Average Error: 0.3 → 0.3
Time: 21.1s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(x \cdot 0.5 - y\right) \cdot \left(e^{\frac{t}{2} \cdot t} \cdot \sqrt{z \cdot 2}\right)\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(x \cdot 0.5 - y\right) \cdot \left(e^{\frac{t}{2} \cdot t} \cdot \sqrt{z \cdot 2}\right)
double f(double x, double y, double z, double t) {
        double r656614 = x;
        double r656615 = 0.5;
        double r656616 = r656614 * r656615;
        double r656617 = y;
        double r656618 = r656616 - r656617;
        double r656619 = z;
        double r656620 = 2.0;
        double r656621 = r656619 * r656620;
        double r656622 = sqrt(r656621);
        double r656623 = r656618 * r656622;
        double r656624 = t;
        double r656625 = r656624 * r656624;
        double r656626 = r656625 / r656620;
        double r656627 = exp(r656626);
        double r656628 = r656623 * r656627;
        return r656628;
}
↓
double f(double x, double y, double z, double t) {
        double r656629 = x;
        double r656630 = 0.5;
        double r656631 = r656629 * r656630;
        double r656632 = y;
        double r656633 = r656631 - r656632;
        double r656634 = t;
        double r656635 = 2.0;
        double r656636 = r656634 / r656635;
        double r656637 = r656636 * r656634;
        double r656638 = exp(r656637);
        double r656639 = z;
        double r656640 = r656639 * r656635;
        double r656641 = sqrt(r656640);
        double r656642 = r656638 * r656641;
        double r656643 = r656633 * r656642;
        return r656643;
}

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. Simplified0.3

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

  3. Final simplification0.3

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

Reproduce

herbie shell --seed 2019174 
(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))))