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 r849553 = x;
        double r849554 = 0.5;
        double r849555 = r849553 * r849554;
        double r849556 = y;
        double r849557 = r849555 - r849556;
        double r849558 = z;
        double r849559 = 2.0;
        double r849560 = r849558 * r849559;
        double r849561 = sqrt(r849560);
        double r849562 = r849557 * r849561;
        double r849563 = t;
        double r849564 = r849563 * r849563;
        double r849565 = r849564 / r849559;
        double r849566 = exp(r849565);
        double r849567 = r849562 * r849566;
        return r849567;
}
↓
double f(double x, double y, double z, double t) {
        double r849568 = x;
        double r849569 = 0.5;
        double r849570 = r849568 * r849569;
        double r849571 = y;
        double r849572 = r849570 - r849571;
        double r849573 = z;
        double r849574 = 2.0;
        double r849575 = r849573 * r849574;
        double r849576 = sqrt(r849575);
        double r849577 = r849572 * r849576;
        double r849578 = t;
        double r849579 = exp(r849578);
        double r849580 = cbrt(r849579);
        double r849581 = r849580 * r849580;
        double r849582 = r849578 / r849574;
        double r849583 = pow(r849581, r849582);
        double r849584 = r849577 * r849583;
        double r849585 = pow(r849580, r849582);
        double r849586 = r849584 * r849585;
        return r849586;
}

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))))