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

# Try it out

Results

 In Out
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)))))