Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D

Average Error: 6.3 → 0.9

Time: 9.6s

Precision: binary64

Cost: 1864

Math

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

↓

\[\begin{array}{l} t_1 := x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+285}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ x (/ (* y (- z x)) t)))

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y (- z x)) t))))
   (if (<= t_1 (- INFINITY))
     (+ x (/ y (/ t (- z x))))
     (if (<= t_1 5e+285) t_1 (+ x (* (- z x) (/ y t)))))))

C

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 t_1 = x + ((y * (z - x)) / t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + (y / (t / (z - x)));
	} else if (t_1 <= 5e+285) {
		tmp = t_1;
	} else {
		tmp = x + ((z - x) * (y / t));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	return x + ((y * (z - x)) / t);
}

↓

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y * (z - x)) / t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + (y / (t / (z - x)));
	} else if (t_1 <= 5e+285) {
		tmp = t_1;
	} else {
		tmp = x + ((z - x) * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	return x + ((y * (z - x)) / t)

↓

def code(x, y, z, t):
	t_1 = x + ((y * (z - x)) / t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + (y / (t / (z - x)))
	elif t_1 <= 5e+285:
		tmp = t_1
	else:
		tmp = x + ((z - x) * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(y * Float64(z - x)) / t))
end

↓

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y * Float64(z - x)) / t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - x))));
	elseif (t_1 <= 5e+285)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(z - x) * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + ((y * (z - x)) / t);
end

↓

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y * (z - x)) / t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + (y / (t / (z - x)));
	elseif (t_1 <= 5e+285)
		tmp = t_1;
	else
		tmp = x + ((z - x) * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := N[(x + N[(N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(y / N[(t / N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+285], t$95$1, N[(x + N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	6.3
Target	2.0
Herbie	0.9

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 64.0

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

   2. Simplified 0.2

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

      [Start] 64.0	\[ x + \frac{y \cdot \left(z - x\right)}{t} \]
      associate-/l* [=>] 0.2	\[ x + \color{blue}{\frac{y}{\frac{t}{z - x}}} \]

   if -inf.0 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < 5.00000000000000016e285

   1. Initial program 0.8

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

   if 5.00000000000000016e285 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

   1. Initial program 42.0

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

   2. Simplified 2.6

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

      [Start] 42.0	\[ x + \frac{y \cdot \left(z - x\right)}{t} \]
      associate-*l/ [<=] 2.6	\[ x + \color{blue}{\frac{y}{t} \cdot \left(z - x\right)} \]

3. Recombined 3 regimes into one program.

4. Final simplification 0.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -\infty:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq 5 \cdot 10^{+285}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \end{array} \]

Alternatives

Alternative 1
Error	29.9
Cost	848

\[\begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+56}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-269}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-197}:\\ \;\;\;\;y \cdot \frac{-x}{t}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+55}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 2
Error	29.9
Cost	848

\[\begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-269}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-197}:\\ \;\;\;\;x \cdot \left(-\frac{y}{t}\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 3
Error	15.6
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq 2.1 \cdot 10^{-269} \lor \neg \left(z \leq 1.9 \cdot 10^{-197}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-\frac{y}{t}\right)\\ \end{array} \]

Alternative 4
Error	13.5
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq 2.1 \cdot 10^{-269} \lor \neg \left(z \leq 1.9 \cdot 10^{-197}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-\frac{y}{t}\right)\\ \end{array} \]

Alternative 5
Error	13.5
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq 2.1 \cdot 10^{-269} \lor \neg \left(z \leq 1.9 \cdot 10^{-197}\right):\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-\frac{y}{t}\right)\\ \end{array} \]

Alternative 6
Error	7.9
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-109} \lor \neg \left(z \leq 1.25 \cdot 10^{-142}\right):\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \end{array} \]

Alternative 7
Error	2.8
Cost	708

\[\begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-191}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \end{array} \]

Alternative 8
Error	28.8
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+52} \lor \neg \left(z \leq 9.2 \cdot 10^{+55}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Error	26.2
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.35 \cdot 10^{-178}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10
Error	28.8
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+58}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 3.65 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 11
Error	2.0
Cost	576

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

Alternative 12
Error	31.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022364 
(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)))