Average Error: 0.3 → 0.3
Time: 26.1s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \left(\sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}} \cdot \sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}}\right)\right) \cdot \sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}}\]
\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]{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}} \cdot \sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}}\right)\right) \cdot \sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}}
double f(double x, double y, double z, double t) {
        double r525719 = x;
        double r525720 = 0.5;
        double r525721 = r525719 * r525720;
        double r525722 = y;
        double r525723 = r525721 - r525722;
        double r525724 = z;
        double r525725 = 2.0;
        double r525726 = r525724 * r525725;
        double r525727 = sqrt(r525726);
        double r525728 = r525723 * r525727;
        double r525729 = t;
        double r525730 = r525729 * r525729;
        double r525731 = r525730 / r525725;
        double r525732 = exp(r525731);
        double r525733 = r525728 * r525732;
        return r525733;
}
↓
double f(double x, double y, double z, double t) {
        double r525734 = x;
        double r525735 = 0.5;
        double r525736 = r525734 * r525735;
        double r525737 = y;
        double r525738 = r525736 - r525737;
        double r525739 = z;
        double r525740 = 2.0;
        double r525741 = r525739 * r525740;
        double r525742 = sqrt(r525741);
        double r525743 = r525738 * r525742;
        double r525744 = t;
        double r525745 = exp(r525744);
        double r525746 = r525744 / r525740;
        double r525747 = pow(r525745, r525746);
        double r525748 = cbrt(r525747);
        double r525749 = r525748 * r525748;
        double r525750 = r525743 * r525749;
        double r525751 = r525750 * r525748;
        return r525751;
}

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

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

  9. Applied associate-*r*0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019323 +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))))