Average Error: 6.8 → 0.9
Time: 4.7s
Precision: binary64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -\infty:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -9.953171815688175 \cdot 10^{+90}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq 2.409171427171004 \cdot 10^{-205}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq 2.6526473394478125 \cdot 10^{+269}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -\infty:\\
\;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\

\mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -9.953171815688175 \cdot 10^{+90}:\\
\;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\

\mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq 2.409171427171004 \cdot 10^{-205}:\\
\;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\

\mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq 2.6526473394478125 \cdot 10^{+269}:\\
\;\;\;\;x + \frac{y \cdot \left(z - x\right)}{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)) (- INFINITY))
   (+ x (* (- z x) (/ y t)))
   (if (<= (+ x (/ (* y (- z x)) t)) -9.953171815688175e+90)
     (+ x (/ (* y (- z x)) t))
     (if (<= (+ x (/ (* y (- z x)) t)) 2.409171427171004e-205)
       (+ x (/ y (/ t (- z x))))
       (if (<= (+ x (/ (* y (- z x)) t)) 2.6526473394478125e+269)
         (+ x (/ (* y (- z x)) 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)) <= -((double) INFINITY)) {
		tmp = x + ((z - x) * (y / t));
	} else if ((x + ((y * (z - x)) / t)) <= -9.953171815688175e+90) {
		tmp = x + ((y * (z - x)) / t);
	} else if ((x + ((y * (z - x)) / t)) <= 2.409171427171004e-205) {
		tmp = x + (y / (t / (z - x)));
	} else if ((x + ((y * (z - x)) / t)) <= 2.6526473394478125e+269) {
		tmp = x + ((y * (z - x)) / 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

Original6.8
Target1.8
Herbie0.9
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 3 regimes

  2. if (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < -inf.0 or 2.6526473394478125e269 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

    1. Initial program 45.8

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

    3. Applied add-cube-cbrt_binary64_887146.0

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

    4. Applied times-frac_binary64_88455.3

      \[\leadsto x + \color{blue}{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z - x}{\sqrt[3]{t}}}\]
    5. Using strategy rm

    6. Applied pow1_binary64_88975.3

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

    7. Applied pow1_binary64_88975.3

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

    8. Applied pow-prod-down_binary64_89075.3

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

    9. Simplified1.9

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

    if -inf.0 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < -9.953171815688175e90 or 2.4091714271710038e-205 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < 2.6526473394478125e269

    1. Initial program 0.3

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

    if -9.953171815688175e90 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < 2.4091714271710038e-205

    1. Initial program 2.1

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

    3. Applied associate-/l*_binary64_87861.7

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -\infty:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -9.953171815688175 \cdot 10^{+90}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq 2.409171427171004 \cdot 10^{-205}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq 2.6526473394478125 \cdot 10^{+269}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020292 
(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)))