Average Error: 7.9 → 5.1
Time: 11.0s
Precision: binary64
\[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -7.349536588218303 \cdot 10^{+171}:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{y}{2}}} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 2.810012605276234 \cdot 10^{+214}:\\ \;\;\;\;\frac{\frac{1}{a}}{\frac{1}{\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{2}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{2} \cdot \frac{x}{a} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array}\]
\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 -7.349536588218303 \cdot 10^{+171}:\\
\;\;\;\;\frac{x}{\frac{a}{\frac{y}{2}}} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\\

\mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 2.810012605276234 \cdot 10^{+214}:\\
\;\;\;\;\frac{\frac{1}{a}}{\frac{1}{\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{2}}}\\

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

\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 (<= (- (* x y) (* (* z 9.0) t)) -7.349536588218303e+171)
   (- (/ x (/ a (/ y 2.0))) (/ (* (* z 9.0) t) (* a 2.0)))
   (if (<= (- (* x y) (* (* z 9.0) t)) 2.810012605276234e+214)
     (/ (/ 1.0 a) (/ 1.0 (/ (- (* x y) (* (* z 9.0) t)) 2.0)))
     (- (* (/ y 2.0) (/ x a)) (/ (* (* z 9.0) t) (* a 2.0))))))
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)) <= -7.349536588218303e+171) {
		tmp = (x / (a / (y / 2.0))) - (((z * 9.0) * t) / (a * 2.0));
	} else if (((x * y) - ((z * 9.0) * t)) <= 2.810012605276234e+214) {
		tmp = (1.0 / a) / (1.0 / (((x * y) - ((z * 9.0) * t)) / 2.0));
	} else {
		tmp = ((y / 2.0) * (x / a)) - (((z * 9.0) * t) / (a * 2.0));
	}
	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

Original7.9
Target5.9
Herbie5.1
\[\begin{array}{l} \mathbf{if}\;a < -2.090464557976709 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a < 2.144030707833976 \cdot 10^{+99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -7.34953658821830306e171

    1. Initial program 23.8

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

    3. Applied div-sub_binary6423.8

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

    5. Applied associate-/l*_binary6413.9

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

    6. Simplified13.8

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

    if -7.34953658821830306e171 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 2.81001260527623391e214

    1. Initial program 1.2

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

    3. Applied clear-num_binary641.5

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

    4. Simplified1.4

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

    6. Applied div-inv_binary641.6

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

    7. Applied associate-/r*_binary641.4

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

    if 2.81001260527623391e214 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

    1. Initial program 29.9

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

    3. Applied div-sub_binary6429.9

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

    5. Applied times-frac_binary6417.5

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

  4. Final simplification5.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -7.349536588218303 \cdot 10^{+171}:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{y}{2}}} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 2.810012605276234 \cdot 10^{+214}:\\ \;\;\;\;\frac{\frac{1}{a}}{\frac{1}{\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{2}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{2} \cdot \frac{x}{a} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array}\]

Reproduce

herbie shell --seed 2020268 
(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)))