Average Error: 6.5 → 1.2
Time: 5.1s
Precision: binary64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -\infty:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -3.403237423270278 \cdot 10^{-168}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(\frac{x}{-1} - \frac{z}{-1}\right)\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -\infty:\\
\;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\

\mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -3.403237423270278 \cdot 10^{-168}:\\
\;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\

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

\end{array}
(FPCore (x y z t) :precision binary64 (+ x (/ (* y (- z x)) t)))
↓
(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x (/ (* y (- z x)) t)) (- INFINITY))
   (+ x (/ y (/ t (- z x))))
   (if (<= (+ x (/ (* y (- z x)) t)) -3.403237423270278e-168)
     (+ x (/ (* y (- z x)) t))
     (+ x (* (/ y t) (- (/ x -1.0) (/ z -1.0)))))))
double code(double x, double y, double z, double t) {
	return x + ((y * (z - x)) / t);
}
↓
double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + ((y * (z - x)) / t)) <= -((double) INFINITY)) {
		tmp = x + (y / (t / (z - x)));
	} else if ((x + ((y * (z - x)) / t)) <= -3.403237423270278e-168) {
		tmp = x + ((y * (z - x)) / t);
	} else {
		tmp = x + ((y / t) * ((x / -1.0) - (z / -1.0)));
	}
	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

Original6.5
Target2.0
Herbie1.2
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 3 regimes

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

    1. Initial program 64.0

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

    3. Applied associate-/l*_binary64_71840.2

      \[\leadsto x + \color{blue}{\frac{y}{\frac{t}{z - x}}}\]

    if -inf.0 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < -3.4032374232702782e-168

    1. Initial program 0.3

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

    if -3.4032374232702782e-168 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

    1. Initial program 6.2

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

    3. Applied add-cube-cbrt_binary64_72746.7

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

    4. Applied times-frac_binary64_72453.0

      \[\leadsto x + \color{blue}{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z - x}{\sqrt[3]{t}}}\]

    5. Taylor expanded around -inf 6.2

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

    6. Simplified2.0

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -\infty:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -3.403237423270278 \cdot 10^{-168}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(\frac{x}{-1} - \frac{z}{-1}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020354 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

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

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