Average Error: 6.0 → 0.1
Time: 42.5s
Precision: 64
\[x \cdot x - \left(y \cdot 4.0\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\left(x \cdot x + \left(t \cdot y\right) \cdot 4.0\right) - 4.0 \cdot \left(\left(z \cdot y\right) \cdot z\right)\]
x \cdot x - \left(y \cdot 4.0\right) \cdot \left(z \cdot z - t\right)
↓
\left(x \cdot x + \left(t \cdot y\right) \cdot 4.0\right) - 4.0 \cdot \left(\left(z \cdot y\right) \cdot z\right)
double f(double x, double y, double z, double t) {
        double r28770549 = x;
        double r28770550 = r28770549 * r28770549;
        double r28770551 = y;
        double r28770552 = 4.0;
        double r28770553 = r28770551 * r28770552;
        double r28770554 = z;
        double r28770555 = r28770554 * r28770554;
        double r28770556 = t;
        double r28770557 = r28770555 - r28770556;
        double r28770558 = r28770553 * r28770557;
        double r28770559 = r28770550 - r28770558;
        return r28770559;
}
↓
double f(double x, double y, double z, double t) {
        double r28770560 = x;
        double r28770561 = r28770560 * r28770560;
        double r28770562 = t;
        double r28770563 = y;
        double r28770564 = r28770562 * r28770563;
        double r28770565 = 4.0;
        double r28770566 = r28770564 * r28770565;
        double r28770567 = r28770561 + r28770566;
        double r28770568 = z;
        double r28770569 = r28770568 * r28770563;
        double r28770570 = r28770569 * r28770568;
        double r28770571 = r28770565 * r28770570;
        double r28770572 = r28770567 - r28770571;
        return r28770572;
}

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

Original6.0
Target6.0
Herbie0.1
\[x \cdot x - 4.0 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Initial program 6.0

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

  2. Taylor expanded around inf 6.0

    \[\leadsto \color{blue}{\left(4.0 \cdot \left(t \cdot y\right) + {x}^{2}\right) - 4.0 \cdot \left({z}^{2} \cdot y\right)}\]

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019165 
(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))))