Average Error: 0.3 → 0.5
Time: 16.3s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z}\right) \cdot \sqrt{2}\right) \cdot e^{t \cdot \frac{t}{2}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z}\right) \cdot \sqrt{2}\right) \cdot e^{t \cdot \frac{t}{2}}
double f(double x, double y, double z, double t) {
        double r496760 = x;
        double r496761 = 0.5;
        double r496762 = r496760 * r496761;
        double r496763 = y;
        double r496764 = r496762 - r496763;
        double r496765 = z;
        double r496766 = 2.0;
        double r496767 = r496765 * r496766;
        double r496768 = sqrt(r496767);
        double r496769 = r496764 * r496768;
        double r496770 = t;
        double r496771 = r496770 * r496770;
        double r496772 = r496771 / r496766;
        double r496773 = exp(r496772);
        double r496774 = r496769 * r496773;
        return r496774;
}
↓
double f(double x, double y, double z, double t) {
        double r496775 = x;
        double r496776 = 0.5;
        double r496777 = r496775 * r496776;
        double r496778 = y;
        double r496779 = r496777 - r496778;
        double r496780 = z;
        double r496781 = sqrt(r496780);
        double r496782 = r496779 * r496781;
        double r496783 = 2.0;
        double r496784 = sqrt(r496783);
        double r496785 = r496782 * r496784;
        double r496786 = t;
        double r496787 = r496786 / r496783;
        double r496788 = r496786 * r496787;
        double r496789 = exp(r496788);
        double r496790 = r496785 * r496789;
        return r496790;
}

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
Herbie0.5
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2}\right)}\]

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 sqrt-prod0.5

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

  4. Applied associate-*r*0.5

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

  6. Applied *-un-lft-identity0.5

    \[\leadsto \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z}\right) \cdot \sqrt{2}\right) \cdot e^{\frac{t \cdot t}{\color{blue}{1 \cdot 2}}}\]

  7. Applied times-frac0.5

    \[\leadsto \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z}\right) \cdot \sqrt{2}\right) \cdot e^{\color{blue}{\frac{t}{1} \cdot \frac{t}{2}}}\]

  8. Simplified0.5

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

  9. Final simplification0.5

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

Reproduce

herbie shell --seed 2020042 
(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))))