Average Error: 0.3 → 0.3
Time: 16.6s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot e^{\frac{t}{\frac{2}{t}}}\right)\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot e^{\frac{t}{\frac{2}{t}}}\right)
double f(double x, double y, double z, double t) {
        double r830871 = x;
        double r830872 = 0.5;
        double r830873 = r830871 * r830872;
        double r830874 = y;
        double r830875 = r830873 - r830874;
        double r830876 = z;
        double r830877 = 2.0;
        double r830878 = r830876 * r830877;
        double r830879 = sqrt(r830878);
        double r830880 = r830875 * r830879;
        double r830881 = t;
        double r830882 = r830881 * r830881;
        double r830883 = r830882 / r830877;
        double r830884 = exp(r830883);
        double r830885 = r830880 * r830884;
        return r830885;
}
↓
double f(double x, double y, double z, double t) {
        double r830886 = x;
        double r830887 = 0.5;
        double r830888 = r830886 * r830887;
        double r830889 = y;
        double r830890 = r830888 - r830889;
        double r830891 = z;
        double r830892 = 2.0;
        double r830893 = r830891 * r830892;
        double r830894 = sqrt(r830893);
        double r830895 = t;
        double r830896 = r830892 / r830895;
        double r830897 = r830895 / r830896;
        double r830898 = exp(r830897);
        double r830899 = r830894 * r830898;
        double r830900 = r830890 * r830899;
        return r830900;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.3
Herbie0.3
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2}\right)}\]

Derivation

  1. Initial program 0.3

    \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
  2. Using strategy rm

  3. Applied associate-*l*0.3

    \[\leadsto \color{blue}{\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot e^{\frac{t \cdot t}{2}}\right)}\]

  4. Simplified0.3

    \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \color{blue}{\left(\sqrt{z \cdot 2} \cdot e^{\frac{t}{\frac{2}{t}}}\right)}\]

  5. Final simplification0.3

    \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot e^{\frac{t}{\frac{2}{t}}}\right)\]

Reproduce

herbie shell --seed 2019350 
(FPCore (x y z t)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, A"
  :precision binary64

  :herbie-target
  (* (* (- (* x 0.5) y) (sqrt (* z 2))) (pow (exp 1) (/ (* t t) 2)))

  (* (* (- (* x 0.5) y) (sqrt (* z 2))) (exp (/ (* t t) 2))))