Average Error: 10.5 → 1.4
Time: 3.3s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)
double f(double x, double y, double z, double t, double a) {
        double r608407 = x;
        double r608408 = y;
        double r608409 = z;
        double r608410 = t;
        double r608411 = r608409 - r608410;
        double r608412 = r608408 * r608411;
        double r608413 = a;
        double r608414 = r608409 - r608413;
        double r608415 = r608412 / r608414;
        double r608416 = r608407 + r608415;
        return r608416;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r608417 = x;
        double r608418 = y;
        double r608419 = z;
        double r608420 = a;
        double r608421 = r608419 - r608420;
        double r608422 = r608419 / r608421;
        double r608423 = t;
        double r608424 = r608423 / r608421;
        double r608425 = r608422 - r608424;
        double r608426 = r608418 * r608425;
        double r608427 = r608417 + r608426;
        return r608427;
}

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

Original10.5
Target1.2
Herbie1.4
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.5

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

  3. Applied *-un-lft-identity10.5

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

  4. Applied times-frac1.4

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

  5. Simplified1.4

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

  7. Applied div-sub1.4

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

  8. Final simplification1.4

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

Reproduce

herbie shell --seed 2020049 
(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))))