Average Error: 0.3 → 0.3
Time: 25.4s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\sqrt{e^{\frac{t \cdot t}{2}}} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right)\right) \cdot \sqrt{e^{\frac{t \cdot t}{2}}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\sqrt{e^{\frac{t \cdot t}{2}}} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right)\right) \cdot \sqrt{e^{\frac{t \cdot t}{2}}}
double f(double x, double y, double z, double t) {
        double r40791703 = x;
        double r40791704 = 0.5;
        double r40791705 = r40791703 * r40791704;
        double r40791706 = y;
        double r40791707 = r40791705 - r40791706;
        double r40791708 = z;
        double r40791709 = 2.0;
        double r40791710 = r40791708 * r40791709;
        double r40791711 = sqrt(r40791710);
        double r40791712 = r40791707 * r40791711;
        double r40791713 = t;
        double r40791714 = r40791713 * r40791713;
        double r40791715 = r40791714 / r40791709;
        double r40791716 = exp(r40791715);
        double r40791717 = r40791712 * r40791716;
        return r40791717;
}
↓
double f(double x, double y, double z, double t) {
        double r40791718 = t;
        double r40791719 = r40791718 * r40791718;
        double r40791720 = 2.0;
        double r40791721 = r40791719 / r40791720;
        double r40791722 = exp(r40791721);
        double r40791723 = sqrt(r40791722);
        double r40791724 = x;
        double r40791725 = 0.5;
        double r40791726 = r40791724 * r40791725;
        double r40791727 = y;
        double r40791728 = r40791726 - r40791727;
        double r40791729 = z;
        double r40791730 = r40791729 * r40791720;
        double r40791731 = sqrt(r40791730);
        double r40791732 = r40791728 * r40791731;
        double r40791733 = r40791723 * r40791732;
        double r40791734 = r40791733 * r40791723;
        return r40791734;
}

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-sqr-sqrt0.3

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

  4. Applied associate-*r*0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(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 1.0) (/ (* t t) 2.0)))

  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))