Average Error: 11.2 → 1.2
Time: 23.7s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\frac{y}{\frac{z - a}{z - t}} + x\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
\frac{y}{\frac{z - a}{z - t}} + x
double f(double x, double y, double z, double t, double a) {
        double r384802 = x;
        double r384803 = y;
        double r384804 = z;
        double r384805 = t;
        double r384806 = r384804 - r384805;
        double r384807 = r384803 * r384806;
        double r384808 = a;
        double r384809 = r384804 - r384808;
        double r384810 = r384807 / r384809;
        double r384811 = r384802 + r384810;
        return r384811;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r384812 = y;
        double r384813 = z;
        double r384814 = a;
        double r384815 = r384813 - r384814;
        double r384816 = t;
        double r384817 = r384813 - r384816;
        double r384818 = r384815 / r384817;
        double r384819 = r384812 / r384818;
        double r384820 = x;
        double r384821 = r384819 + r384820;
        return r384821;
}

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

Original11.2
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 11.2

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

  2. Simplified1.3

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

  4. Applied fma-udef1.3

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

  5. Simplified1.2

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

  6. Final simplification1.2

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"

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

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