Average Error: 45.5 → 45.0
Time: 17.0s
Precision: binary64
\[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\]
↓
\[\left(x \cdot \sqrt[3]{{\left(\cos \left(\frac{\left(y \cdot 2 + 1\right) \cdot \left(z \cdot t\right)}{16}\right)\right)}^{3}}\right) \cdot \sqrt[3]{{\left(\cos \left(\frac{\left(a \cdot 2 + 1\right) \cdot \left(b \cdot t\right)}{16}\right)\right)}^{3}}\]
\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)
↓
\left(x \cdot \sqrt[3]{{\left(\cos \left(\frac{\left(y \cdot 2 + 1\right) \cdot \left(z \cdot t\right)}{16}\right)\right)}^{3}}\right) \cdot \sqrt[3]{{\left(\cos \left(\frac{\left(a \cdot 2 + 1\right) \cdot \left(b \cdot t\right)}{16}\right)\right)}^{3}}
double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (((double) (x * ((double) cos(((double) (((double) (((double) (((double) (((double) (y * 2.0)) + 1.0)) * z)) * t)) / 16.0)))))) * ((double) cos(((double) (((double) (((double) (((double) (((double) (a * 2.0)) + 1.0)) * b)) * t)) / 16.0))))));
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (((double) (x * ((double) cbrt(((double) pow(((double) cos(((double) (((double) (((double) (((double) (y * 2.0)) + 1.0)) * ((double) (z * t)))) / 16.0)))), 3.0)))))) * ((double) cbrt(((double) pow(((double) cos(((double) (((double) (((double) (((double) (a * 2.0)) + 1.0)) * ((double) (b * t)))) / 16.0)))), 3.0))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original45.5
Target43.8
Herbie45.0
\[x \cdot \cos \left(\frac{b}{16} \cdot \frac{t}{\left(1 - a \cdot 2\right) + {\left(a \cdot 2\right)}^{2}}\right)\]

Derivation

  1. Initial program 45.5

    \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\]
  2. Using strategy rm

  3. Applied associate-*l*45.2

    \[\leadsto \left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(a \cdot 2 + 1\right) \cdot \left(b \cdot t\right)}}{16}\right)\]
  4. Using strategy rm

  5. Applied associate-*l*45.0

    \[\leadsto \left(x \cdot \cos \left(\frac{\color{blue}{\left(y \cdot 2 + 1\right) \cdot \left(z \cdot t\right)}}{16}\right)\right) \cdot \cos \left(\frac{\left(a \cdot 2 + 1\right) \cdot \left(b \cdot t\right)}{16}\right)\]
  6. Using strategy rm

  7. Applied add-cbrt-cube45.0

    \[\leadsto \left(x \cdot \color{blue}{\sqrt[3]{\left(\cos \left(\frac{\left(y \cdot 2 + 1\right) \cdot \left(z \cdot t\right)}{16}\right) \cdot \cos \left(\frac{\left(y \cdot 2 + 1\right) \cdot \left(z \cdot t\right)}{16}\right)\right) \cdot \cos \left(\frac{\left(y \cdot 2 + 1\right) \cdot \left(z \cdot t\right)}{16}\right)}}\right) \cdot \cos \left(\frac{\left(a \cdot 2 + 1\right) \cdot \left(b \cdot t\right)}{16}\right)\]

  8. Simplified45.0

    \[\leadsto \left(x \cdot \sqrt[3]{\color{blue}{{\left(\cos \left(\frac{\left(y \cdot 2 + 1\right) \cdot \left(z \cdot t\right)}{16}\right)\right)}^{3}}}\right) \cdot \cos \left(\frac{\left(a \cdot 2 + 1\right) \cdot \left(b \cdot t\right)}{16}\right)\]
  9. Using strategy rm

  10. Applied add-cbrt-cube45.0

    \[\leadsto \left(x \cdot \sqrt[3]{{\left(\cos \left(\frac{\left(y \cdot 2 + 1\right) \cdot \left(z \cdot t\right)}{16}\right)\right)}^{3}}\right) \cdot \color{blue}{\sqrt[3]{\left(\cos \left(\frac{\left(a \cdot 2 + 1\right) \cdot \left(b \cdot t\right)}{16}\right) \cdot \cos \left(\frac{\left(a \cdot 2 + 1\right) \cdot \left(b \cdot t\right)}{16}\right)\right) \cdot \cos \left(\frac{\left(a \cdot 2 + 1\right) \cdot \left(b \cdot t\right)}{16}\right)}}\]

  11. Simplified45.0

    \[\leadsto \left(x \cdot \sqrt[3]{{\left(\cos \left(\frac{\left(y \cdot 2 + 1\right) \cdot \left(z \cdot t\right)}{16}\right)\right)}^{3}}\right) \cdot \sqrt[3]{\color{blue}{{\left(\cos \left(\frac{\left(a \cdot 2 + 1\right) \cdot \left(b \cdot t\right)}{16}\right)\right)}^{3}}}\]

  12. Final simplification45.0

    \[\leadsto \left(x \cdot \sqrt[3]{{\left(\cos \left(\frac{\left(y \cdot 2 + 1\right) \cdot \left(z \cdot t\right)}{16}\right)\right)}^{3}}\right) \cdot \sqrt[3]{{\left(\cos \left(\frac{\left(a \cdot 2 + 1\right) \cdot \left(b \cdot t\right)}{16}\right)\right)}^{3}}\]

Reproduce

herbie shell --seed 2020148 
(FPCore (x y z t a b)
  :name "Codec.Picture.Jpg.FastDct:referenceDct from JuicyPixels-3.2.6.1"
  :precision binary64

  :herbie-target
  (* x (cos (* (/ b 16.0) (/ t (+ (- 1.0 (* a 2.0)) (pow (* a 2.0) 2.0))))))

  (* (* x (cos (/ (* (* (+ (* y 2.0) 1.0) z) t) 16.0))) (cos (/ (* (* (+ (* a 2.0) 1.0) b) t) 16.0))))