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

Average Error: 6.0 → 1.5

Time: 7.7s

Precision: binary64

Math

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

↓

\[\begin{array}{l} t_1 := x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t_1 \leq 10^{-248}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;t_1 \leq 10^{+306}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y}{a}}{\frac{1}{z - t}}\\ \end{array} \]

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 (- x (/ (* y (- z t)) a))))
   (if (<= t_1 1e-248)
     (+ x (* (/ y a) (- t z)))
     (if (<= t_1 1e+306) t_1 (- x (/ (/ y a) (/ 1.0 (- z t))))))))

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 = x - ((y * (z - t)) / a);
	double tmp;
	if (t_1 <= 1e-248) {
		tmp = x + ((y / a) * (t - z));
	} else if (t_1 <= 1e+306) {
		tmp = t_1;
	} else {
		tmp = x - ((y / a) / (1.0 / (z - t)));
	}
	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 = x - ((y * (z - t)) / a)
    if (t_1 <= 1d-248) then
        tmp = x + ((y / a) * (t - z))
    else if (t_1 <= 1d+306) then
        tmp = t_1
    else
        tmp = x - ((y / a) / (1.0d0 / (z - t)))
    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 = x - ((y * (z - t)) / a);
	double tmp;
	if (t_1 <= 1e-248) {
		tmp = x + ((y / a) * (t - z));
	} else if (t_1 <= 1e+306) {
		tmp = t_1;
	} else {
		tmp = x - ((y / a) / (1.0 / (z - t)));
	}
	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 = x - ((y * (z - t)) / a)
	tmp = 0
	if t_1 <= 1e-248:
		tmp = x + ((y / a) * (t - z))
	elif t_1 <= 1e+306:
		tmp = t_1
	else:
		tmp = x - ((y / a) / (1.0 / (z - t)))
	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(x - Float64(Float64(y * Float64(z - t)) / a))
	tmp = 0.0
	if (t_1 <= 1e-248)
		tmp = Float64(x + Float64(Float64(y / a) * Float64(t - z)));
	elseif (t_1 <= 1e+306)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(y / a) / Float64(1.0 / Float64(z - t))));
	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 = x - ((y * (z - t)) / a);
	tmp = 0.0;
	if (t_1 <= 1e-248)
		tmp = x + ((y / a) * (t - z));
	elseif (t_1 <= 1e+306)
		tmp = t_1;
	else
		tmp = x - ((y / a) / (1.0 / (z - t)));
	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[(x - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e-248], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+306], t$95$1, N[(x - N[(N[(y / a), $MachinePrecision] / N[(1.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	6.0
Target	0.6
Herbie	1.5

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

Derivation

1. Split input into 3 regimes

2. if (-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a)) < 9.9999999999999998e-249

   1. Initial program 6.2

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

   2. Applied egg-rr 2.7

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

   if 9.9999999999999998e-249 < (-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a)) < 1.00000000000000002e306

   1. Initial program 0.2

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

   if 1.00000000000000002e306 < (-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

   1. Initial program 60.3

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

   2. Applied egg-rr 0.3

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

   3. Applied egg-rr 0.5

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

4. Final simplification 1.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{y \cdot \left(z - t\right)}{a} \leq 10^{-248}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;x - \frac{y \cdot \left(z - t\right)}{a} \leq 10^{+306}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y}{a}}{\frac{1}{z - t}}\\ \end{array} \]

Reproduce

herbie shell --seed 2022210 
(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)))