Average Error: 0.3 → 0.3
Time: 24.0s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{2 \cdot z}\right)\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{2 \cdot z}\right)
double f(double x, double y, double z, double t) {
        double r611756 = x;
        double r611757 = 0.5;
        double r611758 = r611756 * r611757;
        double r611759 = y;
        double r611760 = r611758 - r611759;
        double r611761 = z;
        double r611762 = 2.0;
        double r611763 = r611761 * r611762;
        double r611764 = sqrt(r611763);
        double r611765 = r611760 * r611764;
        double r611766 = t;
        double r611767 = r611766 * r611766;
        double r611768 = r611767 / r611762;
        double r611769 = exp(r611768);
        double r611770 = r611765 * r611769;
        return r611770;
}
↓
double f(double x, double y, double z, double t) {
        double r611771 = t;
        double r611772 = exp(r611771);
        double r611773 = 2.0;
        double r611774 = r611771 / r611773;
        double r611775 = pow(r611772, r611774);
        double r611776 = x;
        double r611777 = 0.5;
        double r611778 = r611776 * r611777;
        double r611779 = y;
        double r611780 = r611778 - r611779;
        double r611781 = z;
        double r611782 = r611773 * r611781;
        double r611783 = sqrt(r611782);
        double r611784 = r611780 * r611783;
        double r611785 = r611775 * r611784;
        return r611785;
}

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 *-commutative0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019196 
(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))))