Average Error: 25.0 → 6.6
Time: 5.0s
Precision: 64
\[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -5.6665509280114942 \cdot 10^{151}:\\ \;\;\;\;-1 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \le 2.71648771019888003 \cdot 10^{115}:\\ \;\;\;\;\frac{x \cdot y}{\frac{\sqrt{z \cdot z - t \cdot a}}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array}\]
\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}}
↓
\begin{array}{l}
\mathbf{if}\;z \le -5.6665509280114942 \cdot 10^{151}:\\
\;\;\;\;-1 \cdot \left(x \cdot y\right)\\

\mathbf{elif}\;z \le 2.71648771019888003 \cdot 10^{115}:\\
\;\;\;\;\frac{x \cdot y}{\frac{\sqrt{z \cdot z - t \cdot a}}{z}}\\

\mathbf{else}:\\
\;\;\;\;x \cdot y\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r400593 = x;
        double r400594 = y;
        double r400595 = r400593 * r400594;
        double r400596 = z;
        double r400597 = r400595 * r400596;
        double r400598 = r400596 * r400596;
        double r400599 = t;
        double r400600 = a;
        double r400601 = r400599 * r400600;
        double r400602 = r400598 - r400601;
        double r400603 = sqrt(r400602);
        double r400604 = r400597 / r400603;
        return r400604;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r400605 = z;
        double r400606 = -5.666550928011494e+151;
        bool r400607 = r400605 <= r400606;
        double r400608 = -1.0;
        double r400609 = x;
        double r400610 = y;
        double r400611 = r400609 * r400610;
        double r400612 = r400608 * r400611;
        double r400613 = 2.71648771019888e+115;
        bool r400614 = r400605 <= r400613;
        double r400615 = r400605 * r400605;
        double r400616 = t;
        double r400617 = a;
        double r400618 = r400616 * r400617;
        double r400619 = r400615 - r400618;
        double r400620 = sqrt(r400619);
        double r400621 = r400620 / r400605;
        double r400622 = r400611 / r400621;
        double r400623 = r400614 ? r400622 : r400611;
        double r400624 = r400607 ? r400612 : r400623;
        return r400624;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original25.0
Target7.7
Herbie6.6
\[\begin{array}{l} \mathbf{if}\;z \lt -3.1921305903852764 \cdot 10^{46}:\\ \;\;\;\;-y \cdot x\\ \mathbf{elif}\;z \lt 5.9762681209208942 \cdot 10^{90}:\\ \;\;\;\;\frac{x \cdot z}{\frac{\sqrt{z \cdot z - a \cdot t}}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -5.666550928011494e+151

    1. Initial program 53.8

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}}\]

    2. Taylor expanded around -inf 1.1

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot y\right)}\]

    if -5.666550928011494e+151 < z < 2.71648771019888e+115

    1. Initial program 11.2

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}}\]
    2. Using strategy rm

    3. Applied associate-/l*9.4

      \[\leadsto \color{blue}{\frac{x \cdot y}{\frac{\sqrt{z \cdot z - t \cdot a}}{z}}}\]

    if 2.71648771019888e+115 < z

    1. Initial program 46.1

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}}\]

    2. Taylor expanded around inf 1.9

      \[\leadsto \color{blue}{x \cdot y}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification6.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.6665509280114942 \cdot 10^{151}:\\ \;\;\;\;-1 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \le 2.71648771019888003 \cdot 10^{115}:\\ \;\;\;\;\frac{x \cdot y}{\frac{\sqrt{z \cdot z - t \cdot a}}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2020057 
(FPCore (x y z t a)
  :name "Statistics.Math.RootFinding:ridders from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (if (< z -3.1921305903852764e+46) (- (* y x)) (if (< z 5.976268120920894e+90) (/ (* x z) (/ (sqrt (- (* z z) (* a t))) y)) (* y x)))

  (/ (* (* x y) z) (sqrt (- (* z z) (* t a)))))