Average Error: 1.4 → 1.2
Time: 5.2s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\frac{y}{\frac{z - a}{z - t}} + x\]
x + y \cdot \frac{z - t}{z - a}
↓
\frac{y}{\frac{z - a}{z - t}} + x
double f(double x, double y, double z, double t, double a) {
        double r759092 = x;
        double r759093 = y;
        double r759094 = z;
        double r759095 = t;
        double r759096 = r759094 - r759095;
        double r759097 = a;
        double r759098 = r759094 - r759097;
        double r759099 = r759096 / r759098;
        double r759100 = r759093 * r759099;
        double r759101 = r759092 + r759100;
        return r759101;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r759102 = y;
        double r759103 = z;
        double r759104 = a;
        double r759105 = r759103 - r759104;
        double r759106 = t;
        double r759107 = r759103 - r759106;
        double r759108 = r759105 / r759107;
        double r759109 = r759102 / r759108;
        double r759110 = x;
        double r759111 = r759109 + r759110;
        return r759111;
}

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

Original1.4
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.4

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

  2. Simplified1.4

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

  4. Applied add-cube-cbrt1.7

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

  6. Applied fma-udef1.7

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

  7. Simplified10.4

    \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{z - a}} + x\]
  8. Using strategy rm

  9. Applied associate-/l*1.2

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

  10. Final simplification1.2

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

Reproduce

herbie shell --seed 2019362 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

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