Average Error: 10.9 → 1.2
Time: 9.9s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + y \cdot \frac{z - t}{a - t}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + y \cdot \frac{z - t}{a - t}
double f(double x, double y, double z, double t, double a) {
        double r637173 = x;
        double r637174 = y;
        double r637175 = z;
        double r637176 = t;
        double r637177 = r637175 - r637176;
        double r637178 = r637174 * r637177;
        double r637179 = a;
        double r637180 = r637179 - r637176;
        double r637181 = r637178 / r637180;
        double r637182 = r637173 + r637181;
        return r637182;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r637183 = x;
        double r637184 = y;
        double r637185 = z;
        double r637186 = t;
        double r637187 = r637185 - r637186;
        double r637188 = a;
        double r637189 = r637188 - r637186;
        double r637190 = r637187 / r637189;
        double r637191 = r637184 * r637190;
        double r637192 = r637183 + r637191;
        return r637192;
}

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

Original10.9
Target1.0
Herbie1.2
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.9

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

  3. Applied *-un-lft-identity10.9

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

  4. Applied times-frac1.2

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

  5. Simplified1.2

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

  6. Final simplification1.2

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

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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