Average Error: 0.1 → 0.1
Time: 4.5s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[x - \left(\left(\left(\log y \cdot 0.5 + \log y \cdot y\right) + z\right) - y\right)\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
x - \left(\left(\left(\log y \cdot 0.5 + \log y \cdot y\right) + z\right) - y\right)
double f(double x, double y, double z) {
        double r350652 = x;
        double r350653 = y;
        double r350654 = 0.5;
        double r350655 = r350653 + r350654;
        double r350656 = log(r350653);
        double r350657 = r350655 * r350656;
        double r350658 = r350652 - r350657;
        double r350659 = r350658 + r350653;
        double r350660 = z;
        double r350661 = r350659 - r350660;
        return r350661;
}
↓
double f(double x, double y, double z) {
        double r350662 = x;
        double r350663 = y;
        double r350664 = log(r350663);
        double r350665 = 0.5;
        double r350666 = r350664 * r350665;
        double r350667 = r350664 * r350663;
        double r350668 = r350666 + r350667;
        double r350669 = z;
        double r350670 = r350668 + r350669;
        double r350671 = r350670 - r350663;
        double r350672 = r350662 - r350671;
        return r350672;
}

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

Original0.1
Target0.1
Herbie0.1
\[\left(\left(y + x\right) - z\right) - \left(y + 0.5\right) \cdot \log y\]

Derivation

  1. Initial program 0.1

    \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]

  2. Simplified0.1

    \[\leadsto \color{blue}{x - \left(\mathsf{fma}\left(\log y, y + 0.5, z\right) - y\right)}\]
  3. Using strategy rm

  4. Applied fma-udef0.1

    \[\leadsto x - \left(\color{blue}{\left(\log y \cdot \left(y + 0.5\right) + z\right)} - y\right)\]

  5. Simplified0.1

    \[\leadsto x - \left(\left(\color{blue}{\log y \cdot \left(0.5 + y\right)} + z\right) - y\right)\]
  6. Using strategy rm

  7. Applied distribute-lft-in0.1

    \[\leadsto x - \left(\left(\color{blue}{\left(\log y \cdot 0.5 + \log y \cdot y\right)} + z\right) - y\right)\]

  8. Final simplification0.1

    \[\leadsto x - \left(\left(\left(\log y \cdot 0.5 + \log y \cdot y\right) + z\right) - y\right)\]

Reproduce

herbie shell --seed 2020020 +o rules:numerics
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (- (- (+ y x) z) (* (+ y 0.5) (log y)))

  (- (+ (- x (* (+ y 0.5) (log y))) y) z))