Average Error: 1.3 → 1.1
Time: 15.5s
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 r731682 = x;
        double r731683 = y;
        double r731684 = z;
        double r731685 = t;
        double r731686 = r731684 - r731685;
        double r731687 = a;
        double r731688 = r731684 - r731687;
        double r731689 = r731686 / r731688;
        double r731690 = r731683 * r731689;
        double r731691 = r731682 + r731690;
        return r731691;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r731692 = y;
        double r731693 = z;
        double r731694 = a;
        double r731695 = r731693 - r731694;
        double r731696 = t;
        double r731697 = r731693 - r731696;
        double r731698 = r731695 / r731697;
        double r731699 = r731692 / r731698;
        double r731700 = x;
        double r731701 = r731699 + r731700;
        return r731701;
}

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

Original1.3
Target1.1
Herbie1.1
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.3

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

  2. Simplified1.3

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

  4. Applied clear-num1.3

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

  6. Applied add-cube-cbrt1.8

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

  7. Applied *-un-lft-identity1.8

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

  8. Applied times-frac1.8

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

  10. Applied fma-udef1.8

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

  11. Simplified1.1

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

  12. Final simplification1.1

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

Reproduce

herbie shell --seed 2020043 +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)))))