Average Error: 0.3 → 0.3
Time: 24.9s
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 r51504456 = x;
        double r51504457 = 0.5;
        double r51504458 = r51504456 * r51504457;
        double r51504459 = y;
        double r51504460 = r51504458 - r51504459;
        double r51504461 = z;
        double r51504462 = 2.0;
        double r51504463 = r51504461 * r51504462;
        double r51504464 = sqrt(r51504463);
        double r51504465 = r51504460 * r51504464;
        double r51504466 = t;
        double r51504467 = r51504466 * r51504466;
        double r51504468 = r51504467 / r51504462;
        double r51504469 = exp(r51504468);
        double r51504470 = r51504465 * r51504469;
        return r51504470;
}
↓
double f(double x, double y, double z, double t) {
        double r51504471 = t;
        double r51504472 = exp(r51504471);
        double r51504473 = 2.0;
        double r51504474 = r51504471 / r51504473;
        double r51504475 = pow(r51504472, r51504474);
        double r51504476 = sqrt(r51504475);
        double r51504477 = x;
        double r51504478 = 0.5;
        double r51504479 = r51504477 * r51504478;
        double r51504480 = y;
        double r51504481 = r51504479 - r51504480;
        double r51504482 = z;
        double r51504483 = r51504482 * r51504473;
        double r51504484 = sqrt(r51504483);
        double r51504485 = r51504481 * r51504484;
        double r51504486 = r51504476 * r51504485;
        double r51504487 = r51504486 * r51504476;
        return r51504487;
}

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 
(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))))