Average Error: 10.6 → 1.3
Time: 19.1s
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 r24047606 = x;
        double r24047607 = y;
        double r24047608 = z;
        double r24047609 = t;
        double r24047610 = r24047608 - r24047609;
        double r24047611 = r24047607 * r24047610;
        double r24047612 = a;
        double r24047613 = r24047608 - r24047612;
        double r24047614 = r24047611 / r24047613;
        double r24047615 = r24047606 + r24047614;
        return r24047615;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r24047616 = x;
        double r24047617 = y;
        double r24047618 = z;
        double r24047619 = t;
        double r24047620 = r24047618 - r24047619;
        double r24047621 = a;
        double r24047622 = r24047618 - r24047621;
        double r24047623 = r24047620 / r24047622;
        double r24047624 = r24047617 * r24047623;
        double r24047625 = r24047616 + r24047624;
        return r24047625;
}

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

Original10.6
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.6

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

  3. Applied *-un-lft-identity10.6

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

  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 2019172 
(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))))