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

Percentage Accurate: 99.7% → 100.0%

Time: 5.9s

Alternatives: 8

Speedup: 1.4×

• 21.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 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)
    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]

Initial Program: 99.7% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 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)
    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]

Alternative 1: 100.0% accurate, 1.4× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return 4.0 + (4.0 * ((x - 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 = 4.0d0 + (4.0d0 * ((x - z) / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-*l/ 99.8%

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

   2. +-commutative 99.8%

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

   3. associate--l+ 99.8%

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

   4. distribute-lft-in 99.8%

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

   5. associate-+r+ 99.8%

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

   6. *-commutative 99.8%

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

   7. +-commutative 99.8%

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

   8. fma-def 99.8%

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

   9. associate-*r* 99.8%

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

   10. associate-*l/ 99.8%

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

   11. associate-/l* 99.8%

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

   12. *-inverses 99.8%

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

   13. metadata-eval 99.8%

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

   14. metadata-eval 99.8%

       \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \color{blue}{3}\right) \]

   15. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in y around 0 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 53.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \frac{-4}{y}\\ t_1 := 4 \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -2.95 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-85}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-302}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-144}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-110}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+90}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (/ -4.0 y))) (t_1 (* 4.0 (/ x y))))
   (if (<= x -2.95e+32)
     t_1
     (if (<= x -3.1e-85)
       4.0
       (if (<= x 3.8e-302)
         t_0
         (if (<= x 1.2e-144)
           4.0
           (if (<= x 2.05e-110) t_0 (if (<= x 7.8e+90) 4.0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-4.0 / y);
	double t_1 = 4.0 * (x / y);
	double tmp;
	if (x <= -2.95e+32) {
		tmp = t_1;
	} else if (x <= -3.1e-85) {
		tmp = 4.0;
	} else if (x <= 3.8e-302) {
		tmp = t_0;
	} else if (x <= 1.2e-144) {
		tmp = 4.0;
	} else if (x <= 2.05e-110) {
		tmp = t_0;
	} else if (x <= 7.8e+90) {
		tmp = 4.0;
	} else {
		tmp = t_1;
	}
	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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = z * ((-4.0d0) / y)
    t_1 = 4.0d0 * (x / y)
    if (x <= (-2.95d+32)) then
        tmp = t_1
    else if (x <= (-3.1d-85)) then
        tmp = 4.0d0
    else if (x <= 3.8d-302) then
        tmp = t_0
    else if (x <= 1.2d-144) then
        tmp = 4.0d0
    else if (x <= 2.05d-110) then
        tmp = t_0
    else if (x <= 7.8d+90) then
        tmp = 4.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (-4.0 / y);
	double t_1 = 4.0 * (x / y);
	double tmp;
	if (x <= -2.95e+32) {
		tmp = t_1;
	} else if (x <= -3.1e-85) {
		tmp = 4.0;
	} else if (x <= 3.8e-302) {
		tmp = t_0;
	} else if (x <= 1.2e-144) {
		tmp = 4.0;
	} else if (x <= 2.05e-110) {
		tmp = t_0;
	} else if (x <= 7.8e+90) {
		tmp = 4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-4.0 / y)
	t_1 = 4.0 * (x / y)
	tmp = 0
	if x <= -2.95e+32:
		tmp = t_1
	elif x <= -3.1e-85:
		tmp = 4.0
	elif x <= 3.8e-302:
		tmp = t_0
	elif x <= 1.2e-144:
		tmp = 4.0
	elif x <= 2.05e-110:
		tmp = t_0
	elif x <= 7.8e+90:
		tmp = 4.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-4.0 / y))
	t_1 = Float64(4.0 * Float64(x / y))
	tmp = 0.0
	if (x <= -2.95e+32)
		tmp = t_1;
	elseif (x <= -3.1e-85)
		tmp = 4.0;
	elseif (x <= 3.8e-302)
		tmp = t_0;
	elseif (x <= 1.2e-144)
		tmp = 4.0;
	elseif (x <= 2.05e-110)
		tmp = t_0;
	elseif (x <= 7.8e+90)
		tmp = 4.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-4.0 / y);
	t_1 = 4.0 * (x / y);
	tmp = 0.0;
	if (x <= -2.95e+32)
		tmp = t_1;
	elseif (x <= -3.1e-85)
		tmp = 4.0;
	elseif (x <= 3.8e-302)
		tmp = t_0;
	elseif (x <= 1.2e-144)
		tmp = 4.0;
	elseif (x <= 2.05e-110)
		tmp = t_0;
	elseif (x <= 7.8e+90)
		tmp = 4.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.95e+32], t$95$1, If[LessEqual[x, -3.1e-85], 4.0, If[LessEqual[x, 3.8e-302], t$95$0, If[LessEqual[x, 1.2e-144], 4.0, If[LessEqual[x, 2.05e-110], t$95$0, If[LessEqual[x, 7.8e+90], 4.0, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.94999999999999983e32 or 7.8000000000000004e90 < x

   1. Initial program 100.0%

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

      1. associate-*l/ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate--l+ 99.8%

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

      4. distribute-lft-in 99.8%

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

      5. associate-+r+ 99.8%

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

      6. *-commutative 99.8%

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

      7. +-commutative 99.8%

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

      8. fma-def 99.8%

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

      9. associate-*r* 99.8%

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

      10. associate-*l/ 99.8%

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

      11. associate-/l* 99.8%

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

      12. *-inverses 99.8%

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

      13. metadata-eval 99.8%

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

      14. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \color{blue}{3}\right) \]

      15. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in y around 0 87.2%

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

   6. Taylor expanded in x around inf 68.7%

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

      1. *-commutative 68.7%

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

   8. Simplified 68.7%

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

   if -2.94999999999999983e32 < x < -3.1000000000000002e-85 or 3.8e-302 < x < 1.19999999999999997e-144 or 2.04999999999999991e-110 < x < 7.8000000000000004e90

   1. Initial program 99.9%

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

      1. associate-*l/ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate--l+ 99.8%

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

      4. distribute-lft-in 99.8%

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

      5. associate-+r+ 99.8%

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

      6. *-commutative 99.8%

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

      7. +-commutative 99.8%

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

      8. fma-def 99.8%

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

      9. associate-*r* 99.8%

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

      10. associate-*l/ 99.9%

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

      11. associate-/l* 99.9%

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

      12. *-inverses 99.9%

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

      13. metadata-eval 99.9%

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

      14. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \color{blue}{3}\right) \]

      15. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 57.6%

      \[\leadsto \color{blue}{4} \]

   if -3.1000000000000002e-85 < x < 3.8e-302 or 1.19999999999999997e-144 < x < 2.04999999999999991e-110

   1. Initial program 100.0%

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

      1. associate-*l/ 99.7%

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

      2. +-commutative 99.7%

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

      3. associate--l+ 99.7%

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

      4. distribute-lft-in 99.7%

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

      5. associate-+r+ 99.7%

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

      6. *-commutative 99.7%

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

      7. +-commutative 99.7%

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

      8. fma-def 99.7%

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

      9. associate-*r* 99.7%

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

      10. associate-*l/ 99.7%

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

      11. associate-/l* 99.7%

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

      12. *-inverses 99.7%

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

      13. metadata-eval 99.7%

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

      14. metadata-eval 99.7%

          \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \color{blue}{3}\right) \]

      15. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in y around 0 68.4%

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

   6. Taylor expanded in x around 0 64.0%

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

      1. *-commutative 64.0%

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

      2. associate-*l/ 64.0%

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

      3. associate-*r/ 63.8%

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

   8. Simplified 63.8%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.95 \cdot 10^{+32}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-85}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-302}:\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-144}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-110}:\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+90}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 3: 53.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -6.8 \cdot 10^{+31}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -9.7 \cdot 10^{-85}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-296}:\\ \;\;\;\;\frac{z}{y} \cdot -4\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-144}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 1.52 \cdot 10^{-108}:\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{+90}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.0 (/ x y))))
   (if (<= x -6.8e+31)
     t_0
     (if (<= x -9.7e-85)
       4.0
       (if (<= x 1.65e-296)
         (* (/ z y) -4.0)
         (if (<= x 1.4e-144)
           4.0
           (if (<= x 1.52e-108)
             (* z (/ -4.0 y))
             (if (<= x 3.05e+90) 4.0 t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / y);
	double tmp;
	if (x <= -6.8e+31) {
		tmp = t_0;
	} else if (x <= -9.7e-85) {
		tmp = 4.0;
	} else if (x <= 1.65e-296) {
		tmp = (z / y) * -4.0;
	} else if (x <= 1.4e-144) {
		tmp = 4.0;
	} else if (x <= 1.52e-108) {
		tmp = z * (-4.0 / y);
	} else if (x <= 3.05e+90) {
		tmp = 4.0;
	} else {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = 4.0d0 * (x / y)
    if (x <= (-6.8d+31)) then
        tmp = t_0
    else if (x <= (-9.7d-85)) then
        tmp = 4.0d0
    else if (x <= 1.65d-296) then
        tmp = (z / y) * (-4.0d0)
    else if (x <= 1.4d-144) then
        tmp = 4.0d0
    else if (x <= 1.52d-108) then
        tmp = z * ((-4.0d0) / y)
    else if (x <= 3.05d+90) 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 tmp;
	if (x <= -6.8e+31) {
		tmp = t_0;
	} else if (x <= -9.7e-85) {
		tmp = 4.0;
	} else if (x <= 1.65e-296) {
		tmp = (z / y) * -4.0;
	} else if (x <= 1.4e-144) {
		tmp = 4.0;
	} else if (x <= 1.52e-108) {
		tmp = z * (-4.0 / y);
	} else if (x <= 3.05e+90) {
		tmp = 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 * (x / y)
	tmp = 0
	if x <= -6.8e+31:
		tmp = t_0
	elif x <= -9.7e-85:
		tmp = 4.0
	elif x <= 1.65e-296:
		tmp = (z / y) * -4.0
	elif x <= 1.4e-144:
		tmp = 4.0
	elif x <= 1.52e-108:
		tmp = z * (-4.0 / y)
	elif x <= 3.05e+90:
		tmp = 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.0 * Float64(x / y))
	tmp = 0.0
	if (x <= -6.8e+31)
		tmp = t_0;
	elseif (x <= -9.7e-85)
		tmp = 4.0;
	elseif (x <= 1.65e-296)
		tmp = Float64(Float64(z / y) * -4.0);
	elseif (x <= 1.4e-144)
		tmp = 4.0;
	elseif (x <= 1.52e-108)
		tmp = Float64(z * Float64(-4.0 / y));
	elseif (x <= 3.05e+90)
		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);
	tmp = 0.0;
	if (x <= -6.8e+31)
		tmp = t_0;
	elseif (x <= -9.7e-85)
		tmp = 4.0;
	elseif (x <= 1.65e-296)
		tmp = (z / y) * -4.0;
	elseif (x <= 1.4e-144)
		tmp = 4.0;
	elseif (x <= 1.52e-108)
		tmp = z * (-4.0 / y);
	elseif (x <= 3.05e+90)
		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]}, If[LessEqual[x, -6.8e+31], t$95$0, If[LessEqual[x, -9.7e-85], 4.0, If[LessEqual[x, 1.65e-296], N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[x, 1.4e-144], 4.0, If[LessEqual[x, 1.52e-108], N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.05e+90], 4.0, t$95$0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.7999999999999996e31 or 3.0499999999999998e90 < x

   1. Initial program 100.0%

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

      1. associate-*l/ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate--l+ 99.8%

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

      4. distribute-lft-in 99.8%

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

      5. associate-+r+ 99.8%

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

      6. *-commutative 99.8%

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

      7. +-commutative 99.8%

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

      8. fma-def 99.8%

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

      9. associate-*r* 99.8%

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

      10. associate-*l/ 99.8%

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

      11. associate-/l* 99.8%

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

      12. *-inverses 99.8%

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

      13. metadata-eval 99.8%

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

      14. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \color{blue}{3}\right) \]

      15. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in y around 0 87.2%

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

   6. Taylor expanded in x around inf 68.7%

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

      1. *-commutative 68.7%

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

   8. Simplified 68.7%

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

   if -6.7999999999999996e31 < x < -9.6999999999999997e-85 or 1.65e-296 < x < 1.39999999999999999e-144 or 1.52000000000000001e-108 < x < 3.0499999999999998e90

   1. Initial program 99.9%

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

      1. associate-*l/ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate--l+ 99.8%

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

      4. distribute-lft-in 99.8%

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

      5. associate-+r+ 99.8%

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

      6. *-commutative 99.8%

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

      7. +-commutative 99.8%

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

      8. fma-def 99.8%

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

      9. associate-*r* 99.8%

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

      10. associate-*l/ 99.9%

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

      11. associate-/l* 99.9%

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

      12. *-inverses 99.9%

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

      13. metadata-eval 99.9%

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

      14. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \color{blue}{3}\right) \]

      15. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 57.6%

      \[\leadsto \color{blue}{4} \]

   if -9.6999999999999997e-85 < x < 1.65e-296

   1. Initial program 100.0%

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

      1. associate-*l/ 99.7%

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

      2. +-commutative 99.7%

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

      3. associate--l+ 99.7%

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

      4. distribute-lft-in 99.7%

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

      5. associate-+r+ 99.7%

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

      6. *-commutative 99.7%

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

      7. +-commutative 99.7%

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

      8. fma-def 99.7%

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

      9. associate-*r* 99.7%

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

      10. associate-*l/ 99.7%

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

      11. associate-/l* 99.7%

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

      12. *-inverses 99.7%

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

      13. metadata-eval 99.7%

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

      14. metadata-eval 99.7%

          \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \color{blue}{3}\right) \]

      15. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in y around 0 65.3%

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

   6. Taylor expanded in x around 0 60.5%

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

      1. *-commutative 60.5%

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

   8. Simplified 60.5%

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

   if 1.39999999999999999e-144 < x < 1.52000000000000001e-108

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate--l+ 100.0%

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

      4. distribute-lft-in 100.0%

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

      5. associate-+r+ 100.0%

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

      6. *-commutative 100.0%

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

      7. +-commutative 100.0%

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

      8. fma-def 100.0%

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

      9. associate-*r* 100.0%

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

      10. associate-*l/ 100.0%

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

      11. associate-/l* 100.0%

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

      12. *-inverses 100.0%

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

      13. metadata-eval 100.0%

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

      14. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \color{blue}{3}\right) \]

      15. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in y around 0 100.0%

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

   6. Taylor expanded in x around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

      3. associate-*r/ 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+31}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -9.7 \cdot 10^{-85}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-296}:\\ \;\;\;\;\frac{z}{y} \cdot -4\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-144}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 1.52 \cdot 10^{-108}:\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{+90}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 4: 84.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+131} \lor \neg \left(z \leq -1 \cdot 10^{+61} \lor \neg \left(z \leq -1.3 \cdot 10^{+33}\right) \land z \leq 5 \cdot 10^{-51}\right):\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.6e+131)
         (not (or (<= z -1e+61) (and (not (<= z -1.3e+33)) (<= z 5e-51)))))
   (* 4.0 (/ (- x z) y))
   (+ 4.0 (* 4.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.6e+131) || !((z <= -1e+61) || (!(z <= -1.3e+33) && (z <= 5e-51)))) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0 + (4.0 * (x / y));
	}
	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 ((z <= (-3.6d+131)) .or. (.not. (z <= (-1d+61)) .or. (.not. (z <= (-1.3d+33))) .and. (z <= 5d-51))) then
        tmp = 4.0d0 * ((x - z) / y)
    else
        tmp = 4.0d0 + (4.0d0 * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.6e+131) || !((z <= -1e+61) || (!(z <= -1.3e+33) && (z <= 5e-51)))) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.6e+131) or not ((z <= -1e+61) or (not (z <= -1.3e+33) and (z <= 5e-51))):
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = 4.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.6e+131) || !((z <= -1e+61) || (!(z <= -1.3e+33) && (z <= 5e-51))))
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	else
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.6e+131) || ~(((z <= -1e+61) || (~((z <= -1.3e+33)) && (z <= 5e-51)))))
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = 4.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.6e+131], N[Not[Or[LessEqual[z, -1e+61], And[N[Not[LessEqual[z, -1.3e+33]], $MachinePrecision], LessEqual[z, 5e-51]]]], $MachinePrecision]], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.60000000000000031e131 or -9.99999999999999949e60 < z < -1.2999999999999999e33 or 5.00000000000000004e-51 < z

   1. Initial program 99.9%

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

      1. associate-*l/ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate--l+ 99.8%

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

      4. distribute-lft-in 99.8%

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

      5. associate-+r+ 99.8%

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

      6. *-commutative 99.8%

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

      7. +-commutative 99.8%

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

      8. fma-def 99.8%

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

      9. associate-*r* 99.7%

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

      10. associate-*l/ 99.8%

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

      11. associate-/l* 99.8%

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

      12. *-inverses 99.8%

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

      13. metadata-eval 99.8%

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

      14. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \color{blue}{3}\right) \]

      15. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 99.9%

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

   5. Taylor expanded in y around 0 88.2%

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

   if -3.60000000000000031e131 < z < -9.99999999999999949e60 or -1.2999999999999999e33 < z < 5.00000000000000004e-51

   1. Initial program 100.0%

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

      1. associate-*l/ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate--l+ 99.8%

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

      4. distribute-lft-in 99.8%

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

      5. associate-+r+ 99.8%

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

      6. *-commutative 99.8%

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

      7. +-commutative 99.8%

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

      8. fma-def 99.8%

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

      9. associate-*r* 99.8%

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

      10. associate-*l/ 99.9%

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

      11. associate-/l* 99.9%

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

      12. *-inverses 99.9%

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

      13. metadata-eval 99.9%

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

      14. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \color{blue}{3}\right) \]

      15. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 91.9%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+131} \lor \neg \left(z \leq -1 \cdot 10^{+61} \lor \neg \left(z \leq -1.3 \cdot 10^{+33}\right) \land z \leq 5 \cdot 10^{-51}\right):\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 5: 84.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+67} \lor \neg \left(y \leq 7.8 \cdot 10^{+113}\right):\\ \;\;\;\;4 + \frac{z}{y} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.2e+67) (not (<= y 7.8e+113)))
   (+ 4.0 (* (/ z y) -4.0))
   (* 4.0 (/ (- x z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.2e+67) || !(y <= 7.8e+113)) {
		tmp = 4.0 + ((z / y) * -4.0);
	} else {
		tmp = 4.0 * ((x - z) / y);
	}
	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 ((y <= (-5.2d+67)) .or. (.not. (y <= 7.8d+113))) then
        tmp = 4.0d0 + ((z / y) * (-4.0d0))
    else
        tmp = 4.0d0 * ((x - z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.2e+67) || !(y <= 7.8e+113)) {
		tmp = 4.0 + ((z / y) * -4.0);
	} else {
		tmp = 4.0 * ((x - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.2e+67) or not (y <= 7.8e+113):
		tmp = 4.0 + ((z / y) * -4.0)
	else:
		tmp = 4.0 * ((x - z) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.2e+67) || !(y <= 7.8e+113))
		tmp = Float64(4.0 + Float64(Float64(z / y) * -4.0));
	else
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.2e+67) || ~((y <= 7.8e+113)))
		tmp = 4.0 + ((z / y) * -4.0);
	else
		tmp = 4.0 * ((x - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.2e+67], N[Not[LessEqual[y, 7.8e+113]], $MachinePrecision]], N[(4.0 + N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.2000000000000001e67 or 7.80000000000000039e113 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate--l+ 99.8%

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

      4. distribute-lft-in 99.8%

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

      5. associate-+r+ 99.8%

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

      6. *-commutative 99.8%

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

      7. +-commutative 99.8%

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

      8. fma-def 99.8%

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

      9. associate-*r* 99.8%

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

      10. associate-*l/ 99.9%

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

      11. associate-/l* 99.9%

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

      12. *-inverses 99.9%

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

      13. metadata-eval 99.9%

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

      14. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \color{blue}{3}\right) \]

      15. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 90.9%

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

      1. *-commutative 90.9%

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

   6. Simplified 90.9%

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

   if -5.2000000000000001e67 < y < 7.80000000000000039e113

   1. Initial program 100.0%

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

      1. associate-*l/ 99.7%

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

      2. +-commutative 99.7%

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

      3. associate--l+ 99.7%

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

      4. distribute-lft-in 99.7%

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

      5. associate-+r+ 99.7%

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

      6. *-commutative 99.7%

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

      7. +-commutative 99.7%

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

      8. fma-def 99.7%

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

      9. associate-*r* 99.8%

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

      10. associate-*l/ 99.8%

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

      11. associate-/l* 99.8%

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

      12. *-inverses 99.8%

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

      13. metadata-eval 99.8%

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

      14. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \color{blue}{3}\right) \]

      15. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in y around 0 89.4%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+67} \lor \neg \left(y \leq 7.8 \cdot 10^{+113}\right):\\ \;\;\;\;4 + \frac{z}{y} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \]

Alternative 6: 79.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+71}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+147}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.06e+71) 4.0 (if (<= y 1.2e+147) (* 4.0 (/ (- x z) y)) 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.06e+71) {
		tmp = 4.0;
	} else if (y <= 1.2e+147) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 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 (y <= (-1.06d+71)) then
        tmp = 4.0d0
    else if (y <= 1.2d+147) then
        tmp = 4.0d0 * ((x - z) / y)
    else
        tmp = 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.06e+71) {
		tmp = 4.0;
	} else if (y <= 1.2e+147) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.06e+71:
		tmp = 4.0
	elif y <= 1.2e+147:
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.06e+71)
		tmp = 4.0;
	elseif (y <= 1.2e+147)
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.06e+71)
		tmp = 4.0;
	elseif (y <= 1.2e+147)
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.06e+71], 4.0, If[LessEqual[y, 1.2e+147], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.06e71 or 1.20000000000000001e147 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate--l+ 99.8%

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

      4. distribute-lft-in 99.9%

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

      5. associate-+r+ 99.9%

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

      6. *-commutative 99.9%

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

      7. +-commutative 99.9%

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

      8. fma-def 99.9%

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

      9. associate-*r* 99.8%

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

      10. associate-*l/ 99.9%

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

      11. associate-/l* 99.9%

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

      12. *-inverses 99.9%

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

      13. metadata-eval 99.9%

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

      14. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \color{blue}{3}\right) \]

      15. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 74.6%

      \[\leadsto \color{blue}{4} \]

   if -1.06e71 < y < 1.20000000000000001e147

   1. Initial program 100.0%

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

      1. associate-*l/ 99.7%

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

      2. +-commutative 99.7%

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

      3. associate--l+ 99.7%

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

      4. distribute-lft-in 99.7%

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

      5. associate-+r+ 99.7%

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

      6. *-commutative 99.7%

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

      7. +-commutative 99.7%

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

      8. fma-def 99.7%

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

      9. associate-*r* 99.7%

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

      10. associate-*l/ 99.8%

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

      11. associate-/l* 99.8%

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

      12. *-inverses 99.8%

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

      13. metadata-eval 99.8%

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

      14. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \color{blue}{3}\right) \]

      15. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in y around 0 87.8%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+71}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+147}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]

Alternative 7: 51.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{+131} \lor \neg \left(z \leq 1.3 \cdot 10^{-42}\right):\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.95e+131) (not (<= z 1.3e-42))) (* z (/ -4.0 y)) 4.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.95e+131) || !(z <= 1.3e-42)) {
		tmp = z * (-4.0 / y);
	} else {
		tmp = 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 ((z <= (-2.95d+131)) .or. (.not. (z <= 1.3d-42))) then
        tmp = z * ((-4.0d0) / y)
    else
        tmp = 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.95e+131) || !(z <= 1.3e-42)) {
		tmp = z * (-4.0 / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.95e+131) or not (z <= 1.3e-42):
		tmp = z * (-4.0 / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.95e+131) || !(z <= 1.3e-42))
		tmp = Float64(z * Float64(-4.0 / y));
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.95e+131) || ~((z <= 1.3e-42)))
		tmp = z * (-4.0 / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.95e+131], N[Not[LessEqual[z, 1.3e-42]], $MachinePrecision]], N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision], 4.0]

Derivation

1. Split input into 2 regimes

2. if z < -2.94999999999999992e131 or 1.3e-42 < z

   1. Initial program 99.9%

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

      1. associate-*l/ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate--l+ 99.8%

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

      4. distribute-lft-in 99.8%

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

      5. associate-+r+ 99.8%

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

      6. *-commutative 99.8%

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

      7. +-commutative 99.8%

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

      8. fma-def 99.8%

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

      9. associate-*r* 99.7%

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

      10. associate-*l/ 99.8%

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

      11. associate-/l* 99.8%

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

      12. *-inverses 99.8%

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

      13. metadata-eval 99.8%

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

      14. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \color{blue}{3}\right) \]

      15. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 99.9%

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

   5. Taylor expanded in y around 0 87.4%

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

   6. Taylor expanded in x around 0 68.7%

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

      1. *-commutative 68.7%

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

      2. associate-*l/ 68.7%

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

      3. associate-*r/ 68.6%

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

   8. Simplified 68.6%

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

   if -2.94999999999999992e131 < z < 1.3e-42

   1. Initial program 100.0%

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

      1. associate-*l/ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate--l+ 99.8%

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

      4. distribute-lft-in 99.8%

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

      5. associate-+r+ 99.8%

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

      6. *-commutative 99.8%

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

      7. +-commutative 99.8%

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

      8. fma-def 99.8%

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

      9. associate-*r* 99.8%

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

      10. associate-*l/ 99.9%

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

      11. associate-/l* 99.9%

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

      12. *-inverses 99.9%

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

      13. metadata-eval 99.9%

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

      14. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \color{blue}{3}\right) \]

      15. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 48.1%

      \[\leadsto \color{blue}{4} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{+131} \lor \neg \left(z \leq 1.3 \cdot 10^{-42}\right):\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]

Alternative 8: 34.2% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 4 \end{array} \]

FPCore

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

C

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

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
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

Derivation

1. Initial program 99.9%

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

   1. associate-*l/ 99.8%

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

   2. +-commutative 99.8%

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

   3. associate--l+ 99.8%

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

   4. distribute-lft-in 99.8%

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

   5. associate-+r+ 99.8%

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

   6. *-commutative 99.8%

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

   7. +-commutative 99.8%

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

   8. fma-def 99.8%

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

   9. associate-*r* 99.8%

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

   10. associate-*l/ 99.8%

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

   11. associate-/l* 99.8%

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

   12. *-inverses 99.8%

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

   13. metadata-eval 99.8%

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

   14. metadata-eval 99.8%

       \[\leadsto \mathsf{fma}\left(x - z, \frac{4}{y}, 1 + \color{blue}{3}\right) \]

   15. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in y around inf 34.4%

   \[\leadsto \color{blue}{4} \]

5. Final simplification 34.4%

   \[\leadsto 4 \]

Reproduce

herbie shell --seed 2023171 
(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)))