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

Average Error: 6.4 → 0.8

Time: 11.5s

Precision: binary64

Cost: 1352

Math

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

↓

\[\begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+238}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+104}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]

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))))
   (if (<= t_1 -5e+238)
     (- x (/ y (/ a (- z t))))
     (if (<= t_1 5e+104)
       (+ x (/ (* y (- t z)) a))
       (+ x (* (/ y a) (- t z)))))))

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 <= -5e+238) {
		tmp = x - (y / (a / (z - t)));
	} else if (t_1 <= 5e+104) {
		tmp = x + ((y * (t - z)) / a);
	} else {
		tmp = x + ((y / a) * (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x - ((y * (z - t)) / a)
end function

↓

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z - t)
    if (t_1 <= (-5d+238)) then
        tmp = x - (y / (a / (z - t)))
    else if (t_1 <= 5d+104) then
        tmp = x + ((y * (t - z)) / a)
    else
        tmp = x + ((y / a) * (t - z))
    end if
    code = tmp
end function

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 <= -5e+238) {
		tmp = x - (y / (a / (z - t)));
	} else if (t_1 <= 5e+104) {
		tmp = x + ((y * (t - z)) / a);
	} else {
		tmp = x + ((y / a) * (t - z));
	}
	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 <= -5e+238:
		tmp = x - (y / (a / (z - t)))
	elif t_1 <= 5e+104:
		tmp = x + ((y * (t - z)) / a)
	else:
		tmp = x + ((y / a) * (t - z))
	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 <= -5e+238)
		tmp = Float64(x - Float64(y / Float64(a / Float64(z - t))));
	elseif (t_1 <= 5e+104)
		tmp = Float64(x + Float64(Float64(y * Float64(t - z)) / a));
	else
		tmp = Float64(x + Float64(Float64(y / a) * Float64(t - z)));
	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 <= -5e+238)
		tmp = x - (y / (a / (z - t)));
	elseif (t_1 <= 5e+104)
		tmp = x + ((y * (t - z)) / a);
	else
		tmp = x + ((y / a) * (t - z));
	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, -5e+238], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+104], N[(x + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	6.4
Target	0.7
Herbie	0.8

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

Derivation

1. Split input into 3 regimes

2. if (*.f64 y (-.f64 z t)) < -4.99999999999999995e238

   1. Initial program 36.7

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

   2. Applied egg-rr 0.8

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

   3. Applied egg-rr 0.7

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

   if -4.99999999999999995e238 < (*.f64 y (-.f64 z t)) < 4.9999999999999997e104

   1. Initial program 0.4

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

   if 4.9999999999999997e104 < (*.f64 y (-.f64 z t))

   1. Initial program 17.8

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

   2. Applied egg-rr 2.6

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

4. Final simplification 0.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -5 \cdot 10^{+238}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 5 \cdot 10^{+104}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	16.4
Cost	1240

\[\begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ t_2 := \frac{t - z}{\frac{a}{y}}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+162}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.529037133255523 \cdot 10^{-138}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 10^{+29}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+198}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	16.0
Cost	1240

\[\begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ t_2 := y \cdot \frac{t - z}{a}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+162}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+37}:\\ \;\;\;\;\frac{t - z}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 4.529037133255523 \cdot 10^{-138}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 10^{+29}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+191}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	28.5
Cost	912

\[\begin{array}{l} t_1 := \frac{y}{a} \cdot \left(-z\right)\\ \mathbf{if}\;x \leq -1.4907642598393738 \cdot 10^{-101}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.616852343531724 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.704362937307584 \cdot 10^{-171}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;x \leq 7.964073095505046 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Error	5.9
Cost	840

\[\begin{array}{l} t_1 := x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{if}\;y \leq -1.3848615440946353 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.529037133255523 \cdot 10^{-138}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	14.4
Cost	712

\[\begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;x \leq -1.4907642598393738 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.964073095505046 \cdot 10^{-22}:\\ \;\;\;\;\frac{t - z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	12.0
Cost	712

\[\begin{array}{l} t_1 := x - \frac{y \cdot z}{a}\\ \mathbf{if}\;z \leq -56374611294.411865:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.09284142775361 \cdot 10^{-21}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	27.9
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -2.6835423382954547 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.384734278343729 \cdot 10^{-96}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	28.4
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -2.6835423382954547 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.704362937307584 \cdot 10^{-171}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Error	17.8
Cost	580

\[\begin{array}{l} \mathbf{if}\;z \leq -1.0313965022530204 \cdot 10^{+62}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 10
Error	2.5
Cost	576

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

Alternative 11
Error	30.7
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022291 
(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)))