Average Error: 0.3 → 0.3
Time: 11.0s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot {\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}\right)\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot {\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}\right)
double f(double x, double y, double z, double t) {
        double r801129 = x;
        double r801130 = 0.5;
        double r801131 = r801129 * r801130;
        double r801132 = y;
        double r801133 = r801131 - r801132;
        double r801134 = z;
        double r801135 = 2.0;
        double r801136 = r801134 * r801135;
        double r801137 = sqrt(r801136);
        double r801138 = r801133 * r801137;
        double r801139 = t;
        double r801140 = r801139 * r801139;
        double r801141 = r801140 / r801135;
        double r801142 = exp(r801141);
        double r801143 = r801138 * r801142;
        return r801143;
}
↓
double f(double x, double y, double z, double t) {
        double r801144 = x;
        double r801145 = 0.5;
        double r801146 = r801144 * r801145;
        double r801147 = y;
        double r801148 = r801146 - r801147;
        double r801149 = z;
        double r801150 = 2.0;
        double r801151 = r801149 * r801150;
        double r801152 = sqrt(r801151);
        double r801153 = t;
        double r801154 = exp(r801153);
        double r801155 = r801153 / r801150;
        double r801156 = pow(r801154, r801155);
        double r801157 = r801152 * r801156;
        double r801158 = r801148 * r801157;
        return r801158;
}

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. Using strategy rm

  8. Applied associate-*l*0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2020047 +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))))