Average Error: 0.3 → 0.3
Time: 26.1s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(x \cdot 0.5 - y\right) \cdot \left({\left(e^{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right)}^{\left(\sqrt[3]{t} \cdot \frac{t}{2}\right)} \cdot \sqrt{z \cdot 2}\right)\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(x \cdot 0.5 - y\right) \cdot \left({\left(e^{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right)}^{\left(\sqrt[3]{t} \cdot \frac{t}{2}\right)} \cdot \sqrt{z \cdot 2}\right)
double f(double x, double y, double z, double t) {
        double r744374 = x;
        double r744375 = 0.5;
        double r744376 = r744374 * r744375;
        double r744377 = y;
        double r744378 = r744376 - r744377;
        double r744379 = z;
        double r744380 = 2.0;
        double r744381 = r744379 * r744380;
        double r744382 = sqrt(r744381);
        double r744383 = r744378 * r744382;
        double r744384 = t;
        double r744385 = r744384 * r744384;
        double r744386 = r744385 / r744380;
        double r744387 = exp(r744386);
        double r744388 = r744383 * r744387;
        return r744388;
}
↓
double f(double x, double y, double z, double t) {
        double r744389 = x;
        double r744390 = 0.5;
        double r744391 = r744389 * r744390;
        double r744392 = y;
        double r744393 = r744391 - r744392;
        double r744394 = t;
        double r744395 = cbrt(r744394);
        double r744396 = r744395 * r744395;
        double r744397 = exp(r744396);
        double r744398 = 2.0;
        double r744399 = r744394 / r744398;
        double r744400 = r744395 * r744399;
        double r744401 = pow(r744397, r744400);
        double r744402 = z;
        double r744403 = r744402 * r744398;
        double r744404 = sqrt(r744403);
        double r744405 = r744401 * r744404;
        double r744406 = r744393 * r744405;
        return r744406;
}

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 associate-*l*0.3

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

  9. Simplified0.3

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

  11. Applied add-cube-cbrt0.3

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

  12. Applied exp-prod0.3

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

  13. Applied pow-pow0.3

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

  14. Final simplification0.3

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

Reproduce

herbie shell --seed 2019304 +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))))