Average Error: 10.7 → 1.3
Time: 4.3s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{y}{\frac{z}{z - t} - \frac{a}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{y}{\frac{z}{z - t} - \frac{a}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r493189 = x;
        double r493190 = y;
        double r493191 = z;
        double r493192 = t;
        double r493193 = r493191 - r493192;
        double r493194 = r493190 * r493193;
        double r493195 = a;
        double r493196 = r493191 - r493195;
        double r493197 = r493194 / r493196;
        double r493198 = r493189 + r493197;
        return r493198;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r493199 = x;
        double r493200 = y;
        double r493201 = z;
        double r493202 = t;
        double r493203 = r493201 - r493202;
        double r493204 = r493201 / r493203;
        double r493205 = a;
        double r493206 = r493205 / r493203;
        double r493207 = r493204 - r493206;
        double r493208 = r493200 / r493207;
        double r493209 = r493199 + r493208;
        return r493209;
}

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

Original10.7
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.7

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

  3. Applied associate-/l*1.3

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

  5. Applied div-sub1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2020024 +o rules:numerics
(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))))