Average Error: 0.3 → 0.5
Time: 22.6s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}\]
↓
\[\left(\left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \sqrt{2.0}\right) \cdot \sqrt{z}\right) \cdot \left(x \cdot 0.5 - y\right)\]
\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(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \sqrt{2.0}\right) \cdot \sqrt{z}\right) \cdot \left(x \cdot 0.5 - y\right)
double f(double x, double y, double z, double t) {
        double r33323767 = x;
        double r33323768 = 0.5;
        double r33323769 = r33323767 * r33323768;
        double r33323770 = y;
        double r33323771 = r33323769 - r33323770;
        double r33323772 = z;
        double r33323773 = 2.0;
        double r33323774 = r33323772 * r33323773;
        double r33323775 = sqrt(r33323774);
        double r33323776 = r33323771 * r33323775;
        double r33323777 = t;
        double r33323778 = r33323777 * r33323777;
        double r33323779 = r33323778 / r33323773;
        double r33323780 = exp(r33323779);
        double r33323781 = r33323776 * r33323780;
        return r33323781;
}
↓
double f(double x, double y, double z, double t) {
        double r33323782 = t;
        double r33323783 = r33323782 * r33323782;
        double r33323784 = 0.5;
        double r33323785 = r33323783 * r33323784;
        double r33323786 = exp(r33323785);
        double r33323787 = 2.0;
        double r33323788 = sqrt(r33323787);
        double r33323789 = r33323786 * r33323788;
        double r33323790 = z;
        double r33323791 = sqrt(r33323790);
        double r33323792 = r33323789 * r33323791;
        double r33323793 = x;
        double r33323794 = r33323793 * r33323784;
        double r33323795 = y;
        double r33323796 = r33323794 - r33323795;
        double r33323797 = r33323792 * r33323796;
        return r33323797;
}

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
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2.0}\right)}\]

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 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. Using strategy rm

  5. Applied sqrt-prod0.5

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

  6. Applied associate-*l*0.5

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

  7. Taylor expanded around inf 0.5

    \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z} \cdot \left(\sqrt{2.0} \cdot \color{blue}{e^{0.5 \cdot {t}^{2}}}\right)\right)\]

  8. Simplified0.5

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

  9. Final simplification0.5

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

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) (/ (* t t) 2.0)))

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