Average Error: 0.3 → 0.3
Time: 7.5s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(\sqrt[3]{e^{t}} \cdot \sqrt[3]{e^{t}}\right)}^{\left(\frac{t}{2}\right)}\right) \cdot {\left(\sqrt[3]{e^{t}}\right)}^{\left(\frac{t}{2}\right)}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(\sqrt[3]{e^{t}} \cdot \sqrt[3]{e^{t}}\right)}^{\left(\frac{t}{2}\right)}\right) \cdot {\left(\sqrt[3]{e^{t}}\right)}^{\left(\frac{t}{2}\right)}
double f(double x, double y, double z, double t) {
        double r856711 = x;
        double r856712 = 0.5;
        double r856713 = r856711 * r856712;
        double r856714 = y;
        double r856715 = r856713 - r856714;
        double r856716 = z;
        double r856717 = 2.0;
        double r856718 = r856716 * r856717;
        double r856719 = sqrt(r856718);
        double r856720 = r856715 * r856719;
        double r856721 = t;
        double r856722 = r856721 * r856721;
        double r856723 = r856722 / r856717;
        double r856724 = exp(r856723);
        double r856725 = r856720 * r856724;
        return r856725;
}
↓
double f(double x, double y, double z, double t) {
        double r856726 = x;
        double r856727 = 0.5;
        double r856728 = r856726 * r856727;
        double r856729 = y;
        double r856730 = r856728 - r856729;
        double r856731 = z;
        double r856732 = 2.0;
        double r856733 = r856731 * r856732;
        double r856734 = sqrt(r856733);
        double r856735 = r856730 * r856734;
        double r856736 = t;
        double r856737 = exp(r856736);
        double r856738 = cbrt(r856737);
        double r856739 = r856738 * r856738;
        double r856740 = r856736 / r856732;
        double r856741 = pow(r856739, r856740);
        double r856742 = r856735 * r856741;
        double r856743 = pow(r856738, r856740);
        double r856744 = r856742 * r856743;
        return r856744;
}

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. Applied associate-*r*0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2020001 
(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))))