Average Error: 11.7 → 1.4
Time: 6.5s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\frac{\frac{z - t}{z - a}}{\frac{1}{y}} + x\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
\frac{\frac{z - t}{z - a}}{\frac{1}{y}} + x
double f(double x, double y, double z, double t, double a) {
        double r628166 = x;
        double r628167 = y;
        double r628168 = z;
        double r628169 = t;
        double r628170 = r628168 - r628169;
        double r628171 = r628167 * r628170;
        double r628172 = a;
        double r628173 = r628168 - r628172;
        double r628174 = r628171 / r628173;
        double r628175 = r628166 + r628174;
        return r628175;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r628176 = z;
        double r628177 = t;
        double r628178 = r628176 - r628177;
        double r628179 = a;
        double r628180 = r628176 - r628179;
        double r628181 = r628178 / r628180;
        double r628182 = 1.0;
        double r628183 = y;
        double r628184 = r628182 / r628183;
        double r628185 = r628181 / r628184;
        double r628186 = x;
        double r628187 = r628185 + r628186;
        return r628187;
}

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

Original11.7
Target1.3
Herbie1.4
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 11.7

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

  2. Simplified2.7

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

  4. Applied add-cube-cbrt3.2

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

  5. Applied associate-/r*3.2

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

  7. Applied fma-udef3.2

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

  8. Simplified2.8

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

  10. Applied div-inv2.8

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

  11. Applied associate-/r*1.4

    \[\leadsto \color{blue}{\frac{\frac{z - t}{z - a}}{\frac{1}{y}}} + x\]

  12. Final simplification1.4

    \[\leadsto \frac{\frac{z - t}{z - a}}{\frac{1}{y}} + x\]

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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