Average Error: 0.3 → 0.3
Time: 23.5s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}
↓
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}
double f(double x, double y, double z, double t) {
        double r35798754 = x;
        double r35798755 = 0.5;
        double r35798756 = r35798754 * r35798755;
        double r35798757 = y;
        double r35798758 = r35798756 - r35798757;
        double r35798759 = z;
        double r35798760 = 2.0;
        double r35798761 = r35798759 * r35798760;
        double r35798762 = sqrt(r35798761);
        double r35798763 = r35798758 * r35798762;
        double r35798764 = t;
        double r35798765 = r35798764 * r35798764;
        double r35798766 = r35798765 / r35798760;
        double r35798767 = exp(r35798766);
        double r35798768 = r35798763 * r35798767;
        return r35798768;
}
↓
double f(double x, double y, double z, double t) {
        double r35798769 = x;
        double r35798770 = 0.5;
        double r35798771 = r35798769 * r35798770;
        double r35798772 = y;
        double r35798773 = r35798771 - r35798772;
        double r35798774 = z;
        double r35798775 = 2.0;
        double r35798776 = r35798774 * r35798775;
        double r35798777 = sqrt(r35798776);
        double r35798778 = r35798773 * r35798777;
        double r35798779 = t;
        double r35798780 = r35798779 * r35798779;
        double r35798781 = r35798780 / r35798775;
        double r35798782 = exp(r35798781);
        double r35798783 = r35798778 * r35798782;
        return r35798783;
}

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
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2.0}\right)}\]

Derivation

  1. Initial program 0.3

    \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}\]

  2. Final simplification0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}\]

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(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) (/ (* t t) 2.0)))

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