Average Error: 0.3 → 0.3
Time: 8.2s
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 r961845 = x;
        double r961846 = 0.5;
        double r961847 = r961845 * r961846;
        double r961848 = y;
        double r961849 = r961847 - r961848;
        double r961850 = z;
        double r961851 = 2.0;
        double r961852 = r961850 * r961851;
        double r961853 = sqrt(r961852);
        double r961854 = r961849 * r961853;
        double r961855 = t;
        double r961856 = r961855 * r961855;
        double r961857 = r961856 / r961851;
        double r961858 = exp(r961857);
        double r961859 = r961854 * r961858;
        return r961859;
}
↓
double f(double x, double y, double z, double t) {
        double r961860 = x;
        double r961861 = 0.5;
        double r961862 = r961860 * r961861;
        double r961863 = y;
        double r961864 = r961862 - r961863;
        double r961865 = z;
        double r961866 = 2.0;
        double r961867 = r961865 * r961866;
        double r961868 = sqrt(r961867);
        double r961869 = r961864 * r961868;
        double r961870 = t;
        double r961871 = r961870 * r961870;
        double r961872 = -r961871;
        double r961873 = -r961866;
        double r961874 = r961872 / r961873;
        double r961875 = exp(r961874);
        double r961876 = r961869 * r961875;
        return r961876;
}

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 frac-2neg0.3

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

  4. 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 2020046 
(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))))