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 r673544 = x;
        double r673545 = 0.5;
        double r673546 = r673544 * r673545;
        double r673547 = y;
        double r673548 = r673546 - r673547;
        double r673549 = z;
        double r673550 = 2.0;
        double r673551 = r673549 * r673550;
        double r673552 = sqrt(r673551);
        double r673553 = r673548 * r673552;
        double r673554 = t;
        double r673555 = r673554 * r673554;
        double r673556 = r673555 / r673550;
        double r673557 = exp(r673556);
        double r673558 = r673553 * r673557;
        return r673558;
}
↓
double f(double x, double y, double z, double t) {
        double r673559 = x;
        double r673560 = 0.5;
        double r673561 = r673559 * r673560;
        double r673562 = y;
        double r673563 = r673561 - r673562;
        double r673564 = z;
        double r673565 = 2.0;
        double r673566 = r673564 * r673565;
        double r673567 = sqrt(r673566);
        double r673568 = r673563 * r673567;
        double r673569 = t;
        double r673570 = exp(r673569);
        double r673571 = cbrt(r673570);
        double r673572 = r673571 * r673571;
        double r673573 = r673569 / r673565;
        double r673574 = pow(r673572, r673573);
        double r673575 = r673568 * r673574;
        double r673576 = pow(r673571, r673573);
        double r673577 = r673575 * r673576;
        return r673577;
}

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 +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))))