Average Error: 0.3 → 0.3
Time: 1.1m
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\sqrt{z \cdot 2} \cdot \left(0.5 \cdot x - y\right)\right) \cdot e^{\frac{t \cdot t}{2}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\sqrt{z \cdot 2} \cdot \left(0.5 \cdot x - y\right)\right) \cdot e^{\frac{t \cdot t}{2}}
double f(double x, double y, double z, double t) {
        double r41136073 = x;
        double r41136074 = 0.5;
        double r41136075 = r41136073 * r41136074;
        double r41136076 = y;
        double r41136077 = r41136075 - r41136076;
        double r41136078 = z;
        double r41136079 = 2.0;
        double r41136080 = r41136078 * r41136079;
        double r41136081 = sqrt(r41136080);
        double r41136082 = r41136077 * r41136081;
        double r41136083 = t;
        double r41136084 = r41136083 * r41136083;
        double r41136085 = r41136084 / r41136079;
        double r41136086 = exp(r41136085);
        double r41136087 = r41136082 * r41136086;
        return r41136087;
}
↓
double f(double x, double y, double z, double t) {
        double r41136088 = z;
        double r41136089 = 2.0;
        double r41136090 = r41136088 * r41136089;
        double r41136091 = sqrt(r41136090);
        double r41136092 = 0.5;
        double r41136093 = x;
        double r41136094 = r41136092 * r41136093;
        double r41136095 = y;
        double r41136096 = r41136094 - r41136095;
        double r41136097 = r41136091 * r41136096;
        double r41136098 = t;
        double r41136099 = r41136098 * r41136098;
        double r41136100 = r41136099 / r41136089;
        double r41136101 = exp(r41136100);
        double r41136102 = r41136097 * r41136101;
        return r41136102;
}

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

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

Reproduce

herbie shell --seed 2019200 
(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))))