Average Error: 10.0 → 1.3
Time: 20.6s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\frac{z - t}{z - a} \cdot y + x\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
\frac{z - t}{z - a} \cdot y + x
double f(double x, double y, double z, double t, double a) {
        double r24448754 = x;
        double r24448755 = y;
        double r24448756 = z;
        double r24448757 = t;
        double r24448758 = r24448756 - r24448757;
        double r24448759 = r24448755 * r24448758;
        double r24448760 = a;
        double r24448761 = r24448756 - r24448760;
        double r24448762 = r24448759 / r24448761;
        double r24448763 = r24448754 + r24448762;
        return r24448763;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r24448764 = z;
        double r24448765 = t;
        double r24448766 = r24448764 - r24448765;
        double r24448767 = a;
        double r24448768 = r24448764 - r24448767;
        double r24448769 = r24448766 / r24448768;
        double r24448770 = y;
        double r24448771 = r24448769 * r24448770;
        double r24448772 = x;
        double r24448773 = r24448771 + r24448772;
        return r24448773;
}

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

Original10.0
Target1.1
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.0

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

  2. Simplified2.7

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

  4. Applied clear-num3.0

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

  6. Applied fma-udef3.0

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

  7. Simplified1.3

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

  8. Final simplification1.3

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

Reproduce

herbie shell --seed 2019162 +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))))