Average Error: 1.2 → 1.1
Time: 3.4s
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 r595714 = x;
        double r595715 = y;
        double r595716 = z;
        double r595717 = t;
        double r595718 = r595716 - r595717;
        double r595719 = a;
        double r595720 = r595716 - r595719;
        double r595721 = r595718 / r595720;
        double r595722 = r595715 * r595721;
        double r595723 = r595714 + r595722;
        return r595723;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r595724 = y;
        double r595725 = z;
        double r595726 = a;
        double r595727 = r595725 - r595726;
        double r595728 = t;
        double r595729 = r595725 - r595728;
        double r595730 = r595727 / r595729;
        double r595731 = r595724 / r595730;
        double r595732 = x;
        double r595733 = r595731 + r595732;
        return r595733;
}

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

Derivation

  1. Initial program 1.2

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

  2. Simplified1.2

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

  4. Applied clear-num1.3

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

  6. Applied fma-udef1.3

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

  7. Simplified1.1

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

  8. Final simplification1.1

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

Reproduce

herbie shell --seed 2020089 +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)))))