Average Error: 2.2 → 2.2
Time: 27.6s
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 r320749 = x;
        double r320750 = y;
        double r320751 = r320750 - r320749;
        double r320752 = z;
        double r320753 = t;
        double r320754 = r320752 / r320753;
        double r320755 = r320751 * r320754;
        double r320756 = r320749 + r320755;
        return r320756;
}
↓
double f(double x, double y, double z, double t) {
        double r320757 = y;
        double r320758 = t;
        double r320759 = z;
        double r320760 = r320758 / r320759;
        double r320761 = r320757 / r320760;
        double r320762 = x;
        double r320763 = r320762 / r320760;
        double r320764 = r320763 - r320762;
        double r320765 = r320761 - r320764;
        return r320765;
}

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))))