Average Error: 11.1 → 1.4
Time: 3.8s
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 r664569 = x;
        double r664570 = y;
        double r664571 = z;
        double r664572 = t;
        double r664573 = r664571 - r664572;
        double r664574 = r664570 * r664573;
        double r664575 = a;
        double r664576 = r664571 - r664575;
        double r664577 = r664574 / r664576;
        double r664578 = r664569 + r664577;
        return r664578;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r664579 = x;
        double r664580 = y;
        double r664581 = z;
        double r664582 = t;
        double r664583 = r664581 - r664582;
        double r664584 = a;
        double r664585 = r664581 - r664584;
        double r664586 = r664583 / r664585;
        double r664587 = r664580 * r664586;
        double r664588 = r664579 + r664587;
        return r664588;
}

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

Original11.1
Target1.3
Herbie1.4
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 11.1

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

  3. Applied *-un-lft-identity11.1

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

  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. Final simplification1.4

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

Reproduce

herbie shell --seed 2020025 
(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))))