Average Error: 0.3 → 0.3
Time: 6.7s
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 r977713 = x;
        double r977714 = 0.5;
        double r977715 = r977713 * r977714;
        double r977716 = y;
        double r977717 = r977715 - r977716;
        double r977718 = z;
        double r977719 = 2.0;
        double r977720 = r977718 * r977719;
        double r977721 = sqrt(r977720);
        double r977722 = r977717 * r977721;
        double r977723 = t;
        double r977724 = r977723 * r977723;
        double r977725 = r977724 / r977719;
        double r977726 = exp(r977725);
        double r977727 = r977722 * r977726;
        return r977727;
}
↓
double f(double x, double y, double z, double t) {
        double r977728 = x;
        double r977729 = 0.5;
        double r977730 = r977728 * r977729;
        double r977731 = y;
        double r977732 = r977730 - r977731;
        double r977733 = z;
        double r977734 = 2.0;
        double r977735 = r977733 * r977734;
        double r977736 = sqrt(r977735);
        double r977737 = r977732 * r977736;
        double r977738 = t;
        double r977739 = r977738 * r977738;
        double r977740 = r977739 / r977734;
        double r977741 = exp(r977740);
        double r977742 = r977737 * r977741;
        return r977742;
}

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 
(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))))