Average Error: 10.9 → 1.3
Time: 21.5s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + y \cdot \frac{z - t}{z - a}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + y \cdot \frac{z - t}{z - a}
double f(double x, double y, double z, double t, double a) {
        double r25323119 = x;
        double r25323120 = y;
        double r25323121 = z;
        double r25323122 = t;
        double r25323123 = r25323121 - r25323122;
        double r25323124 = r25323120 * r25323123;
        double r25323125 = a;
        double r25323126 = r25323121 - r25323125;
        double r25323127 = r25323124 / r25323126;
        double r25323128 = r25323119 + r25323127;
        return r25323128;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r25323129 = x;
        double r25323130 = y;
        double r25323131 = z;
        double r25323132 = t;
        double r25323133 = r25323131 - r25323132;
        double r25323134 = a;
        double r25323135 = r25323131 - r25323134;
        double r25323136 = r25323133 / r25323135;
        double r25323137 = r25323130 * r25323136;
        double r25323138 = r25323129 + r25323137;
        return r25323138;
}

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

Derivation

  1. Initial program 10.9

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

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

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

  4. Applied times-frac1.3

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

  5. Simplified1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2019169 
(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))))