Average Error: 0.3 → 0.5
Time: 26.3s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left({\left(e^{\frac{t}{2}}\right)}^{t} \cdot \left(\left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right) \cdot \sqrt{z}\right)\right) \cdot \left(0.5 \cdot x - y\right)\right) \cdot \sqrt[3]{\sqrt{2}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\left({\left(e^{\frac{t}{2}}\right)}^{t} \cdot \left(\left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right) \cdot \sqrt{z}\right)\right) \cdot \left(0.5 \cdot x - y\right)\right) \cdot \sqrt[3]{\sqrt{2}}
double f(double x, double y, double z, double t) {
        double r732490 = x;
        double r732491 = 0.5;
        double r732492 = r732490 * r732491;
        double r732493 = y;
        double r732494 = r732492 - r732493;
        double r732495 = z;
        double r732496 = 2.0;
        double r732497 = r732495 * r732496;
        double r732498 = sqrt(r732497);
        double r732499 = r732494 * r732498;
        double r732500 = t;
        double r732501 = r732500 * r732500;
        double r732502 = r732501 / r732496;
        double r732503 = exp(r732502);
        double r732504 = r732499 * r732503;
        return r732504;
}
↓
double f(double x, double y, double z, double t) {
        double r732505 = t;
        double r732506 = 2.0;
        double r732507 = r732505 / r732506;
        double r732508 = exp(r732507);
        double r732509 = pow(r732508, r732505);
        double r732510 = sqrt(r732506);
        double r732511 = cbrt(r732510);
        double r732512 = r732511 * r732511;
        double r732513 = z;
        double r732514 = sqrt(r732513);
        double r732515 = r732512 * r732514;
        double r732516 = r732509 * r732515;
        double r732517 = 0.5;
        double r732518 = x;
        double r732519 = r732517 * r732518;
        double r732520 = y;
        double r732521 = r732519 - r732520;
        double r732522 = r732516 * r732521;
        double r732523 = r732522 * r732511;
        return r732523;
}

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
Herbie0.5
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2}\right)}\]

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. Simplified0.3

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

  4. Applied sqrt-prod0.5

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

  5. Applied associate-*r*0.5

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

  6. Simplified0.5

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

  8. Applied associate-*r*0.5

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

  9. Simplified0.5

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

  11. Applied add-cube-cbrt0.5

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

  12. Applied associate-*r*0.5

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

  13. Simplified0.5

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

  14. Final simplification0.5

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

Reproduce

herbie shell --seed 2019179 
(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))))