Average Error: 0.3 → 0.3
Time: 23.1s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot e^{\frac{t \cdot t}{2}}\right)\]
\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(\sqrt{z \cdot 2} \cdot e^{\frac{t \cdot t}{2}}\right)
double f(double x, double y, double z, double t) {
        double r435769 = x;
        double r435770 = 0.5;
        double r435771 = r435769 * r435770;
        double r435772 = y;
        double r435773 = r435771 - r435772;
        double r435774 = z;
        double r435775 = 2.0;
        double r435776 = r435774 * r435775;
        double r435777 = sqrt(r435776);
        double r435778 = r435773 * r435777;
        double r435779 = t;
        double r435780 = r435779 * r435779;
        double r435781 = r435780 / r435775;
        double r435782 = exp(r435781);
        double r435783 = r435778 * r435782;
        return r435783;
}
↓
double f(double x, double y, double z, double t) {
        double r435784 = x;
        double r435785 = 0.5;
        double r435786 = r435784 * r435785;
        double r435787 = y;
        double r435788 = r435786 - r435787;
        double r435789 = z;
        double r435790 = 2.0;
        double r435791 = r435789 * r435790;
        double r435792 = sqrt(r435791);
        double r435793 = t;
        double r435794 = r435793 * r435793;
        double r435795 = r435794 / r435790;
        double r435796 = exp(r435795);
        double r435797 = r435792 * r435796;
        double r435798 = r435788 * r435797;
        return r435798;
}

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 associate-*l*0.3

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2019212 +o rules:numerics
(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))))