Average Error: 0.3 → 0.3
Time: 7.1s
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 r895691 = x;
        double r895692 = 0.5;
        double r895693 = r895691 * r895692;
        double r895694 = y;
        double r895695 = r895693 - r895694;
        double r895696 = z;
        double r895697 = 2.0;
        double r895698 = r895696 * r895697;
        double r895699 = sqrt(r895698);
        double r895700 = r895695 * r895699;
        double r895701 = t;
        double r895702 = r895701 * r895701;
        double r895703 = r895702 / r895697;
        double r895704 = exp(r895703);
        double r895705 = r895700 * r895704;
        return r895705;
}
↓
double f(double x, double y, double z, double t) {
        double r895706 = x;
        double r895707 = 0.5;
        double r895708 = r895706 * r895707;
        double r895709 = y;
        double r895710 = r895708 - r895709;
        double r895711 = z;
        double r895712 = 2.0;
        double r895713 = r895711 * r895712;
        double r895714 = sqrt(r895713);
        double r895715 = r895710 * r895714;
        double r895716 = t;
        double r895717 = r895716 * r895716;
        double r895718 = r895717 / r895712;
        double r895719 = exp(r895718);
        double r895720 = r895715 * r895719;
        return r895720;
}

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 2020065 
(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))))