Average Error: 5.4 → 0.1
Time: 15.0s
Precision: 64
\[x \cdot x - \left(y \cdot 4.0\right) \cdot \left(z \cdot z - t\right)\]
↓
\[x \cdot x - \left(\left(z \cdot \left(y \cdot 4.0\right)\right) \cdot z + \left(-t \cdot \left(y \cdot 4.0\right)\right)\right)\]
x \cdot x - \left(y \cdot 4.0\right) \cdot \left(z \cdot z - t\right)
↓
x \cdot x - \left(\left(z \cdot \left(y \cdot 4.0\right)\right) \cdot z + \left(-t \cdot \left(y \cdot 4.0\right)\right)\right)
double f(double x, double y, double z, double t) {
        double r34973434 = x;
        double r34973435 = r34973434 * r34973434;
        double r34973436 = y;
        double r34973437 = 4.0;
        double r34973438 = r34973436 * r34973437;
        double r34973439 = z;
        double r34973440 = r34973439 * r34973439;
        double r34973441 = t;
        double r34973442 = r34973440 - r34973441;
        double r34973443 = r34973438 * r34973442;
        double r34973444 = r34973435 - r34973443;
        return r34973444;
}
↓
double f(double x, double y, double z, double t) {
        double r34973445 = x;
        double r34973446 = r34973445 * r34973445;
        double r34973447 = z;
        double r34973448 = y;
        double r34973449 = 4.0;
        double r34973450 = r34973448 * r34973449;
        double r34973451 = r34973447 * r34973450;
        double r34973452 = r34973451 * r34973447;
        double r34973453 = t;
        double r34973454 = r34973453 * r34973450;
        double r34973455 = -r34973454;
        double r34973456 = r34973452 + r34973455;
        double r34973457 = r34973446 - r34973456;
        return r34973457;
}

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

Original5.4
Target5.4
Herbie0.1
\[x \cdot x - 4.0 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Initial program 5.4

    \[x \cdot x - \left(y \cdot 4.0\right) \cdot \left(z \cdot z - t\right)\]
  2. Using strategy rm

  3. Applied sub-neg5.4

    \[\leadsto x \cdot x - \left(y \cdot 4.0\right) \cdot \color{blue}{\left(z \cdot z + \left(-t\right)\right)}\]

  4. Applied distribute-rgt-in5.4

    \[\leadsto x \cdot x - \color{blue}{\left(\left(z \cdot z\right) \cdot \left(y \cdot 4.0\right) + \left(-t\right) \cdot \left(y \cdot 4.0\right)\right)}\]
  5. Using strategy rm

  6. Applied associate-*l*0.1

    \[\leadsto x \cdot x - \left(\color{blue}{z \cdot \left(z \cdot \left(y \cdot 4.0\right)\right)} + \left(-t\right) \cdot \left(y \cdot 4.0\right)\right)\]

  7. Final simplification0.1

    \[\leadsto x \cdot x - \left(\left(z \cdot \left(y \cdot 4.0\right)\right) \cdot z + \left(-t \cdot \left(y \cdot 4.0\right)\right)\right)\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, B"

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

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