Average Error: 0.3 → 0.3
Time: 25.3s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot {\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}
↓
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot {\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}
double f(double x, double y, double z, double t) {
        double r41272729 = x;
        double r41272730 = 0.5;
        double r41272731 = r41272729 * r41272730;
        double r41272732 = y;
        double r41272733 = r41272731 - r41272732;
        double r41272734 = z;
        double r41272735 = 2.0;
        double r41272736 = r41272734 * r41272735;
        double r41272737 = sqrt(r41272736);
        double r41272738 = r41272733 * r41272737;
        double r41272739 = t;
        double r41272740 = r41272739 * r41272739;
        double r41272741 = r41272740 / r41272735;
        double r41272742 = exp(r41272741);
        double r41272743 = r41272738 * r41272742;
        return r41272743;
}
↓
double f(double x, double y, double z, double t) {
        double r41272744 = x;
        double r41272745 = 0.5;
        double r41272746 = r41272744 * r41272745;
        double r41272747 = y;
        double r41272748 = r41272746 - r41272747;
        double r41272749 = z;
        double r41272750 = 2.0;
        double r41272751 = r41272749 * r41272750;
        double r41272752 = sqrt(r41272751);
        double r41272753 = r41272748 * r41272752;
        double r41272754 = t;
        double r41272755 = exp(r41272754);
        double r41272756 = r41272754 / r41272750;
        double r41272757 = pow(r41272755, r41272756);
        double r41272758 = r41272753 * r41272757;
        return r41272758;
}

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019158 
(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))))