Average Error: 0.3 → 0.3
Time: 28.9s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(x \cdot 0.5 - y\right) \cdot \left(e^{\frac{t}{\frac{2}{t}}} \cdot \sqrt{z \cdot 2}\right)\]
\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}{\frac{2}{t}}} \cdot \sqrt{z \cdot 2}\right)
double f(double x, double y, double z, double t) {
        double r579057 = x;
        double r579058 = 0.5;
        double r579059 = r579057 * r579058;
        double r579060 = y;
        double r579061 = r579059 - r579060;
        double r579062 = z;
        double r579063 = 2.0;
        double r579064 = r579062 * r579063;
        double r579065 = sqrt(r579064);
        double r579066 = r579061 * r579065;
        double r579067 = t;
        double r579068 = r579067 * r579067;
        double r579069 = r579068 / r579063;
        double r579070 = exp(r579069);
        double r579071 = r579066 * r579070;
        return r579071;
}
↓
double f(double x, double y, double z, double t) {
        double r579072 = x;
        double r579073 = 0.5;
        double r579074 = r579072 * r579073;
        double r579075 = y;
        double r579076 = r579074 - r579075;
        double r579077 = t;
        double r579078 = 2.0;
        double r579079 = r579078 / r579077;
        double r579080 = r579077 / r579079;
        double r579081 = exp(r579080);
        double r579082 = z;
        double r579083 = r579082 * r579078;
        double r579084 = sqrt(r579083);
        double r579085 = r579081 * r579084;
        double r579086 = r579076 * r579085;
        return r579086;
}

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

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

  3. Final simplification0.3

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

Reproduce

herbie shell --seed 2019174 +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))))