Average Error: 0.3 → 0.3
Time: 22.5s
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 r43799809 = x;
        double r43799810 = 0.5;
        double r43799811 = r43799809 * r43799810;
        double r43799812 = y;
        double r43799813 = r43799811 - r43799812;
        double r43799814 = z;
        double r43799815 = 2.0;
        double r43799816 = r43799814 * r43799815;
        double r43799817 = sqrt(r43799816);
        double r43799818 = r43799813 * r43799817;
        double r43799819 = t;
        double r43799820 = r43799819 * r43799819;
        double r43799821 = r43799820 / r43799815;
        double r43799822 = exp(r43799821);
        double r43799823 = r43799818 * r43799822;
        return r43799823;
}
↓
double f(double x, double y, double z, double t) {
        double r43799824 = x;
        double r43799825 = 0.5;
        double r43799826 = r43799824 * r43799825;
        double r43799827 = y;
        double r43799828 = r43799826 - r43799827;
        double r43799829 = z;
        double r43799830 = 2.0;
        double r43799831 = r43799829 * r43799830;
        double r43799832 = sqrt(r43799831);
        double r43799833 = r43799828 * r43799832;
        double r43799834 = t;
        double r43799835 = r43799834 * r43799834;
        double r43799836 = r43799835 / r43799830;
        double r43799837 = exp(r43799836);
        double r43799838 = r43799833 * r43799837;
        return r43799838;
}

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 2019162 
(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))))