Average Error: 0.3 → 0.3
Time: 43.1s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}\]
↓
\[\left(x \cdot 0.5 - y\right) \cdot \left(e^{\frac{t \cdot t}{2.0}} \cdot \sqrt{z \cdot 2.0}\right)\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}
↓
\left(x \cdot 0.5 - y\right) \cdot \left(e^{\frac{t \cdot t}{2.0}} \cdot \sqrt{z \cdot 2.0}\right)
double f(double x, double y, double z, double t) {
        double r38854744 = x;
        double r38854745 = 0.5;
        double r38854746 = r38854744 * r38854745;
        double r38854747 = y;
        double r38854748 = r38854746 - r38854747;
        double r38854749 = z;
        double r38854750 = 2.0;
        double r38854751 = r38854749 * r38854750;
        double r38854752 = sqrt(r38854751);
        double r38854753 = r38854748 * r38854752;
        double r38854754 = t;
        double r38854755 = r38854754 * r38854754;
        double r38854756 = r38854755 / r38854750;
        double r38854757 = exp(r38854756);
        double r38854758 = r38854753 * r38854757;
        return r38854758;
}
↓
double f(double x, double y, double z, double t) {
        double r38854759 = x;
        double r38854760 = 0.5;
        double r38854761 = r38854759 * r38854760;
        double r38854762 = y;
        double r38854763 = r38854761 - r38854762;
        double r38854764 = t;
        double r38854765 = r38854764 * r38854764;
        double r38854766 = 2.0;
        double r38854767 = r38854765 / r38854766;
        double r38854768 = exp(r38854767);
        double r38854769 = z;
        double r38854770 = r38854769 * r38854766;
        double r38854771 = sqrt(r38854770);
        double r38854772 = r38854768 * r38854771;
        double r38854773 = r38854763 * r38854772;
        return r38854773;
}

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
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot {\left(e^{1.0}\right)}^{\left(\frac{t \cdot t}{2.0}\right)}\]

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 associate-*l*0.3

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2019165 
(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 1.0) (/ (* t t) 2.0)))

  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))