Average Error: 0.3 → 0.3
Time: 31.5s
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 r626038 = x;
        double r626039 = 0.5;
        double r626040 = r626038 * r626039;
        double r626041 = y;
        double r626042 = r626040 - r626041;
        double r626043 = z;
        double r626044 = 2.0;
        double r626045 = r626043 * r626044;
        double r626046 = sqrt(r626045);
        double r626047 = r626042 * r626046;
        double r626048 = t;
        double r626049 = r626048 * r626048;
        double r626050 = r626049 / r626044;
        double r626051 = exp(r626050);
        double r626052 = r626047 * r626051;
        return r626052;
}
↓
double f(double x, double y, double z, double t) {
        double r626053 = x;
        double r626054 = 0.5;
        double r626055 = r626053 * r626054;
        double r626056 = y;
        double r626057 = r626055 - r626056;
        double r626058 = z;
        double r626059 = 2.0;
        double r626060 = r626058 * r626059;
        double r626061 = sqrt(r626060);
        double r626062 = r626057 * r626061;
        double r626063 = t;
        double r626064 = r626063 * r626063;
        double r626065 = r626064 / r626059;
        double r626066 = exp(r626065);
        double r626067 = r626062 * r626066;
        return r626067;
}

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 2019194 +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))))