Average Error: 1.2 → 1.2
Time: 21.7s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\frac{z - t}{a - t} \cdot y + x\]
x + y \cdot \frac{z - t}{a - t}
↓
\frac{z - t}{a - t} \cdot y + x
double f(double x, double y, double z, double t, double a) {
        double r23382130 = x;
        double r23382131 = y;
        double r23382132 = z;
        double r23382133 = t;
        double r23382134 = r23382132 - r23382133;
        double r23382135 = a;
        double r23382136 = r23382135 - r23382133;
        double r23382137 = r23382134 / r23382136;
        double r23382138 = r23382131 * r23382137;
        double r23382139 = r23382130 + r23382138;
        return r23382139;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r23382140 = z;
        double r23382141 = t;
        double r23382142 = r23382140 - r23382141;
        double r23382143 = a;
        double r23382144 = r23382143 - r23382141;
        double r23382145 = r23382142 / r23382144;
        double r23382146 = y;
        double r23382147 = r23382145 * r23382146;
        double r23382148 = x;
        double r23382149 = r23382147 + r23382148;
        return r23382149;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original1.2
Target0.5
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;y \lt -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Initial program 1.2

    \[x + y \cdot \frac{z - t}{a - t}\]

  2. Simplified1.2

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

  4. Applied add-cube-cbrt1.5

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

  6. Applied fma-udef1.5

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

  7. Simplified1.2

    \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot y} + x\]

  8. Final simplification1.2

    \[\leadsto \frac{z - t}{a - t} \cdot y + x\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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