Details

Time bar (total: 2.0m)

sample251.0ms

Algorithm
intervals
Results
220.0ms256×body80valid

simplify995.0ms

Calls
1 calls:
Slowest
994.0ms
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize52.0ms

Local error

Found 4 expressions with local error:

8.3b
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
2.2b
(/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))
0.5b
(/ 4 (/ Om l))
0.4b
(/ 1/2 (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
155×times-frac
75×add-sqr-sqrt
74×*-un-lft-identity add-cube-cbrt
44×div-inv
35×associate-/r*
24×associate-/r/
9×add-cbrt-cube add-exp-log
6×sqrt-prod
4×pow1 sqrt-div insert-posit16 add-log-exp
3×cbrt-undiv clear-num frac-2neg flip3-+ div-exp flip-+ associate-/l* associate-/l/
2×div-sub sqr-sin sin-mult
1×rem-sqrt-square associate-+r- pow1/2 frac-add associate-+l-
Calls
4 calls:
Slowest
31.0ms
(/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))
8.0ms
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
8.0ms
(/ 1/2 (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))))
1.0ms
(/ 4 (/ Om l))

series1.0s

Calls
4 calls:
Slowest
389.0ms
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
319.0ms
(/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))
292.0ms
(/ 1/2 (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))))
18.0ms
(/ 4 (/ Om l))

simplify29.4s

Calls
217 calls:
Slowest
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)))))
507.0ms
(- (log (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (- (log (/ Om l)) (log (/ 4 (/ Om l)))))
498.0ms
(/ (* (* (+ (* (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) (/ 4 (/ Om l))) (/ (/ Om l) (/ 4 (/ Om l)))) (/ (/ Om l) (/ 4 (/ Om l)))))
466.0ms
(/ 1/2 (/ (/ Om l) (/ 4 (/ Om l))))
462.0ms
(/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (/ (/ Om l) (/ 1 (/ Om l))))

prune3.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize44.0ms

Local error

Found 4 expressions with local error:

8.3b
(sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l)))))
2.6b
(/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))
0.4b
(/ 1/2 (sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))))
0.4b
(/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
140×times-frac
75×add-sqr-sqrt
74×*-un-lft-identity add-cube-cbrt
45×div-inv
20×associate-/l*
14×associate-/r*
11×add-cbrt-cube add-exp-log
9×associate-/r/
6×div-sub sqrt-prod
4×pow1 cbrt-undiv sqrt-div div-exp sqr-sin insert-posit16 add-log-exp associate-/l/
3×clear-num frac-2neg flip3-+ flip-+
2×associate-+r- associate-+l- sin-mult
1×rem-sqrt-square pow1/2 frac-add
Calls
4 calls:
Slowest
37.0ms
(/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))
19.0ms
(/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))
1.0ms
(sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l)))))
1.0ms
(/ 1/2 (sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))))

series1.7s

Calls
4 calls:
Slowest
705.0ms
(/ 1/2 (sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))))
387.0ms
(sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l)))))
304.0ms
(/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))
259.0ms
(/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))

simplify18.7s

Calls
226 calls:
Slowest
409.0ms
(cbrt (sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))))
398.0ms
(/ (/ (* (* (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (* (/ Om l) (/ Om l)) (/ Om l))) (* (* (/ Om l) (/ Om l)) (/ Om l)))
348.0ms
(sqrt (* (cbrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))) (cbrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l)))))))
332.0ms
(sqrt (sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))))
331.0ms
(/ (* (* (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))) (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))) (* (* (/ Om l) (/ Om l)) (/ Om l)))

prune3.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize22.0ms

Local error

Found 4 expressions with local error:

2.2b
(/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))
1.7b
(log (exp (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
0.5b
(/ 4 (/ Om l))
0.3b
(* (sin kx) (sin kx))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
290×times-frac
130×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
81×log-pow
80×exp-prod
74×div-inv
38×associate-/r/
29×associate-/r*
11×add-cbrt-cube add-exp-log
10×pow1
5×sqr-sin
4×div-sub insert-posit16 add-log-exp
3×cbrt-undiv log-prod div-exp associate-*r* associate-*l* sin-mult associate-/l* associate-/l/
2×log-div clear-num associate-+r- frac-2neg exp-diff associate-+l-
1×pow2 flip3-+ pow-plus rem-log-exp pow-prod-down frac-add prod-exp *-commutative pow-prod-up cbrt-unprod flip-+
Calls
4 calls:
Slowest
35.0ms
(/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))
34.0ms
(log (exp (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
8.0ms
(* (sin kx) (sin kx))
1.0ms
(/ 4 (/ Om l))

series739.0ms

Calls
4 calls:
Slowest
347.0ms
(log (exp (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
344.0ms
(/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))
25.0ms
(/ 4 (/ Om l))
22.0ms
(* (sin kx) (sin kx))

simplify43.1s

Calls
302 calls:
Slowest
664.0ms
(/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (/ (cbrt (/ Om l)) (/ 4 (/ Om l))))
596.0ms
(- (log (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (- (log (/ Om l)) (log (/ 4 (/ Om l)))))
566.0ms
(/ (* (* (+ (* (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)))))
479.0ms
(/ (cbrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (/ (/ Om l) (/ 1 (/ Om l))))
461.0ms
(/ 1/2 (/ (/ Om l) (/ 4 (/ Om l))))

prune5.8s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.6b

localize65.0ms

Local error

Found 4 expressions with local error:

47.2b
(posit16->real (real->posit16 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))))
8.3b
(sqrt (+ 1 (* 4 (/ (posit16->real (real->posit16 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)))) (/ Om l)))))
2.6b
(/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))
1.5b
(real->posit16 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
12×times-frac
5×add-cbrt-cube add-exp-log div-inv
4×associate-/r*
3×pow1 sqrt-prod insert-posit16 associate-/l* add-log-exp associate-/l/
2×flip3-+ sqrt-div div-sub flip-+ sqr-sin sin-mult
1×cbrt-undiv rem-sqrt-square clear-num associate-+r- frac-2neg pow1/2 div-exp frac-add associate-/r/ associate-+l- remove-posit16
Calls
4 calls:
Slowest
21.0ms
(/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))
1.0ms
(sqrt (+ 1 (* 4 (/ (posit16->real (real->posit16 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)))) (/ Om l)))))
0.0ms
(posit16->real (real->posit16 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))))
0.0ms
(real->posit16 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)))

series842.0ms

Calls
4 calls:
Slowest
380.0ms
(sqrt (+ 1 (* 4 (/ (posit16->real (real->posit16 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)))) (/ Om l)))))
235.0ms
(posit16->real (real->posit16 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))))
226.0ms
(/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))
0.0ms
(real->posit16 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)))

simplify3.7s

Calls
53 calls:
Slowest
480.0ms
(sqrt (* (cbrt (+ 1 (* 4 (/ (posit16->real (real->posit16 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)))) (/ Om l))))) (cbrt (+ 1 (* 4 (/ (posit16->real (real->posit16 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)))) (/ Om l)))))))
391.0ms
(sqrt (sqrt (+ 1 (* 4 (/ (posit16->real (real->posit16 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)))) (/ Om l))))))
338.0ms
(sqrt (+ 1 (* 4 (/ (posit16->real (real->posit16 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)))) (/ Om l)))))
226.0ms
(- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))))
224.0ms
(+ (* (- (cos (- kx kx)) (cos (+ kx kx))) 2) (* 2 (- (cos (- ky ky)) (cos (+ ky ky)))))

prune2.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

regimes669.0ms

Accuracy

0% (0.6b remaining)

Error of 1.4b against oracle of 0.8b and baseline of 1.4b

bsearch9.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
3.3s8000×body80valid