Average Error: 0.4 → 0.1
Time: 38.8s
Precision: 64
Internal Precision: 576
\[0.5 \cdot \left(36.0 \cdot {\left(\sqrt{\left(4.0 \cdot p\right) \cdot \left(1.0 - p\right)}\right)}^{10} + 211 \cdot {\left(\sqrt{\left(4.0 \cdot p\right) \cdot \left(1.0 - p\right)}\right)}^{12}\right)\]
\[\left(211 \cdot {\left(\sqrt{\left(4.0 \cdot p\right) \cdot \left(1.0 - p\right)}\right)}^{12} + 36.0 \cdot \left({\left(4.0 \cdot p\right)}^{\left(10 \cdot \frac{1}{2}\right)} \cdot {\left(1.0 - p\right)}^{\left(10 \cdot \frac{1}{2}\right)}\right)\right) \cdot 0.5\]

Error

Bits error versus p

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.4

    \[0.5 \cdot \left(36.0 \cdot {\left(\sqrt{\left(4.0 \cdot p\right) \cdot \left(1.0 - p\right)}\right)}^{10} + 211 \cdot {\left(\sqrt{\left(4.0 \cdot p\right) \cdot \left(1.0 - p\right)}\right)}^{12}\right)\]
  2. Using strategy rm
  3. Applied pow1/20.4

    \[\leadsto 0.5 \cdot \left(36.0 \cdot {\color{blue}{\left({\left(\left(4.0 \cdot p\right) \cdot \left(1.0 - p\right)\right)}^{\frac{1}{2}}\right)}}^{10} + 211 \cdot {\left(\sqrt{\left(4.0 \cdot p\right) \cdot \left(1.0 - p\right)}\right)}^{12}\right)\]
  4. Applied pow-pow0.1

    \[\leadsto 0.5 \cdot \left(36.0 \cdot \color{blue}{{\left(\left(4.0 \cdot p\right) \cdot \left(1.0 - p\right)\right)}^{\left(\frac{1}{2} \cdot 10\right)}} + 211 \cdot {\left(\sqrt{\left(4.0 \cdot p\right) \cdot \left(1.0 - p\right)}\right)}^{12}\right)\]
  5. Using strategy rm
  6. Applied unpow-prod-down0.1

    \[\leadsto 0.5 \cdot \left(36.0 \cdot \color{blue}{\left({\left(4.0 \cdot p\right)}^{\left(\frac{1}{2} \cdot 10\right)} \cdot {\left(1.0 - p\right)}^{\left(\frac{1}{2} \cdot 10\right)}\right)} + 211 \cdot {\left(\sqrt{\left(4.0 \cdot p\right) \cdot \left(1.0 - p\right)}\right)}^{12}\right)\]
  7. Final simplification0.1

    \[\leadsto \left(211 \cdot {\left(\sqrt{\left(4.0 \cdot p\right) \cdot \left(1.0 - p\right)}\right)}^{12} + 36.0 \cdot \left({\left(4.0 \cdot p\right)}^{\left(10 \cdot \frac{1}{2}\right)} \cdot {\left(1.0 - p\right)}^{\left(10 \cdot \frac{1}{2}\right)}\right)\right) \cdot 0.5\]

Runtime

Time bar (total: 38.8s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (p)
  :name "0.5 * (36.0 * pow(sqrt(4.0 * p * (1.0 - p)), 10)  + 211 * pow(sqrt(4.0 * p * (1.0 - p)), 12) )"
  (* 0.5 (+ (* 36.0 (pow (sqrt (* (* 4.0 p) (- 1.0 p))) 10)) (* 211 (pow (sqrt (* (* 4.0 p) (- 1.0 p))) 12)))))