Average Error: 1.3 → 1.3
Time: 14.7s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[x + y \cdot \frac{z - t}{z - a}\]
x + y \cdot \frac{z - t}{z - a}
↓
x + y \cdot \frac{z - t}{z - a}
double f(double x, double y, double z, double t, double a) {
        double r435653 = x;
        double r435654 = y;
        double r435655 = z;
        double r435656 = t;
        double r435657 = r435655 - r435656;
        double r435658 = a;
        double r435659 = r435655 - r435658;
        double r435660 = r435657 / r435659;
        double r435661 = r435654 * r435660;
        double r435662 = r435653 + r435661;
        return r435662;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r435663 = x;
        double r435664 = y;
        double r435665 = z;
        double r435666 = t;
        double r435667 = r435665 - r435666;
        double r435668 = a;
        double r435669 = r435665 - r435668;
        double r435670 = r435667 / r435669;
        double r435671 = r435664 * r435670;
        double r435672 = r435663 + r435671;
        return r435672;
}

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

Original1.3
Target1.2
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -6.366002923159597e-72 or 1.0253879521988147e-19 < y

    1. Initial program 0.6

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

    if -6.366002923159597e-72 < y < 1.0253879521988147e-19

    1. Initial program 2.1

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

    3. Applied div-inv2.1

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

    4. Applied associate-*r*0.4

      \[\leadsto x + \color{blue}{\left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{z - a}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019291 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

  (+ x (* y (/ (- z t) (- z a)))))