Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 1.1s

Alternatives: 5

Speedup: 1.1×

Specification

Math

\[\left(x + 1\right) \cdot y - x \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (- (* (+ x 1.0) y) x))

C

double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x + 1.0d0) * y) - x
end function

Java

public static double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

Python

def code(x, y):
	return ((x + 1.0) * y) - x

Julia

function code(x, y)
	return Float64(Float64(Float64(x + 1.0) * y) - x)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x + 1.0) * y) - x;
end

Wolfram

code[x_, y_] := N[(N[(N[(x + 1.0), $MachinePrecision] * y), $MachinePrecision] - x), $MachinePrecision]

ReFlow

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\left(x + 1\right) \cdot y - x \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (- (* (+ x 1.0) y) x))

C

double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x + 1.0d0) * y) - x
end function

Java

public static double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

Python

def code(x, y):
	return ((x + 1.0) * y) - x

Julia

function code(x, y)
	return Float64(Float64(Float64(x + 1.0) * y) - x)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x + 1.0) * y) - x;
end

Wolfram

code[x_, y_] := N[(N[(N[(x + 1.0), $MachinePrecision] * y), $MachinePrecision] - x), $MachinePrecision]

ReFlow

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

Alternative 1: 100.0% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

ReFlow

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

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]
2. Step-by-step derivation

3. Applied rewrites 100.0%

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

Alternative 2: 98.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_0 := x \cdot \left(y - 1\right)\\ \mathbf{if}\;x \leq -618.7610523406546:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 246929.50132633775:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* x (- y 1.0))))
  (if (<= x -618.7610523406546)
    t_0
    (if (<= x 246929.50132633775) (- y x) t_0))))

C

double code(double x, double y) {
	double t_0 = x * (y - 1.0);
	double tmp;
	if (x <= -618.7610523406546) {
		tmp = t_0;
	} else if (x <= 246929.50132633775) {
		tmp = y - x;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = x * (y - 1.0d0)
    if (x <= (-618.7610523406546d0)) then
        tmp = t_0
    else if (x <= 246929.50132633775d0) then
        tmp = y - x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x * (y - 1.0);
	double tmp;
	if (x <= -618.7610523406546) {
		tmp = t_0;
	} else if (x <= 246929.50132633775) {
		tmp = y - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * (y - 1.0)
	tmp = 0
	if x <= -618.7610523406546:
		tmp = t_0
	elif x <= 246929.50132633775:
		tmp = y - x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(y - 1.0))
	tmp = 0.0
	if (x <= -618.7610523406546)
		tmp = t_0;
	elseif (x <= 246929.50132633775)
		tmp = Float64(y - x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x * (y - 1.0);
	tmp = 0.0;
	if (x <= -618.7610523406546)
		tmp = t_0;
	elseif (x <= 246929.50132633775)
		tmp = y - x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -618.7610523406546], t$95$0, If[LessEqual[x, 246929.50132633775], N[(y - x), $MachinePrecision], t$95$0]]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET t_0 = (x * (y - (1))) IN
		LET tmp_1 = IF (x <= (2469295013263377477414906024932861328125e-34)) THEN (y - x) ELSE t_0 ENDIF IN
		LET tmp = IF (x <= (-6187610523406546008118311874568462371826171875e-43)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < -618.7610523406546 or 246929.50132633775 < x

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(y - 1\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 63.5%

      \[\leadsto x \cdot \left(y - 1\right) \]

   if -618.7610523406546 < x < 246929.50132633775

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0

      \[\leadsto y - x \]
   3. Step-by-step derivation

   4. Applied rewrites 74.8%

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

Alternative 3: 74.8% accurate, 2.6× speedup

Math

\[y - x \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return y - x

Julia

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

MATLAB

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

Wolfram

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

ReFlow

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

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]

2. Taylor expanded in x around 0

   \[\leadsto y - x \]
3. Step-by-step derivation

4. Applied rewrites 74.8%

   \[\leadsto y - x \]
5. Add Preprocessing

Alternative 4: 62.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -3.712143610141413 \cdot 10^{-15}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 2.394325450771144 \cdot 10^{-33}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= x -3.712143610141413e-15)
  (- x)
  (if (<= x 2.394325450771144e-33) y (- x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.712143610141413e-15) {
		tmp = -x;
	} else if (x <= 2.394325450771144e-33) {
		tmp = y;
	} else {
		tmp = -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 <= (-3.712143610141413d-15)) then
        tmp = -x
    else if (x <= 2.394325450771144d-33) then
        tmp = y
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.712143610141413e-15) {
		tmp = -x;
	} else if (x <= 2.394325450771144e-33) {
		tmp = y;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.712143610141413e-15:
		tmp = -x
	elif x <= 2.394325450771144e-33:
		tmp = y
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.712143610141413e-15)
		tmp = Float64(-x);
	elseif (x <= 2.394325450771144e-33)
		tmp = y;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.712143610141413e-15)
		tmp = -x;
	elseif (x <= 2.394325450771144e-33)
		tmp = y;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.712143610141413e-15], (-x), If[LessEqual[x, 2.394325450771144e-33], y, (-x)]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp_1 = IF (x <= (23943254507711438993143429196243359042823939859644038686053973230752092945912903125516534019734393723410903476178646087646484375e-160)) THEN y ELSE (- x) ENDIF IN
	LET tmp = IF (x <= (-37121436101414133244504551030812255985592254710347948076787361060269176959991455078125e-100)) THEN (- x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < -3.7121436101414133e-15 or 2.3943254507711439e-33 < x

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in y around 0

      \[\leadsto -1 \cdot x \]
   3. Step-by-step derivation

   4. Applied rewrites 39.0%

      \[\leadsto -1 \cdot x \]
   5. Step-by-step derivation

   6. Applied rewrites 39.0%

      \[\leadsto -x \]

   if -3.7121436101414133e-15 < x < 2.3943254507711439e-33

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in y around 0

      \[\leadsto -1 \cdot x \]
   3. Step-by-step derivation

   4. Applied rewrites 39.0%

      \[\leadsto -1 \cdot x \]
   5. Step-by-step derivation

   6. Applied rewrites 39.0%

      \[\leadsto -x \]

   7. Taylor expanded in undef-var around zero

      \[\leadsto -0 \]
   8. Step-by-step derivation

   9. Applied rewrites 2.6%

      \[\leadsto -0 \]

   10. Taylor expanded in x around 0

       \[\leadsto y \]
   11. Step-by-step derivation

   12. Applied rewrites 38.0%

       \[\leadsto y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 38.0% accurate, 9.2× speedup

Math

\[y \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return y

Julia

function code(x, y)
	return y
end

MATLAB

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

Wolfram

code[x_, y_] := y

ReFlow

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

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]

2. Taylor expanded in y around 0

   \[\leadsto -1 \cdot x \]
3. Step-by-step derivation

4. Applied rewrites 39.0%

   \[\leadsto -1 \cdot x \]
5. Step-by-step derivation

6. Applied rewrites 39.0%

   \[\leadsto -x \]

7. Taylor expanded in undef-var around zero

   \[\leadsto -0 \]
8. Step-by-step derivation

9. Applied rewrites 2.6%

   \[\leadsto -0 \]

10. Taylor expanded in x around 0

    \[\leadsto y \]
11. Step-by-step derivation

12. Applied rewrites 38.0%

    \[\leadsto y \]
13. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))