Average Error: 6.7 → 0.6
Time: 7.6s
Precision: binary64
Cost: 3021
\[\frac{x \cdot 2}{y \cdot z - t \cdot z}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot z - z \cdot t \leq -6.473192813480387 \cdot 10^{+190}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 2}{y - t}\\ \mathbf{elif}\;y \cdot z - z \cdot t \leq -1.7542876780262188 \cdot 10^{-189} \lor \neg \left(y \cdot z - z \cdot t \leq 1.494963151258016 \cdot 10^{-125}\right) \land y \cdot z - z \cdot t \leq 2.0363037439895763 \cdot 10^{+189}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot z - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{y - t}}{z}\\ \end{array}\]
\frac{x \cdot 2}{y \cdot z - t \cdot z}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot z - z \cdot t \leq -6.473192813480387 \cdot 10^{+190}:\\
\;\;\;\;\frac{\frac{x}{z} \cdot 2}{y - t}\\

\mathbf{elif}\;y \cdot z - z \cdot t \leq -1.7542876780262188 \cdot 10^{-189} \lor \neg \left(y \cdot z - z \cdot t \leq 1.494963151258016 \cdot 10^{-125}\right) \land y \cdot z - z \cdot t \leq 2.0363037439895763 \cdot 10^{+189}:\\
\;\;\;\;\frac{x \cdot 2}{y \cdot z - z \cdot t}\\

\mathbf{else}:\\
\;\;\;\;\frac{2 \cdot \frac{x}{y - t}}{z}\\

\end{array}
(FPCore (x y z t) :precision binary64 (/ (* x 2.0) (- (* y z) (* t z))))
↓
(FPCore (x y z t)
 :precision binary64
 (if (<= (- (* y z) (* z t)) -6.473192813480387e+190)
   (/ (* (/ x z) 2.0) (- y t))
   (if (or (<= (- (* y z) (* z t)) -1.7542876780262188e-189)
           (and (not (<= (- (* y z) (* z t)) 1.494963151258016e-125))
                (<= (- (* y z) (* z t)) 2.0363037439895763e+189)))
     (/ (* x 2.0) (- (* y z) (* z t)))
     (/ (* 2.0 (/ x (- y t))) z))))
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 tmp;
	if (((y * z) - (z * t)) <= -6.473192813480387e+190) {
		tmp = ((x / z) * 2.0) / (y - t);
	} else if ((((y * z) - (z * t)) <= -1.7542876780262188e-189) || (!(((y * z) - (z * t)) <= 1.494963151258016e-125) && (((y * z) - (z * t)) <= 2.0363037439895763e+189))) {
		tmp = (x * 2.0) / ((y * z) - (z * t));
	} else {
		tmp = (2.0 * (x / (y - t))) / z;
	}
	return tmp;
}

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

Original6.7
Target2.3
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot 2}{y \cdot z - t \cdot z} < -2.559141628295061 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ \mathbf{elif}\;\frac{x \cdot 2}{y \cdot z - t \cdot z} < 1.0450278273301259 \cdot 10^{-269}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 2}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ \end{array}\]

Alternatives

Alternative 1
Error4.1
Cost1218
\[\begin{array}{l} \mathbf{if}\;x \leq -2.650706949139362 \cdot 10^{+282}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y - t}}{z}\\ \mathbf{elif}\;x \leq -8.255599306617066 \cdot 10^{-05}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{y - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 2}{y - t}\\ \end{array}\]
Alternative 2
Error4.1
Cost1218
\[\begin{array}{l} \mathbf{if}\;x \leq -2.3016920786405033 \cdot 10^{+282}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y - t}}{z}\\ \mathbf{elif}\;x \leq -4.376192776233886 \cdot 10^{+21}:\\ \;\;\;\;\frac{x \cdot \frac{2}{y - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 2}{y - t}\\ \end{array}\]
Alternative 3
Error4.1
Cost1218
\[\begin{array}{l} \mathbf{if}\;x \leq -2.1162987229630576 \cdot 10^{+282}:\\ \;\;\;\;x \cdot \frac{2}{z \cdot \left(y - t\right)}\\ \mathbf{elif}\;x \leq -7.872796892558766 \cdot 10^{+21}:\\ \;\;\;\;\frac{x \cdot \frac{2}{y - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 2}{y - t}\\ \end{array}\]
Alternative 4
Error3.0
Cost1036
\[\begin{array}{l} \mathbf{if}\;x \leq -1.8246519112199278 \cdot 10^{+279} \lor \neg \left(x \leq -6.722019486651217 \cdot 10^{+81}\right) \land x \leq 6.525603238109337 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \frac{2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{2}{y - t}}{z}\\ \end{array}\]
Alternative 5
Error5.7
Cost576
\[x \cdot \frac{2}{z \cdot \left(y - t\right)}\]
Alternative 6
Error17.9
Cost776
\[\begin{array}{l} \mathbf{if}\;y \leq -6.844346981378409 \cdot 10^{-09} \lor \neg \left(y \leq 5.546837376841236 \cdot 10^{+101}\right):\\ \;\;\;\;2 \cdot \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \end{array}\]
Alternative 7
Error17.9
Cost776
\[\begin{array}{l} \mathbf{if}\;y \leq -7.817442964121258 \cdot 10^{-06} \lor \neg \left(y \leq 6.807652153826621 \cdot 10^{+101}\right):\\ \;\;\;\;2 \cdot \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \end{array}\]
Alternative 8
Error18.0
Cost776
\[\begin{array}{l} \mathbf{if}\;y \leq -4.107499111857196 \cdot 10^{-09} \lor \neg \left(y \leq 5.4530274300134754 \cdot 10^{+101}\right):\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \end{array}\]
Alternative 9
Error28.9
Cost1090
\[\begin{array}{l} \mathbf{if}\;t \leq -2.2242329676982045 \cdot 10^{+123}:\\ \;\;\;\;0\\ \mathbf{elif}\;t \leq 1.3017903339152738 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]
Alternative 10
Error45.0
Cost64
\[0\]
Alternative 11
Error61.7
Cost64
\[1\]

Error

Derivation

  1. Split input into 3 regimes

  2. if (-.f64 (*.f64 y z) (*.f64 t z)) < -6.47319281348038668e190

    1. Initial program 10.3

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z}\]
    2. Using strategy rm

    3. Applied distribute-rgt-out--_binary64_1571810.3

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

    4. Applied associate-/r*_binary64_157080.8

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

    5. Simplified0.7

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

    6. Simplified0.7

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

    if -6.47319281348038668e190 < (-.f64 (*.f64 y z) (*.f64 t z)) < -1.7542876780262188e-189 or 1.4949631512580159e-125 < (-.f64 (*.f64 y z) (*.f64 t z)) < 2.03630374398957635e189

    1. Initial program 0.3

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

    2. Simplified0.3

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

    if -1.7542876780262188e-189 < (-.f64 (*.f64 y z) (*.f64 t z)) < 1.4949631512580159e-125 or 2.03630374398957635e189 < (-.f64 (*.f64 y z) (*.f64 t z))

    1. Initial program 15.7

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

    2. Simplified11.6

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

    4. Applied *-un-lft-identity_binary64_1576411.6

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

    5. Applied add-cube-cbrt_binary64_1579912.0

      \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(\sqrt[3]{y - t} \cdot \sqrt[3]{y - t}\right) \cdot \sqrt[3]{y - t}}}}{1 \cdot z}\]

    6. Applied *-un-lft-identity_binary64_1576412.0

      \[\leadsto x \cdot \frac{\frac{\color{blue}{1 \cdot 2}}{\left(\sqrt[3]{y - t} \cdot \sqrt[3]{y - t}\right) \cdot \sqrt[3]{y - t}}}{1 \cdot z}\]

    7. Applied times-frac_binary64_1577012.0

      \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{\sqrt[3]{y - t} \cdot \sqrt[3]{y - t}} \cdot \frac{2}{\sqrt[3]{y - t}}}}{1 \cdot z}\]

    8. Applied times-frac_binary64_1577012.0

      \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{\sqrt[3]{y - t} \cdot \sqrt[3]{y - t}}}{1} \cdot \frac{\frac{2}{\sqrt[3]{y - t}}}{z}\right)}\]

    9. Applied associate-*r*_binary64_157043.7

      \[\leadsto \color{blue}{\left(x \cdot \frac{\frac{1}{\sqrt[3]{y - t} \cdot \sqrt[3]{y - t}}}{1}\right) \cdot \frac{\frac{2}{\sqrt[3]{y - t}}}{z}}\]

    10. Simplified3.7

      \[\leadsto \color{blue}{\frac{x}{\sqrt[3]{y - t} \cdot \sqrt[3]{y - t}}} \cdot \frac{\frac{2}{\sqrt[3]{y - t}}}{z}\]
    11. Using strategy rm

    12. Applied associate-*r/_binary64_157061.8

      \[\leadsto \color{blue}{\frac{\frac{x}{\sqrt[3]{y - t} \cdot \sqrt[3]{y - t}} \cdot \frac{2}{\sqrt[3]{y - t}}}{z}}\]

    13. Simplified1.1

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

    14. Simplified1.1

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z - z \cdot t \leq -6.473192813480387 \cdot 10^{+190}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 2}{y - t}\\ \mathbf{elif}\;y \cdot z - z \cdot t \leq -1.7542876780262188 \cdot 10^{-189} \lor \neg \left(y \cdot z - z \cdot t \leq 1.494963151258016 \cdot 10^{-125}\right) \land y \cdot z - z \cdot t \leq 2.0363037439895763 \cdot 10^{+189}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot z - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{y - t}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2021044 
(FPCore (x y z t)
  :name "Linear.Projection:infinitePerspective from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (if (< (/ (* x 2.0) (- (* y z) (* t z))) -2.559141628295061e-13) (* (/ x (* (- y t) z)) 2.0) (if (< (/ (* x 2.0) (- (* y z) (* t z))) 1.0450278273301259e-269) (/ (* (/ x z) 2.0) (- y t)) (* (/ x (* (- y t) z)) 2.0)))

  (/ (* x 2.0) (- (* y z) (* t z))))