Average Error: 6.0 → 0.1
Time: 4.2s
Precision: binary64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[x \cdot x - \left(z \cdot \left(\left(y \cdot 4\right) \cdot z\right) + \left(y \cdot t\right) \cdot -4\right)\]
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) + \left(y \cdot t\right) \cdot -4\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

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Your Program's Arguments

Results

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Target

Original6.0
Target6.0
Herbie0.1
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Initial program 6.0

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

  3. Applied sub-neg_binary646.0

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

  4. Applied distribute-rgt-in_binary646.0

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

  5. Simplified6.0

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

  6. Simplified6.0

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

  8. Applied associate-*r*_binary640.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020253 
(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))))