Details

Time bar (total: 33.7s)

sample75.0ms

Algorithm
intervals
Results
56.0ms256×body80valid

simplify1.0s

Calls
1 calls:
Slowest
1.0s
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

prune75.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize93.0ms

Local error

Found 4 expressions with local error:

8.3b
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
1.5b
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
0.4b
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
0.3b
(* (sin kx) (sin kx))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×pow1 *-un-lft-identity add-cube-cbrt
6×associate-/r* add-cbrt-cube add-exp-log sqrt-prod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
1×pow2 rem-sqrt-square clear-num frac-2neg pow-plus pow1/2 pow-prod-down prod-exp *-commutative pow-prod-up cbrt-unprod fma-udef sqr-sin div-inv sin-mult
Calls
4 calls:
Slowest
10.0ms
(* (sin kx) (sin kx))
5.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
2.0ms
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
0.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)

series925.0ms

Calls
4 calls:
Slowest
386.0ms
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
372.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
143.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
23.0ms
(* (sin kx) (sin kx))

simplify3.6s

Calls
35 calls:
Slowest
372.0ms
(sqrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
356.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
343.0ms
(cbrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
332.0ms
(sqrt (cbrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
319.0ms
(sqrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))

prune1.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize26.0ms

Local error

Found 4 expressions with local error:

8.3b
(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
3.7b
(/ (sin kx) (/ Om l))
3.7b
(/ (sin kx) (/ Om l))
3.2b
(/ (sin ky) (/ Om l))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
33×add-sqr-sqrt
32×*-un-lft-identity add-cube-cbrt
15×div-inv
12×associate-/r*
10×add-cbrt-cube add-exp-log
9×associate-/l*
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv clear-num frac-2neg div-exp associate-/r/ sqrt-prod
1×rem-sqrt-square pow1/2
Calls
4 calls:
Slowest
8.0ms
(/ (sin ky) (/ Om l))
7.0ms
(/ (sin kx) (/ Om l))
4.0ms
(/ (sin kx) (/ Om l))
1.0ms
(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

series610.0ms

Calls
4 calls:
Slowest
328.0ms
(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
97.0ms
(/ (sin kx) (/ Om l))
95.0ms
(/ (sin kx) (/ Om l))
90.0ms
(/ (sin ky) (/ Om l))

simplify4.1s

Calls
112 calls:
Slowest
432.0ms
(/ (* (* (sin kx) (sin kx)) (sin kx)) (* (* (/ Om l) (/ Om l)) (/ Om l)))
423.0ms
(/ (* (* (sin kx) (sin kx)) (sin kx)) (* (* (/ Om l) (/ Om l)) (/ Om l)))
393.0ms
(sqrt (sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))
362.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (/ Om l) (/ Om l)) (/ Om l)))
287.0ms
(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

prune2.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize32.0ms

Local error

Found 4 expressions with local error:

3.9b
(log (exp (/ (sin kx) (/ Om l))))
3.7b
(/ (sin kx) (/ Om l))
3.7b
(/ (sin kx) (/ Om l))
3.2b
(/ (sin ky) (/ Om l))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
40×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
19×div-inv
18×log-pow
17×exp-prod
12×associate-/r*
10×add-cbrt-cube add-exp-log
9×associate-/l*
5×pow1
4×expm1-log1p-u associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv log-prod clear-num frac-2neg div-exp
1×rem-log-exp
Calls
4 calls:
Slowest
5.0ms
(log (exp (/ (sin kx) (/ Om l))))
4.0ms
(/ (sin kx) (/ Om l))
4.0ms
(/ (sin ky) (/ Om l))
4.0ms
(/ (sin kx) (/ Om l))

series336.0ms

Calls
4 calls:
Slowest
119.0ms
(log (exp (/ (sin kx) (/ Om l))))
76.0ms
(/ (sin ky) (/ Om l))
72.0ms
(/ (sin kx) (/ Om l))
68.0ms
(/ (sin kx) (/ Om l))

simplify3.6s

Calls
128 calls:
Slowest
339.0ms
(/ (* (* (sin kx) (sin kx)) (sin kx)) (* (* (/ Om l) (/ Om l)) (/ Om l)))
335.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (/ Om l) (/ Om l)) (/ Om l)))
335.0ms
(/ (* (* (sin kx) (sin kx)) (sin kx)) (* (* (/ Om l) (/ Om l)) (/ Om l)))
149.0ms
(- (/ (* ky l) Om) (* 1/6 (/ (* (pow ky 3) l) Om)))
139.0ms
(- (/ (* kx l) Om) (* 1/6 (/ (* (pow kx 3) l) Om)))

prune3.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize61.0ms

Local error

Found 4 expressions with local error:

46.5b
(posit16->real (real->posit16 (/ (sin ky) (/ Om l))))
3.9b
(log (exp (/ (sin kx) (/ Om l))))
3.7b
(/ (sin kx) (/ Om l))
3.7b
(/ (sin kx) (/ Om l))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
31×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×log-pow
17×exp-prod
14×div-inv
8×associate-/r* add-cbrt-cube add-exp-log
6×associate-/l*
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×log-prod associate-/r/
2×cbrt-undiv clear-num frac-2neg div-exp
1×rem-log-exp remove-posit16
Calls
4 calls:
Slowest
9.0ms
(log (exp (/ (sin kx) (/ Om l))))
9.0ms
(/ (sin kx) (/ Om l))
8.0ms
(/ (sin kx) (/ Om l))
0.0ms
(posit16->real (real->posit16 (/ (sin ky) (/ Om l))))

series345.0ms

Calls
4 calls:
Slowest
96.0ms
(posit16->real (real->posit16 (/ (sin ky) (/ Om l))))
88.0ms
(/ (sin kx) (/ Om l))
82.0ms
(/ (sin kx) (/ Om l))
79.0ms
(log (exp (/ (sin kx) (/ Om l))))

simplify2.8s

Calls
97 calls:
Slowest
409.0ms
(/ (* (* (sin kx) (sin kx)) (sin kx)) (* (* (/ Om l) (/ Om l)) (/ Om l)))
325.0ms
(/ (* (* (sin kx) (sin kx)) (sin kx)) (* (* (/ Om l) (/ Om l)) (/ Om l)))
145.0ms
(- (/ (* kx l) Om) (* 1/6 (/ (* (pow kx 3) l) Om)))
135.0ms
(- (/ (* kx l) Om) (* 1/6 (/ (* (pow kx 3) l) Om)))
130.0ms
(- (/ (* ky l) Om) (* 1/6 (/ (* (pow ky 3) l) Om)))

prune4.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.7b

regimes581.0ms

Accuracy

0% (0.0b remaining)

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

bsearch6.0ms

end0.0ms

sample4.0s

Algorithm
intervals
Results
3.8s8000×body80valid