Average Error: 0.3 → 0.5
Time: 8.1s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z}\right) \cdot \sqrt{2}\right) \cdot {e}^{\left(\frac{t \cdot t}{2}\right)}\]
\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}\right) \cdot \sqrt{2}\right) \cdot {e}^{\left(\frac{t \cdot t}{2}\right)}
double f(double x, double y, double z, double t) {
        double r753803 = x;
        double r753804 = 0.5;
        double r753805 = r753803 * r753804;
        double r753806 = y;
        double r753807 = r753805 - r753806;
        double r753808 = z;
        double r753809 = 2.0;
        double r753810 = r753808 * r753809;
        double r753811 = sqrt(r753810);
        double r753812 = r753807 * r753811;
        double r753813 = t;
        double r753814 = r753813 * r753813;
        double r753815 = r753814 / r753809;
        double r753816 = exp(r753815);
        double r753817 = r753812 * r753816;
        return r753817;
}
↓
double f(double x, double y, double z, double t) {
        double r753818 = x;
        double r753819 = 0.5;
        double r753820 = r753818 * r753819;
        double r753821 = y;
        double r753822 = r753820 - r753821;
        double r753823 = z;
        double r753824 = sqrt(r753823);
        double r753825 = r753822 * r753824;
        double r753826 = 2.0;
        double r753827 = sqrt(r753826);
        double r753828 = r753825 * r753827;
        double r753829 = exp(1.0);
        double r753830 = t;
        double r753831 = r753830 * r753830;
        double r753832 = r753831 / r753826;
        double r753833 = pow(r753829, r753832);
        double r753834 = r753828 * r753833;
        return r753834;
}

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
Herbie0.5
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2}\right)}\]

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 sqrt-prod0.5

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

  4. Applied associate-*r*0.5

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

  6. Applied *-un-lft-identity0.5

    \[\leadsto \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z}\right) \cdot \sqrt{2}\right) \cdot e^{\color{blue}{1 \cdot \frac{t \cdot t}{2}}}\]

  7. Applied exp-prod0.5

    \[\leadsto \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z}\right) \cdot \sqrt{2}\right) \cdot \color{blue}{{\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2}\right)}}\]

  8. Simplified0.5

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

  9. Final simplification0.5

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

Reproduce

herbie shell --seed 2020089 +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))))