Average Error: 2.2 → 2.2
Time: 25.8s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\frac{y}{\frac{t}{z}} - \left(\frac{x}{\frac{t}{z}} - x\right)\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\frac{y}{\frac{t}{z}} - \left(\frac{x}{\frac{t}{z}} - x\right)
double f(double x, double y, double z, double t) {
        double r469259 = x;
        double r469260 = y;
        double r469261 = r469260 - r469259;
        double r469262 = z;
        double r469263 = t;
        double r469264 = r469262 / r469263;
        double r469265 = r469261 * r469264;
        double r469266 = r469259 + r469265;
        return r469266;
}
↓
double f(double x, double y, double z, double t) {
        double r469267 = y;
        double r469268 = t;
        double r469269 = z;
        double r469270 = r469268 / r469269;
        double r469271 = r469267 / r469270;
        double r469272 = x;
        double r469273 = r469272 / r469270;
        double r469274 = r469273 - r469272;
        double r469275 = r469271 - r469274;
        return r469275;
}

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

Original2.2
Target2.4
Herbie2.2
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.88671875:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Initial program 2.2

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

  2. Simplified2.2

    \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z}{t}, x\right)}\]
  3. Using strategy rm

  4. Applied fma-udef2.2

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

  5. Simplified2.2

    \[\leadsto \color{blue}{\frac{y - x}{\frac{t}{z}}} + x\]
  6. Using strategy rm

  7. Applied div-sub2.2

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

  8. Applied associate-+l-2.2

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

  9. Final simplification2.2

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(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))))