Average Error: 1.5 → 0.6
Time: 32.0s
Precision: 64
Internal Precision: 128
\[\sqrt{\frac{1}{2} \cdot \left(1 + \frac{1}{\sqrt{1 + {\left(\frac{2 \cdot \ell}{Om}\right)}^{2} \cdot \left({\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}\right)}}\right)}\]
↓
\[\sqrt{\frac{\frac{1}{2}}{\sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}} \cdot \left(\left(\left(\sqrt[3]{\sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}}\right) \cdot \sqrt[3]{\sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}}\right) \cdot \left(\left(\sqrt[3]{\sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}}\right) \cdot \sqrt[3]{\sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}}\right)\right)} + \frac{1}{2}}\]

Error

Bits error versus l

Bits error versus Om

Bits error versus kx

Bits error versus ky

Derivation

  1. Initial program 1.5

    \[\sqrt{\frac{1}{2} \cdot \left(1 + \frac{1}{\sqrt{1 + {\left(\frac{2 \cdot \ell}{Om}\right)}^{2} \cdot \left({\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}\right)}}\right)}\]

  2. Initial simplification1.5

    \[\leadsto \sqrt{\frac{1}{2} + \frac{\frac{1}{2}}{\sqrt{(\left(\left(\ell \cdot \frac{2}{Om}\right) \cdot \left(\ell \cdot \frac{2}{Om}\right)\right) \cdot \left((\left(\sin ky\right) \cdot \left(\sin ky\right) + \left(\sin kx \cdot \sin kx\right))_*\right) + 1)_*}}}\]

  3. Taylor expanded around -inf 16.8

    \[\leadsto \sqrt{\frac{1}{2} + \frac{\frac{1}{2}}{\sqrt{\color{blue}{4 \cdot \frac{{\ell}^{2} \cdot {\left(\sin ky\right)}^{2}}{{Om}^{2}} + \left(4 \cdot \frac{{\left(\sin kx\right)}^{2} \cdot {\ell}^{2}}{{Om}^{2}} + 1\right)}}}}\]

  4. Simplified0.6

    \[\leadsto \sqrt{\frac{1}{2} + \frac{\frac{1}{2}}{\sqrt{\color{blue}{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}}}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt0.6

    \[\leadsto \sqrt{\frac{1}{2} + \frac{\frac{1}{2}}{\color{blue}{\left(\sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}} \cdot \sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}\right) \cdot \sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}}}}\]
  7. Using strategy rm

  8. Applied add-cube-cbrt0.6

    \[\leadsto \sqrt{\frac{1}{2} + \frac{\frac{1}{2}}{\left(\color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}}\right) \cdot \sqrt[3]{\sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}}\right)} \cdot \sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}\right) \cdot \sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}}}\]
  9. Using strategy rm

  10. Applied add-cube-cbrt0.6

    \[\leadsto \sqrt{\frac{1}{2} + \frac{\frac{1}{2}}{\left(\left(\left(\sqrt[3]{\sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}}\right) \cdot \sqrt[3]{\sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}}\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}}\right) \cdot \sqrt[3]{\sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}}\right)}\right) \cdot \sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}}}\]

  11. Final simplification0.6

    \[\leadsto \sqrt{\frac{\frac{1}{2}}{\sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}} \cdot \left(\left(\left(\sqrt[3]{\sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}}\right) \cdot \sqrt[3]{\sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}}\right) \cdot \left(\left(\sqrt[3]{\sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}}\right) \cdot \sqrt[3]{\sqrt[3]{\sqrt{(4 \cdot \left((\left(\frac{\sin kx}{\frac{Om}{\ell}}\right) \cdot \left(\frac{\sin kx}{\frac{Om}{\ell}}\right) + \left(\frac{\sin ky}{\frac{Om}{\ell}} \cdot \frac{\sin ky}{\frac{Om}{\ell}}\right))_*\right) + 1)_*}}}\right)\right)} + \frac{1}{2}}\]

Reproduce

herbie shell --seed 2018362 +o rules:numerics
(FPCore (l Om kx ky)
  :name "Toniolo and Linder, Equation (3a)"
  (sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))

Details

Time bar (total: 25.9s)Debug log

start179.0ms

Algorithm
intervals

setup434.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.1b

localize46.0ms

Local error

Found 4 expressions with local error:

9.1b
(sqrt (fma (* (* l (/ 2 Om)) (* l (/ 2 Om))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
1.9b
(fma (* (* l (/ 2 Om)) (* l (/ 2 Om))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
1.0b
(/ 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))

rewrite12.0ms

Algorithm
rewrite-expression-head
Counts
4 → 66
Calls

4 calls. Slowest were:

7.0ms
(* (sin kx) (sin kx))
2.0ms
(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)))

series751.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

353.0ms
(/ 1/2 (sqrt (fma (* (* l (/ 2 Om)) (* l (/ 2 Om))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
238.0ms
(sqrt (fma (* (* l (/ 2 Om)) (* l (/ 2 Om))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
134.0ms
(fma (* (* l (/ 2 Om)) (* l (/ 2 Om))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
26.0ms
(* (sin kx) (sin kx))

simplify2.8s

Counts
35 → 78
Calls

35 calls. Slowest were:

355.0ms
(+ (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))) (+ (* 4 (/ (* (pow (sin kx) 2) (pow l 2)) (pow Om 2))) 1))
276.0ms
(+ (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))) (+ (* 4 (/ (* (pow (sin kx) 2) (pow l 2)) (pow Om 2))) 1))
255.0ms
(sqrt (cbrt (fma (* (* l (/ 2 Om)) (* l (/ 2 Om))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))

prune1.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize57.0ms

Local error

Found 4 expressions with local error:

9.1b
(sqrt (fma 4 (fma (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)) (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l)))) 1))
3.5b
(/ (sin kx) (/ Om l))
3.5b
(/ (sin kx) (/ Om l))
3.4b
(/ (sin ky) (/ Om l))

rewrite28.0ms

Algorithm
rewrite-expression-head
Counts
4 → 116
Calls

4 calls. Slowest were:

11.0ms
(/ (sin ky) (/ Om l))
6.0ms
(/ (sin kx) (/ Om l))
6.0ms
(/ (sin kx) (/ Om l))

series567.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

305.0ms
(sqrt (fma 4 (fma (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)) (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l)))) 1))
100.0ms
(/ (sin kx) (/ Om l))
90.0ms
(/ (sin kx) (/ Om l))
71.0ms
(/ (sin ky) (/ Om l))

simplify2.2s

Counts
112 → 128
Calls

112 calls. Slowest were:

248.0ms
(- (/ (* ky l) Om) (* 1/6 (/ (* (pow ky 3) l) Om)))
237.0ms
(- (/ (* kx l) Om) (* 1/6 (/ (* (pow kx 3) l) Om)))
212.0ms
(/ (* (* (sin kx) (sin kx)) (sin kx)) (* (* (/ Om l) (/ Om l)) (/ Om l)))

prune2.8s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize24.0ms

Local error

Found 4 expressions with local error:

10.0b
(cbrt (sqrt (fma 4 (fma (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)) (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l)))) 1)))
10.0b
(cbrt (sqrt (fma 4 (fma (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)) (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l)))) 1)))
10.0b
(cbrt (sqrt (fma 4 (fma (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)) (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l)))) 1)))
9.1b
(sqrt (fma 4 (fma (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)) (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l)))) 1))

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
4 → 62
Calls

4 calls. Slowest were:

2.0ms
(cbrt (sqrt (fma 4 (fma (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)) (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l)))) 1)))
2.0ms
(cbrt (sqrt (fma 4 (fma (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)) (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l)))) 1)))
2.0ms
(cbrt (sqrt (fma 4 (fma (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)) (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l)))) 1)))

series1.2s

Counts
4 → 12
Calls

4 calls. Slowest were:

341.0ms
(cbrt (sqrt (fma 4 (fma (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)) (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l)))) 1)))
323.0ms
(cbrt (sqrt (fma 4 (fma (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)) (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l)))) 1)))
312.0ms
(cbrt (sqrt (fma 4 (fma (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)) (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l)))) 1)))
221.0ms
(sqrt (fma 4 (fma (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)) (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l)))) 1))

simplify3.0s

Counts
34 → 74
Calls

34 calls. Slowest were:

346.0ms
(- (exp (* 1/6 (- (+ (* 2 (log l)) (+ (log 4) (* 2 (log ky)))) (* 2 (log Om))))) (* 55/648 (* (exp (* 1/6 (- (+ (* 10 (log Om)) (log 1/1024)) (+ (* 10 (log l)) (* 10 (log ky)))))) (pow kx 2))))
334.0ms
(- (exp (* 1/6 (- (+ (* 2 (log l)) (+ (log 4) (* 2 (log ky)))) (* 2 (log Om))))) (* 55/648 (* (exp (* 1/6 (- (+ (* 10 (log Om)) (log 1/1024)) (+ (* 10 (log l)) (* 10 (log ky)))))) (pow kx 2))))
332.0ms
(- (exp (* 1/6 (- (+ (* 2 (log l)) (+ (log 4) (* 2 (log ky)))) (* 2 (log Om))))) (* 55/648 (* (exp (* 1/6 (- (+ (* 10 (log Om)) (log 1/1024)) (+ (* 10 (log l)) (* 10 (log ky)))))) (pow kx 2))))

prune1.9s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize49.0ms

Local error

Found 4 expressions with local error:

10.0b
(cbrt (sqrt (fma 4 (fma (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)) (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l)))) 1)))
10.0b
(cbrt (sqrt (fma 4 (fma (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)) (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l)))) 1)))
10.0b
(cbrt (sqrt (fma 4 (fma (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)) (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l)))) 1)))
10.0b
(cbrt (sqrt (fma 4 (fma (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)) (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l)))) 1)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
4 → 64
Calls

4 calls. Slowest were:

2.0ms
(cbrt (sqrt (fma 4 (fma (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)) (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l)))) 1)))
2.0ms
(cbrt (sqrt (fma 4 (fma (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)) (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l)))) 1)))
2.0ms
(cbrt (sqrt (fma 4 (fma (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)) (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l)))) 1)))

series1.4s

Counts
4 → 12
Calls

4 calls. Slowest were:

373.0ms
(cbrt (sqrt (fma 4 (fma (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)) (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l)))) 1)))
371.0ms
(cbrt (sqrt (fma 4 (fma (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)) (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l)))) 1)))
370.0ms
(cbrt (sqrt (fma 4 (fma (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)) (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l)))) 1)))
315.0ms
(cbrt (sqrt (fma 4 (fma (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)) (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l)))) 1)))

simplify4.1s

Counts
36 → 76
Calls

36 calls. Slowest were:

411.0ms
(- (exp (* 1/6 (- (+ (* 2 (log l)) (+ (log 4) (* 2 (log ky)))) (* 2 (log Om))))) (* 55/648 (* (exp (* 1/6 (- (+ (* 10 (log Om)) (log 1/1024)) (+ (* 10 (log l)) (* 10 (log ky)))))) (pow kx 2))))
402.0ms
(- (exp (* 1/6 (- (+ (* 2 (log l)) (+ (log 4) (* 2 (log ky)))) (* 2 (log Om))))) (* 55/648 (* (exp (* 1/6 (- (+ (* 10 (log Om)) (log 1/1024)) (+ (* 10 (log l)) (* 10 (log ky)))))) (pow kx 2))))
363.0ms
(- (exp (* 1/6 (- (+ (* 2 (log l)) (+ (log 4) (* 2 (log ky)))) (* 2 (log Om))))) (* 55/648 (* (exp (* 1/6 (- (+ (* 10 (log Om)) (log 1/1024)) (+ (* 10 (log l)) (* 10 (log ky)))))) (pow kx 2))))

prune2.4s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

regimes360.0ms

Accuracy

0% (0.0b remaining)

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

bsearch4.0ms