Average Error: 32.3 → 12.1
Time: 3.0m
Precision: 64
Internal Precision: 128
\[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]
↓
\[\frac{\sqrt[3]{\frac{2}{t}} \cdot \sqrt[3]{\frac{2}{t}}}{\frac{\sin k}{\frac{\ell}{t}}} \cdot \left(\left(\frac{\sqrt[3]{\frac{2}{t}}}{\sqrt[3]{\frac{\sin k}{\frac{\ell}{t}}}} \cdot \frac{\cos k}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\right) \cdot \frac{1}{\sqrt[3]{\frac{\sin k}{\frac{\ell}{t}}} \cdot \sqrt[3]{\frac{\sin k}{\frac{\ell}{t}}}}\right)\]

Error

Bits error versus t

Bits error versus l

Bits error versus k

Derivation

  1. Initial program 32.3

    \[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]

  2. Initial simplification24.8

    \[\leadsto \frac{\frac{\frac{2}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{\ell}{t}\right)}{\tan k \cdot \sin k}}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity24.8

    \[\leadsto \frac{\frac{\frac{2}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{\ell}{t}\right)}{\tan k \cdot \sin k}}{\color{blue}{1 \cdot (\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}\]

  5. Applied tan-quot24.8

    \[\leadsto \frac{\frac{\frac{2}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{\ell}{t}\right)}{\color{blue}{\frac{\sin k}{\cos k}} \cdot \sin k}}{1 \cdot (\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\]

  6. Applied associate-*l/24.8

    \[\leadsto \frac{\frac{\frac{2}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{\ell}{t}\right)}{\color{blue}{\frac{\sin k \cdot \sin k}{\cos k}}}}{1 \cdot (\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\]

  7. Applied associate-/r/24.8

    \[\leadsto \frac{\color{blue}{\frac{\frac{2}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{\ell}{t}\right)}{\sin k \cdot \sin k} \cdot \cos k}}{1 \cdot (\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\]

  8. Applied times-frac24.8

    \[\leadsto \color{blue}{\frac{\frac{\frac{2}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{\ell}{t}\right)}{\sin k \cdot \sin k}}{1} \cdot \frac{\cos k}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}\]

  9. Simplified16.3

    \[\leadsto \color{blue}{\frac{\frac{2}{t}}{\frac{\sin k}{\frac{\ell}{t}} \cdot \frac{\sin k}{\frac{\ell}{t}}}} \cdot \frac{\cos k}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\]
  10. Using strategy rm

  11. Applied add-cube-cbrt16.5

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{\frac{2}{t}} \cdot \sqrt[3]{\frac{2}{t}}\right) \cdot \sqrt[3]{\frac{2}{t}}}}{\frac{\sin k}{\frac{\ell}{t}} \cdot \frac{\sin k}{\frac{\ell}{t}}} \cdot \frac{\cos k}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\]

  12. Applied times-frac14.6

    \[\leadsto \color{blue}{\left(\frac{\sqrt[3]{\frac{2}{t}} \cdot \sqrt[3]{\frac{2}{t}}}{\frac{\sin k}{\frac{\ell}{t}}} \cdot \frac{\sqrt[3]{\frac{2}{t}}}{\frac{\sin k}{\frac{\ell}{t}}}\right)} \cdot \frac{\cos k}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\]

  13. Applied associate-*l*12.0

    \[\leadsto \color{blue}{\frac{\sqrt[3]{\frac{2}{t}} \cdot \sqrt[3]{\frac{2}{t}}}{\frac{\sin k}{\frac{\ell}{t}}} \cdot \left(\frac{\sqrt[3]{\frac{2}{t}}}{\frac{\sin k}{\frac{\ell}{t}}} \cdot \frac{\cos k}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\right)}\]
  14. Using strategy rm

  15. Applied add-cube-cbrt12.1

    \[\leadsto \frac{\sqrt[3]{\frac{2}{t}} \cdot \sqrt[3]{\frac{2}{t}}}{\frac{\sin k}{\frac{\ell}{t}}} \cdot \left(\frac{\sqrt[3]{\frac{2}{t}}}{\color{blue}{\left(\sqrt[3]{\frac{\sin k}{\frac{\ell}{t}}} \cdot \sqrt[3]{\frac{\sin k}{\frac{\ell}{t}}}\right) \cdot \sqrt[3]{\frac{\sin k}{\frac{\ell}{t}}}}} \cdot \frac{\cos k}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\right)\]

  16. Applied *-un-lft-identity12.1

    \[\leadsto \frac{\sqrt[3]{\frac{2}{t}} \cdot \sqrt[3]{\frac{2}{t}}}{\frac{\sin k}{\frac{\ell}{t}}} \cdot \left(\frac{\sqrt[3]{\color{blue}{1 \cdot \frac{2}{t}}}}{\left(\sqrt[3]{\frac{\sin k}{\frac{\ell}{t}}} \cdot \sqrt[3]{\frac{\sin k}{\frac{\ell}{t}}}\right) \cdot \sqrt[3]{\frac{\sin k}{\frac{\ell}{t}}}} \cdot \frac{\cos k}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\right)\]

  17. Applied cbrt-prod12.1

    \[\leadsto \frac{\sqrt[3]{\frac{2}{t}} \cdot \sqrt[3]{\frac{2}{t}}}{\frac{\sin k}{\frac{\ell}{t}}} \cdot \left(\frac{\color{blue}{\sqrt[3]{1} \cdot \sqrt[3]{\frac{2}{t}}}}{\left(\sqrt[3]{\frac{\sin k}{\frac{\ell}{t}}} \cdot \sqrt[3]{\frac{\sin k}{\frac{\ell}{t}}}\right) \cdot \sqrt[3]{\frac{\sin k}{\frac{\ell}{t}}}} \cdot \frac{\cos k}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\right)\]

  18. Applied times-frac12.1

    \[\leadsto \frac{\sqrt[3]{\frac{2}{t}} \cdot \sqrt[3]{\frac{2}{t}}}{\frac{\sin k}{\frac{\ell}{t}}} \cdot \left(\color{blue}{\left(\frac{\sqrt[3]{1}}{\sqrt[3]{\frac{\sin k}{\frac{\ell}{t}}} \cdot \sqrt[3]{\frac{\sin k}{\frac{\ell}{t}}}} \cdot \frac{\sqrt[3]{\frac{2}{t}}}{\sqrt[3]{\frac{\sin k}{\frac{\ell}{t}}}}\right)} \cdot \frac{\cos k}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\right)\]

  19. Applied associate-*l*12.1

    \[\leadsto \frac{\sqrt[3]{\frac{2}{t}} \cdot \sqrt[3]{\frac{2}{t}}}{\frac{\sin k}{\frac{\ell}{t}}} \cdot \color{blue}{\left(\frac{\sqrt[3]{1}}{\sqrt[3]{\frac{\sin k}{\frac{\ell}{t}}} \cdot \sqrt[3]{\frac{\sin k}{\frac{\ell}{t}}}} \cdot \left(\frac{\sqrt[3]{\frac{2}{t}}}{\sqrt[3]{\frac{\sin k}{\frac{\ell}{t}}}} \cdot \frac{\cos k}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\right)\right)}\]

  20. Simplified12.1

    \[\leadsto \frac{\sqrt[3]{\frac{2}{t}} \cdot \sqrt[3]{\frac{2}{t}}}{\frac{\sin k}{\frac{\ell}{t}}} \cdot \left(\color{blue}{\frac{1}{\sqrt[3]{\frac{\sin k}{\frac{\ell}{t}}} \cdot \sqrt[3]{\frac{\sin k}{\frac{\ell}{t}}}}} \cdot \left(\frac{\sqrt[3]{\frac{2}{t}}}{\sqrt[3]{\frac{\sin k}{\frac{\ell}{t}}}} \cdot \frac{\cos k}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\right)\right)\]

  21. Final simplification12.1

    \[\leadsto \frac{\sqrt[3]{\frac{2}{t}} \cdot \sqrt[3]{\frac{2}{t}}}{\frac{\sin k}{\frac{\ell}{t}}} \cdot \left(\left(\frac{\sqrt[3]{\frac{2}{t}}}{\sqrt[3]{\frac{\sin k}{\frac{\ell}{t}}}} \cdot \frac{\cos k}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\right) \cdot \frac{1}{\sqrt[3]{\frac{\sin k}{\frac{\ell}{t}}} \cdot \sqrt[3]{\frac{\sin k}{\frac{\ell}{t}}}}\right)\]

Reproduce

herbie shell --seed 2018360 +o rules:numerics
(FPCore (t l k)
  :name "Toniolo and Linder, Equation (10+)"
  (/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))))

Details

Time bar (total: 2.5m)Debug log

start692.0ms

Algorithm
intervals

setup601.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.9b

localize67.0ms

Local error

Found 4 expressions with local error:

17.5b
(/ (/ (* (/ 2 t) (* (/ l t) (/ l t))) (* (tan k) (sin k))) (fma (/ k t) (/ k t) 2))
11.2b
(/ (* (/ 2 t) (* (/ l t) (/ l t))) (* (tan k) (sin k)))
2.0b
(* (/ 2 t) (* (/ l t) (/ l t)))
0.2b
(* (tan k) (sin k))

rewrite94.0ms

Algorithm
rewrite-expression-head
Counts
4 → 137
Calls

4 calls. Slowest were:

36.0ms
(/ (* (/ 2 t) (* (/ l t) (/ l t))) (* (tan k) (sin k)))
29.0ms
(/ (/ (* (/ 2 t) (* (/ l t) (/ l t))) (* (tan k) (sin k))) (fma (/ k t) (/ k t) 2))
16.0ms
(* (/ 2 t) (* (/ l t) (/ l t)))

series507.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

229.0ms
(/ (* (/ 2 t) (* (/ l t) (/ l t))) (* (tan k) (sin k)))
200.0ms
(/ (/ (* (/ 2 t) (* (/ l t) (/ l t))) (* (tan k) (sin k))) (fma (/ k t) (/ k t) 2))
51.0ms
(* (tan k) (sin k))
28.0ms
(* (/ 2 t) (* (/ l t) (/ l t)))

simplify23.7s

Counts
121 → 149
Calls

121 calls. Slowest were:

846.0ms
(/ (* (* (* (/ 2 t) (/ 2 t)) (/ 2 t)) (* (* (* (/ l t) (/ l t)) (/ l t)) (* (* (/ l t) (/ l t)) (/ l t)))) (* (* (* (tan k) (sin k)) (* (tan k) (sin k))) (* (tan k) (sin k))))
806.0ms
(/ (/ (* (* (* (/ 2 t) (/ 2 t)) (/ 2 t)) (* (* (* (/ l t) (/ l t)) (/ l t)) (* (* (/ l t) (/ l t)) (/ l t)))) (* (* (* (tan k) (tan k)) (tan k)) (* (* (sin k) (sin k)) (sin k)))) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2)))
793.0ms
(/ (/ (* (* (* (/ 2 t) (/ 2 t)) (/ 2 t)) (* (* (* (/ l t) (/ l t)) (* (/ l t) (/ l t))) (* (/ l t) (/ l t)))) (* (* (* (tan k) (tan k)) (tan k)) (* (* (sin k) (sin k)) (sin k)))) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2)))

prune2.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 15.1b

localize36.0ms

Local error

Found 4 expressions with local error:

17.5b
(* (/ (/ 2 t) (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t)))) (/ (cos k) (fma (/ k t) (/ k t) 2)))
3.1b
(/ (sin k) (/ l t))
3.1b
(/ (sin k) (/ l t))
2.8b
(/ (/ 2 t) (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Counts
4 → 165
Calls

4 calls. Slowest were:

20.0ms
(* (/ (/ 2 t) (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t)))) (/ (cos k) (fma (/ k t) (/ k t) 2)))
8.0ms
(/ (/ 2 t) (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))))
3.0ms
(/ (sin k) (/ l t))

series711.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

385.0ms
(* (/ (/ 2 t) (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t)))) (/ (cos k) (fma (/ k t) (/ k t) 2)))
173.0ms
(/ (/ 2 t) (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))))
94.0ms
(/ (sin k) (/ l t))
58.0ms
(/ (sin k) (/ l t))

simplify17.6s

Counts
152 → 177
Calls

152 calls. Slowest were:

773.0ms
(- (log (/ 2 t)) (+ (log (/ (sin k) (/ l t))) (log (/ (sin k) (/ l t)))))
705.0ms
(* (/ (* (* (/ 2 t) (/ 2 t)) (/ 2 t)) (* (/ (* (* (sin k) (sin k)) (sin k)) (* (* (/ l t) (/ l t)) (/ l t))) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t))))) (* (* (/ (cos k) (fma (/ k t) (/ k t) 2)) (/ (cos k) (fma (/ k t) (/ k t) 2))) (/ (cos k) (fma (/ k t) (/ k t) 2))))
692.0ms
(* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (fma (/ k t) (/ k t) 2))

prune2.4s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 14.1b

localize35.0ms

Local error

Found 4 expressions with local error:

10.4b
(* (/ (* (cbrt (/ 2 t)) (cbrt (/ 2 t))) (/ (sin k) (/ l t))) (* (/ (cbrt (/ 2 t)) (/ (sin k) (/ l t))) (/ (cos k) (fma (/ k t) (/ k t) 2))))
10.0b
(* (/ (cbrt (/ 2 t)) (/ (sin k) (/ l t))) (/ (cos k) (fma (/ k t) (/ k t) 2)))
3.1b
(/ (sin k) (/ l t))
3.1b
(/ (sin k) (/ l t))

rewrite105.0ms

Algorithm
rewrite-expression-head
Counts
4 → 343
Calls

4 calls. Slowest were:

49.0ms
(* (/ (* (cbrt (/ 2 t)) (cbrt (/ 2 t))) (/ (sin k) (/ l t))) (* (/ (cbrt (/ 2 t)) (/ (sin k) (/ l t))) (/ (cos k) (fma (/ k t) (/ k t) 2))))
20.0ms
(* (/ (cbrt (/ 2 t)) (/ (sin k) (/ l t))) (/ (cos k) (fma (/ k t) (/ k t) 2)))
6.0ms
(/ (sin k) (/ l t))

series1.1s

Counts
4 → 12
Calls

4 calls. Slowest were:

584.0ms
(* (/ (cbrt (/ 2 t)) (/ (sin k) (/ l t))) (/ (cos k) (fma (/ k t) (/ k t) 2)))
424.0ms
(* (/ (* (cbrt (/ 2 t)) (cbrt (/ 2 t))) (/ (sin k) (/ l t))) (* (/ (cbrt (/ 2 t)) (/ (sin k) (/ l t))) (/ (cos k) (fma (/ k t) (/ k t) 2))))
80.0ms
(/ (sin k) (/ l t))
57.0ms
(/ (sin k) (/ l t))

simplify44.0s

Counts
333 → 355
Calls

333 calls. Slowest were:

1.0s
(* (/ (* (* (* (cbrt (/ 2 t)) (cbrt (/ 2 t))) (* (cbrt (/ 2 t)) (cbrt (/ 2 t)))) (* (cbrt (/ 2 t)) (cbrt (/ 2 t)))) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (/ (/ 2 t) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (/ (cos k) (fma (/ k t) (/ k t) 2)) (/ (cos k) (fma (/ k t) (/ k t) 2))) (/ (cos k) (fma (/ k t) (/ k t) 2)))))
1.0s
(* (/ (* (/ 2 t) (/ 2 t)) (/ (* (* (sin k) (sin k)) (sin k)) (* (* (/ l t) (/ l t)) (/ l t)))) (* (* (* (/ (cbrt (/ 2 t)) (/ (sin k) (/ l t))) (/ (cbrt (/ 2 t)) (/ (sin k) (/ l t)))) (/ (cbrt (/ 2 t)) (/ (sin k) (/ l t)))) (/ (* (* (cos k) (cos k)) (cos k)) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2)))))
970.0ms
(* (/ (* (* (* (cbrt (/ 2 t)) (cbrt (/ 2 t))) (* (cbrt (/ 2 t)) (cbrt (/ 2 t)))) (* (cbrt (/ 2 t)) (cbrt (/ 2 t)))) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (* (/ (cbrt (/ 2 t)) (/ (sin k) (/ l t))) (/ (cbrt (/ 2 t)) (/ (sin k) (/ l t)))) (/ (cbrt (/ 2 t)) (/ (sin k) (/ l t)))) (/ (* (* (cos k) (cos k)) (cos k)) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2)))))

prune6.7s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.1b

localize31.0ms

Local error

Found 4 expressions with local error:

10.4b
(* (/ (* (cbrt (/ 2 t)) (cbrt (/ 2 t))) (/ (sin k) (/ l t))) (* (/ 1 (* (cbrt (/ (sin k) (/ l t))) (cbrt (/ (sin k) (/ l t))))) (* (/ (cbrt (/ 2 t)) (cbrt (/ (sin k) (/ l t)))) (/ (cos k) (fma (/ k t) (/ k t) 2)))))
9.6b
(cbrt (/ (sin k) (/ l t)))
9.6b
(cbrt (/ (sin k) (/ l t)))
9.6b
(cbrt (/ (sin k) (/ l t)))

rewrite84.0ms

Algorithm
rewrite-expression-head
Counts
4 → 245
Calls

4 calls. Slowest were:

71.0ms
(* (/ (* (cbrt (/ 2 t)) (cbrt (/ 2 t))) (/ (sin k) (/ l t))) (* (/ 1 (* (cbrt (/ (sin k) (/ l t))) (cbrt (/ (sin k) (/ l t))))) (* (/ (cbrt (/ 2 t)) (cbrt (/ (sin k) (/ l t)))) (/ (cos k) (fma (/ k t) (/ k t) 2)))))
2.0ms
(cbrt (/ (sin k) (/ l t)))
2.0ms
(cbrt (/ (sin k) (/ l t)))

series1.3s

Counts
4 → 12
Calls

4 calls. Slowest were:

860.0ms
(* (/ (* (cbrt (/ 2 t)) (cbrt (/ 2 t))) (/ (sin k) (/ l t))) (* (/ 1 (* (cbrt (/ (sin k) (/ l t))) (cbrt (/ (sin k) (/ l t))))) (* (/ (cbrt (/ 2 t)) (cbrt (/ (sin k) (/ l t)))) (/ (cos k) (fma (/ k t) (/ k t) 2)))))
148.0ms
(cbrt (/ (sin k) (/ l t)))
147.0ms
(cbrt (/ (sin k) (/ l t)))
116.0ms
(cbrt (/ (sin k) (/ l t)))

simplify43.8s

Counts
223 → 257
Calls

223 calls. Slowest were:

1.2s
(* (* (* (/ (* (cbrt (/ 2 t)) (cbrt (/ 2 t))) (/ (sin k) (/ l t))) (/ (* (cbrt (/ 2 t)) (cbrt (/ 2 t))) (/ (sin k) (/ l t)))) (/ (* (cbrt (/ 2 t)) (cbrt (/ 2 t))) (/ (sin k) (/ l t)))) (* (* (* (/ 1 (* (cbrt (/ (sin k) (/ l t))) (cbrt (/ (sin k) (/ l t))))) (/ 1 (* (cbrt (/ (sin k) (/ l t))) (cbrt (/ (sin k) (/ l t)))))) (/ 1 (* (cbrt (/ (sin k) (/ l t))) (cbrt (/ (sin k) (/ l t)))))) (* (/ (/ 2 t) (/ (sin k) (/ l t))) (/ (* (* (cos k) (cos k)) (cos k)) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))))))
1.1s
(* (/ (* (/ 2 t) (/ 2 t)) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (* (/ 1 (* (cbrt (/ (sin k) (/ l t))) (cbrt (/ (sin k) (/ l t))))) (/ 1 (* (cbrt (/ (sin k) (/ l t))) (cbrt (/ (sin k) (/ l t)))))) (/ 1 (* (cbrt (/ (sin k) (/ l t))) (cbrt (/ (sin k) (/ l t)))))) (* (/ (/ 2 t) (/ (sin k) (/ l t))) (/ (* (* (cos k) (cos k)) (cos k)) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))))))
959.0ms
(* (/ (* (* (* (cbrt (/ 2 t)) (cbrt (/ 2 t))) (* (cbrt (/ 2 t)) (cbrt (/ 2 t)))) (* (cbrt (/ 2 t)) (cbrt (/ 2 t)))) (/ (* (* (sin k) (sin k)) (sin k)) (* (* (/ l t) (/ l t)) (/ l t)))) (* (* (* (/ 1 (* (cbrt (/ (sin k) (/ l t))) (cbrt (/ (sin k) (/ l t))))) (/ 1 (* (cbrt (/ (sin k) (/ l t))) (cbrt (/ (sin k) (/ l t)))))) (/ 1 (* (cbrt (/ (sin k) (/ l t))) (cbrt (/ (sin k) (/ l t)))))) (* (/ (/ 2 t) (/ (sin k) (/ l t))) (/ (* (* (cos k) (cos k)) (cos k)) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))))))

prune6.1s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 14.1b

regimes771.0ms

Accuracy

0% (1.1b remaining)

Error of 12.1b against oracle of 11.0b and baseline of 12.1b

bsearch5.0ms