Average Error: 0.3 → 0.3
Time: 7.6s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \left(\left(\sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}} \cdot \sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}}\right) \cdot \sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}}\right)\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \left(\left(\sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}} \cdot \sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}}\right) \cdot \sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}}\right)
double f(double x, double y, double z, double t) {
        double r703585 = x;
        double r703586 = 0.5;
        double r703587 = r703585 * r703586;
        double r703588 = y;
        double r703589 = r703587 - r703588;
        double r703590 = z;
        double r703591 = 2.0;
        double r703592 = r703590 * r703591;
        double r703593 = sqrt(r703592);
        double r703594 = r703589 * r703593;
        double r703595 = t;
        double r703596 = r703595 * r703595;
        double r703597 = r703596 / r703591;
        double r703598 = exp(r703597);
        double r703599 = r703594 * r703598;
        return r703599;
}
↓
double f(double x, double y, double z, double t) {
        double r703600 = x;
        double r703601 = 0.5;
        double r703602 = r703600 * r703601;
        double r703603 = y;
        double r703604 = r703602 - r703603;
        double r703605 = z;
        double r703606 = 2.0;
        double r703607 = r703605 * r703606;
        double r703608 = sqrt(r703607);
        double r703609 = r703604 * r703608;
        double r703610 = t;
        double r703611 = exp(r703610);
        double r703612 = r703610 / r703606;
        double r703613 = pow(r703611, r703612);
        double r703614 = cbrt(r703613);
        double r703615 = r703614 * r703614;
        double r703616 = r703615 * r703614;
        double r703617 = r703609 * r703616;
        return r703617;
}

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 add-cube-cbrt0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2020062 +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))))