Average Error: 0.3 → 0.3
Time: 9.7s
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 r898069 = x;
        double r898070 = 0.5;
        double r898071 = r898069 * r898070;
        double r898072 = y;
        double r898073 = r898071 - r898072;
        double r898074 = z;
        double r898075 = 2.0;
        double r898076 = r898074 * r898075;
        double r898077 = sqrt(r898076);
        double r898078 = r898073 * r898077;
        double r898079 = t;
        double r898080 = r898079 * r898079;
        double r898081 = r898080 / r898075;
        double r898082 = exp(r898081);
        double r898083 = r898078 * r898082;
        return r898083;
}
↓
double f(double x, double y, double z, double t) {
        double r898084 = x;
        double r898085 = 0.5;
        double r898086 = r898084 * r898085;
        double r898087 = y;
        double r898088 = r898086 - r898087;
        double r898089 = z;
        double r898090 = 2.0;
        double r898091 = r898089 * r898090;
        double r898092 = sqrt(r898091);
        double r898093 = r898088 * r898092;
        double r898094 = t;
        double r898095 = r898094 * r898094;
        double r898096 = r898095 / r898090;
        double r898097 = exp(r898096);
        double r898098 = r898093 * r898097;
        return r898098;
}

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 2020027 +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))))