Average Error: 0.3 → 0.4
Time: 9.5s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \sqrt[3]{{\left(e^{\frac{t \cdot t}{2}}\right)}^{3}}\]
\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 \sqrt[3]{{\left(e^{\frac{t \cdot t}{2}}\right)}^{3}}
double f(double x, double y, double z, double t) {
        double r1544051 = x;
        double r1544052 = 0.5;
        double r1544053 = r1544051 * r1544052;
        double r1544054 = y;
        double r1544055 = r1544053 - r1544054;
        double r1544056 = z;
        double r1544057 = 2.0;
        double r1544058 = r1544056 * r1544057;
        double r1544059 = sqrt(r1544058);
        double r1544060 = r1544055 * r1544059;
        double r1544061 = t;
        double r1544062 = r1544061 * r1544061;
        double r1544063 = r1544062 / r1544057;
        double r1544064 = exp(r1544063);
        double r1544065 = r1544060 * r1544064;
        return r1544065;
}
↓
double f(double x, double y, double z, double t) {
        double r1544066 = x;
        double r1544067 = 0.5;
        double r1544068 = r1544066 * r1544067;
        double r1544069 = y;
        double r1544070 = r1544068 - r1544069;
        double r1544071 = z;
        double r1544072 = 2.0;
        double r1544073 = r1544071 * r1544072;
        double r1544074 = sqrt(r1544073);
        double r1544075 = r1544070 * r1544074;
        double r1544076 = t;
        double r1544077 = r1544076 * r1544076;
        double r1544078 = r1544077 / r1544072;
        double r1544079 = exp(r1544078);
        double r1544080 = 3.0;
        double r1544081 = pow(r1544079, r1544080);
        double r1544082 = cbrt(r1544081);
        double r1544083 = r1544075 * r1544082;
        return r1544083;
}

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
Herbie0.4
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2}\right)}\]

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. Using strategy rm

  3. Applied add-cbrt-cube0.4

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{\sqrt[3]{\left(e^{\frac{t \cdot t}{2}} \cdot e^{\frac{t \cdot t}{2}}\right) \cdot e^{\frac{t \cdot t}{2}}}}\]

  4. Simplified0.4

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \sqrt[3]{\color{blue}{{\left(e^{\frac{t \cdot t}{2}}\right)}^{3}}}\]

  5. Final simplification0.4

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \sqrt[3]{{\left(e^{\frac{t \cdot t}{2}}\right)}^{3}}\]

Reproduce

herbie shell --seed 2020034 +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))))