Average Error: 1.3 → 1.2
Time: 47.1s
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 r26652059 = x;
        double r26652060 = y;
        double r26652061 = z;
        double r26652062 = t;
        double r26652063 = r26652061 - r26652062;
        double r26652064 = a;
        double r26652065 = r26652061 - r26652064;
        double r26652066 = r26652063 / r26652065;
        double r26652067 = r26652060 * r26652066;
        double r26652068 = r26652059 + r26652067;
        return r26652068;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r26652069 = y;
        double r26652070 = z;
        double r26652071 = a;
        double r26652072 = r26652070 - r26652071;
        double r26652073 = t;
        double r26652074 = r26652070 - r26652073;
        double r26652075 = r26652072 / r26652074;
        double r26652076 = r26652069 / r26652075;
        double r26652077 = x;
        double r26652078 = r26652076 + r26652077;
        return r26652078;
}

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
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{z - a}{z - t}}\]

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 fma-udef1.3

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

  7. Simplified1.2

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

  8. Final simplification1.2

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

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"

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

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