Average Error: 10.2 → 0.0
Time: 12.7s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[y + \left(\left(-y\right) + 1\right) \cdot \frac{x}{z}\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
y + \left(\left(-y\right) + 1\right) \cdot \frac{x}{z}
double f(double x, double y, double z) {
        double r788741 = x;
        double r788742 = y;
        double r788743 = z;
        double r788744 = r788743 - r788741;
        double r788745 = r788742 * r788744;
        double r788746 = r788741 + r788745;
        double r788747 = r788746 / r788743;
        return r788747;
}
↓
double f(double x, double y, double z) {
        double r788748 = y;
        double r788749 = -r788748;
        double r788750 = 1.0;
        double r788751 = r788749 + r788750;
        double r788752 = x;
        double r788753 = z;
        double r788754 = r788752 / r788753;
        double r788755 = r788751 * r788754;
        double r788756 = r788748 + r788755;
        return r788756;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.2
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.2

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

  2. Taylor expanded around 0 3.5

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

  4. Applied *-un-lft-identity3.5

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

  5. Applied *-un-lft-identity3.5

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

  6. Applied distribute-lft-out--3.5

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
  :precision binary64

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

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