Average Error: 0.3 → 0.3
Time: 25.2s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}\]
↓
\[\left(\sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right)\right) \cdot \sqrt{{\left(e^{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right)}^{\left(\frac{t}{2.0} \cdot \sqrt[3]{t}\right)}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}
↓
\left(\sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right)\right) \cdot \sqrt{{\left(e^{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right)}^{\left(\frac{t}{2.0} \cdot \sqrt[3]{t}\right)}}
double f(double x, double y, double z, double t) {
        double r40349630 = x;
        double r40349631 = 0.5;
        double r40349632 = r40349630 * r40349631;
        double r40349633 = y;
        double r40349634 = r40349632 - r40349633;
        double r40349635 = z;
        double r40349636 = 2.0;
        double r40349637 = r40349635 * r40349636;
        double r40349638 = sqrt(r40349637);
        double r40349639 = r40349634 * r40349638;
        double r40349640 = t;
        double r40349641 = r40349640 * r40349640;
        double r40349642 = r40349641 / r40349636;
        double r40349643 = exp(r40349642);
        double r40349644 = r40349639 * r40349643;
        return r40349644;
}
↓
double f(double x, double y, double z, double t) {
        double r40349645 = t;
        double r40349646 = exp(r40349645);
        double r40349647 = 2.0;
        double r40349648 = r40349645 / r40349647;
        double r40349649 = pow(r40349646, r40349648);
        double r40349650 = sqrt(r40349649);
        double r40349651 = x;
        double r40349652 = 0.5;
        double r40349653 = r40349651 * r40349652;
        double r40349654 = y;
        double r40349655 = r40349653 - r40349654;
        double r40349656 = z;
        double r40349657 = r40349656 * r40349647;
        double r40349658 = sqrt(r40349657);
        double r40349659 = r40349655 * r40349658;
        double r40349660 = r40349650 * r40349659;
        double r40349661 = cbrt(r40349645);
        double r40349662 = r40349661 * r40349661;
        double r40349663 = exp(r40349662);
        double r40349664 = r40349648 * r40349661;
        double r40349665 = pow(r40349663, r40349664);
        double r40349666 = sqrt(r40349665);
        double r40349667 = r40349660 * r40349666;
        return r40349667;
}

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-sqr-sqrt0.3

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

  9. Applied associate-*r*0.3

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

  11. Applied add-cube-cbrt0.3

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

  12. Applied exp-prod0.3

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

  13. Applied pow-pow0.3

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

  14. Final simplification0.3

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

Reproduce

herbie shell --seed 2019163 
(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))))