Average Error: 6.8 → 2.6
Time: 3.7s
Precision: 64
\[\frac{x \cdot 2}{y \cdot z - t \cdot z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -6.5010644488975887 \cdot 10^{94} \lor \neg \left(x \le 3.8619926413929668 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x}{y - t} \cdot \left(\frac{1}{z} \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \frac{x}{\frac{z \cdot \left(y - t\right)}{2}}\\ \end{array}\]
\frac{x \cdot 2}{y \cdot z - t \cdot z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -6.5010644488975887 \cdot 10^{94} \lor \neg \left(x \le 3.8619926413929668 \cdot 10^{-62}\right):\\
\;\;\;\;\frac{x}{y - t} \cdot \left(\frac{1}{z} \cdot 2\right)\\

\mathbf{else}:\\
\;\;\;\;1 \cdot \frac{x}{\frac{z \cdot \left(y - t\right)}{2}}\\

\end{array}
double code(double x, double y, double z, double t) {
	return ((x * 2.0) / ((y * z) - (t * z)));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if (((x <= -6.501064448897589e+94) || !(x <= 3.861992641392967e-62))) {
		VAR = ((x / (y - t)) * ((1.0 / z) * 2.0));
	} else {
		VAR = (1.0 * (x / ((z * (y - t)) / 2.0)));
	}
	return VAR;
}

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

Original6.8
Target2.1
Herbie2.6
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot 2}{y \cdot z - t \cdot z} \lt -2.559141628295061 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ \mathbf{elif}\;\frac{x \cdot 2}{y \cdot z - t \cdot z} \lt 1.04502782733012586 \cdot 10^{-269}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 2}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -6.501064448897589e+94 or 3.861992641392967e-62 < x

    1. Initial program 10.9

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z}\]

    2. Simplified10.1

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

    4. Applied *-un-lft-identity10.1

      \[\leadsto \frac{x}{\frac{z \cdot \left(y - t\right)}{\color{blue}{1 \cdot 2}}}\]

    5. Applied times-frac10.1

      \[\leadsto \frac{x}{\color{blue}{\frac{z}{1} \cdot \frac{y - t}{2}}}\]

    6. Applied associate-/r*10.8

      \[\leadsto \color{blue}{\frac{\frac{x}{\frac{z}{1}}}{\frac{y - t}{2}}}\]

    7. Simplified10.8

      \[\leadsto \frac{\color{blue}{\frac{x}{z}}}{\frac{y - t}{2}}\]
    8. Using strategy rm

    9. Applied div-inv10.8

      \[\leadsto \frac{\frac{x}{z}}{\color{blue}{\left(y - t\right) \cdot \frac{1}{2}}}\]

    10. Applied div-inv10.9

      \[\leadsto \frac{\color{blue}{x \cdot \frac{1}{z}}}{\left(y - t\right) \cdot \frac{1}{2}}\]

    11. Applied times-frac3.1

      \[\leadsto \color{blue}{\frac{x}{y - t} \cdot \frac{\frac{1}{z}}{\frac{1}{2}}}\]

    12. Simplified3.1

      \[\leadsto \frac{x}{y - t} \cdot \color{blue}{\left(\frac{1}{z} \cdot 2\right)}\]

    if -6.501064448897589e+94 < x < 3.861992641392967e-62

    1. Initial program 3.7

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z}\]

    2. Simplified2.3

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

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

      \[\leadsto \frac{x}{\color{blue}{1 \cdot \frac{z \cdot \left(y - t\right)}{2}}}\]

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

      \[\leadsto \frac{\color{blue}{1 \cdot x}}{1 \cdot \frac{z \cdot \left(y - t\right)}{2}}\]

    6. Applied times-frac2.3

      \[\leadsto \color{blue}{\frac{1}{1} \cdot \frac{x}{\frac{z \cdot \left(y - t\right)}{2}}}\]

    7. Simplified2.3

      \[\leadsto \color{blue}{1} \cdot \frac{x}{\frac{z \cdot \left(y - t\right)}{2}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -6.5010644488975887 \cdot 10^{94} \lor \neg \left(x \le 3.8619926413929668 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x}{y - t} \cdot \left(\frac{1}{z} \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \frac{x}{\frac{z \cdot \left(y - t\right)}{2}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020078 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.Projection:infinitePerspective from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (if (< (/ (* x 2) (- (* y z) (* t z))) -2.559141628295061e-13) (* (/ x (* (- y t) z)) 2) (if (< (/ (* x 2) (- (* y z) (* t z))) 1.0450278273301259e-269) (/ (* (/ x z) 2) (- y t)) (* (/ x (* (- y t) z)) 2)))

  (/ (* x 2) (- (* y z) (* t z))))