Average Error: 0.3 → 0.3
Time: 19.3s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
\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 \frac{1}{2} - 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 r657744 = x;
        double r657745 = 0.5;
        double r657746 = r657744 * r657745;
        double r657747 = y;
        double r657748 = r657746 - r657747;
        double r657749 = z;
        double r657750 = 2.0;
        double r657751 = r657749 * r657750;
        double r657752 = sqrt(r657751);
        double r657753 = r657748 * r657752;
        double r657754 = t;
        double r657755 = r657754 * r657754;
        double r657756 = r657755 / r657750;
        double r657757 = exp(r657756);
        double r657758 = r657753 * r657757;
        return r657758;
}
↓
double f(double x, double y, double z, double t) {
        double r657759 = x;
        double r657760 = 1.0;
        double r657761 = 2.0;
        double r657762 = r657760 / r657761;
        double r657763 = r657759 * r657762;
        double r657764 = y;
        double r657765 = r657763 - r657764;
        double r657766 = z;
        double r657767 = r657766 * r657761;
        double r657768 = sqrt(r657767);
        double r657769 = r657765 * r657768;
        double r657770 = t;
        double r657771 = r657770 * r657770;
        double r657772 = r657771 / r657761;
        double r657773 = exp(r657772);
        double r657774 = r657769 * r657773;
        return r657774;
}

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. Simplified0.3

    \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}}\]

  3. Final simplification0.3

    \[\leadsto \left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]

Reproduce

herbie shell --seed 2019303 
(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))))