Average Error: 3.6 → 1.2
Time: 8.7s
Precision: binary64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)} \leq -\infty:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{\frac{z}{-0.3333333333333333}}\\ \mathbf{elif}\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)} \leq 1.876860962824293 \cdot 10^{+201}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{\frac{1}{z}}{-3}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)} \leq -\infty:\\
\;\;\;\;x + \frac{y - \frac{t}{y}}{\frac{z}{-0.3333333333333333}}\\

\mathbf{elif}\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)} \leq 1.876860962824293 \cdot 10^{+201}:\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\

\mathbf{else}:\\
\;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{\frac{1}{z}}{-3}\\

\end{array}
(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))
↓
(FPCore (x y z t)
 :precision binary64
 (if (<= (+ (- x (/ y (* z 3.0))) (/ t (* y (* z 3.0)))) (- INFINITY))
   (+ x (/ (- y (/ t y)) (/ z -0.3333333333333333)))
   (if (<=
        (+ (- x (/ y (* z 3.0))) (/ t (* y (* z 3.0))))
        1.876860962824293e+201)
     (+ (- x (/ y (* z 3.0))) (/ t (* y (* z 3.0))))
     (+ x (* (- y (/ t y)) (/ (/ 1.0 z) -3.0))))))
double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}
↓
double code(double x, double y, double z, double t) {
	double tmp;
	if (((x - (y / (z * 3.0))) + (t / (y * (z * 3.0)))) <= -((double) INFINITY)) {
		tmp = x + ((y - (t / y)) / (z / -0.3333333333333333));
	} else if (((x - (y / (z * 3.0))) + (t / (y * (z * 3.0)))) <= 1.876860962824293e+201) {
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	} else {
		tmp = x + ((y - (t / y)) * ((1.0 / z) / -3.0));
	}
	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

Original3.6
Target1.7
Herbie1.2
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 3 regimes

  2. if (+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y))) < -inf.0

    1. Initial program 64.0

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]

    2. Simplified0.4

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)}\]
    3. Using strategy rm

    4. Applied clear-num_binary64_195140.4

      \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right)\]
    5. Using strategy rm

    6. Applied associate-*l/_binary64_194580.4

      \[\leadsto x + \color{blue}{\frac{1 \cdot \left(y - \frac{t}{y}\right)}{\frac{z}{-0.3333333333333333}}}\]

    if -inf.0 < (+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y))) < 1.87686096282429308e201

    1. Initial program 0.5

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]

    if 1.87686096282429308e201 < (+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))

    1. Initial program 8.2

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]

    2. Simplified4.3

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)}\]
    3. Using strategy rm

    4. Applied clear-num_binary64_195144.4

      \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right)\]
    5. Using strategy rm

    6. Applied div-inv_binary64_195124.3

      \[\leadsto x + \frac{1}{\color{blue}{z \cdot \frac{1}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right)\]

    7. Applied associate-/r*_binary64_194594.3

      \[\leadsto x + \color{blue}{\frac{\frac{1}{z}}{\frac{1}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right)\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)} \leq -\infty:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{\frac{z}{-0.3333333333333333}}\\ \mathbf{elif}\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)} \leq 1.876860962824293 \cdot 10^{+201}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{\frac{1}{z}}{-3}\\ \end{array}\]

Reproduce

herbie shell --seed 2021043 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))