Average Error: 27.1 → 0.4
Time: 6.4s
Precision: 64
\[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -4.66503060680459687 \cdot 10^{72} \lor \neg \left(x \le 6.7328323193843391 \cdot 10^{53}\right):\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(\frac{y}{{x}^{3}} + 4.16438922227999964\right) - 101.785145853921094 \cdot \frac{1}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\\ \end{array}\]
\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}
↓
\begin{array}{l}
\mathbf{if}\;x \le -4.66503060680459687 \cdot 10^{72} \lor \neg \left(x \le 6.7328323193843391 \cdot 10^{53}\right):\\
\;\;\;\;\left(x - 2\right) \cdot \left(\left(\frac{y}{{x}^{3}} + 4.16438922227999964\right) - 101.785145853921094 \cdot \frac{1}{x}\right)\\

\mathbf{else}:\\
\;\;\;\;\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\\

\end{array}
double f(double x, double y, double z) {
        double r400552 = x;
        double r400553 = 2.0;
        double r400554 = r400552 - r400553;
        double r400555 = 4.16438922228;
        double r400556 = r400552 * r400555;
        double r400557 = 78.6994924154;
        double r400558 = r400556 + r400557;
        double r400559 = r400558 * r400552;
        double r400560 = 137.519416416;
        double r400561 = r400559 + r400560;
        double r400562 = r400561 * r400552;
        double r400563 = y;
        double r400564 = r400562 + r400563;
        double r400565 = r400564 * r400552;
        double r400566 = z;
        double r400567 = r400565 + r400566;
        double r400568 = r400554 * r400567;
        double r400569 = 43.3400022514;
        double r400570 = r400552 + r400569;
        double r400571 = r400570 * r400552;
        double r400572 = 263.505074721;
        double r400573 = r400571 + r400572;
        double r400574 = r400573 * r400552;
        double r400575 = 313.399215894;
        double r400576 = r400574 + r400575;
        double r400577 = r400576 * r400552;
        double r400578 = 47.066876606;
        double r400579 = r400577 + r400578;
        double r400580 = r400568 / r400579;
        return r400580;
}
↓
double f(double x, double y, double z) {
        double r400581 = x;
        double r400582 = -4.665030606804597e+72;
        bool r400583 = r400581 <= r400582;
        double r400584 = 6.732832319384339e+53;
        bool r400585 = r400581 <= r400584;
        double r400586 = !r400585;
        bool r400587 = r400583 || r400586;
        double r400588 = 2.0;
        double r400589 = r400581 - r400588;
        double r400590 = y;
        double r400591 = 3.0;
        double r400592 = pow(r400581, r400591);
        double r400593 = r400590 / r400592;
        double r400594 = 4.16438922228;
        double r400595 = r400593 + r400594;
        double r400596 = 101.7851458539211;
        double r400597 = 1.0;
        double r400598 = r400597 / r400581;
        double r400599 = r400596 * r400598;
        double r400600 = r400595 - r400599;
        double r400601 = r400589 * r400600;
        double r400602 = r400581 * r400594;
        double r400603 = 78.6994924154;
        double r400604 = r400602 + r400603;
        double r400605 = r400604 * r400581;
        double r400606 = 137.519416416;
        double r400607 = r400605 + r400606;
        double r400608 = r400607 * r400581;
        double r400609 = r400608 + r400590;
        double r400610 = r400609 * r400581;
        double r400611 = z;
        double r400612 = r400610 + r400611;
        double r400613 = 43.3400022514;
        double r400614 = r400581 + r400613;
        double r400615 = r400614 * r400581;
        double r400616 = 263.505074721;
        double r400617 = r400615 + r400616;
        double r400618 = r400617 * r400581;
        double r400619 = 313.399215894;
        double r400620 = r400618 + r400619;
        double r400621 = r400620 * r400581;
        double r400622 = 47.066876606;
        double r400623 = r400621 + r400622;
        double r400624 = r400612 / r400623;
        double r400625 = r400589 * r400624;
        double r400626 = r400587 ? r400601 : r400625;
        return r400626;
}

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

Original27.1
Target0.4
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;x \lt -3.3261287258700048 \cdot 10^{62}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{elif}\;x \lt 9.4299917145546727 \cdot 10^{55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.50507472100003 \cdot x + \left(43.3400022514000014 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606000001}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -4.665030606804597e+72 or 6.732832319384339e+53 < x

    1. Initial program 63.5

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity63.5

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\color{blue}{1 \cdot \left(\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001\right)}}\]

    4. Applied times-frac60.8

      \[\leadsto \color{blue}{\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}}\]

    5. Simplified60.8

      \[\leadsto \color{blue}{\left(x - 2\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]

    6. Taylor expanded around inf 0.3

      \[\leadsto \left(x - 2\right) \cdot \color{blue}{\left(\left(\frac{y}{{x}^{3}} + 4.16438922227999964\right) - 101.785145853921094 \cdot \frac{1}{x}\right)}\]

    if -4.665030606804597e+72 < x < 6.732832319384339e+53

    1. Initial program 2.4

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity2.4

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\color{blue}{1 \cdot \left(\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001\right)}}\]

    4. Applied times-frac0.5

      \[\leadsto \color{blue}{\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}}\]

    5. Simplified0.5

      \[\leadsto \color{blue}{\left(x - 2\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -4.66503060680459687 \cdot 10^{72} \lor \neg \left(x \le 6.7328323193843391 \cdot 10^{53}\right):\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(\frac{y}{{x}^{3}} + 4.16438922227999964\right) - 101.785145853921094 \cdot \frac{1}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :precision binary64

  :herbie-target
  (if (< x -3.326128725870005e+62) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811) (if (< x 9.429991714554673e+55) (* (/ (- x 2) 1) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (+ (* 263.505074721 x) (+ (* 43.3400022514 (* x x)) (* x (* x x)))) 313.399215894) x) 47.066876606))) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811)))

  (/ (* (- x 2) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))