Average Error: 7.6 → 4.4
Time: 28.2s
Precision: binary64
\[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 5.171138758538117 \cdot 10^{+299}\right):\\ \;\;\;\;\left(z \cdot \frac{t}{a}\right) \cdot -4.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y - 9 \cdot \left(z \cdot t\right)}{a}\\ \end{array}\]
\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 5.171138758538117 \cdot 10^{+299}\right):\\
\;\;\;\;\left(z \cdot \frac{t}{a}\right) \cdot -4.5\\

\mathbf{else}:\\
\;\;\;\;0.5 \cdot \frac{x \cdot y - 9 \cdot \left(z \cdot t\right)}{a}\\

\end{array}
(FPCore (x y z t a)
 :precision binary64
 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))
↓
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- (* x y) (* (* z 9.0) t)) (- INFINITY))
         (not (<= (- (* x y) (* (* z 9.0) t)) 5.171138758538117e+299)))
   (* (* z (/ t a)) -4.5)
   (* 0.5 (/ (- (* x y) (* 9.0 (* z t))) a))))
double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}
↓
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((((x * y) - ((z * 9.0) * t)) <= -((double) INFINITY)) || !(((x * y) - ((z * 9.0) * t)) <= 5.171138758538117e+299)) {
		tmp = (z * (t / a)) * -4.5;
	} else {
		tmp = 0.5 * (((x * y) - (9.0 * (z * t))) / a);
	}
	return tmp;
}

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

Original7.6
Target5.7
Herbie4.4
\[\begin{array}{l} \mathbf{if}\;a < -2.090464557976709 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a < 2.144030707833976 \cdot 10^{+99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -inf.0 or 5.1711387585381172e299 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

    1. Initial program 61.7

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity_binary64_1951561.7

      \[\leadsto \frac{\color{blue}{1 \cdot \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)}}{a \cdot 2}\]

    4. Applied times-frac_binary64_1952161.7

      \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{2}}\]

    5. Simplified61.2

      \[\leadsto \frac{1}{a} \cdot \color{blue}{\frac{x \cdot y - \left(t \cdot z\right) \cdot 9}{2}}\]
    6. Using strategy rm

    7. Applied add-sqr-sqrt_binary64_1953761.3

      \[\leadsto \frac{1}{a} \cdot \frac{x \cdot y - \left(t \cdot z\right) \cdot 9}{\color{blue}{\sqrt{2} \cdot \sqrt{2}}}\]

    8. Applied *-un-lft-identity_binary64_1951561.3

      \[\leadsto \frac{1}{a} \cdot \frac{\color{blue}{1 \cdot \left(x \cdot y - \left(t \cdot z\right) \cdot 9\right)}}{\sqrt{2} \cdot \sqrt{2}}\]

    9. Applied times-frac_binary64_1952161.2

      \[\leadsto \frac{1}{a} \cdot \color{blue}{\left(\frac{1}{\sqrt{2}} \cdot \frac{x \cdot y - \left(t \cdot z\right) \cdot 9}{\sqrt{2}}\right)}\]

    10. Simplified61.2

      \[\leadsto \frac{1}{a} \cdot \left(\frac{1}{\sqrt{2}} \cdot \color{blue}{\frac{x \cdot y - 9 \cdot \left(t \cdot z\right)}{\sqrt{2}}}\right)\]

    11. Taylor expanded around 0 61.7

      \[\leadsto \color{blue}{-9 \cdot \frac{t \cdot z}{a \cdot {\left(\sqrt{2}\right)}^{2}}}\]

    12. Simplified32.3

      \[\leadsto \color{blue}{\left(\frac{t}{a} \cdot z\right) \cdot -4.5}\]

    if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 5.1711387585381172e299

    1. Initial program 0.9

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]

    2. Taylor expanded around 0 1.0

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y - 9 \cdot \left(t \cdot z\right)}{a}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification4.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 5.171138758538117 \cdot 10^{+299}\right):\\ \;\;\;\;\left(z \cdot \frac{t}{a}\right) \cdot -4.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y - 9 \cdot \left(z \cdot t\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2021023 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :herbie-target
  (if (< a -2.090464557976709e+86) (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z)))) (if (< a 2.144030707833976e+99) (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0)) (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5)))))

  (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))