Linear.Projection:perspective from linear-1.19.1.3, B

Average Error: 15.2 → 0.1

Time: 5.5s

Precision: binary64

Cost: 840

Math

\[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]

↓

\[\begin{array}{l} t_0 := \left(x \cdot 2\right) \cdot \frac{y}{x - y}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+34}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+17}:\\ \;\;\;\;\left(2 \cdot y\right) \cdot \frac{x}{x - y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* (* x 2.0) y) (- x y)))

↓

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (* x 2.0) (/ y (- x y)))))
   (if (<= y -1e+34) t_0 (if (<= y 5e+17) (* (* 2.0 y) (/ x (- x y))) t_0))))

C

double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

↓

double code(double x, double y) {
	double t_0 = (x * 2.0) * (y / (x - y));
	double tmp;
	if (y <= -1e+34) {
		tmp = t_0;
	} else if (y <= 5e+17) {
		tmp = (2.0 * y) * (x / (x - y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * 2.0d0) * y) / (x - y)
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * 2.0d0) * (y / (x - y))
    if (y <= (-1d+34)) then
        tmp = t_0
    else if (y <= 5d+17) then
        tmp = (2.0d0 * y) * (x / (x - y))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

↓

public static double code(double x, double y) {
	double t_0 = (x * 2.0) * (y / (x - y));
	double tmp;
	if (y <= -1e+34) {
		tmp = t_0;
	} else if (y <= 5e+17) {
		tmp = (2.0 * y) * (x / (x - y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	return ((x * 2.0) * y) / (x - y)

↓

def code(x, y):
	t_0 = (x * 2.0) * (y / (x - y))
	tmp = 0
	if y <= -1e+34:
		tmp = t_0
	elif y <= 5e+17:
		tmp = (2.0 * y) * (x / (x - y))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	return Float64(Float64(Float64(x * 2.0) * y) / Float64(x - y))
end

↓

function code(x, y)
	t_0 = Float64(Float64(x * 2.0) * Float64(y / Float64(x - y)))
	tmp = 0.0
	if (y <= -1e+34)
		tmp = t_0;
	elseif (y <= 5e+17)
		tmp = Float64(Float64(2.0 * y) * Float64(x / Float64(x - y)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * 2.0) * y) / (x - y);
end

↓

function tmp_2 = code(x, y)
	t_0 = (x * 2.0) * (y / (x - y));
	tmp = 0.0;
	if (y <= -1e+34)
		tmp = t_0;
	elseif (y <= 5e+17)
		tmp = (2.0 * y) * (x / (x - y));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := N[(N[(N[(x * 2.0), $MachinePrecision] * y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := Block[{t$95$0 = N[(N[(x * 2.0), $MachinePrecision] * N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+34], t$95$0, If[LessEqual[y, 5e+17], N[(N[(2.0 * y), $MachinePrecision] * N[(x / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Target

Original	15.2
Target	0.3
Herbie	0.1

\[\begin{array}{l} \mathbf{if}\;x < -1.7210442634149447 \cdot 10^{+81}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x < 83645045635564430:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if y < -9.99999999999999946e33 or 5e17 < y

   1. Initial program 17.8

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]

   2. Simplified 0.1

      \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]
      Proof

      [Start] 17.8	\[ \frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
      rational.json-simplify-2 [=>] 17.8	\[ \frac{\color{blue}{y \cdot \left(x \cdot 2\right)}}{x - y} \]
      rational.json-simplify-49 [=>] 0.1	\[ \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]

   if -9.99999999999999946e33 < y < 5e17

   1. Initial program 13.0

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]

   2. Simplified 0.1

      \[\leadsto \color{blue}{\left(2 \cdot y\right) \cdot \frac{x}{x - y}} \]
      Proof

      [Start] 13.0	\[ \frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
      rational.json-simplify-2 [=>] 13.0	\[ \frac{\color{blue}{y \cdot \left(x \cdot 2\right)}}{x - y} \]
      rational.json-simplify-43 [=>] 13.0	\[ \frac{\color{blue}{x \cdot \left(2 \cdot y\right)}}{x - y} \]
      rational.json-simplify-49 [=>] 0.1	\[ \color{blue}{\left(2 \cdot y\right) \cdot \frac{x}{x - y}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 0.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+34}:\\ \;\;\;\;\left(x \cdot 2\right) \cdot \frac{y}{x - y}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+17}:\\ \;\;\;\;\left(2 \cdot y\right) \cdot \frac{x}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2\right) \cdot \frac{y}{x - y}\\ \end{array} \]

Alternatives

Alternative 1
Error	4.2
Cost	840

\[\begin{array}{l} t_0 := \left(2 \cdot y\right) \cdot \frac{x}{x - y}\\ \mathbf{if}\;x \leq -6.4 \cdot 10^{-105}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-143}:\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	16.2
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{+20}:\\ \;\;\;\;y + y\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-29}:\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;y + y\\ \end{array} \]

Alternative 3
Error	31.8
Cost	192

\[x \cdot -2 \]

Reproduce

herbie shell --seed 2023074 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (if (< x -1.7210442634149447e+81) (* (/ (* 2.0 x) (- x y)) y) (if (< x 83645045635564430.0) (/ (* x 2.0) (/ (- x y) y)) (* (/ (* 2.0 x) (- x y)) y)))

  (/ (* (* x 2.0) y) (- x y)))