Average Error: 1.2 → 1.1
Time: 3.9s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\frac{y}{\frac{z - a}{z - t}} + x\]
x + y \cdot \frac{z - t}{z - a}
↓
\frac{y}{\frac{z - a}{z - t}} + x
double f(double x, double y, double z, double t, double a) {
        double r416013 = x;
        double r416014 = y;
        double r416015 = z;
        double r416016 = t;
        double r416017 = r416015 - r416016;
        double r416018 = a;
        double r416019 = r416015 - r416018;
        double r416020 = r416017 / r416019;
        double r416021 = r416014 * r416020;
        double r416022 = r416013 + r416021;
        return r416022;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r416023 = y;
        double r416024 = z;
        double r416025 = a;
        double r416026 = r416024 - r416025;
        double r416027 = t;
        double r416028 = r416024 - r416027;
        double r416029 = r416026 / r416028;
        double r416030 = r416023 / r416029;
        double r416031 = x;
        double r416032 = r416030 + r416031;
        return r416032;
}

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

Original1.2
Target1.1
Herbie1.1
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.2

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

  3. Applied clear-num1.3

    \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{z - a}{z - t}}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity1.3

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

  6. Applied associate-*l*1.3

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

  7. Simplified1.1

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

  8. Final simplification1.1

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

Reproduce

herbie shell --seed 2020089 
(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)))))