Average Error: 1.9 → 6.2
Time: 13.6s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\frac{y \cdot z}{t} + \left(x - \frac{x \cdot z}{t}\right)\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\frac{y \cdot z}{t} + \left(x - \frac{x \cdot z}{t}\right)
double f(double x, double y, double z, double t) {
        double r461355 = x;
        double r461356 = y;
        double r461357 = r461356 - r461355;
        double r461358 = z;
        double r461359 = t;
        double r461360 = r461358 / r461359;
        double r461361 = r461357 * r461360;
        double r461362 = r461355 + r461361;
        return r461362;
}
↓
double f(double x, double y, double z, double t) {
        double r461363 = y;
        double r461364 = z;
        double r461365 = r461363 * r461364;
        double r461366 = t;
        double r461367 = r461365 / r461366;
        double r461368 = x;
        double r461369 = r461368 * r461364;
        double r461370 = r461369 / r461366;
        double r461371 = r461368 - r461370;
        double r461372 = r461367 + r461371;
        return r461372;
}

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

Original1.9
Target2.1
Herbie6.2
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.88671875:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Initial program 1.9

    \[x + \left(y - x\right) \cdot \frac{z}{t}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt2.5

    \[\leadsto x + \left(y - x\right) \cdot \frac{z}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}}\]

  4. Applied add-cube-cbrt2.6

    \[\leadsto x + \left(y - x\right) \cdot \frac{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}\]

  5. Applied times-frac2.6

    \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\left(\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}}\right)}\]

  6. Applied associate-*r*0.9

    \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot \frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right) \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}}}\]

  7. Final simplification6.2

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

Reproduce

herbie shell --seed 2019298 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.887) (+ 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))))