Average Error: 0.3 → 0.3
Time: 22.0s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}\]
\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 {\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}
double f(double x, double y, double z, double t) {
        double r530109 = x;
        double r530110 = 0.5;
        double r530111 = r530109 * r530110;
        double r530112 = y;
        double r530113 = r530111 - r530112;
        double r530114 = z;
        double r530115 = 2.0;
        double r530116 = r530114 * r530115;
        double r530117 = sqrt(r530116);
        double r530118 = r530113 * r530117;
        double r530119 = t;
        double r530120 = r530119 * r530119;
        double r530121 = r530120 / r530115;
        double r530122 = exp(r530121);
        double r530123 = r530118 * r530122;
        return r530123;
}
↓
double f(double x, double y, double z, double t) {
        double r530124 = x;
        double r530125 = 0.5;
        double r530126 = r530124 * r530125;
        double r530127 = y;
        double r530128 = r530126 - r530127;
        double r530129 = z;
        double r530130 = 2.0;
        double r530131 = r530129 * r530130;
        double r530132 = sqrt(r530131);
        double r530133 = r530128 * r530132;
        double r530134 = t;
        double r530135 = exp(r530134);
        double r530136 = r530134 / r530130;
        double r530137 = pow(r530135, r530136);
        double r530138 = r530133 * r530137;
        return r530138;
}

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. Using strategy rm

  3. Applied *-un-lft-identity0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{\color{blue}{1 \cdot 2}}}\]

  4. Applied times-frac0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\color{blue}{\frac{t}{1} \cdot \frac{t}{2}}}\]

  5. Applied exp-prod0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{{\left(e^{\frac{t}{1}}\right)}^{\left(\frac{t}{2}\right)}}\]

  6. Simplified0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019209 
(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))))