Average Error: 0.3 → 0.3
Time: 22.2s
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 r644054 = x;
        double r644055 = 0.5;
        double r644056 = r644054 * r644055;
        double r644057 = y;
        double r644058 = r644056 - r644057;
        double r644059 = z;
        double r644060 = 2.0;
        double r644061 = r644059 * r644060;
        double r644062 = sqrt(r644061);
        double r644063 = r644058 * r644062;
        double r644064 = t;
        double r644065 = r644064 * r644064;
        double r644066 = r644065 / r644060;
        double r644067 = exp(r644066);
        double r644068 = r644063 * r644067;
        return r644068;
}
↓
double f(double x, double y, double z, double t) {
        double r644069 = x;
        double r644070 = 0.5;
        double r644071 = r644069 * r644070;
        double r644072 = y;
        double r644073 = r644071 - r644072;
        double r644074 = z;
        double r644075 = 2.0;
        double r644076 = r644074 * r644075;
        double r644077 = sqrt(r644076);
        double r644078 = r644073 * r644077;
        double r644079 = t;
        double r644080 = r644079 * r644079;
        double r644081 = r644080 / r644075;
        double r644082 = exp(r644081);
        double r644083 = r644078 * r644082;
        return r644083;
}

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 2019303 
(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))))