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

Average Accuracy: 90.3% → 97.2%

Time: 11.2s

Precision: binary64

Cost: 1609

Math

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

↓

\[\begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+193}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \end{array} \]

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)) a)))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+193)))
     (- x (/ y (/ a (- z t))))
     (+ x (/ (* y (- t z)) a)))))

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)) / a;
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+193)) {
		tmp = x - (y / (a / (z - t)));
	} else {
		tmp = x + ((y * (t - z)) / a);
	}
	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)) / a;
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+193)) {
		tmp = x - (y / (a / (z - t)));
	} else {
		tmp = x + ((y * (t - z)) / a);
	}
	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)) / a
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+193):
		tmp = x - (y / (a / (z - t)))
	else:
		tmp = x + ((y * (t - z)) / a)
	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(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+193))
		tmp = Float64(x - Float64(y / Float64(a / Float64(z - t))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(t - z)) / a));
	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)) / a;
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+193)))
		tmp = x - (y / (a / (z - t)));
	else
		tmp = x + ((y * (t - z)) / a);
	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[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+193]], $MachinePrecision]], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Target

Original	90.3%
Target	99.0%
Herbie	97.2%

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -inf.0 or 2.00000000000000013e193 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 41.4%

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

   2. Simplified 85.2%

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

      [Start] 41.4	\[ x - \frac{y \cdot \left(z - t\right)}{a} \]
      associate-/l* [=>] 85.2	\[ x - \color{blue}{\frac{y}{\frac{a}{z - t}}} \]

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) a) < 2.00000000000000013e193

   1. Initial program 99.5%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a} \leq 2 \cdot 10^{+193}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	51.1%
Cost	1376

\[\begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+242}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{+181}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -3.25 \cdot 10^{+118}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-264}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-288}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1800000000:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+151}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 2
Accuracy	51.1%
Cost	1376

\[\begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+241}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{+184}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+121}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-264}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-288}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1860000000:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+147}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 3
Accuracy	51.6%
Cost	1112

\[\begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+243}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{+182}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+118}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1800000000:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 3.05 \cdot 10^{+147}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 4
Accuracy	96.9%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;z - t \leq -2 \cdot 10^{-115} \lor \neg \left(z - t \leq 10^{+123}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 5
Accuracy	53.9%
Cost	850

\[\begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+246} \lor \neg \left(t \leq -1.5 \cdot 10^{+177} \lor \neg \left(t \leq -5 \cdot 10^{+119}\right) \land t \leq 1.25 \cdot 10^{+148}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Accuracy	53.9%
Cost	849

\[\begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+252}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+179}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+121} \lor \neg \left(t \leq 4.4 \cdot 10^{+150}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Accuracy	53.1%
Cost	848

\[\begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+244}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{+183}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{+118}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+151}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 8
Accuracy	72.8%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+146} \lor \neg \left(z \leq 1.72 \cdot 10^{+174}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 9
Accuracy	73.2%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+145} \lor \neg \left(z \leq 9.6 \cdot 10^{+174}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 10
Accuracy	83.4%
Cost	713

\[\begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-58} \lor \neg \left(t \leq 255000000000\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 11
Accuracy	83.9%
Cost	713

\[\begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-58} \lor \neg \left(t \leq 9000000000\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \end{array} \]

Alternative 12
Accuracy	96.2%
Cost	576

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

Alternative 13
Accuracy	51.9%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023129 
(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)))