Average Error: 3.7 → 0.4
Time: 5.7s
Precision: binary64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
↓
\[\begin{array}{l} \mathbf{if}\;t \leq -6.382969987282973 \cdot 10^{+34}:\\ \;\;\;\;\left(x - \frac{1}{z} \cdot \frac{y}{3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;\begin{array}{l} t_1 := x - \frac{\frac{y}{z}}{3}\\ \mathbf{if}\;t \leq 551368187064176000:\\ \;\;\;\;t_1 + \frac{0.3333333333333333}{z} \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{t}{3 \cdot \left(z \cdot y\right)}\\ \end{array}\\ \end{array} \]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;t \leq -6.382969987282973 \cdot 10^{+34}:\\
\;\;\;\;\left(x - \frac{1}{z} \cdot \frac{y}{3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\

\mathbf{else}:\\
\;\;\;\;\begin{array}{l}
t_1 := x - \frac{\frac{y}{z}}{3}\\
\mathbf{if}\;t \leq 551368187064176000:\\
\;\;\;\;t_1 + \frac{0.3333333333333333}{z} \cdot \frac{t}{y}\\

\mathbf{else}:\\
\;\;\;\;t_1 + \frac{t}{3 \cdot \left(z \cdot y\right)}\\


\end{array}\\


\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 (<= t -6.382969987282973e+34)
   (+ (- x (* (/ 1.0 z) (/ y 3.0))) (/ t (* y (* z 3.0))))
   (let* ((t_1 (- x (/ (/ y z) 3.0))))
     (if (<= t 551368187064176000.0)
       (+ t_1 (* (/ 0.3333333333333333 z) (/ t y)))
       (+ t_1 (/ t (* 3.0 (* z y))))))))
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 (t <= -6.382969987282973e+34) {
		tmp = (x - ((1.0 / z) * (y / 3.0))) + (t / (y * (z * 3.0)));
	} else {
		double t_1 = x - ((y / z) / 3.0);
		double tmp_1;
		if (t <= 551368187064176000.0) {
			tmp_1 = t_1 + ((0.3333333333333333 / z) * (t / y));
		} else {
			tmp_1 = t_1 + (t / (3.0 * (z * y)));
		}
		tmp = tmp_1;
	}
	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

Original3.7
Target1.8
Herbie0.4
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y} \]

Derivation

  1. Split input into 3 regimes

  2. if t < -6.3829699872829731e34

    1. Initial program 0.8

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

    2. Applied *-un-lft-identity_binary640.8

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

    3. Applied times-frac_binary640.8

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

    if -6.3829699872829731e34 < t < 551368187064176000

    1. Initial program 5.5

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

    2. Applied associate-/r*_binary645.5

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

    3. Applied *-un-lft-identity_binary645.5

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

    4. Applied times-frac_binary640.2

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

    5. Simplified0.3

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

    if 551368187064176000 < t

    1. Initial program 0.7

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

    2. Applied associate-/r*_binary640.7

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

    3. Taylor expanded in z around 0 0.7

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.382969987282973 \cdot 10^{+34}:\\ \;\;\;\;\left(x - \frac{1}{z} \cdot \frac{y}{3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{elif}\;t \leq 551368187064176000:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{0.3333333333333333}{z} \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{t}{3 \cdot \left(z \cdot y\right)}\\ \end{array} \]

Reproduce

herbie shell --seed 2022081 
(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))))