Average Error: 0.3 → 0.3
Time: 5.9s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{\frac{t \cdot t}{\sqrt[3]{2} \cdot \sqrt[3]{2}}}{\sqrt[3]{2}}}\]
\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{\frac{t \cdot t}{\sqrt[3]{2} \cdot \sqrt[3]{2}}}{\sqrt[3]{2}}}
double f(double x, double y, double z, double t) {
        double r806692 = x;
        double r806693 = 0.5;
        double r806694 = r806692 * r806693;
        double r806695 = y;
        double r806696 = r806694 - r806695;
        double r806697 = z;
        double r806698 = 2.0;
        double r806699 = r806697 * r806698;
        double r806700 = sqrt(r806699);
        double r806701 = r806696 * r806700;
        double r806702 = t;
        double r806703 = r806702 * r806702;
        double r806704 = r806703 / r806698;
        double r806705 = exp(r806704);
        double r806706 = r806701 * r806705;
        return r806706;
}
↓
double f(double x, double y, double z, double t) {
        double r806707 = x;
        double r806708 = 0.5;
        double r806709 = r806707 * r806708;
        double r806710 = y;
        double r806711 = r806709 - r806710;
        double r806712 = z;
        double r806713 = 2.0;
        double r806714 = r806712 * r806713;
        double r806715 = sqrt(r806714);
        double r806716 = r806711 * r806715;
        double r806717 = t;
        double r806718 = r806717 * r806717;
        double r806719 = cbrt(r806713);
        double r806720 = r806719 * r806719;
        double r806721 = r806718 / r806720;
        double r806722 = r806721 / r806719;
        double r806723 = exp(r806722);
        double r806724 = r806716 * r806723;
        return r806724;
}

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. Using strategy rm

  3. Applied add-cube-cbrt0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{\color{blue}{\left(\sqrt[3]{2} \cdot \sqrt[3]{2}\right) \cdot \sqrt[3]{2}}}}\]

  4. Applied associate-/r*0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\color{blue}{\frac{\frac{t \cdot t}{\sqrt[3]{2} \cdot \sqrt[3]{2}}}{\sqrt[3]{2}}}}\]

  5. Final simplification0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{\frac{t \cdot t}{\sqrt[3]{2} \cdot \sqrt[3]{2}}}{\sqrt[3]{2}}}\]

Reproduce

herbie shell --seed 2020049 
(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))))