Average Error: 1.8 → 2.1
Time: 3.0s
Precision: binary64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -7.715468660463849 \cdot 10^{+149}:\\ \;\;\;\;t + \left(\frac{x}{y} \cdot z - \frac{x}{y} \cdot t\right)\\ \mathbf{elif}\;y \leq 3.528241785312015 \cdot 10^{+35}:\\ \;\;\;\;t + \frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;y \leq -7.715468660463849 \cdot 10^{+149}:\\
\;\;\;\;t + \left(\frac{x}{y} \cdot z - \frac{x}{y} \cdot t\right)\\

\mathbf{elif}\;y \leq 3.528241785312015 \cdot 10^{+35}:\\
\;\;\;\;t + \frac{x \cdot \left(z - t\right)}{y}\\

\mathbf{else}:\\
\;\;\;\;t + x \cdot \frac{z - t}{y}\\

\end{array}
(FPCore (x y z t) :precision binary64 (+ (* (/ x y) (- z t)) t))
↓
(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.715468660463849e+149)
   (+ t (- (* (/ x y) z) (* (/ x y) t)))
   (if (<= y 3.528241785312015e+35)
     (+ t (/ (* x (- z t)) y))
     (+ t (* x (/ (- z t) y))))))
double code(double x, double y, double z, double t) {
	return ((x / y) * (z - t)) + t;
}
↓
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.715468660463849e+149) {
		tmp = t + (((x / y) * z) - ((x / y) * t));
	} else if (y <= 3.528241785312015e+35) {
		tmp = t + ((x * (z - t)) / y);
	} else {
		tmp = t + (x * ((z - t) / y));
	}
	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

Original1.8
Target2.1
Herbie2.1
\[\begin{array}{l} \mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -7.7154686604638493e149

    1. Initial program 1.4

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

    3. Applied sub-neg_binary641.4

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

    4. Applied distribute-rgt-in_binary641.4

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

    5. Simplified1.4

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

    6. Simplified1.4

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

    if -7.7154686604638493e149 < y < 3.52824178531201519e35

    1. Initial program 2.3

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

    3. Applied associate-*l/_binary642.9

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

    if 3.52824178531201519e35 < y

    1. Initial program 1.2

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

    3. Applied div-inv_binary641.2

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

    4. Applied associate-*l*_binary641.0

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

    5. Simplified1.0

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

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.715468660463849 \cdot 10^{+149}:\\ \;\;\;\;t + \left(\frac{x}{y} \cdot z - \frac{x}{y} \cdot t\right)\\ \mathbf{elif}\;y \leq 3.528241785312015 \cdot 10^{+35}:\\ \;\;\;\;t + \frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020253 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

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