Average Error: 5.8 → 0.1
Time: 4.1s
Precision: binary64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[x \cdot x - \left(z \cdot \left(\left(y \cdot 4\right) \cdot z\right) + y \cdot \left(t \cdot -4\right)\right)\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
x \cdot x - \left(z \cdot \left(\left(y \cdot 4\right) \cdot z\right) + y \cdot \left(t \cdot -4\right)\right)
(FPCore (x y z t) :precision binary64 (- (* x x) (* (* y 4.0) (- (* z z) t))))
↓
(FPCore (x y z t)
 :precision binary64
 (- (* x x) (+ (* z (* (* y 4.0) z)) (* y (* t -4.0)))))
double code(double x, double y, double z, double t) {
	return (x * x) - ((y * 4.0) * ((z * z) - t));
}
↓
double code(double x, double y, double z, double t) {
	return (x * x) - ((z * ((y * 4.0) * z)) + (y * (t * -4.0)));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.8
Target5.8
Herbie0.1
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Initial program 5.8

    \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
  2. Using strategy rm

  3. Applied sub-neg_binary64_164395.8

    \[\leadsto x \cdot x - \left(y \cdot 4\right) \cdot \color{blue}{\left(z \cdot z + \left(-t\right)\right)}\]

  4. Applied distribute-rgt-in_binary64_163965.8

    \[\leadsto x \cdot x - \color{blue}{\left(\left(z \cdot z\right) \cdot \left(y \cdot 4\right) + \left(-t\right) \cdot \left(y \cdot 4\right)\right)}\]

  5. Simplified5.8

    \[\leadsto x \cdot x - \left(\color{blue}{\left(y \cdot 4\right) \cdot \left(z \cdot z\right)} + \left(-t\right) \cdot \left(y \cdot 4\right)\right)\]

  6. Simplified5.8

    \[\leadsto x \cdot x - \left(\left(y \cdot 4\right) \cdot \left(z \cdot z\right) + \color{blue}{y \cdot \left(t \cdot -4\right)}\right)\]
  7. Using strategy rm

  8. Applied associate-*r*_binary64_163860.1

    \[\leadsto x \cdot x - \left(\color{blue}{\left(\left(y \cdot 4\right) \cdot z\right) \cdot z} + y \cdot \left(t \cdot -4\right)\right)\]

  9. Final simplification0.1

    \[\leadsto x \cdot x - \left(z \cdot \left(\left(y \cdot 4\right) \cdot z\right) + y \cdot \left(t \cdot -4\right)\right)\]

Reproduce

herbie shell --seed 2020346 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, B"
  :precision binary64

  :herbie-target
  (- (* x x) (* 4.0 (* y (- (* z z) t))))

  (- (* x x) (* (* y 4.0) (- (* z z) t))))