Average Error: 11.0 → 1.4
Time: 10.3s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[y \cdot \frac{z - t}{z - a} + x\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
y \cdot \frac{z - t}{z - a} + x
double f(double x, double y, double z, double t, double a) {
        double r468418 = x;
        double r468419 = y;
        double r468420 = z;
        double r468421 = t;
        double r468422 = r468420 - r468421;
        double r468423 = r468419 * r468422;
        double r468424 = a;
        double r468425 = r468420 - r468424;
        double r468426 = r468423 / r468425;
        double r468427 = r468418 + r468426;
        return r468427;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r468428 = y;
        double r468429 = z;
        double r468430 = t;
        double r468431 = r468429 - r468430;
        double r468432 = a;
        double r468433 = r468429 - r468432;
        double r468434 = r468431 / r468433;
        double r468435 = r468428 * r468434;
        double r468436 = x;
        double r468437 = r468435 + r468436;
        return r468437;
}

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

Original11.0
Target1.2
Herbie1.4
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 11.0

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

  2. Simplified2.9

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{z - a}, z - t, x\right)}\]
  3. Using strategy rm

  4. Applied fma-udef2.9

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

  6. Applied div-inv3.0

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

  7. Applied associate-*l*1.4

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

  8. Simplified1.4

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

  9. Final simplification1.4

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

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(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))))