Average Error: 0.3 → 0.3
Time: 27.3s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right)\right) \cdot \sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right)\right) \cdot \sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}}
double f(double x, double y, double z, double t) {
        double r30542685 = x;
        double r30542686 = 0.5;
        double r30542687 = r30542685 * r30542686;
        double r30542688 = y;
        double r30542689 = r30542687 - r30542688;
        double r30542690 = z;
        double r30542691 = 2.0;
        double r30542692 = r30542690 * r30542691;
        double r30542693 = sqrt(r30542692);
        double r30542694 = r30542689 * r30542693;
        double r30542695 = t;
        double r30542696 = r30542695 * r30542695;
        double r30542697 = r30542696 / r30542691;
        double r30542698 = exp(r30542697);
        double r30542699 = r30542694 * r30542698;
        return r30542699;
}
↓
double f(double x, double y, double z, double t) {
        double r30542700 = t;
        double r30542701 = exp(r30542700);
        double r30542702 = 2.0;
        double r30542703 = r30542700 / r30542702;
        double r30542704 = pow(r30542701, r30542703);
        double r30542705 = sqrt(r30542704);
        double r30542706 = x;
        double r30542707 = 0.5;
        double r30542708 = r30542706 * r30542707;
        double r30542709 = y;
        double r30542710 = r30542708 - r30542709;
        double r30542711 = z;
        double r30542712 = r30542711 * r30542702;
        double r30542713 = sqrt(r30542712);
        double r30542714 = r30542710 * r30542713;
        double r30542715 = r30542705 * r30542714;
        double r30542716 = r30542715 * r30542705;
        return r30542716;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

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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 add-sqr-sqrt0.3

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

  9. Applied associate-*r*0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(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))))