Average Error: 1.9 → 6.0
Time: 12.8s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\frac{z}{\frac{t}{y - x}} - \left(-x\right)\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\frac{z}{\frac{t}{y - x}} - \left(-x\right)
double f(double x, double y, double z, double t) {
        double r472270 = x;
        double r472271 = y;
        double r472272 = r472271 - r472270;
        double r472273 = z;
        double r472274 = t;
        double r472275 = r472273 / r472274;
        double r472276 = r472272 * r472275;
        double r472277 = r472270 + r472276;
        return r472277;
}
↓
double f(double x, double y, double z, double t) {
        double r472278 = z;
        double r472279 = t;
        double r472280 = y;
        double r472281 = x;
        double r472282 = r472280 - r472281;
        double r472283 = r472279 / r472282;
        double r472284 = r472278 / r472283;
        double r472285 = -r472281;
        double r472286 = r472284 - r472285;
        return r472286;
}

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
Target2.0
Herbie6.0
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.88671875:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Initial program 1.9

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

  3. Applied add-cube-cbrt2.4

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

  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. Using strategy rm

  8. Applied add-sqr-sqrt0.9

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

  9. Applied associate-*r*0.9

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

  10. Simplified0.9

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

  11. Final simplification6.0

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

Reproduce

herbie shell --seed 2019297 
(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))))