fabs fraction 1

Percentage Accurate: 92.3% → 99.6%

Time: 6.8s

Alternatives: 8

Speedup: 1.0×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+44} \lor \neg \left(x \leq 3.5 \cdot 10^{+89}\right):\\ \;\;\;\;\left|\frac{z + -1}{\frac{y}{x}}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x \cdot \left(1 - z\right)}{y}\right|\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.2e+44) (not (<= x 3.5e+89)))
   (fabs (/ (+ z -1.0) (/ y x)))
   (fabs (/ (+ 4.0 (* x (- 1.0 z))) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.2e+44) || !(x <= 3.5e+89)) {
		tmp = fabs(((z + -1.0) / (y / x)));
	} else {
		tmp = fabs(((4.0 + (x * (1.0 - 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 ((x <= (-1.2d+44)) .or. (.not. (x <= 3.5d+89))) then
        tmp = abs(((z + (-1.0d0)) / (y / x)))
    else
        tmp = abs(((4.0d0 + (x * (1.0d0 - z))) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.2e+44) || !(x <= 3.5e+89)) {
		tmp = Math.abs(((z + -1.0) / (y / x)));
	} else {
		tmp = Math.abs(((4.0 + (x * (1.0 - z))) / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.2e+44) or not (x <= 3.5e+89):
		tmp = math.fabs(((z + -1.0) / (y / x)))
	else:
		tmp = math.fabs(((4.0 + (x * (1.0 - z))) / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.2e+44) || !(x <= 3.5e+89))
		tmp = abs(Float64(Float64(z + -1.0) / Float64(y / x)));
	else
		tmp = abs(Float64(Float64(4.0 + Float64(x * Float64(1.0 - z))) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.2e+44) || ~((x <= 3.5e+89)))
		tmp = abs(((z + -1.0) / (y / x)));
	else
		tmp = abs(((4.0 + (x * (1.0 - z))) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.2e+44], N[Not[LessEqual[x, 3.5e+89]], $MachinePrecision]], N[Abs[N[(N[(z + -1.0), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Abs[N[(N[(4.0 + N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.20000000000000007e44 or 3.5000000000000001e89 < x

   1. Initial program 80.8%

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

      1. *-rgt-identity 80.8%

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

      2. fabs-sub 80.8%

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

      3. metadata-eval 80.8%

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

      4. metadata-eval 80.8%

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

      5. fabs-mul 80.8%

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

      6. metadata-eval 80.8%

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

      7. *-rgt-identity 80.8%

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

      8. associate-*l/ 77.9%

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

      9. div-sub 87.4%

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

      10. sub-neg 87.4%

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

      11. +-commutative 87.4%

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

      12. remove-double-neg 87.4%

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

      13. distribute-neg-in 87.4%

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

      14. sub-neg 87.4%

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

      15. neg-mul-1 87.4%

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

      16. associate-*l/ 87.3%

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

      17. remove-double-neg 87.3%

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

      18. distribute-lft-neg-in 87.3%

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

      19. distribute-rgt-neg-in 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in x around inf 87.4%

      \[\leadsto \left|\color{blue}{\frac{\left(z - 1\right) \cdot x}{y}}\right| \]
   5. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \left|\color{blue}{\frac{z - 1}{\frac{y}{x}}}\right| \]

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

         \[\leadsto \left|\frac{z + \color{blue}{-1}}{\frac{y}{x}}\right| \]

   6. Simplified 99.7%

      \[\leadsto \left|\color{blue}{\frac{z + -1}{\frac{y}{x}}}\right| \]

   if -1.20000000000000007e44 < x < 3.5000000000000001e89

   1. Initial program 98.0%

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

      1. fabs-neg 98.0%

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

      2. sub-neg 98.0%

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

      3. distribute-neg-in 98.0%

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

      4. sub-neg 98.0%

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

      5. distribute-neg-frac 98.0%

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

      6. associate-*l/ 99.2%

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

      7. distribute-neg-frac 99.2%

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

      8. neg-mul-1 99.2%

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

      9. associate-*l/ 99.2%

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

      10. neg-mul-1 99.2%

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

      11. associate-*l/ 99.1%

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

      12. distribute-lft-out-- 99.8%

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

      13. fabs-mul 99.8%

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

      14. fabs-sub 99.8%

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

      15. fabs-mul 99.8%

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

      16. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 99.9%

      \[\leadsto \left|\frac{\color{blue}{4 + \left(1 - z\right) \cdot x}}{y}\right| \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+44} \lor \neg \left(x \leq 3.5 \cdot 10^{+89}\right):\\ \;\;\;\;\left|\frac{z + -1}{\frac{y}{x}}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x \cdot \left(1 - z\right)}{y}\right|\\ \end{array} \]

Alternative 2: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\\ \mathbf{if}\;t_0 \leq 10^{+301}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x \cdot \left(z + -1\right)}{y}\right|\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fabs (- (/ (+ x 4.0) y) (* (/ x y) z)))))
   (if (<= t_0 1e+301) t_0 (fabs (/ (* x (+ z -1.0)) y)))))

C

double code(double x, double y, double z) {
	double t_0 = fabs((((x + 4.0) / y) - ((x / y) * z)));
	double tmp;
	if (t_0 <= 1e+301) {
		tmp = t_0;
	} else {
		tmp = fabs(((x * (z + -1.0)) / 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) :: t_0
    real(8) :: tmp
    t_0 = abs((((x + 4.0d0) / y) - ((x / y) * z)))
    if (t_0 <= 1d+301) then
        tmp = t_0
    else
        tmp = abs(((x * (z + (-1.0d0))) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs((((x + 4.0) / y) - ((x / y) * z)));
	double tmp;
	if (t_0 <= 1e+301) {
		tmp = t_0;
	} else {
		tmp = Math.abs(((x * (z + -1.0)) / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs((((x + 4.0) / y) - ((x / y) * z)))
	tmp = 0
	if t_0 <= 1e+301:
		tmp = t_0
	else:
		tmp = math.fabs(((x * (z + -1.0)) / y))
	return tmp

Julia

function code(x, y, z)
	t_0 = abs(Float64(Float64(Float64(x + 4.0) / y) - Float64(Float64(x / y) * z)))
	tmp = 0.0
	if (t_0 <= 1e+301)
		tmp = t_0;
	else
		tmp = abs(Float64(Float64(x * Float64(z + -1.0)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs((((x + 4.0) / y) - ((x / y) * z)));
	tmp = 0.0;
	if (t_0 <= 1e+301)
		tmp = t_0;
	else
		tmp = abs(((x * (z + -1.0)) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Abs[N[(N[(N[(x + 4.0), $MachinePrecision] / y), $MachinePrecision] - N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t$95$0, 1e+301], t$95$0, N[Abs[N[(N[(x * N[(z + -1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))) < 1.00000000000000005e301

   1. Initial program 99.0%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   if 1.00000000000000005e301 < (fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

   1. Initial program 61.8%

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

      1. *-rgt-identity 61.8%

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

      2. fabs-sub 61.8%

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

      3. metadata-eval 61.8%

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

      4. metadata-eval 61.8%

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

      5. fabs-mul 61.8%

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

      6. metadata-eval 61.8%

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

      7. *-rgt-identity 61.8%

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

      8. associate-*l/ 80.0%

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

      9. div-sub 100.0%

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

      10. sub-neg 100.0%

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

      11. +-commutative 100.0%

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

      12. remove-double-neg 100.0%

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

      13. distribute-neg-in 100.0%

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

      14. sub-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. associate-*l/ 100.0%

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

      17. remove-double-neg 100.0%

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

      18. distribute-lft-neg-in 100.0%

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

      19. distribute-rgt-neg-in 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

      \[\leadsto \left|\color{blue}{\frac{\left(z - 1\right) \cdot x}{y}}\right| \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \leq 10^{+301}:\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x \cdot \left(z + -1\right)}{y}\right|\\ \end{array} \]

Alternative 3: 98.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -155000000000 \lor \neg \left(x \leq 2.25 \cdot 10^{-10}\right):\\ \;\;\;\;\left|\frac{z + -1}{\frac{y}{x}}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 - x \cdot z}{y}\right|\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -155000000000.0) (not (<= x 2.25e-10)))
   (fabs (/ (+ z -1.0) (/ y x)))
   (fabs (/ (- 4.0 (* x z)) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -155000000000.0) || !(x <= 2.25e-10)) {
		tmp = fabs(((z + -1.0) / (y / x)));
	} else {
		tmp = fabs(((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 ((x <= (-155000000000.0d0)) .or. (.not. (x <= 2.25d-10))) then
        tmp = abs(((z + (-1.0d0)) / (y / x)))
    else
        tmp = abs(((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 ((x <= -155000000000.0) || !(x <= 2.25e-10)) {
		tmp = Math.abs(((z + -1.0) / (y / x)));
	} else {
		tmp = Math.abs(((4.0 - (x * z)) / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -155000000000.0) or not (x <= 2.25e-10):
		tmp = math.fabs(((z + -1.0) / (y / x)))
	else:
		tmp = math.fabs(((4.0 - (x * z)) / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -155000000000.0) || !(x <= 2.25e-10))
		tmp = abs(Float64(Float64(z + -1.0) / Float64(y / x)));
	else
		tmp = abs(Float64(Float64(4.0 - Float64(x * z)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -155000000000.0) || ~((x <= 2.25e-10)))
		tmp = abs(((z + -1.0) / (y / x)));
	else
		tmp = abs(((4.0 - (x * z)) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -155000000000.0], N[Not[LessEqual[x, 2.25e-10]], $MachinePrecision]], N[Abs[N[(N[(z + -1.0), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Abs[N[(N[(4.0 - N[(x * z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.55e11 or 2.25e-10 < x

   1. Initial program 83.6%

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

      1. *-rgt-identity 83.6%

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

      2. fabs-sub 83.6%

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

      3. metadata-eval 83.6%

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

      4. metadata-eval 83.6%

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

      5. fabs-mul 83.6%

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

      6. metadata-eval 83.6%

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

      7. *-rgt-identity 83.6%

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

      8. associate-*l/ 81.2%

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

      9. div-sub 89.7%

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

      10. sub-neg 89.7%

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

      11. +-commutative 89.7%

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

      12. remove-double-neg 89.7%

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

      13. distribute-neg-in 89.7%

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

      14. sub-neg 89.7%

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

      15. neg-mul-1 89.7%

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

      16. associate-*l/ 89.6%

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

      17. remove-double-neg 89.6%

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

      18. distribute-lft-neg-in 89.6%

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

      19. distribute-rgt-neg-in 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in x around inf 88.1%

      \[\leadsto \left|\color{blue}{\frac{\left(z - 1\right) \cdot x}{y}}\right| \]
   5. Step-by-step derivation

      1. associate-/l* 98.1%

         \[\leadsto \left|\color{blue}{\frac{z - 1}{\frac{y}{x}}}\right| \]

      2. sub-neg 98.1%

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

      3. metadata-eval 98.1%

         \[\leadsto \left|\frac{z + \color{blue}{-1}}{\frac{y}{x}}\right| \]

   6. Simplified 98.1%

      \[\leadsto \left|\color{blue}{\frac{z + -1}{\frac{y}{x}}}\right| \]

   if -1.55e11 < x < 2.25e-10

   1. Initial program 98.4%

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

      1. fabs-neg 98.4%

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

      2. sub-neg 98.4%

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

      3. distribute-neg-in 98.4%

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

      4. sub-neg 98.4%

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

      5. distribute-neg-frac 98.4%

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

      6. associate-*l/ 99.9%

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

      7. distribute-neg-frac 99.9%

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

      8. neg-mul-1 99.9%

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

      9. associate-*l/ 99.9%

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

      10. neg-mul-1 99.9%

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

      11. associate-*l/ 99.8%

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

      12. distribute-lft-out-- 99.8%

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

      13. fabs-mul 99.8%

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

      14. fabs-sub 99.8%

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

      15. fabs-mul 99.8%

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

      16. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 99.9%

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

   5. Taylor expanded in z around inf 98.8%

      \[\leadsto \left|\frac{4 + \color{blue}{-1 \cdot \left(z \cdot x\right)}}{y}\right| \]
   6. Step-by-step derivation

      1. neg-mul-1 98.8%

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

      2. distribute-lft-neg-in 98.8%

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

      3. *-commutative 98.8%

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

   7. Simplified 98.8%

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

   8. Taylor expanded in x around 0 98.8%

      \[\leadsto \left|\color{blue}{4 \cdot \frac{1}{y} + -1 \cdot \frac{z \cdot x}{y}}\right| \]
   9. Step-by-step derivation

      1. associate-*l/ 92.3%

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

      2. *-commutative 92.3%

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

      3. neg-mul-1 92.3%

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

      4. unsub-neg 92.3%

         \[\leadsto \left|\color{blue}{4 \cdot \frac{1}{y} - x \cdot \frac{z}{y}}\right| \]

      5. associate-*r/ 92.3%

         \[\leadsto \left|\color{blue}{\frac{4 \cdot 1}{y}} - x \cdot \frac{z}{y}\right| \]

      6. metadata-eval 92.3%

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

      7. *-commutative 92.3%

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

      8. associate-*l/ 98.8%

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

      9. div-sub 98.8%

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

   10. Simplified 98.8%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -155000000000 \lor \neg \left(x \leq 2.25 \cdot 10^{-10}\right):\\ \;\;\;\;\left|\frac{z + -1}{\frac{y}{x}}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 - x \cdot z}{y}\right|\\ \end{array} \]

Alternative 4: 68.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\frac{x}{y}\right|\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+209}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-6}:\\ \;\;\;\;\left|x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \leq 4:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fabs (/ x y))))
   (if (<= x -1.2e+209)
     t_0
     (if (<= x -2.9e-6)
       (fabs (* x (/ z y)))
       (if (<= x 4.0) (fabs (/ 4.0 y)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = fabs((x / y));
	double tmp;
	if (x <= -1.2e+209) {
		tmp = t_0;
	} else if (x <= -2.9e-6) {
		tmp = fabs((x * (z / y)));
	} else if (x <= 4.0) {
		tmp = fabs((4.0 / y));
	} 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 = abs((x / y))
    if (x <= (-1.2d+209)) then
        tmp = t_0
    else if (x <= (-2.9d-6)) then
        tmp = abs((x * (z / y)))
    else if (x <= 4.0d0) then
        tmp = abs((4.0d0 / 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 = Math.abs((x / y));
	double tmp;
	if (x <= -1.2e+209) {
		tmp = t_0;
	} else if (x <= -2.9e-6) {
		tmp = Math.abs((x * (z / y)));
	} else if (x <= 4.0) {
		tmp = Math.abs((4.0 / y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs((x / y))
	tmp = 0
	if x <= -1.2e+209:
		tmp = t_0
	elif x <= -2.9e-6:
		tmp = math.fabs((x * (z / y)))
	elif x <= 4.0:
		tmp = math.fabs((4.0 / y))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = abs(Float64(x / y))
	tmp = 0.0
	if (x <= -1.2e+209)
		tmp = t_0;
	elseif (x <= -2.9e-6)
		tmp = abs(Float64(x * Float64(z / y)));
	elseif (x <= 4.0)
		tmp = abs(Float64(4.0 / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs((x / y));
	tmp = 0.0;
	if (x <= -1.2e+209)
		tmp = t_0;
	elseif (x <= -2.9e-6)
		tmp = abs((x * (z / y)));
	elseif (x <= 4.0)
		tmp = abs((4.0 / y));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Abs[N[(x / y), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -1.2e+209], t$95$0, If[LessEqual[x, -2.9e-6], N[Abs[N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 4.0], N[Abs[N[(4.0 / y), $MachinePrecision]], $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.19999999999999998e209 or 4 < x

   1. Initial program 82.9%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   2. Taylor expanded in z around 0 74.5%

      \[\leadsto \left|\color{blue}{4 \cdot \frac{1}{y} + \frac{x}{y}}\right| \]
   3. Step-by-step derivation

      1. associate-*r/ 74.5%

         \[\leadsto \left|\color{blue}{\frac{4 \cdot 1}{y}} + \frac{x}{y}\right| \]

      2. metadata-eval 74.5%

         \[\leadsto \left|\frac{\color{blue}{4}}{y} + \frac{x}{y}\right| \]

   4. Simplified 74.5%

      \[\leadsto \left|\color{blue}{\frac{4}{y} + \frac{x}{y}}\right| \]

   5. Taylor expanded in x around inf 72.4%

      \[\leadsto \left|\color{blue}{\frac{x}{y}}\right| \]

   if -1.19999999999999998e209 < x < -2.9000000000000002e-6

   1. Initial program 84.9%

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

      1. *-rgt-identity 84.9%

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

      2. fabs-sub 84.9%

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

      3. metadata-eval 84.9%

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

      4. metadata-eval 84.9%

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

      5. fabs-mul 84.9%

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

      6. metadata-eval 84.9%

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

      7. *-rgt-identity 84.9%

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

      8. associate-*l/ 83.0%

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

      9. div-sub 90.5%

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

      10. sub-neg 90.5%

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

      11. +-commutative 90.5%

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

      12. remove-double-neg 90.5%

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

      13. distribute-neg-in 90.5%

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

      14. sub-neg 90.5%

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

      15. neg-mul-1 90.5%

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

      16. associate-*l/ 90.3%

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

      17. remove-double-neg 90.3%

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

      18. distribute-lft-neg-in 90.3%

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

      19. distribute-rgt-neg-in 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in z around inf 51.5%

      \[\leadsto \left|\color{blue}{\frac{z \cdot x}{y}}\right| \]
   5. Step-by-step derivation

      1. associate-*l/ 61.0%

         \[\leadsto \left|\color{blue}{\frac{z}{y} \cdot x}\right| \]

      2. *-commutative 61.0%

         \[\leadsto \left|\color{blue}{x \cdot \frac{z}{y}}\right| \]

   6. Simplified 61.0%

      \[\leadsto \left|\color{blue}{x \cdot \frac{z}{y}}\right| \]

   if -2.9000000000000002e-6 < x < 4

   1. Initial program 98.4%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   2. Taylor expanded in x around 0 76.6%

      \[\leadsto \left|\color{blue}{\frac{4}{y}}\right| \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+209}:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-6}:\\ \;\;\;\;\left|x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \leq 4:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \end{array} \]

Alternative 5: 85.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+95} \lor \neg \left(z \leq 8.2 \cdot 10^{+36}\right):\\ \;\;\;\;\left|\frac{x}{y} \cdot z\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{-4 - x}{y}\right|\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.8e+95) (not (<= z 8.2e+36)))
   (fabs (* (/ x y) z))
   (fabs (/ (- -4.0 x) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.8e+95) || !(z <= 8.2e+36)) {
		tmp = fabs(((x / y) * z));
	} else {
		tmp = fabs(((-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 <= (-3.8d+95)) .or. (.not. (z <= 8.2d+36))) then
        tmp = abs(((x / y) * z))
    else
        tmp = abs((((-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 <= -3.8e+95) || !(z <= 8.2e+36)) {
		tmp = Math.abs(((x / y) * z));
	} else {
		tmp = Math.abs(((-4.0 - x) / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.8e+95) or not (z <= 8.2e+36):
		tmp = math.fabs(((x / y) * z))
	else:
		tmp = math.fabs(((-4.0 - x) / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.8e+95) || !(z <= 8.2e+36))
		tmp = abs(Float64(Float64(x / y) * z));
	else
		tmp = abs(Float64(Float64(-4.0 - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.8e+95) || ~((z <= 8.2e+36)))
		tmp = abs(((x / y) * z));
	else
		tmp = abs(((-4.0 - x) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.8e+95], N[Not[LessEqual[z, 8.2e+36]], $MachinePrecision]], N[Abs[N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]], $MachinePrecision], N[Abs[N[(N[(-4.0 - x), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7999999999999999e95 or 8.20000000000000026e36 < z

   1. Initial program 87.4%

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

      1. *-rgt-identity 87.4%

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

      2. fabs-sub 87.4%

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

      3. metadata-eval 87.4%

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

      4. metadata-eval 87.4%

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

      5. fabs-mul 87.4%

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

      6. metadata-eval 87.4%

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

      7. *-rgt-identity 87.4%

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

      8. associate-*l/ 75.5%

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

      9. div-sub 86.0%

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

      10. sub-neg 86.0%

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

      11. +-commutative 86.0%

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

      12. remove-double-neg 86.0%

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

      13. distribute-neg-in 86.0%

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

      14. sub-neg 86.0%

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

      15. neg-mul-1 86.0%

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

      16. associate-*l/ 85.9%

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

      17. remove-double-neg 85.9%

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

      18. distribute-lft-neg-in 85.9%

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

      19. distribute-rgt-neg-in 85.9%

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

   3. Simplified 85.9%

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

   4. Taylor expanded in z around inf 71.2%

      \[\leadsto \left|\color{blue}{\frac{z \cdot x}{y}}\right| \]
   5. Step-by-step derivation

      1. *-commutative 71.2%

         \[\leadsto \left|\frac{\color{blue}{x \cdot z}}{y}\right| \]

      2. associate-*l/ 83.0%

         \[\leadsto \left|\color{blue}{\frac{x}{y} \cdot z}\right| \]

      3. *-commutative 83.0%

         \[\leadsto \left|\color{blue}{z \cdot \frac{x}{y}}\right| \]

   6. Simplified 83.0%

      \[\leadsto \left|\color{blue}{z \cdot \frac{x}{y}}\right| \]

   if -3.7999999999999999e95 < z < 8.20000000000000026e36

   1. Initial program 93.1%

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

      1. *-rgt-identity 93.1%

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

      2. fabs-sub 93.1%

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

      3. metadata-eval 93.1%

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

      4. metadata-eval 93.1%

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

      5. fabs-mul 93.1%

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

      6. metadata-eval 93.1%

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

      7. *-rgt-identity 93.1%

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

      8. associate-*l/ 99.3%

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

      9. div-sub 99.9%

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

      10. sub-neg 99.9%

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

      11. +-commutative 99.9%

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

      12. remove-double-neg 99.9%

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

      13. distribute-neg-in 99.9%

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

      14. sub-neg 99.9%

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

      15. neg-mul-1 99.9%

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

      16. associate-*l/ 99.8%

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

      17. remove-double-neg 99.8%

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

      18. distribute-lft-neg-in 99.8%

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

      19. distribute-rgt-neg-in 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 95.0%

      \[\leadsto \left|\color{blue}{-1 \cdot \frac{4 + x}{y}}\right| \]
   5. Step-by-step derivation

      1. associate-*r/ 95.0%

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

      2. distribute-lft-in 95.0%

         \[\leadsto \left|\frac{\color{blue}{-1 \cdot 4 + -1 \cdot x}}{y}\right| \]

      3. metadata-eval 95.0%

         \[\leadsto \left|\frac{\color{blue}{-4} + -1 \cdot x}{y}\right| \]

      4. neg-mul-1 95.0%

         \[\leadsto \left|\frac{-4 + \color{blue}{\left(-x\right)}}{y}\right| \]

      5. sub-neg 95.0%

         \[\leadsto \left|\frac{\color{blue}{-4 - x}}{y}\right| \]

   6. Simplified 95.0%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+95} \lor \neg \left(z \leq 8.2 \cdot 10^{+36}\right):\\ \;\;\;\;\left|\frac{x}{y} \cdot z\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{-4 - x}{y}\right|\\ \end{array} \]

Alternative 6: 68.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -10.5 \lor \neg \left(x \leq 4\right):\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -10.5) (not (<= x 4.0))) (fabs (/ x y)) (fabs (/ 4.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -10.5) || !(x <= 4.0)) {
		tmp = fabs((x / y));
	} else {
		tmp = fabs((4.0 / 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 ((x <= (-10.5d0)) .or. (.not. (x <= 4.0d0))) then
        tmp = abs((x / y))
    else
        tmp = abs((4.0d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -10.5) || !(x <= 4.0)) {
		tmp = Math.abs((x / y));
	} else {
		tmp = Math.abs((4.0 / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -10.5) or not (x <= 4.0):
		tmp = math.fabs((x / y))
	else:
		tmp = math.fabs((4.0 / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -10.5) || !(x <= 4.0))
		tmp = abs(Float64(x / y));
	else
		tmp = abs(Float64(4.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -10.5) || ~((x <= 4.0)))
		tmp = abs((x / y));
	else
		tmp = abs((4.0 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -10.5], N[Not[LessEqual[x, 4.0]], $MachinePrecision]], N[Abs[N[(x / y), $MachinePrecision]], $MachinePrecision], N[Abs[N[(4.0 / y), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -10.5 or 4 < x

   1. Initial program 83.4%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   2. Taylor expanded in z around 0 66.6%

      \[\leadsto \left|\color{blue}{4 \cdot \frac{1}{y} + \frac{x}{y}}\right| \]
   3. Step-by-step derivation

      1. associate-*r/ 66.6%

         \[\leadsto \left|\color{blue}{\frac{4 \cdot 1}{y}} + \frac{x}{y}\right| \]

      2. metadata-eval 66.6%

         \[\leadsto \left|\frac{\color{blue}{4}}{y} + \frac{x}{y}\right| \]

   4. Simplified 66.6%

      \[\leadsto \left|\color{blue}{\frac{4}{y} + \frac{x}{y}}\right| \]

   5. Taylor expanded in x around inf 65.8%

      \[\leadsto \left|\color{blue}{\frac{x}{y}}\right| \]

   if -10.5 < x < 4

   1. Initial program 98.5%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   2. Taylor expanded in x around 0 76.1%

      \[\leadsto \left|\color{blue}{\frac{4}{y}}\right| \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -10.5 \lor \neg \left(x \leq 4\right):\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \end{array} \]

Alternative 7: 68.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-6}:\\ \;\;\;\;\left|\frac{x}{y} \cdot z\right|\\ \mathbf{elif}\;x \leq 4:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.7e-6)
   (fabs (* (/ x y) z))
   (if (<= x 4.0) (fabs (/ 4.0 y)) (fabs (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.7e-6) {
		tmp = fabs(((x / y) * z));
	} else if (x <= 4.0) {
		tmp = fabs((4.0 / y));
	} else {
		tmp = fabs((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 (x <= (-2.7d-6)) then
        tmp = abs(((x / y) * z))
    else if (x <= 4.0d0) then
        tmp = abs((4.0d0 / y))
    else
        tmp = abs((x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.7e-6) {
		tmp = Math.abs(((x / y) * z));
	} else if (x <= 4.0) {
		tmp = Math.abs((4.0 / y));
	} else {
		tmp = Math.abs((x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.7e-6:
		tmp = math.fabs(((x / y) * z))
	elif x <= 4.0:
		tmp = math.fabs((4.0 / y))
	else:
		tmp = math.fabs((x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.7e-6)
		tmp = abs(Float64(Float64(x / y) * z));
	elseif (x <= 4.0)
		tmp = abs(Float64(4.0 / y));
	else
		tmp = abs(Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.7e-6)
		tmp = abs(((x / y) * z));
	elseif (x <= 4.0)
		tmp = abs((4.0 / y));
	else
		tmp = abs((x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.7e-6], N[Abs[N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 4.0], N[Abs[N[(4.0 / y), $MachinePrecision]], $MachinePrecision], N[Abs[N[(x / y), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.69999999999999998e-6

   1. Initial program 81.3%

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

      1. *-rgt-identity 81.3%

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

      2. fabs-sub 81.3%

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

      3. metadata-eval 81.3%

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

      4. metadata-eval 81.3%

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

      5. fabs-mul 81.3%

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

      6. metadata-eval 81.3%

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

      7. *-rgt-identity 81.3%

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

      8. associate-*l/ 83.5%

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

      9. div-sub 92.0%

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

      10. sub-neg 92.0%

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

      11. +-commutative 92.0%

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

      12. remove-double-neg 92.0%

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

      13. distribute-neg-in 92.0%

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

      14. sub-neg 92.0%

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

      15. neg-mul-1 92.0%

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

      16. associate-*l/ 91.9%

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

      17. remove-double-neg 91.9%

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

      18. distribute-lft-neg-in 91.9%

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

      19. distribute-rgt-neg-in 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in z around inf 47.1%

      \[\leadsto \left|\color{blue}{\frac{z \cdot x}{y}}\right| \]
   5. Step-by-step derivation

      1. *-commutative 47.1%

         \[\leadsto \left|\frac{\color{blue}{x \cdot z}}{y}\right| \]

      2. associate-*l/ 69.2%

         \[\leadsto \left|\color{blue}{\frac{x}{y} \cdot z}\right| \]

      3. *-commutative 69.2%

         \[\leadsto \left|\color{blue}{z \cdot \frac{x}{y}}\right| \]

   6. Simplified 69.2%

      \[\leadsto \left|\color{blue}{z \cdot \frac{x}{y}}\right| \]

   if -2.69999999999999998e-6 < x < 4

   1. Initial program 98.4%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   2. Taylor expanded in x around 0 76.6%

      \[\leadsto \left|\color{blue}{\frac{4}{y}}\right| \]

   if 4 < x

   1. Initial program 85.4%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   2. Taylor expanded in z around 0 72.7%

      \[\leadsto \left|\color{blue}{4 \cdot \frac{1}{y} + \frac{x}{y}}\right| \]
   3. Step-by-step derivation

      1. associate-*r/ 72.7%

         \[\leadsto \left|\color{blue}{\frac{4 \cdot 1}{y}} + \frac{x}{y}\right| \]

      2. metadata-eval 72.7%

         \[\leadsto \left|\frac{\color{blue}{4}}{y} + \frac{x}{y}\right| \]

   4. Simplified 72.7%

      \[\leadsto \left|\color{blue}{\frac{4}{y} + \frac{x}{y}}\right| \]

   5. Taylor expanded in x around inf 70.1%

      \[\leadsto \left|\color{blue}{\frac{x}{y}}\right| \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-6}:\\ \;\;\;\;\left|\frac{x}{y} \cdot z\right|\\ \mathbf{elif}\;x \leq 4:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \end{array} \]

Alternative 8: 39.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \left|\frac{4}{y}\right| \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return fabs((4.0 / 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 = abs((4.0d0 / y))
end function

Java

public static double code(double x, double y, double z) {
	return Math.abs((4.0 / y));
}

Python

def code(x, y, z):
	return math.fabs((4.0 / y))

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[Abs[N[(4.0 / y), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 91.0%

   \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

2. Taylor expanded in x around 0 41.3%

   \[\leadsto \left|\color{blue}{\frac{4}{y}}\right| \]

3. Final simplification 41.3%

   \[\leadsto \left|\frac{4}{y}\right| \]

Reproduce

herbie shell --seed 2023174 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4.0) y) (* (/ x y) z))))