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

Average Error: 6.1 → 0.4

Time: 16.0s

Precision: binary64

Cost: 1352

Math

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

↓

\[\begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;t_1 \leq 10^{+258}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (<= t_1 (- INFINITY))
     (+ x (* (/ y a) (- t z)))
     (if (<= t_1 1e+258)
       (+ x (/ (* y (- t z)) a))
       (+ x (/ (- t z) (/ a y)))))))

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + ((y / a) * (t - z));
	} else if (t_1 <= 1e+258) {
		tmp = x + ((y * (t - z)) / a);
	} else {
		tmp = x + ((t - z) / (a / y));
	}
	return tmp;
}

Java

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

↓

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + ((y / a) * (t - z));
	} else if (t_1 <= 1e+258) {
		tmp = x + ((y * (t - z)) / a);
	} else {
		tmp = x + ((t - z) / (a / y));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + ((y / a) * (t - z))
	elif t_1 <= 1e+258:
		tmp = x + ((y * (t - z)) / a)
	else:
		tmp = x + ((t - z) / (a / y))
	return tmp

Julia

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

↓

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(y / a) * Float64(t - z)));
	elseif (t_1 <= 1e+258)
		tmp = Float64(x + Float64(Float64(y * Float64(t - z)) / a));
	else
		tmp = Float64(x + Float64(Float64(t - z) / Float64(a / y)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z - t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + ((y / a) * (t - z));
	elseif (t_1 <= 1e+258)
		tmp = x + ((y * (t - z)) / a);
	else
		tmp = x + ((t - z) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+258], N[(x + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - z), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	6.1
Target	0.7
Herbie	0.4

\[\begin{array}{l} \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array} \]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 64.0

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

   2. Applied egg-rr 0.2

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

   if -inf.0 < (*.f64 y (-.f64 z t)) < 1.00000000000000006e258

   1. Initial program 0.4

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

   if 1.00000000000000006e258 < (*.f64 y (-.f64 z t))

   1. Initial program 41.0

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

   2. Applied egg-rr 0.3

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

   3. Applied egg-rr 0.2

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

4. Final simplification 0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -\infty:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 10^{+258}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \end{array} \]

Alternatives

Alternative 1
Error	28.7
Cost	1176

\[\begin{array}{l} t_1 := \frac{y \cdot t}{a}\\ \mathbf{if}\;x \leq -1.8954520519956108 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.6921908829357644 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.568883944281374 \cdot 10^{-177}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.232673380960908 \cdot 10^{-254}:\\ \;\;\;\;\frac{y}{\frac{-a}{z}}\\ \mathbf{elif}\;x \leq 4.4514340365244966 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.2385765153333963 \cdot 10^{-11}:\\ \;\;\;\;\frac{y \cdot z}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Error	28.5
Cost	980

\[\begin{array}{l} t_1 := \frac{y \cdot t}{a}\\ \mathbf{if}\;x \leq -1.8954520519956108 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.6921908829357644 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.568883944281374 \cdot 10^{-177}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.232673380960908 \cdot 10^{-254}:\\ \;\;\;\;\frac{y}{\frac{-a}{z}}\\ \mathbf{elif}\;x \leq 1.985376065078264 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Error	16.1
Cost	976

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ t_2 := z \cdot \frac{-y}{a}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+201}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.54561367847326 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.436165999433957 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	16.2
Cost	976

\[\begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ t_2 := z \cdot \frac{-y}{a}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+201}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.54561367847326 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.436165999433957 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	9.0
Cost	712

\[\begin{array}{l} t_1 := x - z \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -3.436165999433957 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.0004215942389499532:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	9.9
Cost	712

\[\begin{array}{l} t_1 := x - z \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -3.436165999433957 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.0004215942389499532:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	28.1
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -1.8954520519956108 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.985376065078264 \cdot 10^{-38}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	29.5
Cost	584

\[\begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+164}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+139}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 9
Error	29.5
Cost	584

\[\begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+164}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+139}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 10
Error	2.3
Cost	576

\[x + \frac{t - z}{\frac{a}{y}} \]

Alternative 11
Error	30.7
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022316 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (- x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

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