Average Error: 0.3 → 0.3
Time: 7.0s
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 r850375 = x;
        double r850376 = 0.5;
        double r850377 = r850375 * r850376;
        double r850378 = y;
        double r850379 = r850377 - r850378;
        double r850380 = z;
        double r850381 = 2.0;
        double r850382 = r850380 * r850381;
        double r850383 = sqrt(r850382);
        double r850384 = r850379 * r850383;
        double r850385 = t;
        double r850386 = r850385 * r850385;
        double r850387 = r850386 / r850381;
        double r850388 = exp(r850387);
        double r850389 = r850384 * r850388;
        return r850389;
}
↓
double f(double x, double y, double z, double t) {
        double r850390 = x;
        double r850391 = 0.5;
        double r850392 = r850390 * r850391;
        double r850393 = y;
        double r850394 = r850392 - r850393;
        double r850395 = z;
        double r850396 = 2.0;
        double r850397 = r850395 * r850396;
        double r850398 = sqrt(r850397);
        double r850399 = r850394 * r850398;
        double r850400 = t;
        double r850401 = exp(r850400);
        double r850402 = r850400 / r850396;
        double r850403 = pow(r850401, r850402);
        double r850404 = cbrt(r850403);
        double r850405 = r850404 * r850404;
        double r850406 = r850405 * r850404;
        double r850407 = r850399 * r850406;
        return r850407;
}

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 
(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))))