Details

Time bar (total: 1.5m)

sample860.0ms

Algorithm
intervals
Results
625.0ms88×body1280valid
75.0ms62×body640valid
23.0ms79×body80valid
17.0ms21×body320valid
4.0ms6×body160valid

simplify324.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
323.0ms
(* (/ (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: 8.6b

localize21.0ms

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

rewrite39.0ms

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
24.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
13.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
0.0ms
(hypot (sin kx) (sin ky))

series724.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
313.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
236.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
175.0ms
(hypot (sin kx) (sin ky))

simplify3.6s

Counts
59 → 85
Calls
59 calls:
Slowest
418.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
383.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
350.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
347.0ms
(* (* (* (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)))))
278.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 8.3b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

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
26.0ms
(* (sin th) (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky))))
15.0ms
(/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))
5.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))
0.0ms
(hypot (sin kx) (sin ky))

series941.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
317.0ms
(* (sin th) (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky))))
266.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))
179.0ms
(hypot (sin kx) (sin ky))
179.0ms
(/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))

simplify14.2s

Counts
207 → 208
Calls
207 calls:
Slowest
653.0ms
(* (* (* (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)))))
615.0ms
(* (* (* (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)))))
466.0ms
(/ (* (* 1 1) 1) (* (* (/ (hypot (sin kx) (sin ky)) (sin ky)) (/ (hypot (sin kx) (sin ky)) (sin ky))) (/ (hypot (sin kx) (sin ky)) (sin ky))))
426.0ms
(/ (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))) (* (* (sin ky) (sin ky)) (sin ky)))
399.0ms
(* (sqrt (+ (pow (sin ky) 2) (pow (sin kx) 2))) (/ 1 (sin ky)))

prune2.6s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 8.3b

localize26.0ms

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))

rewrite42.0ms

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
23.0ms
(/ (sin th) (/ (hypot (sin kx) (sin ky)) (sin ky)))
16.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))
0.0ms
(hypot (sin kx) (sin ky))

series646.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
279.0ms
(/ (sin th) (/ (hypot (sin kx) (sin ky)) (sin ky)))
216.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))
151.0ms
(hypot (sin kx) (sin ky))

simplify7.7s

Counts
132 → 123
Calls
132 calls:
Slowest
502.0ms
(* (sqrt (+ (pow (sin ky) 2) (pow (sin kx) 2))) (/ 1 (sin ky)))
488.0ms
(/ (* (cbrt (sin th)) (cbrt (sin th))) (/ (* (cbrt (hypot (sin kx) (sin ky))) (cbrt (hypot (sin kx) (sin ky)))) (* (cbrt (sin ky)) (cbrt (sin ky)))))
446.0ms
(/ (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))) (* (* (sin ky) (sin ky)) (sin ky)))
442.0ms
(* (sqrt (+ (pow (sin ky) 2) (pow (sin kx) 2))) (/ 1 (sin ky)))
396.0ms
(/ (* (* (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))))

prune1.7s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 8.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (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))

rewrite60.0ms

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
27.0ms
(/ (/ (sin th) (hypot (sin kx) (sin ky))) (/ 1 (sin ky)))
15.0ms
(/ (sin th) (hypot (sin kx) (sin ky)))
10.0ms
(/ 1 (sin ky))
0.0ms
(hypot (sin kx) (sin ky))

series828.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
332.0ms
(/ (/ (sin th) (hypot (sin kx) (sin ky))) (/ 1 (sin ky)))
277.0ms
(/ (sin th) (hypot (sin kx) (sin ky)))
187.0ms
(hypot (sin kx) (sin ky))
32.0ms
(/ 1 (sin ky))

simplify38.5s

Counts
441 → 309
Calls
441 calls:
Slowest
664.0ms
(/ (* (* (/ (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))))
587.0ms
(/ (/ 1 (* (cbrt (hypot (sin kx) (sin ky))) (cbrt (hypot (sin kx) (sin ky))))) (/ 1 (* (cbrt (sin ky)) (cbrt (sin ky)))))
520.0ms
(/ (/ (* (cbrt (sin th)) (cbrt (sin th))) (* (cbrt (hypot (sin kx) (sin ky))) (cbrt (hypot (sin kx) (sin ky))))) (/ (* (cbrt 1) (cbrt 1)) (sqrt (sin ky))))
502.0ms
(/ (/ (sqrt (sin th)) (* (cbrt (hypot (sin kx) (sin ky))) (cbrt (hypot (sin kx) (sin ky))))) (/ 1 (* (cbrt (sin ky)) (cbrt (sin ky)))))
496.0ms
(/ (/ (cbrt (sin th)) (cbrt (hypot (sin kx) (sin ky)))) (/ (cbrt 1) (sin ky)))

prune3.8s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 8.3b

regimes1.3s

Accuracy

0% (0.2b remaining)

Error of 8.4b against oracle of 8.2b and baseline of 8.4b

bsearch2.0ms

end0.0ms

sample12.2s

Algorithm
intervals
Results
6.6s2794×body1280valid
3.5s1883×body640valid
838.0ms2255×body80valid
722.0ms734×body320valid
257.0ms334×body160valid