Details

Time bar (total: 2.4m)

sample685.0ms

Algorithm
intervals
Results
314.0ms67×body640valid
224.0ms81×body1280valid
19.0ms75×body80valid
17.0ms19×body320valid
9.0ms14×body160valid

simplify804.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
803.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.9b

localize27.0ms

Local error

Found 3 expressions with local error:

3.2b
(/ (* (sin th) (sin ky)) (hypot (sin kx) (sin ky)))
0.2b
(* (sin th) (sin ky))
0.1b
(hypot (sin kx) (sin ky))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
10×add-cbrt-cube add-exp-log
9×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
5×pow1
3×expm1-log1p-u associate-/r* times-frac associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod sin-mult
1×hypot-udef clear-num frac-2neg pow-prod-down *-commutative div-inv associate-/l* unswap-sqr associate-/l/
Counts
3 → 58
Calls
3 calls:
Slowest
16.0ms
(/ (* (sin th) (sin ky)) (hypot (sin kx) (sin ky)))
11.0ms
(* (sin th) (sin ky))
0.0ms
(hypot (sin kx) (sin ky))

series448.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
274.0ms
(/ (* (sin th) (sin ky)) (hypot (sin kx) (sin ky)))
123.0ms
(hypot (sin kx) (sin ky))
50.0ms
(* (sin th) (sin ky))

simplify3.8s

Counts
71 → 67
Calls
71 calls:
Slowest
409.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
407.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
381.0ms
(* (* (* (sin th) (sin th)) (sin th)) (* (* (sin ky) (sin ky)) (sin ky)))
361.0ms
(* (* (/ (* (sin th) (sin ky)) (hypot (sin kx) (sin ky))) (/ (* (sin th) (sin ky)) (hypot (sin kx) (sin ky)))) (/ (* (sin th) (sin ky)) (hypot (sin kx) (sin ky))))
223.0ms
(/ (* (* (* (sin th) (sin ky)) (* (sin th) (sin ky))) (* (sin th) (sin ky))) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))

prune894.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 8.7b

localize27.0ms

Local error

Found 3 expressions with local error:

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

rewrite24.0ms

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
16.0ms
(/ (sin th) (/ (hypot (sin kx) (sin ky)) (sin ky)))
5.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))
0.0ms
(hypot (sin kx) (sin ky))

series683.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
284.0ms
(/ (sin th) (/ (hypot (sin kx) (sin ky)) (sin ky)))
242.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))
157.0ms
(hypot (sin kx) (sin ky))

simplify9.9s

Counts
173 → 123
Calls
173 calls:
Slowest
555.0ms
(/ (* (cbrt (sin th)) (cbrt (sin th))) (/ (* (cbrt (hypot (sin kx) (sin ky))) (cbrt (hypot (sin kx) (sin ky)))) (* (cbrt (sin ky)) (cbrt (sin ky)))))
498.0ms
(* (sqrt (+ (pow (sin ky) 2) (pow (sin kx) 2))) (/ 1 (sin ky)))
478.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
475.0ms
(* (sqrt (+ (pow (sin ky) 2) (pow (sin kx) 2))) (/ 1 (sin ky)))
460.0ms
(/ (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))) (* (* (sin ky) (sin ky)) (sin ky)))

prune1.6s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 8.7b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
480×times-frac
239×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
60×associate-/r*
36×add-exp-log
23×div-inv
22×div-exp
20×add-cbrt-cube
10×cbrt-undiv
9×associate-/l*
6×associate-/r/
5×pow1
4×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×hypot-udef pow-flip inv-pow
Counts
4 → 323
Calls
4 calls:
Slowest
16.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
12.0ms
(/ (sin th) (/ 1 (/ (sin ky) (hypot (sin kx) (sin ky)))))
10.0ms
(/ 1 (/ (sin ky) (hypot (sin kx) (sin ky))))
0.0ms
(hypot (sin kx) (sin ky))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
379.0ms
(/ (sin th) (/ 1 (/ (sin ky) (hypot (sin kx) (sin ky)))))
248.0ms
(/ 1 (/ (sin ky) (hypot (sin kx) (sin ky))))
222.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
161.0ms
(hypot (sin kx) (sin ky))

simplify53.2s

Counts
517 → 335
Calls
517 calls:
Slowest
964.0ms
(* (* (/ (sin th) (/ 1 (/ (sin ky) (hypot (sin kx) (sin ky))))) (/ (sin th) (/ 1 (/ (sin ky) (hypot (sin kx) (sin ky)))))) (/ (sin th) (/ 1 (/ (sin ky) (hypot (sin kx) (sin ky))))))
863.0ms
(/ (* (* (sin th) (sin th)) (sin th)) (/ (* (* 1 1) 1) (* (* (/ (sin ky) (hypot (sin kx) (sin ky))) (/ (sin ky) (hypot (sin kx) (sin ky)))) (/ (sin ky) (hypot (sin kx) (sin ky))))))
669.0ms
(/ 1 (/ (* (cbrt (sin ky)) (cbrt (sin ky))) (* (cbrt (hypot (sin kx) (sin ky))) (cbrt (hypot (sin kx) (sin ky))))))
571.0ms
(/ 1 (/ 1 (/ (* (cbrt (sin ky)) (cbrt (sin ky))) (* (cbrt (hypot (sin kx) (sin ky))) (cbrt (hypot (sin kx) (sin ky)))))))
567.0ms
(* (* (/ 1 (/ (sin ky) (hypot (sin kx) (sin ky)))) (/ 1 (/ (sin ky) (hypot (sin kx) (sin ky))))) (/ 1 (/ (sin ky) (hypot (sin kx) (sin ky)))))

prune4.4s

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 8.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ (sin th) (hypot (sin kx) (sin ky))) (/ 1 (sin ky)))
0.3b
(/ (sin th) (hypot (sin kx) (sin ky)))
0.1b
(/ 1 (sin ky))
0.1b
(hypot (sin kx) (sin ky))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
439×times-frac
216×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
32×add-exp-log
31×div-inv
20×add-cbrt-cube
19×associate-/r* div-exp associate-/l*
10×cbrt-undiv
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×rec-exp clear-num frac-2neg 1-exp
1×hypot-udef associate-/r/ pow-flip inv-pow associate-/l/
Counts
4 → 297
Calls
4 calls:
Slowest
13.0ms
(/ (/ (sin th) (hypot (sin kx) (sin ky))) (/ 1 (sin ky)))
7.0ms
(/ (sin th) (hypot (sin kx) (sin ky)))
5.0ms
(/ 1 (sin ky))
0.0ms
(hypot (sin kx) (sin ky))

series733.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
296.0ms
(/ (/ (sin th) (hypot (sin kx) (sin ky))) (/ 1 (sin ky)))
259.0ms
(/ (sin th) (hypot (sin kx) (sin ky)))
156.0ms
(hypot (sin kx) (sin ky))
22.0ms
(/ 1 (sin ky))

simplify45.9s

Counts
498 → 309
Calls
498 calls:
Slowest
827.0ms
(/ (* (* (/ (sin th) (hypot (sin kx) (sin ky))) (/ (sin th) (hypot (sin kx) (sin ky)))) (/ (sin th) (hypot (sin kx) (sin ky)))) (/ (* (* 1 1) 1) (* (* (sin ky) (sin ky)) (sin ky))))
646.0ms
(/ (/ 1 (* (cbrt (hypot (sin kx) (sin ky))) (cbrt (hypot (sin kx) (sin ky))))) (/ 1 (* (cbrt (sin ky)) (cbrt (sin ky)))))
623.0ms
(* (* (/ (/ (sin th) (hypot (sin kx) (sin ky))) (/ 1 (sin ky))) (/ (/ (sin th) (hypot (sin kx) (sin ky))) (/ 1 (sin ky)))) (/ (/ (sin th) (hypot (sin kx) (sin ky))) (/ 1 (sin ky))))
541.0ms
(+ (* 7/360 (pow ky 3)) (+ (/ 1 ky) (* 1/6 ky)))
538.0ms
(/ (/ 1 (* (cbrt (hypot (sin kx) (sin ky))) (cbrt (hypot (sin kx) (sin ky))))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sin ky)) (cbrt (sin ky)))))

prune3.9s

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 8.7b

regimes1.4s

Accuracy

0% (0.3b remaining)

Error of 8.9b against oracle of 8.6b and baseline of 8.9b

bsearch3.0ms

end0.0ms

sample11.8s

Algorithm
intervals
Results
7.3s2781×body1280valid
2.7s1839×body640valid
731.0ms725×body320valid
671.0ms2301×body80valid
200.0ms354×body160valid