Average Error: 7.5 → 5.0
Time: 3.4s
Precision: 64
\[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \le -4.37551561696799226 \cdot 10^{226}:\\ \;\;\;\;\frac{x}{\frac{a \cdot 2}{y}} - \frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \le 2.03134039541453595 \cdot 10^{72}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2} - 4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2} - \frac{z \cdot 9}{\frac{a \cdot 2}{t}}\\ \end{array}\]
\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 \le -4.37551561696799226 \cdot 10^{226}:\\
\;\;\;\;\frac{x}{\frac{a \cdot 2}{y}} - \frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\

\mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \le 2.03134039541453595 \cdot 10^{72}:\\
\;\;\;\;\frac{x \cdot y}{a \cdot 2} - 4.5 \cdot \frac{t \cdot z}{a}\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot y}{a \cdot 2} - \frac{z \cdot 9}{\frac{a \cdot 2}{t}}\\

\end{array}
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 temp;
	if ((((x * y) - ((z * 9.0) * t)) <= -4.375515616967992e+226)) {
		temp = ((x / ((a * 2.0) / y)) - ((z * (9.0 * t)) / (a * 2.0)));
	} else {
		double temp_1;
		if ((((x * y) - ((z * 9.0) * t)) <= 2.031340395414536e+72)) {
			temp_1 = (((x * y) / (a * 2.0)) - (4.5 * ((t * z) / a)));
		} else {
			temp_1 = (((x * y) / (a * 2.0)) - ((z * 9.0) / ((a * 2.0) / t)));
		}
		temp = temp_1;
	}
	return temp;
}

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

Original7.5
Target5.8
Herbie5.0
\[\begin{array}{l} \mathbf{if}\;a \lt -2.090464557976709 \cdot 10^{86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a \lt 2.14403070783397609 \cdot 10^{99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (* x y) (* (* z 9.0) t)) < -4.375515616967992e+226

    1. Initial program 31.7

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

    3. Applied associate-*l*31.6

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

    5. Applied div-sub31.6

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

    7. Applied associate-/l*16.7

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

    if -4.375515616967992e+226 < (- (* x y) (* (* z 9.0) t)) < 2.031340395414536e+72

    1. Initial program 0.9

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

    3. Applied associate-*l*1.0

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

    5. Applied div-sub1.0

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

    6. Taylor expanded around 0 0.9

      \[\leadsto \frac{x \cdot y}{a \cdot 2} - \color{blue}{4.5 \cdot \frac{t \cdot z}{a}}\]

    if 2.031340395414536e+72 < (- (* x y) (* (* z 9.0) t))

    1. Initial program 14.7

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

    3. Applied associate-*l*14.8

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

    5. Applied div-sub14.8

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

    7. Applied associate-*r*14.7

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

    9. Applied associate-/l*10.8

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

  4. Final simplification5.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \le -4.37551561696799226 \cdot 10^{226}:\\ \;\;\;\;\frac{x}{\frac{a \cdot 2}{y}} - \frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \le 2.03134039541453595 \cdot 10^{72}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2} - 4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2} - \frac{z \cdot 9}{\frac{a \cdot 2}{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020058 
(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 t))) (* a 2)) (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5)))))

  (/ (- (* x y) (* (* z 9) t)) (* a 2)))