Average Error: 0.3 → 0.3
Time: 24.0s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
double f(double x, double y, double z, double t) {
        double r679890 = x;
        double r679891 = 0.5;
        double r679892 = r679890 * r679891;
        double r679893 = y;
        double r679894 = r679892 - r679893;
        double r679895 = z;
        double r679896 = 2.0;
        double r679897 = r679895 * r679896;
        double r679898 = sqrt(r679897);
        double r679899 = r679894 * r679898;
        double r679900 = t;
        double r679901 = r679900 * r679900;
        double r679902 = r679901 / r679896;
        double r679903 = exp(r679902);
        double r679904 = r679899 * r679903;
        return r679904;
}
↓
double f(double x, double y, double z, double t) {
        double r679905 = x;
        double r679906 = 0.5;
        double r679907 = r679905 * r679906;
        double r679908 = y;
        double r679909 = r679907 - r679908;
        double r679910 = z;
        double r679911 = 2.0;
        double r679912 = r679910 * r679911;
        double r679913 = sqrt(r679912);
        double r679914 = r679909 * r679913;
        double r679915 = t;
        double r679916 = r679915 * r679915;
        double r679917 = r679916 / r679911;
        double r679918 = exp(r679917);
        double r679919 = r679914 * r679918;
        return r679919;
}

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019305 
(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))))