Average Error: 0.3 → 0.3
Time: 29.5s
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 r656824 = x;
        double r656825 = 0.5;
        double r656826 = r656824 * r656825;
        double r656827 = y;
        double r656828 = r656826 - r656827;
        double r656829 = z;
        double r656830 = 2.0;
        double r656831 = r656829 * r656830;
        double r656832 = sqrt(r656831);
        double r656833 = r656828 * r656832;
        double r656834 = t;
        double r656835 = r656834 * r656834;
        double r656836 = r656835 / r656830;
        double r656837 = exp(r656836);
        double r656838 = r656833 * r656837;
        return r656838;
}
↓
double f(double x, double y, double z, double t) {
        double r656839 = x;
        double r656840 = 0.5;
        double r656841 = r656839 * r656840;
        double r656842 = y;
        double r656843 = r656841 - r656842;
        double r656844 = z;
        double r656845 = 2.0;
        double r656846 = r656844 * r656845;
        double r656847 = sqrt(r656846);
        double r656848 = r656843 * r656847;
        double r656849 = t;
        double r656850 = r656849 * r656849;
        double r656851 = r656850 / r656845;
        double r656852 = exp(r656851);
        double r656853 = r656848 * r656852;
        return r656853;
}

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 2019194 
(FPCore (x y z t)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, A"

  :herbie-target
  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (pow (exp 1.0) (/ (* t t) 2.0)))

  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))