Average Error: 0.3 → 0.3
Time: 7.0s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot \left(\left(\sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}} \cdot \sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}}\right) \cdot \sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}}\right)\right)\]
\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(\left(\sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}} \cdot \sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}}\right) \cdot \sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}}\right)\right)
double f(double x, double y, double z, double t) {
        double r931620 = x;
        double r931621 = 0.5;
        double r931622 = r931620 * r931621;
        double r931623 = y;
        double r931624 = r931622 - r931623;
        double r931625 = z;
        double r931626 = 2.0;
        double r931627 = r931625 * r931626;
        double r931628 = sqrt(r931627);
        double r931629 = r931624 * r931628;
        double r931630 = t;
        double r931631 = r931630 * r931630;
        double r931632 = r931631 / r931626;
        double r931633 = exp(r931632);
        double r931634 = r931629 * r931633;
        return r931634;
}
↓
double f(double x, double y, double z, double t) {
        double r931635 = x;
        double r931636 = 0.5;
        double r931637 = r931635 * r931636;
        double r931638 = y;
        double r931639 = r931637 - r931638;
        double r931640 = z;
        double r931641 = 2.0;
        double r931642 = r931640 * r931641;
        double r931643 = sqrt(r931642);
        double r931644 = t;
        double r931645 = exp(r931644);
        double r931646 = r931644 / r931641;
        double r931647 = pow(r931645, r931646);
        double r931648 = cbrt(r931647);
        double r931649 = r931648 * r931648;
        double r931650 = r931649 * r931648;
        double r931651 = r931643 * r931650;
        double r931652 = r931639 * r931651;
        return r931652;
}

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 associate-*l*0.3

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

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

    \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot e^{\frac{t \cdot t}{\color{blue}{1 \cdot 2}}}\right)\]

  6. Applied times-frac0.3

    \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot e^{\color{blue}{\frac{t}{1} \cdot \frac{t}{2}}}\right)\]

  7. Applied exp-prod0.3

    \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot \color{blue}{{\left(e^{\frac{t}{1}}\right)}^{\left(\frac{t}{2}\right)}}\right)\]

  8. Simplified0.3

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

  10. Applied add-cube-cbrt0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2020057 
(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))))