Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B

Percentage Accurate: 99.8% → 100.0%

Time: 1.5s

Alternatives: 7

Speedup: 1.3×

• 79.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (/ (* 4.0 (- (- x y) (* z 0.5))) z))

C

double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / z;
}

Fortran

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (4.0d0 * ((x - y) - (z * 0.5d0))) / z
end function

Java

public static double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / z;
}

Python

def code(x, y, z):
	return (4.0 * ((x - y) - (z * 0.5))) / z

Julia

function code(x, y, z)
	return Float64(Float64(4.0 * Float64(Float64(x - y) - Float64(z * 0.5))) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (4.0 * ((x - y) - (z * 0.5))) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(4.0 * N[(N[(x - y), $MachinePrecision] - N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

ReFlow

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (/ (* 4.0 (- (- x y) (* z 0.5))) z))

C

double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / z;
}

Fortran

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (4.0d0 * ((x - y) - (z * 0.5d0))) / z
end function

Java

public static double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / z;
}

Python

def code(x, y, z):
	return (4.0 * ((x - y) - (z * 0.5))) / z

Julia

function code(x, y, z)
	return Float64(Float64(4.0 * Float64(Float64(x - y) - Float64(z * 0.5))) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (4.0 * ((x - y) - (z * 0.5))) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(4.0 * N[(N[(x - y), $MachinePrecision] - N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

ReFlow

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

Alternative 1: 100.0% accurate, 1.3× speedup

Math

\[\mathsf{fma}\left(4, \frac{x - y}{z}, -2\right) \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (fma 4.0 (/ (- x y) z) -2.0))

C

double code(double x, double y, double z) {
	return fma(4.0, ((x - y) / z), -2.0);
}

Julia

function code(x, y, z)
	return fma(4.0, Float64(Float64(x - y) / z), -2.0)
end

Wolfram

code[x_, y_, z_] := N[(4.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] + -2.0), $MachinePrecision]

ReFlow

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

Derivation

1. Initial program 99.8%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
2. Step-by-step derivation

3. Applied rewrites 100.0%

   \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, -2\right) \]
4. Add Preprocessing

Alternative 2: 97.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \frac{4 \cdot \left(x - y\right)}{z}\\ t_1 := \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+18}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 5000:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z}, -4, -2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (/ (* 4.0 (- x y)) z))
       (t_1 (/ (* 4.0 (- (- x y) (* z 0.5))) z)))
  (if (<= t_1 -4e+18)
    t_0
    (if (<= t_1 5000.0) (fma (/ y z) -4.0 -2.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.0 * (x - y)) / z;
	double t_1 = (4.0 * ((x - y) - (z * 0.5))) / z;
	double tmp;
	if (t_1 <= -4e+18) {
		tmp = t_0;
	} else if (t_1 <= 5000.0) {
		tmp = fma((y / z), -4.0, -2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.0 * Float64(x - y)) / z)
	t_1 = Float64(Float64(4.0 * Float64(Float64(x - y) - Float64(z * 0.5))) / z)
	tmp = 0.0
	if (t_1 <= -4e+18)
		tmp = t_0;
	elseif (t_1 <= 5000.0)
		tmp = fma(Float64(y / z), -4.0, -2.0);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(4.0 * N[(N[(x - y), $MachinePrecision] - N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+18], t$95$0, If[LessEqual[t$95$1, 5000.0], N[(N[(y / z), $MachinePrecision] * -4.0 + -2.0), $MachinePrecision], t$95$0]]]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET t_0 = (((4) * (x - y)) / z) IN
		LET t_1 = (((4) * ((x - y) - (z * (5e-1)))) / z) IN
			LET tmp_1 = IF (t_1 <= (5000)) THEN (((y / z) * (-4)) + (-2)) ELSE t_0 ENDIF IN
			LET tmp = IF (t_1 <= (-4e18)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (*.f64 z #s(literal 1/2 binary64)))) z) < -4e18 or 5e3 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (*.f64 z #s(literal 1/2 binary64)))) z)

   1. Initial program 99.8%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

   2. Taylor expanded in z around 0

      \[\leadsto \frac{4 \cdot \left(x - y\right)}{z} \]
   3. Step-by-step derivation

   4. Applied rewrites 66.3%

      \[\leadsto \frac{4 \cdot \left(x - y\right)}{z} \]

   if -4e18 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (*.f64 z #s(literal 1/2 binary64)))) z) < 5e3

   1. Initial program 99.8%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

   3. Applied rewrites 100.0%

      \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, -2\right) \]

   4. Taylor expanded in x around 0

      \[\leadsto -4 \cdot \frac{y}{z} - 2 \]
   5. Step-by-step derivation

   6. Applied rewrites 67.7%

      \[\leadsto -4 \cdot \frac{y}{z} - 2 \]
   7. Step-by-step derivation

   8. Applied rewrites 67.7%

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

Alternative 3: 86.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{fma}\left(4, \frac{x}{z}, -2\right)\\ \mathbf{if}\;x \leq -0.003879612161427806:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 474010.7854988907:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z}, -4, -2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (fma 4.0 (/ x z) -2.0)))
  (if (<= x -0.003879612161427806)
    t_0
    (if (<= x 474010.7854988907) (fma (/ y z) -4.0 -2.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma(4.0, (x / z), -2.0);
	double tmp;
	if (x <= -0.003879612161427806) {
		tmp = t_0;
	} else if (x <= 474010.7854988907) {
		tmp = fma((y / z), -4.0, -2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(4.0, Float64(x / z), -2.0)
	tmp = 0.0
	if (x <= -0.003879612161427806)
		tmp = t_0;
	elseif (x <= 474010.7854988907)
		tmp = fma(Float64(y / z), -4.0, -2.0);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(4.0 * N[(x / z), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[x, -0.003879612161427806], t$95$0, If[LessEqual[x, 474010.7854988907], N[(N[(y / z), $MachinePrecision] * -4.0 + -2.0), $MachinePrecision], t$95$0]]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET t_0 = (((4) * (x / z)) + (-2)) IN
		LET tmp_1 = IF (x <= (474010785498890676535665988922119140625e-33)) THEN (((y / z) * (-4)) + (-2)) ELSE t_0 ENDIF IN
		LET tmp = IF (x <= (-387961216142780618287844163205591030418872833251953125e-56)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < -0.0038796121614278062 or 474010.78549889068 < x

   1. Initial program 99.8%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

   3. Applied rewrites 100.0%

      \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, -2\right) \]

   4. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(4, \frac{x}{z}, -2\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 68.3%

      \[\leadsto \mathsf{fma}\left(4, \frac{x}{z}, -2\right) \]

   if -0.0038796121614278062 < x < 474010.78549889068

   1. Initial program 99.8%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

   3. Applied rewrites 100.0%

      \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, -2\right) \]

   4. Taylor expanded in x around 0

      \[\leadsto -4 \cdot \frac{y}{z} - 2 \]
   5. Step-by-step derivation

   6. Applied rewrites 67.7%

      \[\leadsto -4 \cdot \frac{y}{z} - 2 \]
   7. Step-by-step derivation

   8. Applied rewrites 67.7%

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

Alternative 4: 80.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_0 := \frac{4 \cdot x}{z}\\ \mathbf{if}\;x \leq -1.5154749511009043 \cdot 10^{+102}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.3064649686083533 \cdot 10^{+147}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z}, -4, -2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (/ (* 4.0 x) z)))
  (if (<= x -1.5154749511009043e+102)
    t_0
    (if (<= x 1.3064649686083533e+147) (fma (/ y z) -4.0 -2.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.0 * x) / z;
	double tmp;
	if (x <= -1.5154749511009043e+102) {
		tmp = t_0;
	} else if (x <= 1.3064649686083533e+147) {
		tmp = fma((y / z), -4.0, -2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.0 * x) / z)
	tmp = 0.0
	if (x <= -1.5154749511009043e+102)
		tmp = t_0;
	elseif (x <= 1.3064649686083533e+147)
		tmp = fma(Float64(y / z), -4.0, -2.0);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.0 * x), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[x, -1.5154749511009043e+102], t$95$0, If[LessEqual[x, 1.3064649686083533e+147], N[(N[(y / z), $MachinePrecision] * -4.0 + -2.0), $MachinePrecision], t$95$0]]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET t_0 = (((4) * x) / z) IN
		LET tmp_1 = IF (x <= (1306464968608353291917552759654382600582940896221174479734158802198310852262413427002729117057911732841890700755877960701217930113429315076552130560)) THEN (((y / z) * (-4)) + (-2)) ELSE t_0 ENDIF IN
		LET tmp = IF (x <= (-1515474951100904265797726916768202718528404263409534502959203922947084940691542789719649840481777483776)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < -1.5154749511009043e102 or 1.3064649686083533e147 < x

   1. Initial program 99.8%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

   2. Taylor expanded in x around inf

      \[\leadsto \frac{4 \cdot x}{z} \]
   3. Step-by-step derivation

   4. Applied rewrites 35.6%

      \[\leadsto \frac{4 \cdot x}{z} \]

   if -1.5154749511009043e102 < x < 1.3064649686083533e147

   1. Initial program 99.8%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

   3. Applied rewrites 100.0%

      \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, -2\right) \]

   4. Taylor expanded in x around 0

      \[\leadsto -4 \cdot \frac{y}{z} - 2 \]
   5. Step-by-step derivation

   6. Applied rewrites 67.7%

      \[\leadsto -4 \cdot \frac{y}{z} - 2 \]
   7. Step-by-step derivation

   8. Applied rewrites 67.7%

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

Alternative 5: 66.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_0 := \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\\ t_1 := \frac{-4 \cdot y}{z}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{+173}:\\ \;\;\;\;\frac{4 \cdot x}{z}\\ \mathbf{elif}\;t\_0 \leq -5 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq -1:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (/ (* 4.0 (- (- x y) (* z 0.5))) z))
       (t_1 (/ (* -4.0 y) z)))
  (if (<= t_0 -2e+173)
    (/ (* 4.0 x) z)
    (if (<= t_0 -5e+15) t_1 (if (<= t_0 -1.0) -2.0 t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = (4.0 * ((x - y) - (z * 0.5))) / z;
	double t_1 = (-4.0 * y) / z;
	double tmp;
	if (t_0 <= -2e+173) {
		tmp = (4.0 * x) / z;
	} else if (t_0 <= -5e+15) {
		tmp = t_1;
	} else if (t_0 <= -1.0) {
		tmp = -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (4.0d0 * ((x - y) - (z * 0.5d0))) / z
    t_1 = ((-4.0d0) * y) / z
    if (t_0 <= (-2d+173)) then
        tmp = (4.0d0 * x) / z
    else if (t_0 <= (-5d+15)) then
        tmp = t_1
    else if (t_0 <= (-1.0d0)) then
        tmp = -2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (4.0 * ((x - y) - (z * 0.5))) / z;
	double t_1 = (-4.0 * y) / z;
	double tmp;
	if (t_0 <= -2e+173) {
		tmp = (4.0 * x) / z;
	} else if (t_0 <= -5e+15) {
		tmp = t_1;
	} else if (t_0 <= -1.0) {
		tmp = -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.0 * ((x - y) - (z * 0.5))) / z
	t_1 = (-4.0 * y) / z
	tmp = 0
	if t_0 <= -2e+173:
		tmp = (4.0 * x) / z
	elif t_0 <= -5e+15:
		tmp = t_1
	elif t_0 <= -1.0:
		tmp = -2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.0 * Float64(Float64(x - y) - Float64(z * 0.5))) / z)
	t_1 = Float64(Float64(-4.0 * y) / z)
	tmp = 0.0
	if (t_0 <= -2e+173)
		tmp = Float64(Float64(4.0 * x) / z);
	elseif (t_0 <= -5e+15)
		tmp = t_1;
	elseif (t_0 <= -1.0)
		tmp = -2.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.0 * ((x - y) - (z * 0.5))) / z;
	t_1 = (-4.0 * y) / z;
	tmp = 0.0;
	if (t_0 <= -2e+173)
		tmp = (4.0 * x) / z;
	elseif (t_0 <= -5e+15)
		tmp = t_1;
	elseif (t_0 <= -1.0)
		tmp = -2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.0 * N[(N[(x - y), $MachinePrecision] - N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(-4.0 * y), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+173], N[(N[(4.0 * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$0, -5e+15], t$95$1, If[LessEqual[t$95$0, -1.0], -2.0, t$95$1]]]]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET t_0 = (((4) * ((x - y) - (z * (5e-1)))) / z) IN
		LET t_1 = (((-4) * y) / z) IN
			LET tmp_2 = IF (t_0 <= (-1)) THEN (-2) ELSE t_1 ENDIF IN
			LET tmp_1 = IF (t_0 <= (-5e15)) THEN t_1 ELSE tmp_2 ENDIF IN
			LET tmp = IF (t_0 <= (-200000000000000002807837251159941043564923941140258272187660085890042609097300216216368266487131373689224571527556203812385978553726279379745535544168843379433521211366178816)) THEN (((4) * x) / z) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (*.f64 z #s(literal 1/2 binary64)))) z) < -2e173

   1. Initial program 99.8%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

   2. Taylor expanded in x around inf

      \[\leadsto \frac{4 \cdot x}{z} \]
   3. Step-by-step derivation

   4. Applied rewrites 35.6%

      \[\leadsto \frac{4 \cdot x}{z} \]

   if -2e173 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (*.f64 z #s(literal 1/2 binary64)))) z) < -5e15 or -1 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (*.f64 z #s(literal 1/2 binary64)))) z)

   1. Initial program 99.8%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \frac{-4 \cdot y}{z} \]
   3. Step-by-step derivation

   4. Applied rewrites 35.1%

      \[\leadsto \frac{-4 \cdot y}{z} \]

   if -5e15 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (*.f64 z #s(literal 1/2 binary64)))) z) < -1

   1. Initial program 99.8%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

   2. Taylor expanded in z around inf

      \[\leadsto -2 \]
   3. Step-by-step derivation

   4. Applied rewrites 34.5%

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

Alternative 6: 66.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := \frac{-4 \cdot y}{z}\\ t_1 := \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+15}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq -1:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (/ (* -4.0 y) z))
       (t_1 (/ (* 4.0 (- (- x y) (* z 0.5))) z)))
  (if (<= t_1 -5e+15) t_0 (if (<= t_1 -1.0) -2.0 t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (-4.0 * y) / z;
	double t_1 = (4.0 * ((x - y) - (z * 0.5))) / z;
	double tmp;
	if (t_1 <= -5e+15) {
		tmp = t_0;
	} else if (t_1 <= -1.0) {
		tmp = -2.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ((-4.0d0) * y) / z
    t_1 = (4.0d0 * ((x - y) - (z * 0.5d0))) / z
    if (t_1 <= (-5d+15)) then
        tmp = t_0
    else if (t_1 <= (-1.0d0)) then
        tmp = -2.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (-4.0 * y) / z;
	double t_1 = (4.0 * ((x - y) - (z * 0.5))) / z;
	double tmp;
	if (t_1 <= -5e+15) {
		tmp = t_0;
	} else if (t_1 <= -1.0) {
		tmp = -2.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (-4.0 * y) / z
	t_1 = (4.0 * ((x - y) - (z * 0.5))) / z
	tmp = 0
	if t_1 <= -5e+15:
		tmp = t_0
	elif t_1 <= -1.0:
		tmp = -2.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-4.0 * y) / z)
	t_1 = Float64(Float64(4.0 * Float64(Float64(x - y) - Float64(z * 0.5))) / z)
	tmp = 0.0
	if (t_1 <= -5e+15)
		tmp = t_0;
	elseif (t_1 <= -1.0)
		tmp = -2.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (-4.0 * y) / z;
	t_1 = (4.0 * ((x - y) - (z * 0.5))) / z;
	tmp = 0.0;
	if (t_1 <= -5e+15)
		tmp = t_0;
	elseif (t_1 <= -1.0)
		tmp = -2.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-4.0 * y), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(4.0 * N[(N[(x - y), $MachinePrecision] - N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+15], t$95$0, If[LessEqual[t$95$1, -1.0], -2.0, t$95$0]]]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET t_0 = (((-4) * y) / z) IN
		LET t_1 = (((4) * ((x - y) - (z * (5e-1)))) / z) IN
			LET tmp_1 = IF (t_1 <= (-1)) THEN (-2) ELSE t_0 ENDIF IN
			LET tmp = IF (t_1 <= (-5e15)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (*.f64 z #s(literal 1/2 binary64)))) z) < -5e15 or -1 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (*.f64 z #s(literal 1/2 binary64)))) z)

   1. Initial program 99.8%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \frac{-4 \cdot y}{z} \]
   3. Step-by-step derivation

   4. Applied rewrites 35.1%

      \[\leadsto \frac{-4 \cdot y}{z} \]

   if -5e15 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (*.f64 z #s(literal 1/2 binary64)))) z) < -1

   1. Initial program 99.8%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

   2. Taylor expanded in z around inf

      \[\leadsto -2 \]
   3. Step-by-step derivation

   4. Applied rewrites 34.5%

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

Alternative 7: 34.5% accurate, 16.0× speedup

Math

\[-2 \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return -2.0

Julia

function code(x, y, z)
	return -2.0
end

MATLAB

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

Wolfram

code[x_, y_, z_] := -2.0

ReFlow

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

Derivation

1. Initial program 99.8%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

2. Taylor expanded in z around inf

   \[\leadsto -2 \]
3. Step-by-step derivation

4. Applied rewrites 34.5%

   \[\leadsto -2 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"
  :precision binary64
  (/ (* 4.0 (- (- x y) (* z 0.5))) z))