Average Error: 0.1 → 0.1
Time: 18.3s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[\left(\left(x + y\right) - \left(y + 0.5\right) \cdot \log y\right) - z\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
\left(\left(x + y\right) - \left(y + 0.5\right) \cdot \log y\right) - z
double f(double x, double y, double z) {
        double r268096 = x;
        double r268097 = y;
        double r268098 = 0.5;
        double r268099 = r268097 + r268098;
        double r268100 = log(r268097);
        double r268101 = r268099 * r268100;
        double r268102 = r268096 - r268101;
        double r268103 = r268102 + r268097;
        double r268104 = z;
        double r268105 = r268103 - r268104;
        return r268105;
}
↓
double f(double x, double y, double z) {
        double r268106 = x;
        double r268107 = y;
        double r268108 = r268106 + r268107;
        double r268109 = 0.5;
        double r268110 = r268107 + r268109;
        double r268111 = log(r268107);
        double r268112 = r268110 * r268111;
        double r268113 = r268108 - r268112;
        double r268114 = z;
        double r268115 = r268113 - r268114;
        return r268115;
}

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. Using strategy rm

  3. Applied *-un-lft-identity0.1

    \[\leadsto \left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + \color{blue}{1 \cdot y}\right) - z\]

  4. Applied *-un-lft-identity0.1

    \[\leadsto \left(\color{blue}{1 \cdot \left(x - \left(y + 0.5\right) \cdot \log y\right)} + 1 \cdot y\right) - z\]

  5. Applied distribute-lft-out0.1

    \[\leadsto \color{blue}{1 \cdot \left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right)} - z\]

  6. Simplified0.1

    \[\leadsto 1 \cdot \color{blue}{\left(\left(x + y\right) - \left(y + 0.5\right) \cdot \log y\right)} - z\]

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019198 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"

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

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