Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 1.7s

Alternatives: 9

Speedup: 0.8×

Specification

Math

\[\frac{x + y}{y + 1} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return (x + y) / (y + 1.0)

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(N[(x + y), $MachinePrecision] / N[(y + 1.0), $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 + (1))
END code

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\frac{x + y}{y + 1} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return (x + y) / (y + 1.0)

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(N[(x + y), $MachinePrecision] / N[(y + 1.0), $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 + (1))
END code

Alternative 1: 100.0% accurate, 0.8× speedup

Math

\[\frac{x + y}{0.5 + \left(0.5 + y\right)} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (/ (+ x y) (+ 0.5 (+ 0.5 y))))

C

double code(double x, double y) {
	return (x + y) / (0.5 + (0.5 + y));
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x + y) / (0.5d0 + (0.5d0 + y))
end function

Java

public static double code(double x, double y) {
	return (x + y) / (0.5 + (0.5 + y));
}

Python

def code(x, y):
	return (x + y) / (0.5 + (0.5 + y))

Julia

function code(x, y)
	return Float64(Float64(x + y) / Float64(0.5 + Float64(0.5 + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x + y) / (0.5 + (0.5 + y));
end

Wolfram

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

ReFlow

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

Derivation

1. Initial program 100.0%

   \[\frac{x + y}{y + 1} \]
2. Step-by-step derivation

3. Applied rewrites 100.0%

   \[\leadsto \frac{x + y}{0.5 + \left(0.5 + y\right)} \]
4. Add Preprocessing

Alternative 2: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_0 := \frac{x - 1}{y} - -1\\ \mathbf{if}\;y \leq -6333.314074973118:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 546.1926757848701:\\ \;\;\;\;\frac{x + y}{1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (- (/ (- x 1.0) y) -1.0)))
  (if (<= y -6333.314074973118)
    t_0
    (if (<= y 546.1926757848701) (/ (+ x y) 1.0) t_0))))

C

double code(double x, double y) {
	double t_0 = ((x - 1.0) / y) - -1.0;
	double tmp;
	if (y <= -6333.314074973118) {
		tmp = t_0;
	} else if (y <= 546.1926757848701) {
		tmp = (x + y) / 1.0;
	} 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 - 1.0d0) / y) - (-1.0d0)
    if (y <= (-6333.314074973118d0)) then
        tmp = t_0
    else if (y <= 546.1926757848701d0) then
        tmp = (x + y) / 1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = ((x - 1.0) / y) - -1.0;
	double tmp;
	if (y <= -6333.314074973118) {
		tmp = t_0;
	} else if (y <= 546.1926757848701) {
		tmp = (x + y) / 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = ((x - 1.0) / y) - -1.0
	tmp = 0
	if y <= -6333.314074973118:
		tmp = t_0
	elif y <= 546.1926757848701:
		tmp = (x + y) / 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(x - 1.0) / y) - -1.0)
	tmp = 0.0
	if (y <= -6333.314074973118)
		tmp = t_0;
	elseif (y <= 546.1926757848701)
		tmp = Float64(Float64(x + y) / 1.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = ((x - 1.0) / y) - -1.0;
	tmp = 0.0;
	if (y <= -6333.314074973118)
		tmp = t_0;
	elseif (y <= 546.1926757848701)
		tmp = (x + y) / 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(x - 1.0), $MachinePrecision] / y), $MachinePrecision] - -1.0), $MachinePrecision]}, If[LessEqual[y, -6333.314074973118], t$95$0, If[LessEqual[y, 546.1926757848701], N[(N[(x + y), $MachinePrecision] / 1.0), $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 - (1)) / y) - (-1)) IN
		LET tmp_1 = IF (y <= (54619267578487006176146678626537322998046875e-41)) THEN ((x + y) / (1)) ELSE t_0 ENDIF IN
		LET tmp = IF (y <= (-63333140749731182950199581682682037353515625e-40)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -6333.3140749731183 or 546.19267578487006 < y

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 51.1%

      \[\leadsto \left(1 + \frac{x}{y}\right) - \frac{1}{y} \]
   5. Step-by-step derivation

   6. Applied rewrites 51.1%

      \[\leadsto \frac{x - 1}{y} - -1 \]

   if -6333.3140749731183 < y < 546.19267578487006

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around 0

      \[\leadsto \frac{x + y}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 50.0%

      \[\leadsto \frac{x + y}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 98.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_0 := \frac{x + y}{y + 1}\\ t_1 := \frac{x}{1 + y}\\ \mathbf{if}\;t\_0 \leq -200:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 0.05:\\ \;\;\;\;\frac{x + y}{1}\\ \mathbf{elif}\;t\_0 \leq 2:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (/ (+ x y) (+ y 1.0))) (t_1 (/ x (+ 1.0 y))))
  (if (<= t_0 -200.0)
    t_1
    (if (<= t_0 0.05)
      (/ (+ x y) 1.0)
      (if (<= t_0 2.0) (/ y (+ y 1.0)) t_1)))))

C

double code(double x, double y) {
	double t_0 = (x + y) / (y + 1.0);
	double t_1 = x / (1.0 + y);
	double tmp;
	if (t_0 <= -200.0) {
		tmp = t_1;
	} else if (t_0 <= 0.05) {
		tmp = (x + y) / 1.0;
	} else if (t_0 <= 2.0) {
		tmp = y / (y + 1.0);
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = (x + y) / (y + 1.0d0)
    t_1 = x / (1.0d0 + y)
    if (t_0 <= (-200.0d0)) then
        tmp = t_1
    else if (t_0 <= 0.05d0) then
        tmp = (x + y) / 1.0d0
    else if (t_0 <= 2.0d0) then
        tmp = y / (y + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x + y) / (y + 1.0);
	double t_1 = x / (1.0 + y);
	double tmp;
	if (t_0 <= -200.0) {
		tmp = t_1;
	} else if (t_0 <= 0.05) {
		tmp = (x + y) / 1.0;
	} else if (t_0 <= 2.0) {
		tmp = y / (y + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x + y) / (y + 1.0)
	t_1 = x / (1.0 + y)
	tmp = 0
	if t_0 <= -200.0:
		tmp = t_1
	elif t_0 <= 0.05:
		tmp = (x + y) / 1.0
	elif t_0 <= 2.0:
		tmp = y / (y + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x + y) / Float64(y + 1.0))
	t_1 = Float64(x / Float64(1.0 + y))
	tmp = 0.0
	if (t_0 <= -200.0)
		tmp = t_1;
	elseif (t_0 <= 0.05)
		tmp = Float64(Float64(x + y) / 1.0);
	elseif (t_0 <= 2.0)
		tmp = Float64(y / Float64(y + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x + y) / (y + 1.0);
	t_1 = x / (1.0 + y);
	tmp = 0.0;
	if (t_0 <= -200.0)
		tmp = t_1;
	elseif (t_0 <= 0.05)
		tmp = (x + y) / 1.0;
	elseif (t_0 <= 2.0)
		tmp = y / (y + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(1.0 + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -200.0], t$95$1, If[LessEqual[t$95$0, 0.05], N[(N[(x + y), $MachinePrecision] / 1.0), $MachinePrecision], If[LessEqual[t$95$0, 2.0], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

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) / (y + (1))) IN
		LET t_1 = (x / ((1) + y)) IN
			LET tmp_2 = IF (t_0 <= (2)) THEN (y / (y + (1))) ELSE t_1 ENDIF IN
			LET tmp_1 = IF (t_0 <= (5000000000000000277555756156289135105907917022705078125e-56)) THEN ((x + y) / (1)) ELSE tmp_2 ENDIF IN
			LET tmp = IF (t_0 <= (-200)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x y) (+.f64 y #s(literal 1 binary64))) < -200 or 2 < (/.f64 (+.f64 x y) (+.f64 y #s(literal 1 binary64)))

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in x around inf

      \[\leadsto \frac{x}{1 + y} \]
   3. Step-by-step derivation

   4. Applied rewrites 50.2%

      \[\leadsto \frac{x}{1 + y} \]

   if -200 < (/.f64 (+.f64 x y) (+.f64 y #s(literal 1 binary64))) < 0.050000000000000003

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around 0

      \[\leadsto \frac{x + y}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 50.0%

      \[\leadsto \frac{x + y}{1} \]

   if 0.050000000000000003 < (/.f64 (+.f64 x y) (+.f64 y #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{y}{y + 1} \]
   3. Step-by-step derivation

   4. Applied rewrites 51.3%

      \[\leadsto \frac{y}{y + 1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 97.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := \frac{x}{y} - -1\\ \mathbf{if}\;y \leq -0.02470192540250247:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.227028658029451:\\ \;\;\;\;\frac{x + y}{1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (- (/ x y) -1.0)))
  (if (<= y -0.02470192540250247)
    t_0
    (if (<= y 3.227028658029451) (/ (+ x y) 1.0) t_0))))

C

double code(double x, double y) {
	double t_0 = (x / y) - -1.0;
	double tmp;
	if (y <= -0.02470192540250247) {
		tmp = t_0;
	} else if (y <= 3.227028658029451) {
		tmp = (x + y) / 1.0;
	} 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 (y <= (-0.02470192540250247d0)) then
        tmp = t_0
    else if (y <= 3.227028658029451d0) then
        tmp = (x + y) / 1.0d0
    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 (y <= -0.02470192540250247) {
		tmp = t_0;
	} else if (y <= 3.227028658029451) {
		tmp = (x + y) / 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x / y) - -1.0
	tmp = 0
	if y <= -0.02470192540250247:
		tmp = t_0
	elif y <= 3.227028658029451:
		tmp = (x + y) / 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x / y) - -1.0)
	tmp = 0.0
	if (y <= -0.02470192540250247)
		tmp = t_0;
	elseif (y <= 3.227028658029451)
		tmp = Float64(Float64(x + y) / 1.0);
	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 (y <= -0.02470192540250247)
		tmp = t_0;
	elseif (y <= 3.227028658029451)
		tmp = (x + y) / 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x / y), $MachinePrecision] - -1.0), $MachinePrecision]}, If[LessEqual[y, -0.02470192540250247], t$95$0, If[LessEqual[y, 3.227028658029451], N[(N[(x + y), $MachinePrecision] / 1.0), $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 (y <= (322702865802945115802913278457708656787872314453125e-50)) THEN ((x + y) / (1)) ELSE t_0 ENDIF IN
		LET tmp = IF (y <= (-24701925402502468431809035109836258925497531890869140625e-57)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -0.024701925402502468 or 3.2270286580294512 < y

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 51.1%

      \[\leadsto \left(1 + \frac{x}{y}\right) - \frac{1}{y} \]
   5. Step-by-step derivation

   6. Applied rewrites 51.1%

      \[\leadsto \frac{x - 1}{y} - -1 \]

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 51.1%

      \[\leadsto \frac{x}{y} - -1 \]

   if -0.024701925402502468 < y < 3.2270286580294512

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around 0

      \[\leadsto \frac{x + y}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 50.0%

      \[\leadsto \frac{x + y}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 86.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \frac{x + y}{y + 1}\\ t_1 := \frac{x}{1 + y}\\ \mathbf{if}\;t\_0 \leq 5 \cdot 10^{-134}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (/ (+ x y) (+ y 1.0))) (t_1 (/ x (+ 1.0 y))))
  (if (<= t_0 5e-134) t_1 (if (<= t_0 2.0) (/ y (+ y 1.0)) t_1))))

C

double code(double x, double y) {
	double t_0 = (x + y) / (y + 1.0);
	double t_1 = x / (1.0 + y);
	double tmp;
	if (t_0 <= 5e-134) {
		tmp = t_1;
	} else if (t_0 <= 2.0) {
		tmp = y / (y + 1.0);
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = (x + y) / (y + 1.0d0)
    t_1 = x / (1.0d0 + y)
    if (t_0 <= 5d-134) then
        tmp = t_1
    else if (t_0 <= 2.0d0) then
        tmp = y / (y + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x + y) / (y + 1.0);
	double t_1 = x / (1.0 + y);
	double tmp;
	if (t_0 <= 5e-134) {
		tmp = t_1;
	} else if (t_0 <= 2.0) {
		tmp = y / (y + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x + y) / (y + 1.0)
	t_1 = x / (1.0 + y)
	tmp = 0
	if t_0 <= 5e-134:
		tmp = t_1
	elif t_0 <= 2.0:
		tmp = y / (y + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x + y) / Float64(y + 1.0))
	t_1 = Float64(x / Float64(1.0 + y))
	tmp = 0.0
	if (t_0 <= 5e-134)
		tmp = t_1;
	elseif (t_0 <= 2.0)
		tmp = Float64(y / Float64(y + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x + y) / (y + 1.0);
	t_1 = x / (1.0 + y);
	tmp = 0.0;
	if (t_0 <= 5e-134)
		tmp = t_1;
	elseif (t_0 <= 2.0)
		tmp = y / (y + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(1.0 + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 5e-134], t$95$1, If[LessEqual[t$95$0, 2.0], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

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) / (y + (1))) IN
		LET t_1 = (x / ((1) + y)) IN
			LET tmp_1 = IF (t_0 <= (2)) THEN (y / (y + (1))) ELSE t_1 ENDIF IN
			LET tmp = IF (t_0 <= (5000000000000000320748171325227407602265583029471801419809593512473507099237019991411223221120531020560880949660340328963055617707357760006409658941734521084366182056151828897429570144449678740321014602295052267721788818054326005599506438550205322516652098864567339603526120051278434163878998570228560286230286314809322274765879257074630004353821277618408203125e-494)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (+.f64 y #s(literal 1 binary64))) < 5.0000000000000003e-134 or 2 < (/.f64 (+.f64 x y) (+.f64 y #s(literal 1 binary64)))

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in x around inf

      \[\leadsto \frac{x}{1 + y} \]
   3. Step-by-step derivation

   4. Applied rewrites 50.2%

      \[\leadsto \frac{x}{1 + y} \]

   if 5.0000000000000003e-134 < (/.f64 (+.f64 x y) (+.f64 y #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{y}{y + 1} \]
   3. Step-by-step derivation

   4. Applied rewrites 51.3%

      \[\leadsto \frac{y}{y + 1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 85.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \frac{x + y}{y + 1}\\ t_1 := \frac{x}{1 + y}\\ \mathbf{if}\;t\_0 \leq 0.05:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (/ (+ x y) (+ y 1.0))) (t_1 (/ x (+ 1.0 y))))
  (if (<= t_0 0.05) t_1 (if (<= t_0 2.0) 1.0 t_1))))

C

double code(double x, double y) {
	double t_0 = (x + y) / (y + 1.0);
	double t_1 = x / (1.0 + y);
	double tmp;
	if (t_0 <= 0.05) {
		tmp = t_1;
	} else if (t_0 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = (x + y) / (y + 1.0d0)
    t_1 = x / (1.0d0 + y)
    if (t_0 <= 0.05d0) then
        tmp = t_1
    else if (t_0 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x + y) / (y + 1.0);
	double t_1 = x / (1.0 + y);
	double tmp;
	if (t_0 <= 0.05) {
		tmp = t_1;
	} else if (t_0 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x + y) / (y + 1.0)
	t_1 = x / (1.0 + y)
	tmp = 0
	if t_0 <= 0.05:
		tmp = t_1
	elif t_0 <= 2.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x + y) / Float64(y + 1.0))
	t_1 = Float64(x / Float64(1.0 + y))
	tmp = 0.0
	if (t_0 <= 0.05)
		tmp = t_1;
	elseif (t_0 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x + y) / (y + 1.0);
	t_1 = x / (1.0 + y);
	tmp = 0.0;
	if (t_0 <= 0.05)
		tmp = t_1;
	elseif (t_0 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(1.0 + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 0.05], t$95$1, If[LessEqual[t$95$0, 2.0], 1.0, t$95$1]]]]

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) / (y + (1))) IN
		LET t_1 = (x / ((1) + y)) IN
			LET tmp_1 = IF (t_0 <= (2)) THEN (1) ELSE t_1 ENDIF IN
			LET tmp = IF (t_0 <= (5000000000000000277555756156289135105907917022705078125e-56)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (+.f64 y #s(literal 1 binary64))) < 0.050000000000000003 or 2 < (/.f64 (+.f64 x y) (+.f64 y #s(literal 1 binary64)))

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in x around inf

      \[\leadsto \frac{x}{1 + y} \]
   3. Step-by-step derivation

   4. Applied rewrites 50.2%

      \[\leadsto \frac{x}{1 + y} \]

   if 0.050000000000000003 < (/.f64 (+.f64 x y) (+.f64 y #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 51.1%

      \[\leadsto \left(1 + \frac{x}{y}\right) - \frac{1}{y} \]
   5. Step-by-step derivation

   6. Applied rewrites 51.1%

      \[\leadsto \frac{x - 1}{y} - -1 \]

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 51.1%

      \[\leadsto \frac{x}{y} - -1 \]

   10. Taylor expanded in y around inf

       \[\leadsto 1 \]
   11. Step-by-step derivation

   12. Applied rewrites 39.5%

       \[\leadsto 1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 50.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{x + y}{y + 1} \leq 10^{-13}:\\ \;\;\;\;\frac{y}{1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= (/ (+ x y) (+ y 1.0)) 1e-13) (/ y 1.0) 1.0))

C

double code(double x, double y) {
	double tmp;
	if (((x + y) / (y + 1.0)) <= 1e-13) {
		tmp = y / 1.0;
	} else {
		tmp = 1.0;
	}
	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) :: tmp
    if (((x + y) / (y + 1.0d0)) <= 1d-13) then
        tmp = y / 1.0d0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((x + y) / (y + 1.0)) <= 1e-13) {
		tmp = y / 1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((x + y) / (y + 1.0)) <= 1e-13:
		tmp = y / 1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(x + y) / Float64(y + 1.0)) <= 1e-13)
		tmp = Float64(y / 1.0);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((x + y) / (y + 1.0)) <= 1e-13)
		tmp = y / 1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(x + y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], 1e-13], N[(y / 1.0), $MachinePrecision], 1.0]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp = IF (((x + y) / (y + (1))) <= (10000000000000000303737455634003709136034716842278413651001756079494953155517578125e-95)) THEN (y / (1)) ELSE (1) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (+.f64 y #s(literal 1 binary64))) < 1e-13

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around 0

      \[\leadsto \frac{x + y}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 50.0%

      \[\leadsto \frac{x + y}{1} \]

   5. Taylor expanded in x around 0

      \[\leadsto \frac{y}{1} \]
   6. Step-by-step derivation

   7. Applied rewrites 14.3%

      \[\leadsto \frac{y}{1} \]

   if 1e-13 < (/.f64 (+.f64 x y) (+.f64 y #s(literal 1 binary64)))

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 51.1%

      \[\leadsto \left(1 + \frac{x}{y}\right) - \frac{1}{y} \]
   5. Step-by-step derivation

   6. Applied rewrites 51.1%

      \[\leadsto \frac{x - 1}{y} - -1 \]

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 51.1%

      \[\leadsto \frac{x}{y} - -1 \]

   10. Taylor expanded in y around inf

       \[\leadsto 1 \]
   11. Step-by-step derivation

   12. Applied rewrites 39.5%

       \[\leadsto 1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 39.5% accurate, 10.0× speedup

Math

\[1 \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  1.0)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

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

Wolfram

code[x_, y_] := 1.0

ReFlow

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

Derivation

1. Initial program 100.0%

   \[\frac{x + y}{y + 1} \]

2. Taylor expanded in y around inf

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

4. Applied rewrites 51.1%

   \[\leadsto \left(1 + \frac{x}{y}\right) - \frac{1}{y} \]
5. Step-by-step derivation

6. Applied rewrites 51.1%

   \[\leadsto \frac{x - 1}{y} - -1 \]

7. Taylor expanded in x around inf

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

9. Applied rewrites 51.1%

   \[\leadsto \frac{x}{y} - -1 \]

10. Taylor expanded in y around inf

    \[\leadsto 1 \]
11. Step-by-step derivation

12. Applied rewrites 39.5%

    \[\leadsto 1 \]
13. Add Preprocessing

Reproduce

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