Average Error: 10.4 → 1.3
Time: 4.6s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{y}{\frac{z - a}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{y}{\frac{z - a}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r342204 = x;
        double r342205 = y;
        double r342206 = z;
        double r342207 = t;
        double r342208 = r342206 - r342207;
        double r342209 = r342205 * r342208;
        double r342210 = a;
        double r342211 = r342206 - r342210;
        double r342212 = r342209 / r342211;
        double r342213 = r342204 + r342212;
        return r342213;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r342214 = x;
        double r342215 = y;
        double r342216 = z;
        double r342217 = a;
        double r342218 = r342216 - r342217;
        double r342219 = t;
        double r342220 = r342216 - r342219;
        double r342221 = r342218 / r342220;
        double r342222 = r342215 / r342221;
        double r342223 = r342214 + r342222;
        return r342223;
}

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

Original10.4
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.4

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

  3. Applied associate-/l*1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019304 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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