Average Error: 0.3 → 0.3
Time: 25.5s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\sqrt{e^{\frac{t \cdot t}{2}}} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right)\right) \cdot \sqrt{e^{\frac{t \cdot t}{2}}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\sqrt{e^{\frac{t \cdot t}{2}}} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right)\right) \cdot \sqrt{e^{\frac{t \cdot t}{2}}}
double f(double x, double y, double z, double t) {
        double r32358099 = x;
        double r32358100 = 0.5;
        double r32358101 = r32358099 * r32358100;
        double r32358102 = y;
        double r32358103 = r32358101 - r32358102;
        double r32358104 = z;
        double r32358105 = 2.0;
        double r32358106 = r32358104 * r32358105;
        double r32358107 = sqrt(r32358106);
        double r32358108 = r32358103 * r32358107;
        double r32358109 = t;
        double r32358110 = r32358109 * r32358109;
        double r32358111 = r32358110 / r32358105;
        double r32358112 = exp(r32358111);
        double r32358113 = r32358108 * r32358112;
        return r32358113;
}
↓
double f(double x, double y, double z, double t) {
        double r32358114 = t;
        double r32358115 = r32358114 * r32358114;
        double r32358116 = 2.0;
        double r32358117 = r32358115 / r32358116;
        double r32358118 = exp(r32358117);
        double r32358119 = sqrt(r32358118);
        double r32358120 = x;
        double r32358121 = 0.5;
        double r32358122 = r32358120 * r32358121;
        double r32358123 = y;
        double r32358124 = r32358122 - r32358123;
        double r32358125 = z;
        double r32358126 = r32358125 * r32358116;
        double r32358127 = sqrt(r32358126);
        double r32358128 = r32358124 * r32358127;
        double r32358129 = r32358119 * r32358128;
        double r32358130 = r32358129 * r32358119;
        return r32358130;
}

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 add-sqr-sqrt0.3

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

  4. Applied associate-*r*0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(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))))