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

Percentage Accurate: 99.7% → 100.0%

Time: 2.4s

Alternatives: 8

Speedup: 1.5×

• 79.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}

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 = 1.0d0 + ((4.0d0 * ((x + (y * 0.75d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $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 =
	(1) + (((4) * ((x + (y * (75e-2))) - z)) / y)
END code

Initial Program: 99.7% accurate, 1.0× speedup

Math

\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}

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 = 1.0d0 + ((4.0d0 * ((x + (y * 0.75d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $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 =
	(1) + (((4) * ((x + (y * (75e-2))) - z)) / y)
END code

Alternative 1: 100.0% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision] * 4.0 + 4.0), $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 =
	(((x - z) / y) * (4)) + (4)
END code

Derivation

1. Initial program 99.7%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]

2. Taylor expanded in y around inf

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

4. Applied rewrites 100.0%

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

6. Applied rewrites 100.0%

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

Alternative 2: 98.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := -4 \cdot \frac{z - x}{y}\\ t_1 := \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\\ \mathbf{if}\;t\_1 \leq -40000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 5:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* -4.0 (/ (- z x) y)))
       (t_1 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))
  (if (<= t_1 -40000000.0)
    t_0
    (if (<= t_1 5.0) (+ 4.0 (* 4.0 (/ x y))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -4.0 * ((z - x) / y);
	double t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	double tmp;
	if (t_1 <= -40000000.0) {
		tmp = t_0;
	} else if (t_1 <= 5.0) {
		tmp = 4.0 + (4.0 * (x / y));
	} 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) * ((z - x) / y)
    t_1 = (4.0d0 * ((x + (y * 0.75d0)) - z)) / y
    if (t_1 <= (-40000000.0d0)) then
        tmp = t_0
    else if (t_1 <= 5.0d0) then
        tmp = 4.0d0 + (4.0d0 * (x / y))
    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 * ((z - x) / y);
	double t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	double tmp;
	if (t_1 <= -40000000.0) {
		tmp = t_0;
	} else if (t_1 <= 5.0) {
		tmp = 4.0 + (4.0 * (x / y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -4.0 * ((z - x) / y)
	t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y
	tmp = 0
	if t_1 <= -40000000.0:
		tmp = t_0
	elif t_1 <= 5.0:
		tmp = 4.0 + (4.0 * (x / y))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-4.0 * Float64(Float64(z - x) / y))
	t_1 = Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y)
	tmp = 0.0
	if (t_1 <= -40000000.0)
		tmp = t_0;
	elseif (t_1 <= 5.0)
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -4.0 * ((z - x) / y);
	t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	tmp = 0.0;
	if (t_1 <= -40000000.0)
		tmp = t_0;
	elseif (t_1 <= 5.0)
		tmp = 4.0 + (4.0 * (x / y));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-4.0 * N[(N[(z - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -40000000.0], t$95$0, If[LessEqual[t$95$1, 5.0], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $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) * ((z - x) / y)) IN
		LET t_1 = (((4) * ((x + (y * (75e-2))) - z)) / y) IN
			LET tmp_1 = IF (t_1 <= (5)) THEN ((4) + ((4) * (x / y))) ELSE t_0 ENDIF IN
			LET tmp = IF (t_1 <= (-4e7)) 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 (*.f64 y #s(literal 3/4 binary64))) z)) y) < -4e7 or 5 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y)

   1. Initial program 99.7%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

   3. Applied rewrites 99.7%

      \[\leadsto \mathsf{fma}\left(z - \mathsf{fma}\left(0.75, y, x\right), \frac{-4}{y}, 1\right) \]

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 67.0%

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

   if -4e7 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y) < 5

   1. Initial program 99.7%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in x around inf

      \[\leadsto 4 + 4 \cdot \frac{x}{y} \]
   6. Step-by-step derivation

   7. Applied rewrites 67.9%

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

Alternative 3: 98.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := -4 \cdot \frac{z - x}{y}\\ t_1 := \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\\ \mathbf{if}\;t\_1 \leq -1000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+15}:\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* -4.0 (/ (- z x) y)))
       (t_1 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))
  (if (<= t_1 -1000000.0)
    t_0
    (if (<= t_1 2e+15) (+ 4.0 (* -4.0 (/ z y))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -4.0 * ((z - x) / y);
	double t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	double tmp;
	if (t_1 <= -1000000.0) {
		tmp = t_0;
	} else if (t_1 <= 2e+15) {
		tmp = 4.0 + (-4.0 * (z / y));
	} 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) * ((z - x) / y)
    t_1 = (4.0d0 * ((x + (y * 0.75d0)) - z)) / y
    if (t_1 <= (-1000000.0d0)) then
        tmp = t_0
    else if (t_1 <= 2d+15) then
        tmp = 4.0d0 + ((-4.0d0) * (z / y))
    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 * ((z - x) / y);
	double t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	double tmp;
	if (t_1 <= -1000000.0) {
		tmp = t_0;
	} else if (t_1 <= 2e+15) {
		tmp = 4.0 + (-4.0 * (z / y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -4.0 * ((z - x) / y)
	t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y
	tmp = 0
	if t_1 <= -1000000.0:
		tmp = t_0
	elif t_1 <= 2e+15:
		tmp = 4.0 + (-4.0 * (z / y))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-4.0 * Float64(Float64(z - x) / y))
	t_1 = Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y)
	tmp = 0.0
	if (t_1 <= -1000000.0)
		tmp = t_0;
	elseif (t_1 <= 2e+15)
		tmp = Float64(4.0 + Float64(-4.0 * Float64(z / y)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -4.0 * ((z - x) / y);
	t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	tmp = 0.0;
	if (t_1 <= -1000000.0)
		tmp = t_0;
	elseif (t_1 <= 2e+15)
		tmp = 4.0 + (-4.0 * (z / y));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-4.0 * N[(N[(z - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -1000000.0], t$95$0, If[LessEqual[t$95$1, 2e+15], N[(4.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $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) * ((z - x) / y)) IN
		LET t_1 = (((4) * ((x + (y * (75e-2))) - z)) / y) IN
			LET tmp_1 = IF (t_1 <= (2e15)) THEN ((4) + ((-4) * (z / y))) ELSE t_0 ENDIF IN
			LET tmp = IF (t_1 <= (-1e6)) 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 (*.f64 y #s(literal 3/4 binary64))) z)) y) < -1e6 or 2e15 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y)

   1. Initial program 99.7%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

   3. Applied rewrites 99.7%

      \[\leadsto \mathsf{fma}\left(z - \mathsf{fma}\left(0.75, y, x\right), \frac{-4}{y}, 1\right) \]

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 67.0%

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

   if -1e6 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y) < 2e15

   1. Initial program 99.7%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 67.7%

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

Alternative 4: 97.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := -4 \cdot \frac{z - x}{y}\\ t_1 := \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\\ \mathbf{if}\;t\_1 \leq -50:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 5:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* -4.0 (/ (- z x) y)))
       (t_1 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))
  (if (<= t_1 -50.0) t_0 (if (<= t_1 5.0) 4.0 t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -4.0 * ((z - x) / y);
	double t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	double tmp;
	if (t_1 <= -50.0) {
		tmp = t_0;
	} else if (t_1 <= 5.0) {
		tmp = 4.0;
	} 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) * ((z - x) / y)
    t_1 = (4.0d0 * ((x + (y * 0.75d0)) - z)) / y
    if (t_1 <= (-50.0d0)) then
        tmp = t_0
    else if (t_1 <= 5.0d0) then
        tmp = 4.0d0
    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 * ((z - x) / y);
	double t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	double tmp;
	if (t_1 <= -50.0) {
		tmp = t_0;
	} else if (t_1 <= 5.0) {
		tmp = 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -4.0 * ((z - x) / y)
	t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y
	tmp = 0
	if t_1 <= -50.0:
		tmp = t_0
	elif t_1 <= 5.0:
		tmp = 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-4.0 * Float64(Float64(z - x) / y))
	t_1 = Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y)
	tmp = 0.0
	if (t_1 <= -50.0)
		tmp = t_0;
	elseif (t_1 <= 5.0)
		tmp = 4.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -4.0 * ((z - x) / y);
	t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	tmp = 0.0;
	if (t_1 <= -50.0)
		tmp = t_0;
	elseif (t_1 <= 5.0)
		tmp = 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-4.0 * N[(N[(z - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -50.0], t$95$0, If[LessEqual[t$95$1, 5.0], 4.0, 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) * ((z - x) / y)) IN
		LET t_1 = (((4) * ((x + (y * (75e-2))) - z)) / y) IN
			LET tmp_1 = IF (t_1 <= (5)) THEN (4) ELSE t_0 ENDIF IN
			LET tmp = IF (t_1 <= (-50)) 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 (*.f64 y #s(literal 3/4 binary64))) z)) y) < -50 or 5 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y)

   1. Initial program 99.7%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

   3. Applied rewrites 99.7%

      \[\leadsto \mathsf{fma}\left(z - \mathsf{fma}\left(0.75, y, x\right), \frac{-4}{y}, 1\right) \]

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 67.0%

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

   if -50 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y) < 5

   1. Initial program 99.7%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]

   2. Taylor expanded in y around inf

      \[\leadsto 4 \]
   3. Step-by-step derivation

   4. Applied rewrites 34.2%

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

Alternative 5: 66.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := 4 \cdot \frac{x}{y}\\ t_1 := \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\\ \mathbf{if}\;t\_1 \leq -50:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+17}:\\ \;\;\;\;4\\ \mathbf{elif}\;t\_1 \leq 10^{+171}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, -4, y\right)}{y}\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* 4.0 (/ x y)))
       (t_1 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))
  (if (<= t_1 -50.0)
    t_0
    (if (<= t_1 5e+17)
      4.0
      (if (<= t_1 1e+171) t_0 (/ (fma z -4.0 y) y))))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / y);
	double t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	double tmp;
	if (t_1 <= -50.0) {
		tmp = t_0;
	} else if (t_1 <= 5e+17) {
		tmp = 4.0;
	} else if (t_1 <= 1e+171) {
		tmp = t_0;
	} else {
		tmp = fma(z, -4.0, y) / y;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(4.0 * Float64(x / y))
	t_1 = Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y)
	tmp = 0.0
	if (t_1 <= -50.0)
		tmp = t_0;
	elseif (t_1 <= 5e+17)
		tmp = 4.0;
	elseif (t_1 <= 1e+171)
		tmp = t_0;
	else
		tmp = Float64(fma(z, -4.0, y) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -50.0], t$95$0, If[LessEqual[t$95$1, 5e+17], 4.0, If[LessEqual[t$95$1, 1e+171], t$95$0, N[(N[(z * -4.0 + y), $MachinePrecision] / y), $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 =
	LET t_0 = ((4) * (x / y)) IN
		LET t_1 = (((4) * ((x + (y * (75e-2))) - z)) / y) IN
			LET tmp_2 = IF (t_1 <= (999999999999999953972206729656870211732987713739100709830741553196290713284945813208338477706166412373726001850053663010587168093173889073910282723323583537144858509574144)) THEN t_0 ELSE (((z * (-4)) + y) / y) ENDIF IN
			LET tmp_1 = IF (t_1 <= (5e17)) THEN (4) ELSE tmp_2 ENDIF IN
			LET tmp = IF (t_1 <= (-50)) THEN t_0 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 (*.f64 y #s(literal 3/4 binary64))) z)) y) < -50 or 5e17 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y) < 9.9999999999999995e170

   1. Initial program 99.7%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

   3. Applied rewrites 99.7%

      \[\leadsto \mathsf{fma}\left(z - \mathsf{fma}\left(0.75, y, x\right), \frac{-4}{y}, 1\right) \]

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 67.0%

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

   8. Applied rewrites 66.9%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 35.7%

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

   if -50 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y) < 5e17

   1. Initial program 99.7%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]

   2. Taylor expanded in y around inf

      \[\leadsto 4 \]
   3. Step-by-step derivation

   4. Applied rewrites 34.2%

      \[\leadsto 4 \]

   if 9.9999999999999995e170 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y)

   1. Initial program 99.7%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

   3. Applied rewrites 99.7%

      \[\leadsto \mathsf{fma}\left(z - \mathsf{fma}\left(0.75, y, x\right), \frac{-4}{y}, 1\right) \]

   4. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(z - x, \frac{-4}{y}, 1\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 71.3%

      \[\leadsto \mathsf{fma}\left(z - x, \frac{-4}{y}, 1\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(z, \frac{-4}{y}, 1\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 40.1%

      \[\leadsto \mathsf{fma}\left(z, \frac{-4}{y}, 1\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 40.1%

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

Alternative 6: 66.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := 4 \cdot \frac{x}{y}\\ t_1 := \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\\ \mathbf{if}\;t\_1 \leq -50:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+17}:\\ \;\;\;\;4\\ \mathbf{elif}\;t\_1 \leq 10^{+171}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{z}{y}\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* 4.0 (/ x y)))
       (t_1 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))
  (if (<= t_1 -50.0)
    t_0
    (if (<= t_1 5e+17)
      4.0
      (if (<= t_1 1e+171) t_0 (* -4.0 (/ z y)))))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / y);
	double t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	double tmp;
	if (t_1 <= -50.0) {
		tmp = t_0;
	} else if (t_1 <= 5e+17) {
		tmp = 4.0;
	} else if (t_1 <= 1e+171) {
		tmp = t_0;
	} else {
		tmp = -4.0 * (z / y);
	}
	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)
    t_1 = (4.0d0 * ((x + (y * 0.75d0)) - z)) / y
    if (t_1 <= (-50.0d0)) then
        tmp = t_0
    else if (t_1 <= 5d+17) then
        tmp = 4.0d0
    else if (t_1 <= 1d+171) then
        tmp = t_0
    else
        tmp = (-4.0d0) * (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / y);
	double t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	double tmp;
	if (t_1 <= -50.0) {
		tmp = t_0;
	} else if (t_1 <= 5e+17) {
		tmp = 4.0;
	} else if (t_1 <= 1e+171) {
		tmp = t_0;
	} else {
		tmp = -4.0 * (z / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 * (x / y)
	t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y
	tmp = 0
	if t_1 <= -50.0:
		tmp = t_0
	elif t_1 <= 5e+17:
		tmp = 4.0
	elif t_1 <= 1e+171:
		tmp = t_0
	else:
		tmp = -4.0 * (z / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.0 * Float64(x / y))
	t_1 = Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y)
	tmp = 0.0
	if (t_1 <= -50.0)
		tmp = t_0;
	elseif (t_1 <= 5e+17)
		tmp = 4.0;
	elseif (t_1 <= 1e+171)
		tmp = t_0;
	else
		tmp = Float64(-4.0 * Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.0 * (x / y);
	t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	tmp = 0.0;
	if (t_1 <= -50.0)
		tmp = t_0;
	elseif (t_1 <= 5e+17)
		tmp = 4.0;
	elseif (t_1 <= 1e+171)
		tmp = t_0;
	else
		tmp = -4.0 * (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -50.0], t$95$0, If[LessEqual[t$95$1, 5e+17], 4.0, If[LessEqual[t$95$1, 1e+171], t$95$0, N[(-4.0 * N[(z / y), $MachinePrecision]), $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 =
	LET t_0 = ((4) * (x / y)) IN
		LET t_1 = (((4) * ((x + (y * (75e-2))) - z)) / y) IN
			LET tmp_2 = IF (t_1 <= (999999999999999953972206729656870211732987713739100709830741553196290713284945813208338477706166412373726001850053663010587168093173889073910282723323583537144858509574144)) THEN t_0 ELSE ((-4) * (z / y)) ENDIF IN
			LET tmp_1 = IF (t_1 <= (5e17)) THEN (4) ELSE tmp_2 ENDIF IN
			LET tmp = IF (t_1 <= (-50)) THEN t_0 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 (*.f64 y #s(literal 3/4 binary64))) z)) y) < -50 or 5e17 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y) < 9.9999999999999995e170

   1. Initial program 99.7%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

   3. Applied rewrites 99.7%

      \[\leadsto \mathsf{fma}\left(z - \mathsf{fma}\left(0.75, y, x\right), \frac{-4}{y}, 1\right) \]

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 67.0%

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

   8. Applied rewrites 66.9%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 35.7%

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

   if -50 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y) < 5e17

   1. Initial program 99.7%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]

   2. Taylor expanded in y around inf

      \[\leadsto 4 \]
   3. Step-by-step derivation

   4. Applied rewrites 34.2%

      \[\leadsto 4 \]

   if 9.9999999999999995e170 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y)

   1. Initial program 99.7%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

   3. Applied rewrites 99.7%

      \[\leadsto \mathsf{fma}\left(z - \mathsf{fma}\left(0.75, y, x\right), \frac{-4}{y}, 1\right) \]

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 67.0%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 35.5%

      \[\leadsto -4 \cdot \frac{z}{y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 66.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := 4 \cdot \frac{x}{y}\\ t_1 := \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\\ \mathbf{if}\;t\_1 \leq -50:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+17}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* 4.0 (/ x y)))
       (t_1 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))
  (if (<= t_1 -50.0) t_0 (if (<= t_1 5e+17) 4.0 t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / y);
	double t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	double tmp;
	if (t_1 <= -50.0) {
		tmp = t_0;
	} else if (t_1 <= 5e+17) {
		tmp = 4.0;
	} 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 * (x / y)
    t_1 = (4.0d0 * ((x + (y * 0.75d0)) - z)) / y
    if (t_1 <= (-50.0d0)) then
        tmp = t_0
    else if (t_1 <= 5d+17) then
        tmp = 4.0d0
    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 * (x / y);
	double t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	double tmp;
	if (t_1 <= -50.0) {
		tmp = t_0;
	} else if (t_1 <= 5e+17) {
		tmp = 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 * (x / y)
	t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y
	tmp = 0
	if t_1 <= -50.0:
		tmp = t_0
	elif t_1 <= 5e+17:
		tmp = 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.0 * Float64(x / y))
	t_1 = Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y)
	tmp = 0.0
	if (t_1 <= -50.0)
		tmp = t_0;
	elseif (t_1 <= 5e+17)
		tmp = 4.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.0 * (x / y);
	t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	tmp = 0.0;
	if (t_1 <= -50.0)
		tmp = t_0;
	elseif (t_1 <= 5e+17)
		tmp = 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -50.0], t$95$0, If[LessEqual[t$95$1, 5e+17], 4.0, 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) * (x / y)) IN
		LET t_1 = (((4) * ((x + (y * (75e-2))) - z)) / y) IN
			LET tmp_1 = IF (t_1 <= (5e17)) THEN (4) ELSE t_0 ENDIF IN
			LET tmp = IF (t_1 <= (-50)) 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 (*.f64 y #s(literal 3/4 binary64))) z)) y) < -50 or 5e17 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y)

   1. Initial program 99.7%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

   3. Applied rewrites 99.7%

      \[\leadsto \mathsf{fma}\left(z - \mathsf{fma}\left(0.75, y, x\right), \frac{-4}{y}, 1\right) \]

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 67.0%

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

   8. Applied rewrites 66.9%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 35.7%

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

   if -50 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y) < 5e17

   1. Initial program 99.7%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]

   2. Taylor expanded in y around inf

      \[\leadsto 4 \]
   3. Step-by-step derivation

   4. Applied rewrites 34.2%

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

Alternative 8: 34.2% accurate, 18.6× speedup

Math

\[4 \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  4.0)

C

double code(double x, double y, double z) {
	return 4.0;
}

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 = 4.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 4.0;
}

Python

def code(x, y, z):
	return 4.0

Julia

function code(x, y, z)
	return 4.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 4.0;
end

Wolfram

code[x_, y_, z_] := 4.0

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 =
	4
END code

Derivation

1. Initial program 99.7%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]

2. Taylor expanded in y around inf

   \[\leadsto 4 \]
3. Step-by-step derivation

4. Applied rewrites 34.2%

   \[\leadsto 4 \]
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, A"
  :precision binary64
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))