Average Error: 1.6 → 1.6
Time: 42.7s
Precision: 64
Internal Precision: 128
\[\sqrt{\frac{1}{2} \cdot \left(1 + \frac{1}{\sqrt{1 + {\left(\frac{2 \cdot \ell}{Om}\right)}^{2} \cdot \left({\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}\right)}}\right)}\]
↓
\[\sqrt{\left(\frac{\frac{1}{\sqrt[3]{\sqrt{\left({\left(\sin ky\right)}^{2} + {\left(\sin kx\right)}^{2}\right) \cdot {\left(\frac{\ell \cdot 2}{Om}\right)}^{2} + 1}} \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt{\left({\left(\sin ky\right)}^{2} + {\left(\sin kx\right)}^{2}\right) \cdot {\left(\frac{\ell \cdot 2}{Om}\right)}^{2} + 1}}} \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt{\left({\left(\sin ky\right)}^{2} + {\left(\sin kx\right)}^{2}\right) \cdot {\left(\frac{\ell \cdot 2}{Om}\right)}^{2} + 1}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt{\left({\left(\sin ky\right)}^{2} + {\left(\sin kx\right)}^{2}\right) \cdot {\left(\frac{\ell \cdot 2}{Om}\right)}^{2} + 1}}}\right)\right)}}{\sqrt[3]{\sqrt[3]{\sqrt{\left({\left(\sin ky\right)}^{2} + {\left(\sin kx\right)}^{2}\right) \cdot {\left(\frac{\ell \cdot 2}{Om}\right)}^{2} + 1}}} \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt{\left({\left(\sin ky\right)}^{2} + {\left(\sin kx\right)}^{2}\right) \cdot {\left(\frac{\ell \cdot 2}{Om}\right)}^{2} + 1}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt{\left({\left(\sin ky\right)}^{2} + {\left(\sin kx\right)}^{2}\right) \cdot {\left(\frac{\ell \cdot 2}{Om}\right)}^{2} + 1}}}\right)} + 1\right) \cdot \frac{1}{2}}\]

Error

Bits error versus l

Bits error versus Om

Bits error versus kx

Bits error versus ky

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.6

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

  3. Applied add-cube-cbrt1.6

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

  4. Applied associate-/r*1.6

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

  6. Applied add-cube-cbrt1.6

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

  8. Applied add-cube-cbrt1.6

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

  9. Final simplification1.6

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

Reproduce

herbie shell --seed 2019022 
(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: 41.7s)Debug log

sample184.0ms

Algorithm
intervals
Results
111.0ms256×body80valid

simplify288.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
287.0ms
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.3b

localize82.0ms

Local error

Found 4 expressions with local error:

7.5b
(sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
3.1b
(* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.6b
(/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
0.3b
(pow (sin kx) 2)

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
12×add-sqr-sqrt
11×add-cube-cbrt
11×add-exp-log
9×unpow-prod-down
8×associate-*l*
6×sqrt-prod
6×add-cbrt-cube
6×associate-/r*
6×pow1
5×associate-*r*
4×add-log-exp
4×sqrt-div
3×flip-+
3×prod-exp
3×flip3-+
2×unpow2
2×distribute-lft-out
2×pow-flip
2×div-inv
2×associate-/r/
2×associate-*r/
2×pow-exp
2×pow1/2
2×pow-to-exp
1×inv-pow
1×cbrt-unprod
1×*-commutative
1×distribute-lft-in
1×frac-2neg
1×pow-pow
1×clear-num
1×rec-exp
1×rem-sqrt-square
1×distribute-rgt-in
Counts
4 → 79
Calls
4 calls:
Slowest
26.0ms
(* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))
3.0ms
(sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
2.0ms
(/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
2.0ms
(pow (sin kx) 2)

series774.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
305.0ms
(/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
274.0ms
(sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
170.0ms
(* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))
26.0ms
(pow (sin kx) 2)

simplify5.9s

Counts
53 → 91
Calls
53 calls:
Slowest
566.0ms
(* (pow (/ (* 2 l) Om) 2) (pow (sin ky) 2))
499.0ms
(* (pow (sin ky) 2) (pow (/ (* 2 l) Om) 2))
339.0ms
(+ (* 4 (/ (* (pow kx 2) (pow l 2)) (pow Om 2))) (* 4 (/ (* (pow ky 2) (pow l 2)) (pow Om 2))))
318.0ms
(sqrt (- 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
255.0ms
(sqrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))

prune1.7s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize43.0ms

Local error

Found 4 expressions with local error:

8.3b
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
8.3b
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
8.3b
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
7.5b
(sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-prod
12×sqrt-prod
12×add-sqr-sqrt
11×add-cube-cbrt
11×*-un-lft-identity
8×sqrt-div
6×cbrt-div
4×add-log-exp
4×flip-+
4×add-exp-log
4×add-cbrt-cube
4×flip3-+
4×pow1
3×pow1/3
1×pow1/2
1×rem-sqrt-square
Counts
4 → 62
Calls
4 calls:
Slowest
2.0ms
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
2.0ms
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
2.0ms
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
1.0ms
(sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
411.0ms
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
363.0ms
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
339.0ms
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
244.0ms
(sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))

simplify5.9s

Counts
42 → 74
Calls
42 calls:
Slowest
562.0ms
(sqrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
369.0ms
(exp (* 1/6 (- (+ (* 2 (log (/ 1 Om))) (log (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2))))) (* 2 (log (/ 1 l))))))
326.0ms
(exp (* 1/6 (- (+ (* 2 (log (/ 1 Om))) (log (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2))))) (* 2 (log (/ 1 l))))))
247.0ms
(cbrt (sqrt (* (cbrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (cbrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
244.0ms
(cbrt (sqrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))

prune2.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize57.0ms

Local error

Found 4 expressions with local error:

8.3b
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
8.3b
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
8.3b
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
8.3b
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-prod
12×sqrt-prod
12×add-cube-cbrt
12×*-un-lft-identity
12×add-sqr-sqrt
8×sqrt-div
8×cbrt-div
4×add-log-exp
4×flip-+
4×add-exp-log
4×pow1/3
4×add-cbrt-cube
4×flip3-+
4×pow1
Counts
4 → 64
Calls
4 calls:
Slowest
1.0ms
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
1.0ms
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
1.0ms
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
1.0ms
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
366.0ms
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
335.0ms
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
322.0ms
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
309.0ms
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))

simplify5.8s

Counts
44 → 76
Calls
44 calls:
Slowest
299.0ms
(exp (* 1/6 (- (+ (* 2 (log (/ 1 Om))) (log (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2))))) (* 2 (log (/ 1 l))))))
291.0ms
(exp (* 1/6 (- (+ (* 2 (log (/ 1 Om))) (log (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2))))) (* 2 (log (/ 1 l))))))
271.0ms
(exp (* 1/6 (- (+ (* 2 (log (/ 1 Om))) (log (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2))))) (* 2 (log (/ 1 l))))))
252.0ms
(exp (* 1/6 (- (+ (* 2 (log (/ 1 Om))) (log (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2))))) (* 2 (log (/ 1 l))))))
237.0ms
(cbrt (* (cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))

prune2.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize49.0ms

Local error

Found 4 expressions with local error:

8.3b
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
8.3b
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
8.3b
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
8.3b
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-prod
12×sqrt-prod
12×add-cube-cbrt
12×*-un-lft-identity
12×add-sqr-sqrt
8×sqrt-div
8×cbrt-div
4×add-log-exp
4×flip-+
4×add-exp-log
4×pow1/3
4×add-cbrt-cube
4×flip3-+
4×pow1
Counts
4 → 64
Calls
4 calls:
Slowest
2.0ms
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
2.0ms
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
2.0ms
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
1.0ms
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
391.0ms
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
344.0ms
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
329.0ms
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
316.0ms
(cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))

simplify5.5s

Counts
44 → 76
Calls
44 calls:
Slowest
332.0ms
(exp (* 1/6 (- (+ (* 2 (log (/ 1 Om))) (log (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2))))) (* 2 (log (/ 1 l))))))
304.0ms
(exp (* 1/6 (- (+ (* 2 (log (/ 1 Om))) (log (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2))))) (* 2 (log (/ 1 l))))))
268.0ms
(exp (* 1/6 (- (+ (* 2 (log (/ 1 Om))) (log (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2))))) (* 2 (log (/ 1 l))))))
239.0ms
(exp (* 1/6 (- (+ (* 2 (log (/ 1 Om))) (log (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2))))) (* 2 (log (/ 1 l))))))
229.0ms
(cbrt (* (cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (cbrt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))

prune2.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

regimes1.5s

Accuracy

0% (0.9b remaining)

Error of 1.6b against oracle of 0.7b and baseline of 1.6b

bsearch5.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
3.3s7998×body80valid
1.0ms2×body160valid