Graphics.Rendering.Chart.Axis.Types:hBufferRect from Chart-1.5.3

Percentage Accurate: 99.9% → 100.0%

Time: 1.8s

Alternatives: 5

Speedup: 1.2×

Specification

Math

\[x + \frac{x - y}{2} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (+ x (/ (- x y) 2.0)))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	x + ((x - y) / (2))
END code

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[x + \frac{x - y}{2} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (+ x (/ (- x y) 2.0)))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	x + ((x - y) / (2))
END code

Alternative 1: 100.0% accurate, 1.1× speedup

Math

\[\mathsf{fma}\left(1.5, x, -0.5 \cdot y\right) \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (fma 1.5 x (* -0.5 y)))

C

double code(double x, double y) {
	return fma(1.5, x, (-0.5 * y));
}

Julia

function code(x, y)
	return fma(1.5, x, Float64(-0.5 * y))
end

Wolfram

code[x_, y_] := N[(1.5 * x + N[(-0.5 * y), $MachinePrecision]), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	((15e-1) * x) + ((-5e-1) * y)
END code

Derivation

1. Initial program 99.9%

   \[x + \frac{x - y}{2} \]
2. Step-by-step derivation

3. Applied rewrites 100.0%

   \[\leadsto \mathsf{fma}\left(1.5, x, -0.5 \cdot y\right) \]
4. Add Preprocessing

Alternative 2: 99.9% accurate, 1.2× speedup

Math

\[\mathsf{fma}\left(-0.5, y - x, x\right) \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (fma -0.5 (- y x) x))

C

double code(double x, double y) {
	return fma(-0.5, (y - x), x);
}

Julia

function code(x, y)
	return fma(-0.5, Float64(y - x), x)
end

Wolfram

code[x_, y_] := N[(-0.5 * N[(y - x), $MachinePrecision] + x), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	((-5e-1) * (y - x)) + x
END code

Derivation

1. Initial program 99.9%

   \[x + \frac{x - y}{2} \]
2. Step-by-step derivation

3. Applied rewrites 99.9%

   \[\leadsto \mathsf{fma}\left(-0.5, y - x, x\right) \]
4. Add Preprocessing

Alternative 3: 76.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -1.1623226477154053 \cdot 10^{-26}:\\ \;\;\;\;\mathsf{fma}\left(-0.5, y, x\right)\\ \mathbf{elif}\;y \leq 2.426229654520916 \cdot 10^{+48}:\\ \;\;\;\;1.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.5, y, x\right)\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= y -1.1623226477154053e-26)
  (fma -0.5 y x)
  (if (<= y 2.426229654520916e+48) (* 1.5 x) (fma -0.5 y x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.1623226477154053e-26) {
		tmp = fma(-0.5, y, x);
	} else if (y <= 2.426229654520916e+48) {
		tmp = 1.5 * x;
	} else {
		tmp = fma(-0.5, y, x);
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.1623226477154053e-26)
		tmp = fma(-0.5, y, x);
	elseif (y <= 2.426229654520916e+48)
		tmp = Float64(1.5 * x);
	else
		tmp = fma(-0.5, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.1623226477154053e-26], N[(-0.5 * y + x), $MachinePrecision], If[LessEqual[y, 2.426229654520916e+48], N[(1.5 * x), $MachinePrecision], N[(-0.5 * y + x), $MachinePrecision]]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp_1 = IF (y <= (2426229654520915891643607200729785382101422440448)) THEN ((15e-1) * x) ELSE (((-5e-1) * y) + x) ENDIF IN
	LET tmp = IF (y <= (-11623226477154053309672337016807098596194572553602347814800057447127815991871901957210866385139524936676025390625e-138)) THEN (((-5e-1) * y) + x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -1.1623226477154053e-26 or 2.4262296545209159e48 < y

   1. Initial program 99.9%

      \[x + \frac{x - y}{2} \]
   2. Step-by-step derivation

   3. Applied rewrites 99.9%

      \[\leadsto \mathsf{fma}\left(-0.5, y - x, x\right) \]

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(-0.5, y, x\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 58.6%

      \[\leadsto \mathsf{fma}\left(-0.5, y, x\right) \]

   if -1.1623226477154053e-26 < y < 2.4262296545209159e48

   1. Initial program 99.9%

      \[x + \frac{x - y}{2} \]

   2. Taylor expanded in x around inf

      \[\leadsto \frac{3}{2} \cdot x \]
   3. Step-by-step derivation

   4. Applied rewrites 51.2%

      \[\leadsto 1.5 \cdot x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 74.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -4.155509726251822 \cdot 10^{+46}:\\ \;\;\;\;-0.5 \cdot y\\ \mathbf{elif}\;y \leq 2.426229654520916 \cdot 10^{+48}:\\ \;\;\;\;1.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot y\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= y -4.155509726251822e+46)
  (* -0.5 y)
  (if (<= y 2.426229654520916e+48) (* 1.5 x) (* -0.5 y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.155509726251822e+46) {
		tmp = -0.5 * y;
	} else if (y <= 2.426229654520916e+48) {
		tmp = 1.5 * x;
	} else {
		tmp = -0.5 * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-4.155509726251822d+46)) then
        tmp = (-0.5d0) * y
    else if (y <= 2.426229654520916d+48) then
        tmp = 1.5d0 * x
    else
        tmp = (-0.5d0) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -4.155509726251822e+46) {
		tmp = -0.5 * y;
	} else if (y <= 2.426229654520916e+48) {
		tmp = 1.5 * x;
	} else {
		tmp = -0.5 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.155509726251822e+46:
		tmp = -0.5 * y
	elif y <= 2.426229654520916e+48:
		tmp = 1.5 * x
	else:
		tmp = -0.5 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.155509726251822e+46)
		tmp = Float64(-0.5 * y);
	elseif (y <= 2.426229654520916e+48)
		tmp = Float64(1.5 * x);
	else
		tmp = Float64(-0.5 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.155509726251822e+46)
		tmp = -0.5 * y;
	elseif (y <= 2.426229654520916e+48)
		tmp = 1.5 * x;
	else
		tmp = -0.5 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.155509726251822e+46], N[(-0.5 * y), $MachinePrecision], If[LessEqual[y, 2.426229654520916e+48], N[(1.5 * x), $MachinePrecision], N[(-0.5 * y), $MachinePrecision]]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp_1 = IF (y <= (2426229654520915891643607200729785382101422440448)) THEN ((15e-1) * x) ELSE ((-5e-1) * y) ENDIF IN
	LET tmp = IF (y <= (-41555097262518219140230899091581622926874509312)) THEN ((-5e-1) * y) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -4.1555097262518219e46 or 2.4262296545209159e48 < y

   1. Initial program 99.9%

      \[x + \frac{x - y}{2} \]
   2. Step-by-step derivation

   3. Applied rewrites 99.9%

      \[\leadsto \mathsf{fma}\left(-0.5, y - x, x\right) \]

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(-0.5, y, x\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 58.6%

      \[\leadsto \mathsf{fma}\left(-0.5, y, x\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto \frac{-1}{2} \cdot y \]
   8. Step-by-step derivation

   9. Applied rewrites 50.1%

      \[\leadsto -0.5 \cdot y \]

   if -4.1555097262518219e46 < y < 2.4262296545209159e48

   1. Initial program 99.9%

      \[x + \frac{x - y}{2} \]

   2. Taylor expanded in x around inf

      \[\leadsto \frac{3}{2} \cdot x \]
   3. Step-by-step derivation

   4. Applied rewrites 51.2%

      \[\leadsto 1.5 \cdot x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 51.2% accurate, 2.5× speedup

Math

\[1.5 \cdot x \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (* 1.5 x))

C

double code(double x, double y) {
	return 1.5 * x;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.5d0 * x
end function

Java

public static double code(double x, double y) {
	return 1.5 * x;
}

Python

def code(x, y):
	return 1.5 * x

Julia

function code(x, y)
	return Float64(1.5 * x)
end

MATLAB

function tmp = code(x, y)
	tmp = 1.5 * x;
end

Wolfram

code[x_, y_] := N[(1.5 * x), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	(15e-1) * x
END code

Derivation

1. Initial program 99.9%

   \[x + \frac{x - y}{2} \]

2. Taylor expanded in x around inf

   \[\leadsto \frac{3}{2} \cdot x \]
3. Step-by-step derivation

4. Applied rewrites 51.2%

   \[\leadsto 1.5 \cdot x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Axis.Types:hBufferRect from Chart-1.5.3"
  :precision binary64
  (+ x (/ (- x y) 2.0)))