Average Error: 1.4 → 1.4
Time: 20.4s
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 r351176 = x;
        double r351177 = y;
        double r351178 = z;
        double r351179 = t;
        double r351180 = r351178 - r351179;
        double r351181 = a;
        double r351182 = r351178 - r351181;
        double r351183 = r351180 / r351182;
        double r351184 = r351177 * r351183;
        double r351185 = r351176 + r351184;
        return r351185;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r351186 = y;
        double r351187 = z;
        double r351188 = a;
        double r351189 = r351187 - r351188;
        double r351190 = t;
        double r351191 = r351187 - r351190;
        double r351192 = r351189 / r351191;
        double r351193 = r351186 / r351192;
        double r351194 = x;
        double r351195 = r351193 + r351194;
        return r351195;
}

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

Derivation

  1. Initial program 1.4

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

  2. Simplified1.4

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

  4. Applied clear-num1.5

    \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{z - a}{z - t}}}, y, x\right)\]
  5. Using strategy rm

  6. Applied add-cube-cbrt1.7

    \[\leadsto \mathsf{fma}\left(\frac{1}{\color{blue}{\left(\sqrt[3]{\frac{z - a}{z - t}} \cdot \sqrt[3]{\frac{z - a}{z - t}}\right) \cdot \sqrt[3]{\frac{z - a}{z - t}}}}, y, x\right)\]

  7. Applied add-cube-cbrt1.7

    \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\left(\sqrt[3]{\frac{z - a}{z - t}} \cdot \sqrt[3]{\frac{z - a}{z - t}}\right) \cdot \sqrt[3]{\frac{z - a}{z - t}}}, y, x\right)\]

  8. Applied times-frac1.7

    \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{\frac{z - a}{z - t}} \cdot \sqrt[3]{\frac{z - a}{z - t}}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{\frac{z - a}{z - t}}}}, y, x\right)\]

  9. Simplified1.7

    \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{\frac{1}{\sqrt[3]{\frac{z - a}{z - t}}}}{\sqrt[3]{\frac{z - a}{z - t}}}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{\frac{z - a}{z - t}}}, y, x\right)\]

  10. Simplified1.7

    \[\leadsto \mathsf{fma}\left(\frac{\frac{1}{\sqrt[3]{\frac{z - a}{z - t}}}}{\sqrt[3]{\frac{z - a}{z - t}}} \cdot \color{blue}{\frac{1}{\sqrt[3]{\frac{z - a}{z - t}}}}, y, x\right)\]
  11. Using strategy rm

  12. Applied fma-udef1.7

    \[\leadsto \color{blue}{\left(\frac{\frac{1}{\sqrt[3]{\frac{z - a}{z - t}}}}{\sqrt[3]{\frac{z - a}{z - t}}} \cdot \frac{1}{\sqrt[3]{\frac{z - a}{z - t}}}\right) \cdot y + x}\]

  13. Simplified1.4

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

  14. Final simplification1.4

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

Reproduce

herbie shell --seed 2019325 +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)))))