Average Error: 0.3 → 0.3
Time: 23.2s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}\]
↓
\[\sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}} \cdot \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot \left(\sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}} \cdot \sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}}\right)\right)\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}
↓
\sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}} \cdot \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot \left(\sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}} \cdot \sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}}\right)\right)
double f(double x, double y, double z, double t) {
        double r39950149 = x;
        double r39950150 = 0.5;
        double r39950151 = r39950149 * r39950150;
        double r39950152 = y;
        double r39950153 = r39950151 - r39950152;
        double r39950154 = z;
        double r39950155 = 2.0;
        double r39950156 = r39950154 * r39950155;
        double r39950157 = sqrt(r39950156);
        double r39950158 = r39950153 * r39950157;
        double r39950159 = t;
        double r39950160 = r39950159 * r39950159;
        double r39950161 = r39950160 / r39950155;
        double r39950162 = exp(r39950161);
        double r39950163 = r39950158 * r39950162;
        return r39950163;
}
↓
double f(double x, double y, double z, double t) {
        double r39950164 = t;
        double r39950165 = exp(r39950164);
        double r39950166 = 2.0;
        double r39950167 = r39950164 / r39950166;
        double r39950168 = pow(r39950165, r39950167);
        double r39950169 = cbrt(r39950168);
        double r39950170 = x;
        double r39950171 = 0.5;
        double r39950172 = r39950170 * r39950171;
        double r39950173 = y;
        double r39950174 = r39950172 - r39950173;
        double r39950175 = z;
        double r39950176 = r39950175 * r39950166;
        double r39950177 = sqrt(r39950176);
        double r39950178 = r39950174 * r39950177;
        double r39950179 = r39950169 * r39950169;
        double r39950180 = r39950178 * r39950179;
        double r39950181 = r39950169 * r39950180;
        return r39950181;
}

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
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2.0}\right)}\]

Derivation

  1. Initial program 0.3

    \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}\]
  2. Using strategy rm

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

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{\color{blue}{1 \cdot 2.0}}}\]

  4. Applied times-frac0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\color{blue}{\frac{t}{1} \cdot \frac{t}{2.0}}}\]

  5. Applied exp-prod0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot \color{blue}{{\left(e^{\frac{t}{1}}\right)}^{\left(\frac{t}{2.0}\right)}}\]

  6. Simplified0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot {\color{blue}{\left(e^{t}\right)}}^{\left(\frac{t}{2.0}\right)}\]
  7. Using strategy rm

  8. Applied add-cube-cbrt0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot \color{blue}{\left(\left(\sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}} \cdot \sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}}\right) \cdot \sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}}\right)}\]

  9. Applied associate-*r*0.3

    \[\leadsto \color{blue}{\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot \left(\sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}} \cdot \sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}}\right)\right) \cdot \sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}}}\]

  10. Final simplification0.3

    \[\leadsto \sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}} \cdot \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot \left(\sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}} \cdot \sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}}\right)\right)\]

Reproduce

herbie shell --seed 2019164 
(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) (/ (* t t) 2.0)))

  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))