Average Error: 19.5 → 19.5
Time: 5.4s
Precision: 64
\[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\]
↓
\[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\]
2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}
↓
2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}
double f(double x, double y, double z) {
        double r1211452 = 2.0;
        double r1211453 = x;
        double r1211454 = y;
        double r1211455 = r1211453 * r1211454;
        double r1211456 = z;
        double r1211457 = r1211453 * r1211456;
        double r1211458 = r1211455 + r1211457;
        double r1211459 = r1211454 * r1211456;
        double r1211460 = r1211458 + r1211459;
        double r1211461 = sqrt(r1211460);
        double r1211462 = r1211452 * r1211461;
        return r1211462;
}
↓
double f(double x, double y, double z) {
        double r1211463 = 2.0;
        double r1211464 = x;
        double r1211465 = y;
        double r1211466 = r1211464 * r1211465;
        double r1211467 = z;
        double r1211468 = r1211464 * r1211467;
        double r1211469 = r1211466 + r1211468;
        double r1211470 = r1211465 * r1211467;
        double r1211471 = r1211469 + r1211470;
        double r1211472 = sqrt(r1211471);
        double r1211473 = r1211463 * r1211472;
        return r1211473;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original19.5
Target19.0
Herbie19.5
\[\begin{array}{l} \mathbf{if}\;z \lt 7.6369500905736745 \cdot 10^{176}:\\ \;\;\;\;2 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right) \cdot \left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right)\right) \cdot 2\\ \end{array}\]

Derivation

  1. Initial program 19.5

    \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\]

  2. Final simplification19.5

    \[\leadsto 2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\]

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:descartes from diagrams-contrib-1.3.0.5"
  :precision binary64

  :herbie-target
  (if (< z 7.636950090573675e+176) (* 2 (sqrt (+ (* (+ x y) z) (* x y)))) (* (* (+ (* 0.25 (* (* (pow y -0.75) (* (pow z -0.75) x)) (+ y z))) (* (pow z 0.25) (pow y 0.25))) (+ (* 0.25 (* (* (pow y -0.75) (* (pow z -0.75) x)) (+ y z))) (* (pow z 0.25) (pow y 0.25)))) 2))

  (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))))