Average Error: 19.2 → 0.2
Time: 23.8s
Precision: 64
\[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -0.612073400392309:\\ \;\;\;\;\left(\left(y \cdot 0.0692910599291889 + \frac{y}{z} \cdot 0.07512208616047561\right) - \frac{0.40462203869992125}{z} \cdot \frac{y}{z}\right) + x\\ \mathbf{elif}\;z \le 540034.0694215782:\\ \;\;\;\;x + y \cdot \frac{\frac{0.279195317918525 + z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)}{\sqrt{3.350343815022304 + z \cdot \left(6.012459259764103 + z\right)}}}{\sqrt{3.350343815022304 + z \cdot \left(6.012459259764103 + z\right)}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot 0.0692910599291889 + \frac{y}{z} \cdot 0.07512208616047561\right) - \frac{0.40462203869992125}{z} \cdot \frac{y}{z}\right) + x\\ \end{array}\]
x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}
↓
\begin{array}{l}
\mathbf{if}\;z \le -0.612073400392309:\\
\;\;\;\;\left(\left(y \cdot 0.0692910599291889 + \frac{y}{z} \cdot 0.07512208616047561\right) - \frac{0.40462203869992125}{z} \cdot \frac{y}{z}\right) + x\\

\mathbf{elif}\;z \le 540034.0694215782:\\
\;\;\;\;x + y \cdot \frac{\frac{0.279195317918525 + z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)}{\sqrt{3.350343815022304 + z \cdot \left(6.012459259764103 + z\right)}}}{\sqrt{3.350343815022304 + z \cdot \left(6.012459259764103 + z\right)}}\\

\mathbf{else}:\\
\;\;\;\;\left(\left(y \cdot 0.0692910599291889 + \frac{y}{z} \cdot 0.07512208616047561\right) - \frac{0.40462203869992125}{z} \cdot \frac{y}{z}\right) + x\\

\end{array}
double f(double x, double y, double z) {
        double r17821508 = x;
        double r17821509 = y;
        double r17821510 = z;
        double r17821511 = 0.0692910599291889;
        double r17821512 = r17821510 * r17821511;
        double r17821513 = 0.4917317610505968;
        double r17821514 = r17821512 + r17821513;
        double r17821515 = r17821514 * r17821510;
        double r17821516 = 0.279195317918525;
        double r17821517 = r17821515 + r17821516;
        double r17821518 = r17821509 * r17821517;
        double r17821519 = 6.012459259764103;
        double r17821520 = r17821510 + r17821519;
        double r17821521 = r17821520 * r17821510;
        double r17821522 = 3.350343815022304;
        double r17821523 = r17821521 + r17821522;
        double r17821524 = r17821518 / r17821523;
        double r17821525 = r17821508 + r17821524;
        return r17821525;
}
↓
double f(double x, double y, double z) {
        double r17821526 = z;
        double r17821527 = -0.612073400392309;
        bool r17821528 = r17821526 <= r17821527;
        double r17821529 = y;
        double r17821530 = 0.0692910599291889;
        double r17821531 = r17821529 * r17821530;
        double r17821532 = r17821529 / r17821526;
        double r17821533 = 0.07512208616047561;
        double r17821534 = r17821532 * r17821533;
        double r17821535 = r17821531 + r17821534;
        double r17821536 = 0.40462203869992125;
        double r17821537 = r17821536 / r17821526;
        double r17821538 = r17821537 * r17821532;
        double r17821539 = r17821535 - r17821538;
        double r17821540 = x;
        double r17821541 = r17821539 + r17821540;
        double r17821542 = 540034.0694215782;
        bool r17821543 = r17821526 <= r17821542;
        double r17821544 = 0.279195317918525;
        double r17821545 = r17821526 * r17821530;
        double r17821546 = 0.4917317610505968;
        double r17821547 = r17821545 + r17821546;
        double r17821548 = r17821526 * r17821547;
        double r17821549 = r17821544 + r17821548;
        double r17821550 = 3.350343815022304;
        double r17821551 = 6.012459259764103;
        double r17821552 = r17821551 + r17821526;
        double r17821553 = r17821526 * r17821552;
        double r17821554 = r17821550 + r17821553;
        double r17821555 = sqrt(r17821554);
        double r17821556 = r17821549 / r17821555;
        double r17821557 = r17821556 / r17821555;
        double r17821558 = r17821529 * r17821557;
        double r17821559 = r17821540 + r17821558;
        double r17821560 = r17821543 ? r17821559 : r17821541;
        double r17821561 = r17821528 ? r17821541 : r17821560;
        return r17821561;
}

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

Original19.2
Target0.2
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;z \lt -8120153.652456675:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291889\right) \cdot y - \left(\frac{0.40462203869992125 \cdot y}{z \cdot z} - x\right)\\ \mathbf{elif}\;z \lt 6.576118972787377 \cdot 10^{+20}:\\ \;\;\;\;x + \left(y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)\right) \cdot \frac{1}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291889\right) \cdot y - \left(\frac{0.40462203869992125 \cdot y}{z \cdot z} - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -0.612073400392309 or 540034.0694215782 < z

    1. Initial program 39.4

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\]
    2. Using strategy rm

    3. Applied associate-/l*31.6

      \[\leadsto x + \color{blue}{\frac{y}{\frac{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}}}\]

    4. Taylor expanded around inf 0.2

      \[\leadsto x + \color{blue}{\left(\left(0.0692910599291889 \cdot y + 0.07512208616047561 \cdot \frac{y}{z}\right) - 0.40462203869992125 \cdot \frac{y}{{z}^{2}}\right)}\]

    5. Simplified0.2

      \[\leadsto x + \color{blue}{\left(\left(\frac{y}{z} \cdot 0.07512208616047561 + y \cdot 0.0692910599291889\right) - \frac{0.40462203869992125}{z} \cdot \frac{y}{z}\right)}\]

    if -0.612073400392309 < z < 540034.0694215782

    1. Initial program 0.2

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\]
    2. Using strategy rm

    3. Applied add-sqr-sqrt0.4

      \[\leadsto x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\color{blue}{\sqrt{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \cdot \sqrt{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}}}\]

    4. Applied times-frac0.1

      \[\leadsto x + \color{blue}{\frac{y}{\sqrt{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} \cdot \frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\sqrt{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}}}\]
    5. Using strategy rm

    6. Applied div-inv0.2

      \[\leadsto x + \color{blue}{\left(y \cdot \frac{1}{\sqrt{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}}\right)} \cdot \frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\sqrt{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}}\]

    7. Applied associate-*l*0.1

      \[\leadsto x + \color{blue}{y \cdot \left(\frac{1}{\sqrt{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} \cdot \frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\sqrt{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}}\right)}\]

    8. Simplified0.1

      \[\leadsto x + y \cdot \color{blue}{\frac{\frac{\left(0.4917317610505968 + z \cdot 0.0692910599291889\right) \cdot z + 0.279195317918525}{\sqrt{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}}}{\sqrt{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -0.612073400392309:\\ \;\;\;\;\left(\left(y \cdot 0.0692910599291889 + \frac{y}{z} \cdot 0.07512208616047561\right) - \frac{0.40462203869992125}{z} \cdot \frac{y}{z}\right) + x\\ \mathbf{elif}\;z \le 540034.0694215782:\\ \;\;\;\;x + y \cdot \frac{\frac{0.279195317918525 + z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)}{\sqrt{3.350343815022304 + z \cdot \left(6.012459259764103 + z\right)}}}{\sqrt{3.350343815022304 + z \cdot \left(6.012459259764103 + z\right)}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot 0.0692910599291889 + \frac{y}{z} \cdot 0.07512208616047561\right) - \frac{0.40462203869992125}{z} \cdot \frac{y}{z}\right) + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, B"

  :herbie-target
  (if (< z -8120153.652456675) (- (* (+ (/ 0.07512208616047561 z) 0.0692910599291889) y) (- (/ (* 0.40462203869992125 y) (* z z)) x)) (if (< z 6.576118972787377e+20) (+ x (* (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (/ 1 (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (- (* (+ (/ 0.07512208616047561 z) 0.0692910599291889) y) (- (/ (* 0.40462203869992125 y) (* z z)) x))))

  (+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))