Average Error: 0.3 → 0.3
Time: 20.8s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(e^{\frac{t \cdot t}{2}} \cdot \sqrt{z \cdot 2}\right) \cdot \left(x \cdot 0.5 - y\right)\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(e^{\frac{t \cdot t}{2}} \cdot \sqrt{z \cdot 2}\right) \cdot \left(x \cdot 0.5 - y\right)
double f(double x, double y, double z, double t) {
        double r591621 = x;
        double r591622 = 0.5;
        double r591623 = r591621 * r591622;
        double r591624 = y;
        double r591625 = r591623 - r591624;
        double r591626 = z;
        double r591627 = 2.0;
        double r591628 = r591626 * r591627;
        double r591629 = sqrt(r591628);
        double r591630 = r591625 * r591629;
        double r591631 = t;
        double r591632 = r591631 * r591631;
        double r591633 = r591632 / r591627;
        double r591634 = exp(r591633);
        double r591635 = r591630 * r591634;
        return r591635;
}
↓
double f(double x, double y, double z, double t) {
        double r591636 = t;
        double r591637 = r591636 * r591636;
        double r591638 = 2.0;
        double r591639 = r591637 / r591638;
        double r591640 = exp(r591639);
        double r591641 = z;
        double r591642 = r591641 * r591638;
        double r591643 = sqrt(r591642);
        double r591644 = r591640 * r591643;
        double r591645 = x;
        double r591646 = 0.5;
        double r591647 = r591645 * r591646;
        double r591648 = y;
        double r591649 = r591647 - r591648;
        double r591650 = r591644 * r591649;
        return r591650;
}

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 add-cube-cbrt0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{\left(\left(\sqrt[3]{e^{\frac{t \cdot t}{2}}} \cdot \sqrt[3]{e^{\frac{t \cdot t}{2}}}\right) \cdot \sqrt[3]{e^{\frac{t \cdot t}{2}}}\right)}\]

  4. Applied associate-*r*0.3

    \[\leadsto \color{blue}{\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \left(\sqrt[3]{e^{\frac{t \cdot t}{2}}} \cdot \sqrt[3]{e^{\frac{t \cdot t}{2}}}\right)\right) \cdot \sqrt[3]{e^{\frac{t \cdot t}{2}}}}\]
  5. Using strategy rm

  6. Applied add-sqr-sqrt0.3

    \[\leadsto \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \left(\sqrt[3]{e^{\frac{t \cdot t}{2}}} \cdot \sqrt[3]{e^{\frac{t \cdot t}{2}}}\right)\right) \cdot \color{blue}{\left(\sqrt{\sqrt[3]{e^{\frac{t \cdot t}{2}}}} \cdot \sqrt{\sqrt[3]{e^{\frac{t \cdot t}{2}}}}\right)}\]

  7. Applied associate-*r*0.3

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \left(\sqrt[3]{e^{\frac{t \cdot t}{2}}} \cdot \sqrt[3]{e^{\frac{t \cdot t}{2}}}\right)\right) \cdot \sqrt{\sqrt[3]{e^{\frac{t \cdot t}{2}}}}\right) \cdot \sqrt{\sqrt[3]{e^{\frac{t \cdot t}{2}}}}}\]

  8. Simplified0.3

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \sqrt[3]{e^{\frac{t \cdot t}{2}}}\right) \cdot {\left(\sqrt{\sqrt[3]{e^{\frac{t \cdot t}{2}}}}\right)}^{3}\right)} \cdot \sqrt{\sqrt[3]{e^{\frac{t \cdot t}{2}}}}\]

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019294 
(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))))