Average Error: 0.3 → 0.3
Time: 17.3s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
\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 r949149 = x;
        double r949150 = 0.5;
        double r949151 = r949149 * r949150;
        double r949152 = y;
        double r949153 = r949151 - r949152;
        double r949154 = z;
        double r949155 = 2.0;
        double r949156 = r949154 * r949155;
        double r949157 = sqrt(r949156);
        double r949158 = r949153 * r949157;
        double r949159 = t;
        double r949160 = r949159 * r949159;
        double r949161 = r949160 / r949155;
        double r949162 = exp(r949161);
        double r949163 = r949158 * r949162;
        return r949163;
}
↓
double f(double x, double y, double z, double t) {
        double r949164 = x;
        double r949165 = 0.5;
        double r949166 = r949164 * r949165;
        double r949167 = y;
        double r949168 = r949166 - r949167;
        double r949169 = z;
        double r949170 = 2.0;
        double r949171 = r949169 * r949170;
        double r949172 = sqrt(r949171);
        double r949173 = r949168 * r949172;
        double r949174 = t;
        double r949175 = r949174 * r949174;
        double r949176 = r949175 / r949170;
        double r949177 = exp(r949176);
        double r949178 = r949173 * r949177;
        return r949178;
}

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 2020043 +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))))