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

Percentage Accurate: 99.9% → 99.9%

Time: 2.5s

Alternatives: 4

Speedup: 1.0×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + ((4.0d0 * ((x + (y * 0.25d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + ((4.0d0 * ((x + (y * 0.25d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + ((4.0d0 * ((x + (y * 0.25d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]

2. Final simplification 100.0%

   \[\leadsto 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]

Alternative 2: 85.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.066 \lor \neg \left(x \leq 2.35 \cdot 10^{+95}\right):\\ \;\;\;\;4 \cdot \frac{x}{y} + 2\\ \mathbf{else}:\\ \;\;\;\;2 + \frac{z}{y} \cdot -4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.066) (not (<= x 2.35e+95)))
   (+ (* 4.0 (/ x y)) 2.0)
   (+ 2.0 (* (/ z y) -4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.066) || !(x <= 2.35e+95)) {
		tmp = (4.0 * (x / y)) + 2.0;
	} else {
		tmp = 2.0 + ((z / y) * -4.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-0.066d0)) .or. (.not. (x <= 2.35d+95))) then
        tmp = (4.0d0 * (x / y)) + 2.0d0
    else
        tmp = 2.0d0 + ((z / y) * (-4.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.066) || !(x <= 2.35e+95)) {
		tmp = (4.0 * (x / y)) + 2.0;
	} else {
		tmp = 2.0 + ((z / y) * -4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.066) or not (x <= 2.35e+95):
		tmp = (4.0 * (x / y)) + 2.0
	else:
		tmp = 2.0 + ((z / y) * -4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.066) || !(x <= 2.35e+95))
		tmp = Float64(Float64(4.0 * Float64(x / y)) + 2.0);
	else
		tmp = Float64(2.0 + Float64(Float64(z / y) * -4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.066) || ~((x <= 2.35e+95)))
		tmp = (4.0 * (x / y)) + 2.0;
	else
		tmp = 2.0 + ((z / y) * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.066], N[Not[LessEqual[x, 2.35e+95]], $MachinePrecision]], N[(N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision], N[(2.0 + N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.066000000000000003 or 2.34999999999999986e95 < x

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

         \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} \]

      2. +-commutative 99.8%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) \]

      3. associate--l+ 99.8%

         \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(y \cdot 0.25 + \left(x - z\right)\right)} \]

      4. distribute-lft-in 99.8%

         \[\leadsto 1 + \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot 0.25\right) + \frac{4}{y} \cdot \left(x - z\right)\right)} \]

      5. associate-+r+ 99.8%

         \[\leadsto \color{blue}{\left(1 + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right) + \frac{4}{y} \cdot \left(x - z\right)} \]

      6. *-commutative 99.8%

         \[\leadsto \left(1 + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right) + \color{blue}{\left(x - z\right) \cdot \frac{4}{y}} \]

      7. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(x - z\right) \cdot \frac{4}{y} + \left(1 + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right)} \]

      8. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right)} \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \color{blue}{\left(y \cdot 0.25\right) \cdot \frac{4}{y}}\right) \]

      10. associate-*l* 99.8%

          \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \color{blue}{y \cdot \left(0.25 \cdot \frac{4}{y}\right)}\right) \]

      11. associate-*r/ 99.8%

          \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + y \cdot \color{blue}{\frac{0.25 \cdot 4}{y}}\right) \]

      12. metadata-eval 99.8%

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

      13. rgt-mult-inverse 99.8%

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

      14. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 88.4%

      \[\leadsto \color{blue}{2 + 4 \cdot \frac{x}{y}} \]
   5. Step-by-step derivation

      1. +-commutative 88.4%

         \[\leadsto \color{blue}{4 \cdot \frac{x}{y} + 2} \]

   6. Simplified 88.4%

      \[\leadsto \color{blue}{4 \cdot \frac{x}{y} + 2} \]

   if -0.066000000000000003 < x < 2.34999999999999986e95

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

         \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} \]

      2. +-commutative 99.8%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) \]

      3. associate--l+ 99.8%

         \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(y \cdot 0.25 + \left(x - z\right)\right)} \]

      4. distribute-lft-in 99.8%

         \[\leadsto 1 + \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot 0.25\right) + \frac{4}{y} \cdot \left(x - z\right)\right)} \]

      5. associate-+r+ 99.8%

         \[\leadsto \color{blue}{\left(1 + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right) + \frac{4}{y} \cdot \left(x - z\right)} \]

      6. *-commutative 99.8%

         \[\leadsto \left(1 + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right) + \color{blue}{\left(x - z\right) \cdot \frac{4}{y}} \]

      7. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(x - z\right) \cdot \frac{4}{y} + \left(1 + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right)} \]

      8. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right)} \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \color{blue}{\left(y \cdot 0.25\right) \cdot \frac{4}{y}}\right) \]

      10. associate-*l* 99.8%

          \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \color{blue}{y \cdot \left(0.25 \cdot \frac{4}{y}\right)}\right) \]

      11. associate-*r/ 99.8%

          \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + y \cdot \color{blue}{\frac{0.25 \cdot 4}{y}}\right) \]

      12. metadata-eval 99.8%

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

      13. rgt-mult-inverse 99.8%

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

      14. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 90.6%

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

      1. +-commutative 90.6%

         \[\leadsto \color{blue}{-4 \cdot \frac{z}{y} + 2} \]

      2. *-commutative 90.6%

         \[\leadsto \color{blue}{\frac{z}{y} \cdot -4} + 2 \]

   6. Simplified 90.6%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.066 \lor \neg \left(x \leq 2.35 \cdot 10^{+95}\right):\\ \;\;\;\;4 \cdot \frac{x}{y} + 2\\ \mathbf{else}:\\ \;\;\;\;2 + \frac{z}{y} \cdot -4\\ \end{array} \]

Alternative 3: 67.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ 4 \cdot \frac{x}{y} + 2 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* 4.0 (/ x y)) 2.0))

C

double code(double x, double y, double z) {
	return (4.0 * (x / y)) + 2.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (4.0d0 * (x / y)) + 2.0d0
end function

Java

public static double code(double x, double y, double z) {
	return (4.0 * (x / y)) + 2.0;
}

Python

def code(x, y, z):
	return (4.0 * (x / y)) + 2.0

Julia

function code(x, y, z)
	return Float64(Float64(4.0 * Float64(x / y)) + 2.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (4.0 * (x / y)) + 2.0;
end

Wolfram

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

Derivation

1. Initial program 100.0%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. associate-*l/ 99.8%

      \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} \]

   2. +-commutative 99.8%

      \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) \]

   3. associate--l+ 99.8%

      \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(y \cdot 0.25 + \left(x - z\right)\right)} \]

   4. distribute-lft-in 99.8%

      \[\leadsto 1 + \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot 0.25\right) + \frac{4}{y} \cdot \left(x - z\right)\right)} \]

   5. associate-+r+ 99.8%

      \[\leadsto \color{blue}{\left(1 + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right) + \frac{4}{y} \cdot \left(x - z\right)} \]

   6. *-commutative 99.8%

      \[\leadsto \left(1 + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right) + \color{blue}{\left(x - z\right) \cdot \frac{4}{y}} \]

   7. +-commutative 99.8%

      \[\leadsto \color{blue}{\left(x - z\right) \cdot \frac{4}{y} + \left(1 + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right)} \]

   8. fma-def 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right)} \]

   9. *-commutative 99.8%

      \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \color{blue}{\left(y \cdot 0.25\right) \cdot \frac{4}{y}}\right) \]

   10. associate-*l* 99.8%

       \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \color{blue}{y \cdot \left(0.25 \cdot \frac{4}{y}\right)}\right) \]

   11. associate-*r/ 99.8%

       \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + y \cdot \color{blue}{\frac{0.25 \cdot 4}{y}}\right) \]

   12. metadata-eval 99.8%

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

   13. rgt-mult-inverse 99.8%

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

   14. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in z around 0 68.4%

   \[\leadsto \color{blue}{2 + 4 \cdot \frac{x}{y}} \]
5. Step-by-step derivation

   1. +-commutative 68.4%

      \[\leadsto \color{blue}{4 \cdot \frac{x}{y} + 2} \]

6. Simplified 68.4%

   \[\leadsto \color{blue}{4 \cdot \frac{x}{y} + 2} \]

7. Final simplification 68.4%

   \[\leadsto 4 \cdot \frac{x}{y} + 2 \]

Alternative 4: 33.9% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 2 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 2.0)

C

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

Fortran

real(8) function code(x, y, z)
    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

Derivation

1. Initial program 100.0%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. associate-*l/ 99.8%

      \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} \]

   2. +-commutative 99.8%

      \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) \]

   3. associate--l+ 99.8%

      \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(y \cdot 0.25 + \left(x - z\right)\right)} \]

   4. distribute-lft-in 99.8%

      \[\leadsto 1 + \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot 0.25\right) + \frac{4}{y} \cdot \left(x - z\right)\right)} \]

   5. associate-+r+ 99.8%

      \[\leadsto \color{blue}{\left(1 + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right) + \frac{4}{y} \cdot \left(x - z\right)} \]

   6. *-commutative 99.8%

      \[\leadsto \left(1 + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right) + \color{blue}{\left(x - z\right) \cdot \frac{4}{y}} \]

   7. +-commutative 99.8%

      \[\leadsto \color{blue}{\left(x - z\right) \cdot \frac{4}{y} + \left(1 + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right)} \]

   8. fma-def 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right)} \]

   9. *-commutative 99.8%

      \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \color{blue}{\left(y \cdot 0.25\right) \cdot \frac{4}{y}}\right) \]

   10. associate-*l* 99.8%

       \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \color{blue}{y \cdot \left(0.25 \cdot \frac{4}{y}\right)}\right) \]

   11. associate-*r/ 99.8%

       \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + y \cdot \color{blue}{\frac{0.25 \cdot 4}{y}}\right) \]

   12. metadata-eval 99.8%

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

   13. rgt-mult-inverse 99.8%

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

   14. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in y around inf 33.1%

   \[\leadsto \color{blue}{2} \]

5. Final simplification 33.1%

   \[\leadsto 2 \]

Reproduce

herbie shell --seed 2023208 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  :precision binary64
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))