0ms
(hypot (sin kx) (sin ky))

simplify6.2s

Counts
81 → 121
Calls
81 calls:
Slowest
538.0ms
(* (* (* (/ 1 (hypot (sin kx) (sin ky))) (/ 1 (hypot (sin kx) (sin ky)))) (/ 1 (hypot (sin kx) (sin ky)))) (* (* (sin th) (sin th)) (sin th)))
363.0ms
(* (/ (* (* 1 1) 1) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky)))) (* (* (sin th) (sin th)) (sin th)))
331.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
317.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
314.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin th))

prune1.6s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 10.0b

regimes1.2s

Accuracy

0% (0.3b remaining)

Error of 8.8b against oracle of 8.5b and baseline of 8.8b

bsearch3.0ms

end0.0ms

sample12.5s

Algorithm
intervals
Results
6.8s2797×body1280valid
3.1s1773×body640valid
1.3s2324×body80valid
730.0ms767×body320valid
215.0ms339×body160valid