Average Error: 0.3 → 0.3
Time: 7.2s
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 r848697 = x;
        double r848698 = 0.5;
        double r848699 = r848697 * r848698;
        double r848700 = y;
        double r848701 = r848699 - r848700;
        double r848702 = z;
        double r848703 = 2.0;
        double r848704 = r848702 * r848703;
        double r848705 = sqrt(r848704);
        double r848706 = r848701 * r848705;
        double r848707 = t;
        double r848708 = r848707 * r848707;
        double r848709 = r848708 / r848703;
        double r848710 = exp(r848709);
        double r848711 = r848706 * r848710;
        return r848711;
}
↓
double f(double x, double y, double z, double t) {
        double r848712 = x;
        double r848713 = 0.5;
        double r848714 = r848712 * r848713;
        double r848715 = y;
        double r848716 = r848714 - r848715;
        double r848717 = z;
        double r848718 = 2.0;
        double r848719 = r848717 * r848718;
        double r848720 = sqrt(r848719);
        double r848721 = r848716 * r848720;
        double r848722 = t;
        double r848723 = r848722 * r848722;
        double r848724 = r848723 / r848718;
        double r848725 = exp(r848724);
        double r848726 = r848721 * r848725;
        return r848726;
}

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. 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 2020060 +o rules:numerics
(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))))