Details

Time bar (total: 21.3s)

sample143.0ms

Algorithm
intervals
Results
108.0ms256×body80valid

simplify254.0ms

Calls
1 calls:
Slowest
253.0ms
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.6b

localize73.0ms

Local error

Found 4 expressions with local error:

11.7b
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
2.6b
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
0.5b
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
0.2b
(* (sin kx) (sin kx))

rewrite11.0ms

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
4.0ms
(* (sin kx) (sin kx))
3.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
1.0ms
(/ 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)

series1.0s

Calls
4 calls:
Slowest
448.0ms
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
338.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
185.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
34.0ms
(* (sin kx) (sin kx))

simplify3.9s

Calls
35 calls:
Slowest
397.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
390.0ms
(sqrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
368.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
361.0ms
(sqrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
331.0ms
(sqrt (* (cbrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)) (cbrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.0b

localize56.0ms

Local error

Found 4 expressions with local error:

11.7b
(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
4.2b
(/ (sin kx) (/ Om l))
4.2b
(/ (sin kx) (/ Om l))
3.1b
(/ (sin ky) (/ Om l))

rewrite20.0ms

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 kx) (/ Om l))
5.0ms
(/ (sin kx) (/ Om l))
4.0ms
(/ (sin ky) (/ Om l))
2.0ms
(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

series582.0ms

Calls
4 calls:
Slowest
310.0ms
(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
101.0ms
(/ (sin kx) (/ Om l))
96.0ms
(/ (sin ky) (/ Om l))
75.0ms
(/ (sin kx) (/ Om l))

simplify3.8s

Calls
112 calls:
Slowest
366.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (/ Om l) (/ Om l)) (/ Om l)))
357.0ms
(/ (* (* (sin kx) (sin kx)) (sin kx)) (* (* (/ Om l) (/ Om l)) (/ Om l)))
335.0ms
(/ (* (* (sin kx) (sin kx)) (sin kx)) (* (* (/ Om l) (/ Om l)) (/ Om l)))
316.0ms
(sqrt (sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))
274.0ms
(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

prune2.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.0b

localize43.0ms

Local error

Found 4 expressions with local error:

11.7b
(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
11.7b
(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
11.7b
(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
6.9b
(cbrt (sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×*-un-lft-identity add-cube-cbrt
6×cbrt-prod
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square pow1/2
1×pow1/3
Calls
4 calls:
Slowest
2.0ms
(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
2.0ms
(cbrt (sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))
2.0ms
(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
2.0ms
(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

series1.4s

Calls
4 calls:
Slowest
384.0ms
(cbrt (sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))
358.0ms
(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
341.0ms
(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
298.0ms
(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

simplify4.3s

Calls
30 calls:
Slowest
360.0ms
(cbrt (sqrt (sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))))
356.0ms
(cbrt (sqrt (* (cbrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)) (cbrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))))
349.0ms
(sqrt (* (cbrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)) (cbrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))))
346.0ms
(cbrt (* (cbrt (sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))) (cbrt (sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))))
322.0ms
(sqrt (sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))

prune1.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.0b