Average Error: 0.3 → 0.3
Time: 12.3s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \left({\left(\sqrt[3]{e^{t}} \cdot \sqrt[3]{e^{t}}\right)}^{\left(\frac{t}{2}\right)} \cdot {\left(\sqrt[3]{e^{t}}\right)}^{\left(\frac{t}{2}\right)}\right)\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \left({\left(\sqrt[3]{e^{t}} \cdot \sqrt[3]{e^{t}}\right)}^{\left(\frac{t}{2}\right)} \cdot {\left(\sqrt[3]{e^{t}}\right)}^{\left(\frac{t}{2}\right)}\right)
double f(double x, double y, double z, double t) {
        double r821714 = x;
        double r821715 = 0.5;
        double r821716 = r821714 * r821715;
        double r821717 = y;
        double r821718 = r821716 - r821717;
        double r821719 = z;
        double r821720 = 2.0;
        double r821721 = r821719 * r821720;
        double r821722 = sqrt(r821721);
        double r821723 = r821718 * r821722;
        double r821724 = t;
        double r821725 = r821724 * r821724;
        double r821726 = r821725 / r821720;
        double r821727 = exp(r821726);
        double r821728 = r821723 * r821727;
        return r821728;
}
↓
double f(double x, double y, double z, double t) {
        double r821729 = x;
        double r821730 = 0.5;
        double r821731 = r821729 * r821730;
        double r821732 = y;
        double r821733 = r821731 - r821732;
        double r821734 = z;
        double r821735 = 2.0;
        double r821736 = r821734 * r821735;
        double r821737 = sqrt(r821736);
        double r821738 = r821733 * r821737;
        double r821739 = t;
        double r821740 = exp(r821739);
        double r821741 = cbrt(r821740);
        double r821742 = r821741 * r821741;
        double r821743 = r821739 / r821735;
        double r821744 = pow(r821742, r821743);
        double r821745 = pow(r821741, r821743);
        double r821746 = r821744 * r821745;
        double r821747 = r821738 * r821746;
        return r821747;
}

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 add-cube-cbrt0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\color{blue}{\left(\left(\sqrt[3]{e^{t}} \cdot \sqrt[3]{e^{t}}\right) \cdot \sqrt[3]{e^{t}}\right)}}^{\left(\frac{t}{2}\right)}\]

  9. Applied unpow-prod-down0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{\left({\left(\sqrt[3]{e^{t}} \cdot \sqrt[3]{e^{t}}\right)}^{\left(\frac{t}{2}\right)} \cdot {\left(\sqrt[3]{e^{t}}\right)}^{\left(\frac{t}{2}\right)}\right)}\]

  10. Final simplification0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \left({\left(\sqrt[3]{e^{t}} \cdot \sqrt[3]{e^{t}}\right)}^{\left(\frac{t}{2}\right)} \cdot {\left(\sqrt[3]{e^{t}}\right)}^{\left(\frac{t}{2}\right)}\right)\]

Reproduce

herbie shell --seed 2020045 +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))))