Details

Time bar (total: 1.3m)

sample148.0ms

Algorithm
intervals
Results
116.0ms256×body80valid

simplify594.0ms

Calls
1 calls:
Slowest
593.0ms
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.4b

localize47.0ms

Local error

Found 4 expressions with local error:

10.8b
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
2.0b
(/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))
0.9b
(/ 4 (/ Om l))
0.3b
(* (sin ky) (sin ky))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
155×times-frac
75×add-sqr-sqrt
74×*-un-lft-identity add-cube-cbrt
43×div-inv
29×associate-/r*
22×associate-/r/
11×add-cbrt-cube add-exp-log
9×pow1
4×insert-posit16 add-log-exp
3×cbrt-undiv div-exp associate-*r* associate-*l* sqrt-prod sqr-sin sin-mult associate-/l* associate-/l/
2×clear-num frac-2neg flip3-+ sqrt-div div-sub flip-+
1×pow2 rem-sqrt-square associate-+r- pow-plus pow1/2 pow-prod-down frac-add prod-exp *-commutative pow-prod-up associate-+l- cbrt-unprod
Calls
4 calls:
Slowest
37.0ms
(/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))
9.0ms
(* (sin ky) (sin ky))
8.0ms
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
1.0ms
(/ 4 (/ Om l))

series696.0ms

Calls
4 calls:
Slowest
373.0ms
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
284.0ms
(/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))
24.0ms
(* (sin ky) (sin ky))
15.0ms
(/ 4 (/ Om l))

simplify28.2s

Calls
222 calls:
Slowest
697.0ms
(/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ 1 l) (/ 4 (/ Om l))))
591.0ms
(/ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (/ (* (* (/ Om l) (/ Om l)) (/ Om l)) (* (* (/ 4 (/ Om l)) (/ 4 (/ Om l))) (/ 4 (/ Om l)))))
558.0ms
(- (log (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (- (log (/ Om l)) (log (/ 4 (/ Om l)))))
496.0ms
(/ 1/2 (/ (/ Om l) (/ 4 (/ Om l))))
490.0ms
(/ (* (cbrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (cbrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/ (* (cbrt (/ Om l)) (cbrt (/ Om l))) (/ 4 Om)))

prune3.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

10.8b
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
10.8b
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
10.8b
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
7.2b
(cbrt (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×*-un-lft-identity add-cube-cbrt
8×sqrt-div
6×cbrt-prod
4×pow1 flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 add-log-exp
3×rem-sqrt-square pow1/2
2×cbrt-div
1×pow1/3
Calls
4 calls:
Slowest
11.0ms
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
10.0ms
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
7.0ms
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
4.0ms
(cbrt (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))))

series1.1s

Calls
4 calls:
Slowest
340.0ms
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
310.0ms
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
279.0ms
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
193.0ms
(cbrt (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))))

simplify5.2s

Calls
38 calls:
Slowest
351.0ms
(cbrt (* (cbrt (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))) (cbrt (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))))))
344.0ms
(sqrt (* (cbrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))) (cbrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))))
323.0ms
(sqrt (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))))
301.0ms
(sqrt (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))))
292.0ms
(sqrt (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))))

prune1.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize51.0ms

Local error

Found 4 expressions with local error:

29.1b
(posit16->real (real->posit16 (cbrt (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))))))
10.8b
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
10.8b
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
10.8b
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×*-un-lft-identity add-cube-cbrt
6×sqrt-div
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×rem-sqrt-square flip3-+ pow1/2 flip-+
1×remove-posit16
Calls
4 calls:
Slowest
16.0ms
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
12.0ms
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
6.0ms
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
0.0ms
(posit16->real (real->posit16 (cbrt (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))))))

series1.0s

Calls
4 calls:
Slowest
292.0ms
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
276.0ms
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
265.0ms
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
212.0ms
(posit16->real (real->posit16 (cbrt (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))))))

simplify4.0s

Calls
31 calls:
Slowest
327.0ms
(sqrt (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))))
326.0ms
(sqrt (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))))
304.0ms
(sqrt (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))))
296.0ms
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
287.0ms
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))

prune2.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize40.0ms

Local error

Found 4 expressions with local error:

52.2b
(posit16->real (real->posit16 (/ 4 (/ Om l))))
10.8b
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (posit16->real (real->posit16 (/ 4 (/ Om l))))))))
2.0b
(/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (posit16->real (real->posit16 (/ 4 (/ Om l))))))
1.9b
(real->posit16 (/ 4 (/ Om l)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
96×times-frac
54×add-sqr-sqrt
53×*-un-lft-identity add-cube-cbrt
17×div-inv
16×associate-/r*
8×add-cbrt-cube add-exp-log
3×pow1 cbrt-undiv div-exp sqrt-prod insert-posit16 associate-/l* add-log-exp associate-/l/
2×flip3-+ sqrt-div div-sub flip-+ sqr-sin sin-mult
1×rem-sqrt-square clear-num associate-+r- frac-2neg pow1/2 frac-add associate-/r/ associate-+l- remove-posit16
Calls
4 calls:
Slowest
28.0ms
(/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (posit16->real (real->posit16 (/ 4 (/ Om l))))))
7.0ms
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (posit16->real (real->posit16 (/ 4 (/ Om l))))))))
0.0ms
(posit16->real (real->posit16 (/ 4 (/ Om l))))
0.0ms
(real->posit16 (/ 4 (/ Om l)))

series565.0ms

Calls
4 calls:
Slowest
293.0ms
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (posit16->real (real->posit16 (/ 4 (/ Om l))))))))
263.0ms
(/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (posit16->real (real->posit16 (/ 4 (/ Om l))))))
9.0ms
(posit16->real (real->posit16 (/ 4 (/ Om l))))
0.0ms
(real->posit16 (/ 4 (/ Om l)))

simplify18.8s

Calls
139 calls:
Slowest
599.0ms
(/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (/ (cbrt (/ Om l)) (posit16->real (real->posit16 (/ 4 (/ Om l))))))
558.0ms
(/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (/ (/ Om l) (posit16->real (real->posit16 (/ 4 (/ Om l))))))
494.0ms
(/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (/ (/ Om l) (posit16->real (real->posit16 (/ 4 (/ Om l))))))
434.0ms
(/ (cbrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (/ (/ Om l) (posit16->real (real->posit16 (/ 4 (/ Om l))))))
431.0ms
(/ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (/ (* (* (/ Om l) (/ Om l)) (/ Om l)) (* (* (posit16->real (real->posit16 (/ 4 (/ Om l)))) (posit16->real (real->posit16 (/ 4 (/ Om l))))) (posit16->real (real->posit16 (/ 4 (/ Om l)))))))

prune3.8s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.2b

regimes454.0ms

Accuracy

0% (0.9b remaining)

Error of 1.7b against oracle of 0.7b and baseline of 1.7b

bsearch11.0ms

end0.0ms

sample3.9s

Algorithm
intervals
Results
3.6s8000×body80valid