Average Error: 0.1 → 0.1
Time: 7.0s
Precision: binary64
Cost: 576
\[\frac{\left(x + y\right) - z}{t \cdot 2}\]
↓
\[\frac{\left(y + x\right) - z}{t \cdot 2}\]
\frac{\left(x + y\right) - z}{t \cdot 2}
↓
\frac{\left(y + x\right) - z}{t \cdot 2}
(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))
↓
(FPCore (x y z t) :precision binary64 (/ (- (+ y x) z) (* t 2.0)))
double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}
↓
double code(double x, double y, double z, double t) {
	return ((y + x) - z) / (t * 2.0);
}

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

Alternatives

Alternative 1
Error9.7
Cost1090
\[\begin{array}{l} \mathbf{if}\;y \leq -9.969725377039779 \cdot 10^{-34}:\\ \;\;\;\;0.5 \cdot \frac{y + x}{t}\\ \mathbf{elif}\;y \leq 6.660466595584249 \cdot 10^{+47}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array}\]
Alternative 2
Error9.8
Cost1090
\[\begin{array}{l} \mathbf{if}\;y \leq -8.076273135266442 \cdot 10^{-34}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y + x}}\\ \mathbf{elif}\;y \leq 4.603379997977828 \cdot 10^{+47}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array}\]
Alternative 3
Error9.6
Cost776
\[\begin{array}{l} \mathbf{if}\;y \leq -6.767582456960509 \cdot 10^{-06} \lor \neg \left(y \leq 2.2645429233024365 \cdot 10^{+48}\right):\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \end{array}\]
Alternative 4
Error14.1
Cost1041
\[\begin{array}{l} \mathbf{if}\;x \leq -1.4435994313317343 \cdot 10^{+69} \lor \neg \left(x \leq -2.0991720734114232 \cdot 10^{-05} \lor \neg \left(x \leq -5.181320044185506 \cdot 10^{-47}\right) \land x \leq 1.4232674036982547 \cdot 10^{+98}\right):\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array}\]
Alternative 5
Error14.2
Cost1041
\[\begin{array}{l} \mathbf{if}\;x \leq -1.6130218207256159 \cdot 10^{+69} \lor \neg \left(x \leq -2.0991720734114232 \cdot 10^{-05} \lor \neg \left(x \leq -5.181320044185506 \cdot 10^{-47}\right) \land x \leq 1.2405534337742625 \cdot 10^{+99}\right):\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y - z}}\\ \end{array}\]
Alternative 6
Error29.8
Cost2246
\[\begin{array}{l} \mathbf{if}\;y \leq -0.0054705429156708275:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq -4.373394034678171 \cdot 10^{-141}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;y \leq -1.2421280067327076 \cdot 10^{-149}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{elif}\;y \leq -8.048573680854262 \cdot 10^{-178}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;y \leq 2.045059115964639 \cdot 10^{-252}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{elif}\;y \leq 3.9176844654423535 \cdot 10^{+47}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array}\]
Alternative 7
Error30.2
Cost648
\[\begin{array}{l} \mathbf{if}\;z \leq -2.612609035955256 \cdot 10^{+38} \lor \neg \left(z \leq 2.9130137260212836 \cdot 10^{+100}\right):\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \end{array}\]
Alternative 8
Error40.9
Cost320
\[0.5 \cdot \frac{x}{t}\]
Alternative 9
Error60.8
Cost64
\[0\]
Alternative 10
Error61.7
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.1

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

  2. Simplified0.1

    \[\leadsto \color{blue}{\frac{\left(y + x\right) - z}{t \cdot 2}}\]

  3. Final simplification0.1

    \[\leadsto \frac{\left(y + x\right) - z}{t \cdot 2}\]

Reproduce

herbie shell --seed 2021044 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2.0)))