Average Error: 2.0 → 2.0
Time: 11.1s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[x - \frac{z}{t} \cdot \left(x - y\right)\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
x - \frac{z}{t} \cdot \left(x - y\right)
double f(double x, double y, double z, double t) {
        double r502820 = x;
        double r502821 = y;
        double r502822 = r502821 - r502820;
        double r502823 = z;
        double r502824 = t;
        double r502825 = r502823 / r502824;
        double r502826 = r502822 * r502825;
        double r502827 = r502820 + r502826;
        return r502827;
}
↓
double f(double x, double y, double z, double t) {
        double r502828 = x;
        double r502829 = z;
        double r502830 = t;
        double r502831 = r502829 / r502830;
        double r502832 = y;
        double r502833 = r502828 - r502832;
        double r502834 = r502831 * r502833;
        double r502835 = r502828 - r502834;
        return r502835;
}

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

Original2.0
Target2.1
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.88671875:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Initial program 2.0

    \[x + \left(y - x\right) \cdot \frac{z}{t}\]

  2. Simplified2.0

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

  3. Final simplification2.0

    \[\leadsto x - \frac{z}{t} \cdot \left(x - y\right)\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.8867) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) -0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

  (+ x (* (- y x) (/ z t))))