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

Average Error: 6.0 → 0.5

Time: 16.5s

Precision: binary64

Cost: 1736

Math

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

↓

\[\begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{\frac{t - z}{a}}{\frac{1}{y}}\\ \mathbf{elif}\;t_1 \leq 10^{+285}:\\ \;\;\;\;x - \frac{y \cdot z - y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \left(z - t\right) \cdot \left(y \cdot \frac{1}{a}\right)\\ \end{array} \]

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 (<= t_1 (- INFINITY))
     (+ x (/ (/ (- t z) a) (/ 1.0 y)))
     (if (<= t_1 1e+285)
       (- x (/ (- (* y z) (* y t)) a))
       (- x (* (- z t) (* y (/ 1.0 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)) {
		tmp = x + (((t - z) / a) / (1.0 / y));
	} else if (t_1 <= 1e+285) {
		tmp = x - (((y * z) - (y * t)) / a);
	} else {
		tmp = x - ((z - t) * (y * (1.0 / 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) {
		tmp = x + (((t - z) / a) / (1.0 / y));
	} else if (t_1 <= 1e+285) {
		tmp = x - (((y * z) - (y * t)) / a);
	} else {
		tmp = x - ((z - t) * (y * (1.0 / 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:
		tmp = x + (((t - z) / a) / (1.0 / y))
	elif t_1 <= 1e+285:
		tmp = x - (((y * z) - (y * t)) / a)
	else:
		tmp = x - ((z - t) * (y * (1.0 / 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))
		tmp = Float64(x + Float64(Float64(Float64(t - z) / a) / Float64(1.0 / y)));
	elseif (t_1 <= 1e+285)
		tmp = Float64(x - Float64(Float64(Float64(y * z) - Float64(y * t)) / a));
	else
		tmp = Float64(x - Float64(Float64(z - t) * Float64(y * Float64(1.0 / 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)
		tmp = x + (((t - z) / a) / (1.0 / y));
	elseif (t_1 <= 1e+285)
		tmp = x - (((y * z) - (y * t)) / a);
	else
		tmp = x - ((z - t) * (y * (1.0 / 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[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision] / N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+285], N[(x - N[(N[(N[(y * z), $MachinePrecision] - N[(y * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z - t), $MachinePrecision] * N[(y * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	6.0
Target	0.7
Herbie	0.5

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 64.0

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

   2. Applied egg-rr 0.3

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

   3. Applied egg-rr 0.3

      \[\leadsto x - \color{blue}{\frac{\frac{z - t}{a}}{\frac{1}{y}}} \]

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) a) < 9.9999999999999998e284

   1. Initial program 0.4

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

   2. Applied egg-rr 0.4

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

   if 9.9999999999999998e284 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 50.4

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

   2. Applied egg-rr 2.6

      \[\leadsto x - \color{blue}{\left(z - t\right) \cdot \left(y \cdot \frac{1}{a}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 0.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -\infty:\\ \;\;\;\;x + \frac{\frac{t - z}{a}}{\frac{1}{y}}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \leq 10^{+285}:\\ \;\;\;\;x - \frac{y \cdot z - y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \left(z - t\right) \cdot \left(y \cdot \frac{1}{a}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	15.2
Cost	1768

\[\begin{array}{l} t_1 := x - z \cdot \frac{y}{a}\\ t_2 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;y \leq -8 \cdot 10^{+177}:\\ \;\;\;\;\frac{y}{\frac{a}{t - z}}\\ \mathbf{elif}\;y \leq -2100:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq -1.6825670056781524 \cdot 10^{-31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.2047231834097209 \cdot 10^{-153}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{elif}\;y \leq -9.32571828322306 \cdot 10^{-208}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.881546688603803 \cdot 10^{-294}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.125698437305244 \cdot 10^{-204}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.4465064286752424 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+189}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - z}{\frac{a}{y}}\\ \end{array} \]

Alternative 2
Error	0.5
Cost	1736

\[\begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{\frac{t - z}{a}}{\frac{1}{y}}\\ \mathbf{elif}\;t_1 \leq 10^{+285}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \left(z - t\right) \cdot \left(y \cdot \frac{1}{a}\right)\\ \end{array} \]

Alternative 3
Error	0.4
Cost	1480

\[\begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ t_2 := x + \frac{\frac{t - z}{a}}{\frac{1}{y}}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+236}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	0.6
Cost	1352

\[\begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ t_2 := x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 10^{+120}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	31.2
Cost	1112

\[\begin{array}{l} t_1 := \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;y \leq -8 \cdot 10^{+177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -0.135:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.6825670056781524 \cdot 10^{-31}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq -1.0928223288333191 \cdot 10^{-180}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.383264538104988 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+189}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	19.6
Cost	976

\[\begin{array}{l} t_1 := \frac{y}{\frac{a}{t - z}}\\ \mathbf{if}\;x \leq -6.7 \cdot 10^{-42}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.814322678296673 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.6439344744918075 \cdot 10^{-78}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.2918685449798716 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Error	18.8
Cost	976

\[\begin{array}{l} \mathbf{if}\;x \leq -6.648862388264716 \cdot 10^{-42}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.760596792115033 \cdot 10^{-122}:\\ \;\;\;\;\frac{t - z}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq 3.6439344744918075 \cdot 10^{-78}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.2918685449798716 \cdot 10^{-29}:\\ \;\;\;\;\frac{y}{\frac{a}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	16.4
Cost	976

\[\begin{array}{l} t_1 := x - z \cdot \frac{y}{a}\\ t_2 := \frac{t - z}{\frac{a}{y}}\\ \mathbf{if}\;y \leq -8 \cdot 10^{+177}:\\ \;\;\;\;\frac{y}{\frac{a}{t - z}}\\ \mathbf{elif}\;y \leq -2200:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.6825670056781524 \cdot 10^{-31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+189}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	16.3
Cost	976

\[\begin{array}{l} t_1 := \frac{t - z}{\frac{a}{y}}\\ \mathbf{if}\;y \leq -8 \cdot 10^{+177}:\\ \;\;\;\;\frac{y}{\frac{a}{t - z}}\\ \mathbf{elif}\;y \leq -2200:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq -1.6825670056781524 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+189}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	30.0
Cost	848

\[\begin{array}{l} t_1 := \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;y \leq -8 \cdot 10^{+177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -0.135:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.6825670056781524 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+189}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	30.0
Cost	848

\[\begin{array}{l} t_1 := \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;y \leq -8 \cdot 10^{+177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -0.135:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.6825670056781524 \cdot 10^{-31}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+189}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	27.5
Cost	780

\[\begin{array}{l} \mathbf{if}\;x \leq -1.4893988804110956 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.1870925662703923 \cdot 10^{-227}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;x \leq 9.435992693415405 \cdot 10^{-174}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13
Error	10.0
Cost	712

\[\begin{array}{l} t_1 := x - z \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.9839249830848782 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.3928591157141355 \cdot 10^{+58}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	2.2
Cost	576

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

Alternative 15
Error	30.3
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022295 
(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)))