Average Error: 1.3 → 1.3
Time: 4.3s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[x + y \cdot \left(\frac{1}{\frac{z - a}{z}} - \frac{t}{z - a}\right)\]
x + y \cdot \frac{z - t}{z - a}
↓
x + y \cdot \left(\frac{1}{\frac{z - a}{z}} - \frac{t}{z - a}\right)
double f(double x, double y, double z, double t, double a) {
        double r797940 = x;
        double r797941 = y;
        double r797942 = z;
        double r797943 = t;
        double r797944 = r797942 - r797943;
        double r797945 = a;
        double r797946 = r797942 - r797945;
        double r797947 = r797944 / r797946;
        double r797948 = r797941 * r797947;
        double r797949 = r797940 + r797948;
        return r797949;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r797950 = x;
        double r797951 = y;
        double r797952 = 1.0;
        double r797953 = z;
        double r797954 = a;
        double r797955 = r797953 - r797954;
        double r797956 = r797955 / r797953;
        double r797957 = r797952 / r797956;
        double r797958 = t;
        double r797959 = r797958 / r797955;
        double r797960 = r797957 - r797959;
        double r797961 = r797951 * r797960;
        double r797962 = r797950 + r797961;
        return r797962;
}

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

Derivation

  1. Initial program 1.3

    \[x + y \cdot \frac{z - t}{z - a}\]
  2. Using strategy rm

  3. Applied div-sub1.3

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

  5. Applied clear-num1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2020056 
(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)))))