Average Error: 0.3 → 0.3
Time: 10.0s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(x \cdot 0.5 - y\right) \cdot \left(e^{\frac{t \cdot t}{2}} \cdot \sqrt{z \cdot 2}\right)\]
\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(e^{\frac{t \cdot t}{2}} \cdot \sqrt{z \cdot 2}\right)
double f(double x, double y, double z, double t) {
        double r1542838 = x;
        double r1542839 = 0.5;
        double r1542840 = r1542838 * r1542839;
        double r1542841 = y;
        double r1542842 = r1542840 - r1542841;
        double r1542843 = z;
        double r1542844 = 2.0;
        double r1542845 = r1542843 * r1542844;
        double r1542846 = sqrt(r1542845);
        double r1542847 = r1542842 * r1542846;
        double r1542848 = t;
        double r1542849 = r1542848 * r1542848;
        double r1542850 = r1542849 / r1542844;
        double r1542851 = exp(r1542850);
        double r1542852 = r1542847 * r1542851;
        return r1542852;
}
↓
double f(double x, double y, double z, double t) {
        double r1542853 = x;
        double r1542854 = 0.5;
        double r1542855 = r1542853 * r1542854;
        double r1542856 = y;
        double r1542857 = r1542855 - r1542856;
        double r1542858 = t;
        double r1542859 = r1542858 * r1542858;
        double r1542860 = 2.0;
        double r1542861 = r1542859 / r1542860;
        double r1542862 = exp(r1542861);
        double r1542863 = z;
        double r1542864 = r1542863 * r1542860;
        double r1542865 = sqrt(r1542864);
        double r1542866 = r1542862 * r1542865;
        double r1542867 = r1542857 * r1542866;
        return r1542867;
}

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

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2020047 
(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))))