Average Error: 6.3 → 1.1
Time: 13.0s
Precision: binary64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -3.727600063252794 \cdot 10^{+300}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq 7.99301336581688 \cdot 10^{+277}:\\ \;\;\;\;x + \frac{y \cdot z - x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -3.727600063252794 \cdot 10^{+300}:\\
\;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\

\mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq 7.99301336581688 \cdot 10^{+277}:\\
\;\;\;\;x + \frac{y \cdot z - x \cdot y}{t}\\

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

\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)) -3.727600063252794e+300)
   (+ x (/ y (/ t (- z x))))
   (if (<= (+ x (/ (* y (- z x)) t)) 7.99301336581688e+277)
     (+ x (/ (- (* y z) (* x y)) t))
     (+ x (* (- z x) (/ y t))))))
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)) <= -3.727600063252794e+300) {
		tmp = x + (y / (t / (z - x)));
	} else if ((x + ((y * (z - x)) / t)) <= 7.99301336581688e+277) {
		tmp = x + (((y * z) - (x * y)) / t);
	} else {
		tmp = x + ((z - x) * (y / t));
	}
	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

Original6.3
Target2.1
Herbie1.1
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 3 regimes

  2. if (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < -3.7276000632527938e300

    1. Initial program 55.0

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

    2. Simplified3.3

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

    if -3.7276000632527938e300 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < 7.9930133658168799e277

    1. Initial program 0.9

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

    2. Simplified2.1

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

    3. Taylor expanded around inf 0.9

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

    if 7.9930133658168799e277 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

    1. Initial program 39.5

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

    2. Simplified2.9

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

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -3.727600063252794 \cdot 10^{+300}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq 7.99301336581688 \cdot 10^{+277}:\\ \;\;\;\;x + \frac{y \cdot z - x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2021176 
(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)))