Graphics.Rendering.Chart.Plot.AreaSpots:renderSpotLegend from Chart-1.5.3

Percentage Accurate: 99.9% → 99.9%

Time: 2.6s

Alternatives: 5

Speedup: 1.1×

Specification

Math

\[x + \frac{\left|y - x\right|}{2} \]

FPCore

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

C

double code(double x, double y) {
	return x + (fabs((y - x)) / 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 + (abs((y - x)) / 2.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(x + N[(N[Abs[N[(y - x), $MachinePrecision]], $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 + ((abs((y - x))) / (2))
END code

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[x + \frac{\left|y - x\right|}{2} \]

FPCore

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

C

double code(double x, double y) {
	return x + (fabs((y - x)) / 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 + (abs((y - x)) / 2.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(x + N[(N[Abs[N[(y - x), $MachinePrecision]], $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 + ((abs((y - x))) / (2))
END code

Alternative 1: 99.9% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Applied rewrites 99.9%

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

Alternative 2: 78.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x + \frac{\left|y - x\right|}{2} \leq 5 \cdot 10^{-194}:\\ \;\;\;\;\mathsf{fma}\left(\left|x\right|, 0.5, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.5, \left|y\right|, x\right)\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= (+ x (/ (fabs (- y x)) 2.0)) 5e-194)
  (fma (fabs x) 0.5 x)
  (fma 0.5 (fabs y) x)))

C

double code(double x, double y) {
	double tmp;
	if ((x + (fabs((y - x)) / 2.0)) <= 5e-194) {
		tmp = fma(fabs(x), 0.5, x);
	} else {
		tmp = fma(0.5, fabs(y), x);
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(x + Float64(abs(Float64(y - x)) / 2.0)) <= 5e-194)
		tmp = fma(abs(x), 0.5, x);
	else
		tmp = fma(0.5, abs(y), x);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[N[(x + N[(N[Abs[N[(y - x), $MachinePrecision]], $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision], 5e-194], N[(N[Abs[x], $MachinePrecision] * 0.5 + x), $MachinePrecision], N[(0.5 * N[Abs[y], $MachinePrecision] + x), $MachinePrecision]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp = IF ((x + ((abs((y - x))) / (2))) <= (500000000000000024025901121938478221147045809140089786880419736238950243745519939537454010864879495441296908907856491643658165580987505294446731832247650320925424270286857547130615491904230130177316749940482583783112397332246112980463360875015550554640174019551764103769427671211535168442701887771577450785234144342878468552851093186158299048532468929990642960399829866861547980369048689070909724364996636934641233277441370338964559834891463775097391839471214040890867380539930309168994426727294921875e-694)) THEN (((abs(x)) * (5e-1)) + x) ELSE (((5e-1) * (abs(y))) + x) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) < 5.0000000000000002e-194

   1. Initial program 99.9%

      \[x + \frac{\left|y - x\right|}{2} \]

   2. Taylor expanded in x around -inf

      \[\leadsto {x}^{2} \cdot \left(\frac{1}{2} \cdot \left|\frac{-1}{x}\right| + \frac{1}{x}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 28.5%

      \[\leadsto {x}^{2} \cdot \mathsf{fma}\left(0.5, \left|\frac{-1}{x}\right|, \frac{1}{x}\right) \]

   6. Applied rewrites 51.2%

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

   if 5.0000000000000002e-194 < (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))

   1. Initial program 99.9%

      \[x + \frac{\left|y - x\right|}{2} \]

   2. Taylor expanded in x around 0

      \[\leadsto x + \frac{\left|y\right|}{2} \]
   3. Step-by-step derivation

   4. Applied rewrites 58.3%

      \[\leadsto x + \frac{\left|y\right|}{2} \]
   5. Step-by-step derivation

   6. Applied rewrites 58.3%

      \[\leadsto \mathsf{fma}\left(0.5, \left|y\right|, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 51.2% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Julia

function code(x, y)
	return fma(abs(x), 0.5, x)
end

Wolfram

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

ReFlow

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

Derivation

1. Initial program 99.9%

   \[x + \frac{\left|y - x\right|}{2} \]

2. Taylor expanded in x around -inf

   \[\leadsto {x}^{2} \cdot \left(\frac{1}{2} \cdot \left|\frac{-1}{x}\right| + \frac{1}{x}\right) \]
3. Step-by-step derivation

4. Applied rewrites 28.5%

   \[\leadsto {x}^{2} \cdot \mathsf{fma}\left(0.5, \left|\frac{-1}{x}\right|, \frac{1}{x}\right) \]

6. Applied rewrites 51.2%

   \[\leadsto \mathsf{fma}\left(\left|x\right|, 0.5, x\right) \]
7. Add Preprocessing

Alternative 4: 30.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x + \frac{\left|y - x\right|}{2} \leq -1 \cdot 10^{-169}:\\ \;\;\;\;-0.5 \cdot \left|x\right|\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left|x\right|\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= (+ x (/ (fabs (- y x)) 2.0)) -1e-169)
  (* -0.5 (fabs x))
  (* 0.5 (fabs x))))

C

double code(double x, double y) {
	double tmp;
	if ((x + (fabs((y - x)) / 2.0)) <= -1e-169) {
		tmp = -0.5 * fabs(x);
	} else {
		tmp = 0.5 * fabs(x);
	}
	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 ((x + (abs((y - x)) / 2.0d0)) <= (-1d-169)) then
        tmp = (-0.5d0) * abs(x)
    else
        tmp = 0.5d0 * abs(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x + (Math.abs((y - x)) / 2.0)) <= -1e-169) {
		tmp = -0.5 * Math.abs(x);
	} else {
		tmp = 0.5 * Math.abs(x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x + (math.fabs((y - x)) / 2.0)) <= -1e-169:
		tmp = -0.5 * math.fabs(x)
	else:
		tmp = 0.5 * math.fabs(x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(x + Float64(abs(Float64(y - x)) / 2.0)) <= -1e-169)
		tmp = Float64(-0.5 * abs(x));
	else
		tmp = Float64(0.5 * abs(x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x + (abs((y - x)) / 2.0)) <= -1e-169)
		tmp = -0.5 * abs(x);
	else
		tmp = 0.5 * abs(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(x + N[(N[Abs[N[(y - x), $MachinePrecision]], $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision], -1e-169], N[(-0.5 * N[Abs[x], $MachinePrecision]), $MachinePrecision], N[(0.5 * N[Abs[x], $MachinePrecision]), $MachinePrecision]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp = IF ((x + ((abs((y - x))) / (2))) <= (-10000000000000000201179579279951889494332706650336297646126334616435798702446775408390300828267543734556479114876743872147869225462564480958602997490296631147190646714427999744304638141648645677568293476605921373886828801707213576973104942065303602800152996738639009092824083236212756882922294542672246320073171719768219062755043188870164156569825065005551127725431170669760491634397165652335013242654640323869852380767042632214725017547607421875e-614)) THEN ((-5e-1) * (abs(x))) ELSE ((5e-1) * (abs(x))) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) < -1e-169

   1. Initial program 99.9%

      \[x + \frac{\left|y - x\right|}{2} \]

   2. Taylor expanded in x around -inf

      \[\leadsto {x}^{2} \cdot \left(\frac{1}{2} \cdot \left|\frac{-1}{x}\right| + \frac{1}{x}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 28.5%

      \[\leadsto {x}^{2} \cdot \mathsf{fma}\left(0.5, \left|\frac{-1}{x}\right|, \frac{1}{x}\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \frac{-1}{2} \cdot \left|x\right| \]
   6. Step-by-step derivation

   7. Applied rewrites 26.4%

      \[\leadsto -0.5 \cdot \left|x\right| \]

   if -1e-169 < (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))

   1. Initial program 99.9%

      \[x + \frac{\left|y - x\right|}{2} \]

   2. Taylor expanded in x around -inf

      \[\leadsto {x}^{2} \cdot \left(\frac{1}{2} \cdot \left|\frac{-1}{x}\right| + \frac{1}{x}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 28.5%

      \[\leadsto {x}^{2} \cdot \mathsf{fma}\left(0.5, \left|\frac{-1}{x}\right|, \frac{1}{x}\right) \]

   6. Applied rewrites 51.2%

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

   7. Taylor expanded in x around 0

      \[\leadsto \frac{1}{2} \cdot \left|x\right| \]
   8. Step-by-step derivation

   9. Applied rewrites 7.1%

      \[\leadsto 0.5 \cdot \left|x\right| \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 26.4% accurate, 2.2× speedup

Math

\[-0.5 \cdot \left|x\right| \]

FPCore

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

C

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

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (-0.5d0) * abs(x)
end function

Java

public static double code(double x, double y) {
	return -0.5 * Math.abs(x);
}

Python

def code(x, y):
	return -0.5 * math.fabs(x)

Julia

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

MATLAB

function tmp = code(x, y)
	tmp = -0.5 * abs(x);
end

Wolfram

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

ReFlow

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

Derivation

1. Initial program 99.9%

   \[x + \frac{\left|y - x\right|}{2} \]

2. Taylor expanded in x around -inf

   \[\leadsto {x}^{2} \cdot \left(\frac{1}{2} \cdot \left|\frac{-1}{x}\right| + \frac{1}{x}\right) \]
3. Step-by-step derivation

4. Applied rewrites 28.5%

   \[\leadsto {x}^{2} \cdot \mathsf{fma}\left(0.5, \left|\frac{-1}{x}\right|, \frac{1}{x}\right) \]

5. Taylor expanded in x around 0

   \[\leadsto \frac{-1}{2} \cdot \left|x\right| \]
6. Step-by-step derivation

7. Applied rewrites 26.4%

   \[\leadsto -0.5 \cdot \left|x\right| \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderSpotLegend from Chart-1.5.3"
  :precision binary64
  (+ x (/ (fabs (- y x)) 2.0)))