Average Error: 0.3 → 0.3
Time: 10.4s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{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}}
double f(double x, double y, double z, double t) {
        double r729821 = x;
        double r729822 = 0.5;
        double r729823 = r729821 * r729822;
        double r729824 = y;
        double r729825 = r729823 - r729824;
        double r729826 = z;
        double r729827 = 2.0;
        double r729828 = r729826 * r729827;
        double r729829 = sqrt(r729828);
        double r729830 = r729825 * r729829;
        double r729831 = t;
        double r729832 = r729831 * r729831;
        double r729833 = r729832 / r729827;
        double r729834 = exp(r729833);
        double r729835 = r729830 * r729834;
        return r729835;
}
↓
double f(double x, double y, double z, double t) {
        double r729836 = x;
        double r729837 = 0.5;
        double r729838 = r729836 * r729837;
        double r729839 = y;
        double r729840 = r729838 - r729839;
        double r729841 = z;
        double r729842 = 2.0;
        double r729843 = r729841 * r729842;
        double r729844 = sqrt(r729843);
        double r729845 = r729840 * r729844;
        double r729846 = t;
        double r729847 = r729846 * r729846;
        double r729848 = r729847 / r729842;
        double r729849 = exp(r729848);
        double r729850 = r729845 * r729849;
        return r729850;
}

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019353 +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))))