Details

Time bar (total: 3.4m)

sample1.0s

Algorithm
intervals
Results
763.0ms256×body80valid

simplify950.0ms

Calls
1 calls:
Slowest
937.0ms
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.5b

localize92.0ms

Local error

Found 4 expressions with local error:

5.9b
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
2.8b
(/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))
0.6b
(/ 1/2 (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))))
0.5b
(/ 4 (/ Om l))

rewrite63.0ms

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
37.0ms
(/ (+ (* (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
(/ 1/2 (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))))
1.0ms
(/ 4 (/ Om l))

series1.1s

Calls
4 calls:
Slowest
404.0ms
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
360.0ms
(/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))
298.0ms
(/ 1/2 (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))))
16.0ms
(/ 4 (/ Om l))

simplify52.3s

Calls
217 calls:
Slowest
1.9s
(/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (/ (sqrt (/ Om l)) (/ 4 (/ Om l))))
1.3s
(/ (* (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)))
1.2s
(- (log (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (- (log (/ Om l)) (log (/ 4 (/ Om l)))))
938.0ms
(/ (cbrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (/ (/ 1 l) (/ 1 (/ Om l))))
863.0ms
(/ (cbrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (/ (sqrt (/ Om l)) (/ 4 (/ Om l))))

prune7.9s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize116.0ms

Local error

Found 4 expressions with local error:

5.9b
(sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l)))))
2.9b
(/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))
0.6b
(/ 1/2 (sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))))
0.6b
(/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))

rewrite97.0ms

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
43.0ms
(/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))
31.0ms
(/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))
2.0ms
(sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l)))))
2.0ms
(/ 1/2 (sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))))

series1.6s

Calls
4 calls:
Slowest
513.0ms
(sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l)))))
409.0ms
(/ 1/2 (sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))))
392.0ms
(/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))
282.0ms
(/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))

simplify37.4s

Calls
226 calls:
Slowest
1.5s
(/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))
1.1s
(sqrt (sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))))
1.1s
(sqrt (cbrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))))
1.1s
(/ (* (* (/ (+ (* (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)))
1.1s
(sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l)))))

prune8.9s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize293.0ms

Local error

Found 4 expressions with local error:

18.0b
(posit16->real (real->posit16 (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))))
5.9b
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
2.8b
(/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))
2.4b
(real->posit16 (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))))

rewrite211.0ms

Algorithm
rewrite-expression-head
Rules
155×times-frac
71×add-sqr-sqrt
70×*-un-lft-identity add-cube-cbrt
41×div-inv
25×associate-/r*
21×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-+l- remove-posit16
Calls
4 calls:
Slowest
105.0ms
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
84.0ms
(/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))
0.0ms
(posit16->real (real->posit16 (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))))
0.0ms
(real->posit16 (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))))

series1.2s

Calls
4 calls:
Slowest
448.0ms
(posit16->real (real->posit16 (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))))
439.0ms
(/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))
340.0ms
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
0.0ms
(real->posit16 (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))))

simplify54.2s

Calls
203 calls:
Slowest
1.4s
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
1.3s
(/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (cbrt (/ Om l)) (/ 4 (/ Om l))))
1.1s
(/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (/ (/ Om l) (/ 1 (/ Om l))))
1.1s
(/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ 1 l) (/ 1 (/ Om l))))
1.1s
(/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (/ (/ Om l) (/ 4 (/ Om l))))

prune16.5s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.7b

localize84.0ms

Local error

Found 4 expressions with local error:

43.7b
(posit16->real (real->posit16 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))))
5.9b
(sqrt (+ 1 (* 4 (/ (posit16->real (real->posit16 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)))) (/ Om l)))))
2.9b
(/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))
2.3b
(real->posit16 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)))

rewrite42.0ms

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
39.0ms
(/ (+ (* (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)))

series1.0s

Calls
4 calls:
Slowest
388.0ms
(sqrt (+ 1 (* 4 (/ (posit16->real (real->posit16 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)))) (/ Om l)))))
388.0ms
(posit16->real (real->posit16 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))))
255.0ms
(/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))
0.0ms
(real->posit16 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)))

simplify5.9s

Calls
53 calls:
Slowest
832.0ms
(sqrt (+ 1 (* 4 (/ (posit16->real (real->posit16 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)))) (/ Om l)))))
778.0ms
(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)))))))
589.0ms
(sqrt (sqrt (+ 1 (* 4 (/ (posit16->real (real->posit16 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)))) (/ Om l))))))
468.0ms
(sqrt (+ (pow 1 3) (pow (* 4 (/ (posit16->real (real->posit16 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)))) (/ Om l))) 3)))
295.0ms
(- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))))

prune4.4s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.7b

regimes930.0ms

Accuracy

0% (0.7b remaining)

Error of 1.4b against oracle of 0.6b and baseline of 1.4b

bsearch6.0ms

end0.0ms

sample6.2s

Algorithm
intervals
Results
5.9s8000×body80valid