fabs fraction 1

Percentage Accurate: 91.7% → 99.9%

Time: 25.0s

Alternatives: 8

Speedup: 1.0×

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: 91.7% 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: 99.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\frac{x}{y} \cdot \left(1 - z\right)\right|\\ \mathbf{if}\;x \leq -2 \cdot 10^{+24}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+15}:\\ \;\;\;\;\left|\frac{\left(4 + x\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fabs (* (/ x y) (- 1.0 z)))))
   (if (<= x -2e+24)
     t_0
     (if (<= x 8e+15) (fabs (/ (- (+ 4.0 x) (* x z)) y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(((x / y) * (1.0 - z)));
	double tmp;
	if (x <= -2e+24) {
		tmp = t_0;
	} else if (x <= 8e+15) {
		tmp = fabs((((4.0 + x) - (x * z)) / 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) * (1.0d0 - z)))
    if (x <= (-2d+24)) then
        tmp = t_0
    else if (x <= 8d+15) then
        tmp = abs((((4.0d0 + x) - (x * z)) / y))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs(((x / y) * (1.0 - z)));
	double tmp;
	if (x <= -2e+24) {
		tmp = t_0;
	} else if (x <= 8e+15) {
		tmp = Math.abs((((4.0 + x) - (x * z)) / y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs(((x / y) * (1.0 - z)))
	tmp = 0
	if x <= -2e+24:
		tmp = t_0
	elif x <= 8e+15:
		tmp = math.fabs((((4.0 + x) - (x * z)) / y))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = abs(Float64(Float64(x / y) * Float64(1.0 - z)))
	tmp = 0.0
	if (x <= -2e+24)
		tmp = t_0;
	elseif (x <= 8e+15)
		tmp = abs(Float64(Float64(Float64(4.0 + x) - Float64(x * z)) / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs(((x / y) * (1.0 - z)));
	tmp = 0.0;
	if (x <= -2e+24)
		tmp = t_0;
	elseif (x <= 8e+15)
		tmp = abs((((4.0 + x) - (x * z)) / y));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Abs[N[(N[(x / y), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -2e+24], t$95$0, If[LessEqual[x, 8e+15], N[Abs[N[(N[(N[(4.0 + x), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2e24 or 8e15 < x

   1. Initial program 91.1%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \left(z \cdot \frac{x}{y}\right)\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \left(z \cdot \frac{1}{\frac{y}{x}}\right)\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \left(\frac{z}{\frac{y}{x}}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \mathsf{/.f64}\left(z, \left(\frac{y}{x}\right)\right)\right)\right) \]

      5. /-lowering-/.f64 91.1%

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(y, x\right)\right)\right)\right) \]

   4. Applied egg-rr 91.1%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{fabs.f64}\left(\color{blue}{\left(x \cdot \left(\frac{1}{y} - \frac{z}{y}\right)\right)}\right) \]
   6. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(x \cdot \frac{1}{y} - x \cdot \frac{z}{y}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(x \cdot \frac{1}{y} - \frac{x \cdot z}{y}\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x \cdot 1}{y} - \frac{x \cdot z}{y}\right)\right) \]

      4. *-rgt-identity N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x}{y} - \frac{x \cdot z}{y}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x}{y} - \frac{z \cdot x}{y}\right)\right) \]

      6. associate-/l* N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x}{y} - z \cdot \frac{x}{y}\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x}{y} + \left(\mathsf{neg}\left(z\right)\right) \cdot \frac{x}{y}\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x}{y} + \left(-1 \cdot z\right) \cdot \frac{x}{y}\right)\right) \]

      9. distribute-rgt1-in N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\left(-1 \cdot z + 1\right) \cdot \frac{x}{y}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x}{y} \cdot \left(-1 \cdot z + 1\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\left(\frac{x}{y}\right), \left(-1 \cdot z + 1\right)\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(-1 \cdot z + 1\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(1 + -1 \cdot z\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(1 + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(1 - z\right)\right)\right) \]

      16. --lowering--.f64 99.9%

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{\_.f64}\left(1, z\right)\right)\right) \]

   7. Simplified 99.9%

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

   if -2e24 < x < 8e15

   1. Initial program 97.8%

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

      1. fabs-lowering-fabs.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x + 4}{y} - \frac{x}{y} \cdot z\right)\right) \]

      2. associate-*l/ N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x + 4}{y} - \frac{x \cdot z}{y}\right)\right) \]

      3. sub-div N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{\left(x + 4\right) - x \cdot z}{y}\right)\right) \]

      4. flip3-+ N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{\frac{{x}^{3} + {4}^{3}}{x \cdot x + \left(4 \cdot 4 - x \cdot 4\right)} - x \cdot z}{y}\right)\right) \]

      5. div-inv N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{\left({x}^{3} + {4}^{3}\right) \cdot \frac{1}{x \cdot x + \left(4 \cdot 4 - x \cdot 4\right)} - x \cdot z}{y}\right)\right) \]

      6. fmm-def N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{\mathsf{fma}\left({x}^{3} + {4}^{3}, \frac{1}{x \cdot x + \left(4 \cdot 4 - x \cdot 4\right)}, \mathsf{neg}\left(x \cdot z\right)\right)}{y}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{\mathsf{fma}\left({x}^{3} + {4}^{3}, \frac{1}{x \cdot x + \left(4 \cdot 4 - x \cdot 4\right)}, \mathsf{neg}\left(z \cdot x\right)\right)}{y}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{fma}\left({x}^{3} + {4}^{3}, \frac{1}{x \cdot x + \left(4 \cdot 4 - x \cdot 4\right)}, \mathsf{neg}\left(z \cdot x\right)\right)\right), y\right)\right) \]

   4. Applied egg-rr 99.9%

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

Alternative 2: 68.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\frac{x}{y} \cdot z\right|\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{-84}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-27}:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+237}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fabs (* (/ x y) z))))
   (if (<= x -1.05e-84)
     t_0
     (if (<= x 1.85e-27)
       (fabs (/ 4.0 y))
       (if (<= x 1.05e+237) t_0 (fabs (/ x y)))))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(((x / y) * z));
	double tmp;
	if (x <= -1.05e-84) {
		tmp = t_0;
	} else if (x <= 1.85e-27) {
		tmp = fabs((4.0 / y));
	} else if (x <= 1.05e+237) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = abs(((x / y) * z))
    if (x <= (-1.05d-84)) then
        tmp = t_0
    else if (x <= 1.85d-27) then
        tmp = abs((4.0d0 / y))
    else if (x <= 1.05d+237) then
        tmp = t_0
    else
        tmp = abs((x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs(((x / y) * z));
	double tmp;
	if (x <= -1.05e-84) {
		tmp = t_0;
	} else if (x <= 1.85e-27) {
		tmp = Math.abs((4.0 / y));
	} else if (x <= 1.05e+237) {
		tmp = t_0;
	} else {
		tmp = Math.abs((x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs(((x / y) * z))
	tmp = 0
	if x <= -1.05e-84:
		tmp = t_0
	elif x <= 1.85e-27:
		tmp = math.fabs((4.0 / y))
	elif x <= 1.05e+237:
		tmp = t_0
	else:
		tmp = math.fabs((x / y))
	return tmp

Julia

function code(x, y, z)
	t_0 = abs(Float64(Float64(x / y) * z))
	tmp = 0.0
	if (x <= -1.05e-84)
		tmp = t_0;
	elseif (x <= 1.85e-27)
		tmp = abs(Float64(4.0 / y));
	elseif (x <= 1.05e+237)
		tmp = t_0;
	else
		tmp = abs(Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs(((x / y) * z));
	tmp = 0.0;
	if (x <= -1.05e-84)
		tmp = t_0;
	elseif (x <= 1.85e-27)
		tmp = abs((4.0 / y));
	elseif (x <= 1.05e+237)
		tmp = t_0;
	else
		tmp = abs((x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Abs[N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -1.05e-84], t$95$0, If[LessEqual[x, 1.85e-27], N[Abs[N[(4.0 / y), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 1.05e+237], t$95$0, N[Abs[N[(x / y), $MachinePrecision]], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.04999999999999999e-84 or 1.85000000000000014e-27 < x < 1.05000000000000007e237

   1. Initial program 93.4%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \left(z \cdot \frac{x}{y}\right)\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \left(z \cdot \frac{1}{\frac{y}{x}}\right)\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \left(\frac{z}{\frac{y}{x}}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \mathsf{/.f64}\left(z, \left(\frac{y}{x}\right)\right)\right)\right) \]

      5. /-lowering-/.f64 93.4%

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(y, x\right)\right)\right)\right) \]

   4. Applied egg-rr 93.4%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{fabs.f64}\left(\color{blue}{\left(-1 \cdot \frac{x \cdot z}{y}\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\mathsf{neg}\left(\frac{x \cdot z}{y}\right)\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\mathsf{neg}\left(x \cdot \frac{z}{y}\right)\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(x \cdot \left(\mathsf{neg}\left(\frac{z}{y}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\frac{z}{y}\right)\right)\right)\right) \]

      5. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{z}{\mathsf{neg}\left(y\right)}\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(z, \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      7. neg-sub0 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(z, \left(0 - y\right)\right)\right)\right) \]

      8. --lowering--.f64 55.6%

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(z, \mathsf{\_.f64}\left(0, y\right)\right)\right)\right) \]

   7. Simplified 55.6%

      \[\leadsto \left|\color{blue}{x \cdot \frac{z}{0 - y}}\right| \]
   8. Step-by-step derivation

      1. neg-fabs N/A

         \[\leadsto \left|\mathsf{neg}\left(x \cdot \frac{z}{0 - y}\right)\right| \]

      2. sub0-neg N/A

         \[\leadsto \left|\mathsf{neg}\left(x \cdot \frac{z}{\mathsf{neg}\left(y\right)}\right)\right| \]

      3. associate-*r/ N/A

         \[\leadsto \left|\mathsf{neg}\left(\frac{x \cdot z}{\mathsf{neg}\left(y\right)}\right)\right| \]

      4. distribute-neg-frac2 N/A

         \[\leadsto \left|\frac{x \cdot z}{\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)}\right| \]

      5. remove-double-neg N/A

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

      6. associate-*l/ N/A

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

      7. associate-/r/ N/A

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

      8. fabs-lowering-fabs.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x}{\frac{y}{z}}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{/.f64}\left(x, \left(\frac{y}{z}\right)\right)\right) \]

      10. /-lowering-/.f64 56.2%

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, z\right)\right)\right) \]

   9. Applied egg-rr 56.2%

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

       1. associate-/r/ N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x}{y} \cdot z\right)\right) \]

       2. clear-num N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{1}{\frac{y}{x}} \cdot z\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{\frac{y}{x}}\right), z\right)\right) \]

       4. clear-num N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\left(\frac{x}{y}\right), z\right)\right) \]

       5. /-lowering-/.f64 61.8%

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), z\right)\right) \]

   11. Applied egg-rr 61.8%

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

   if -1.04999999999999999e-84 < x < 1.85000000000000014e-27

   1. Initial program 97.2%

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

      1. fabs-lowering-fabs.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x + 4}{y} - \frac{x}{y} \cdot z\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x + 4}{y} + \left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) + \frac{x + 4}{y}\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\left(0 - \frac{x}{y} \cdot z\right) + \frac{x + 4}{y}\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(0 - \left(\frac{x}{y} \cdot z - \frac{x + 4}{y}\right)\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\mathsf{neg}\left(\left(\frac{x}{y} \cdot z - \frac{x + 4}{y}\right)\right)\right)\right) \]

      7. neg-mul-1 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(-1 \cdot \left(\frac{x}{y} \cdot z - \frac{x + 4}{y}\right)\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\frac{x}{y} \cdot z\right) \cdot -1 - \frac{x + 4}{y} \cdot -1\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(-1 \cdot \left(\frac{x}{y} \cdot z\right) - \frac{x + 4}{y} \cdot -1\right)\right) \]

      10. neg-mul-1 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{x + 4}{y} \cdot -1\right)\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\left(x + 4\right) \cdot -1}{y}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{-1 \cdot \left(x + 4\right)}{y}\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\mathsf{neg}\left(\left(x + 4\right)\right)}{y}\right)\right) \]

      14. distribute-neg-in N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\left(\mathsf{neg}\left(x\right)\right) + \left(\mathsf{neg}\left(4\right)\right)}{y}\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\left(\mathsf{neg}\left(x\right)\right) - 4}{y}\right)\right) \]

      16. div-sub N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\frac{\mathsf{neg}\left(x\right)}{y} - \frac{4}{y}\right)\right)\right) \]

      17. distribute-neg-frac N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\left(\mathsf{neg}\left(\frac{x}{y}\right)\right) - \frac{4}{y}\right)\right)\right) \]

      18. associate--r- N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right) + \frac{4}{y}\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{4}{y} + \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\left(\frac{4}{y}\right), \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

      21. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(4, y\right), \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

      22. sub-neg N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(4, y\right), \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 97.2%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fabs.f64}\left(\color{blue}{\left(\frac{4}{y}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 84.2%

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{/.f64}\left(4, y\right)\right) \]

   7. Simplified 84.2%

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

   if 1.05000000000000007e237 < x

   1. Initial program 86.6%

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

      1. fabs-lowering-fabs.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x + 4}{y} - \frac{x}{y} \cdot z\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x + 4}{y} + \left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) + \frac{x + 4}{y}\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\left(0 - \frac{x}{y} \cdot z\right) + \frac{x + 4}{y}\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(0 - \left(\frac{x}{y} \cdot z - \frac{x + 4}{y}\right)\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\mathsf{neg}\left(\left(\frac{x}{y} \cdot z - \frac{x + 4}{y}\right)\right)\right)\right) \]

      7. neg-mul-1 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(-1 \cdot \left(\frac{x}{y} \cdot z - \frac{x + 4}{y}\right)\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\frac{x}{y} \cdot z\right) \cdot -1 - \frac{x + 4}{y} \cdot -1\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(-1 \cdot \left(\frac{x}{y} \cdot z\right) - \frac{x + 4}{y} \cdot -1\right)\right) \]

      10. neg-mul-1 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{x + 4}{y} \cdot -1\right)\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\left(x + 4\right) \cdot -1}{y}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{-1 \cdot \left(x + 4\right)}{y}\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\mathsf{neg}\left(\left(x + 4\right)\right)}{y}\right)\right) \]

      14. distribute-neg-in N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\left(\mathsf{neg}\left(x\right)\right) + \left(\mathsf{neg}\left(4\right)\right)}{y}\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\left(\mathsf{neg}\left(x\right)\right) - 4}{y}\right)\right) \]

      16. div-sub N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\frac{\mathsf{neg}\left(x\right)}{y} - \frac{4}{y}\right)\right)\right) \]

      17. distribute-neg-frac N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\left(\mathsf{neg}\left(\frac{x}{y}\right)\right) - \frac{4}{y}\right)\right)\right) \]

      18. associate--r- N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right) + \frac{4}{y}\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{4}{y} + \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\left(\frac{4}{y}\right), \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

      21. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(4, y\right), \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

      22. sub-neg N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(4, y\right), \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(4, y\right), \color{blue}{\left(\frac{x}{y}\right)}\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 84.4%

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(4, y\right), \mathsf{/.f64}\left(x, y\right)\right)\right) \]

   7. Simplified 84.4%

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

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{fabs.f64}\left(\color{blue}{\left(\frac{x}{y}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 84.4%

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{/.f64}\left(x, y\right)\right) \]

   10. Simplified 84.4%

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

Alternative 3: 98.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\frac{x}{y} \cdot \left(1 - z\right)\right|\\ \mathbf{if}\;x \leq -5.6 \cdot 10^{+23}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5:\\ \;\;\;\;\left|\frac{x \cdot z - 4}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fabs (* (/ x y) (- 1.0 z)))))
   (if (<= x -5.6e+23) t_0 (if (<= x 5.0) (fabs (/ (- (* x z) 4.0) y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(((x / y) * (1.0 - z)));
	double tmp;
	if (x <= -5.6e+23) {
		tmp = t_0;
	} else if (x <= 5.0) {
		tmp = fabs((((x * z) - 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) * (1.0d0 - z)))
    if (x <= (-5.6d+23)) then
        tmp = t_0
    else if (x <= 5.0d0) then
        tmp = abs((((x * z) - 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) * (1.0 - z)));
	double tmp;
	if (x <= -5.6e+23) {
		tmp = t_0;
	} else if (x <= 5.0) {
		tmp = Math.abs((((x * z) - 4.0) / y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs(((x / y) * (1.0 - z)))
	tmp = 0
	if x <= -5.6e+23:
		tmp = t_0
	elif x <= 5.0:
		tmp = math.fabs((((x * z) - 4.0) / y))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = abs(Float64(Float64(x / y) * Float64(1.0 - z)))
	tmp = 0.0
	if (x <= -5.6e+23)
		tmp = t_0;
	elseif (x <= 5.0)
		tmp = abs(Float64(Float64(Float64(x * z) - 4.0) / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs(((x / y) * (1.0 - z)));
	tmp = 0.0;
	if (x <= -5.6e+23)
		tmp = t_0;
	elseif (x <= 5.0)
		tmp = abs((((x * z) - 4.0) / y));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Abs[N[(N[(x / y), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -5.6e+23], t$95$0, If[LessEqual[x, 5.0], N[Abs[N[(N[(N[(x * z), $MachinePrecision] - 4.0), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.6e23 or 5 < x

   1. Initial program 91.4%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \left(z \cdot \frac{x}{y}\right)\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \left(z \cdot \frac{1}{\frac{y}{x}}\right)\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \left(\frac{z}{\frac{y}{x}}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \mathsf{/.f64}\left(z, \left(\frac{y}{x}\right)\right)\right)\right) \]

      5. /-lowering-/.f64 91.4%

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(y, x\right)\right)\right)\right) \]

   4. Applied egg-rr 91.4%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{fabs.f64}\left(\color{blue}{\left(x \cdot \left(\frac{1}{y} - \frac{z}{y}\right)\right)}\right) \]
   6. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(x \cdot \frac{1}{y} - x \cdot \frac{z}{y}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(x \cdot \frac{1}{y} - \frac{x \cdot z}{y}\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x \cdot 1}{y} - \frac{x \cdot z}{y}\right)\right) \]

      4. *-rgt-identity N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x}{y} - \frac{x \cdot z}{y}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x}{y} - \frac{z \cdot x}{y}\right)\right) \]

      6. associate-/l* N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x}{y} - z \cdot \frac{x}{y}\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x}{y} + \left(\mathsf{neg}\left(z\right)\right) \cdot \frac{x}{y}\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x}{y} + \left(-1 \cdot z\right) \cdot \frac{x}{y}\right)\right) \]

      9. distribute-rgt1-in N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\left(-1 \cdot z + 1\right) \cdot \frac{x}{y}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x}{y} \cdot \left(-1 \cdot z + 1\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\left(\frac{x}{y}\right), \left(-1 \cdot z + 1\right)\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(-1 \cdot z + 1\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(1 + -1 \cdot z\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(1 + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(1 - z\right)\right)\right) \]

      16. --lowering--.f64 98.8%

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{\_.f64}\left(1, z\right)\right)\right) \]

   7. Simplified 98.8%

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

   if -5.6e23 < x < 5

   1. Initial program 97.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(\frac{4}{y}\right)}, \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), z\right)\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 96.2%

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(4, y\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), z\right)\right)\right) \]

   5. Simplified 96.2%

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

      1. fabs-sub N/A

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

      2. fabs-lowering-fabs.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x}{y} \cdot z - \frac{4}{y}\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x \cdot z}{y} - \frac{4}{y}\right)\right) \]

      4. sub-div N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x \cdot z - 4}{y}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{/.f64}\left(\left(x \cdot z - 4\right), y\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(x \cdot z\right), 4\right), y\right)\right) \]

      7. *-lowering-*.f64 98.3%

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, z\right), 4\right), y\right)\right) \]

   7. Applied egg-rr 98.3%

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

Alternative 4: 85.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0073:\\ \;\;\;\;\left|\frac{x}{y} \cdot \left(1 - z\right)\right|\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+70}:\\ \;\;\;\;\left|\frac{4 + x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x}{y} \cdot z\right|\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.0073)
   (fabs (* (/ x y) (- 1.0 z)))
   (if (<= z 7e+70) (fabs (/ (+ 4.0 x) y)) (fabs (* (/ x y) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.0073) {
		tmp = fabs(((x / y) * (1.0 - z)));
	} else if (z <= 7e+70) {
		tmp = fabs(((4.0 + x) / y));
	} else {
		tmp = fabs(((x / y) * z));
	}
	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 <= (-0.0073d0)) then
        tmp = abs(((x / y) * (1.0d0 - z)))
    else if (z <= 7d+70) then
        tmp = abs(((4.0d0 + x) / y))
    else
        tmp = abs(((x / y) * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.0073) {
		tmp = Math.abs(((x / y) * (1.0 - z)));
	} else if (z <= 7e+70) {
		tmp = Math.abs(((4.0 + x) / y));
	} else {
		tmp = Math.abs(((x / y) * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.0073:
		tmp = math.fabs(((x / y) * (1.0 - z)))
	elif z <= 7e+70:
		tmp = math.fabs(((4.0 + x) / y))
	else:
		tmp = math.fabs(((x / y) * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.0073)
		tmp = abs(Float64(Float64(x / y) * Float64(1.0 - z)));
	elseif (z <= 7e+70)
		tmp = abs(Float64(Float64(4.0 + x) / y));
	else
		tmp = abs(Float64(Float64(x / y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.0073)
		tmp = abs(((x / y) * (1.0 - z)));
	elseif (z <= 7e+70)
		tmp = abs(((4.0 + x) / y));
	else
		tmp = abs(((x / y) * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.0073], N[Abs[N[(N[(x / y), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[z, 7e+70], N[Abs[N[(N[(4.0 + x), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision], N[Abs[N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.00730000000000000007

   1. Initial program 96.9%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \left(z \cdot \frac{x}{y}\right)\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \left(z \cdot \frac{1}{\frac{y}{x}}\right)\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \left(\frac{z}{\frac{y}{x}}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \mathsf{/.f64}\left(z, \left(\frac{y}{x}\right)\right)\right)\right) \]

      5. /-lowering-/.f64 96.9%

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(y, x\right)\right)\right)\right) \]

   4. Applied egg-rr 96.9%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{fabs.f64}\left(\color{blue}{\left(x \cdot \left(\frac{1}{y} - \frac{z}{y}\right)\right)}\right) \]
   6. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(x \cdot \frac{1}{y} - x \cdot \frac{z}{y}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(x \cdot \frac{1}{y} - \frac{x \cdot z}{y}\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x \cdot 1}{y} - \frac{x \cdot z}{y}\right)\right) \]

      4. *-rgt-identity N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x}{y} - \frac{x \cdot z}{y}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x}{y} - \frac{z \cdot x}{y}\right)\right) \]

      6. associate-/l* N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x}{y} - z \cdot \frac{x}{y}\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x}{y} + \left(\mathsf{neg}\left(z\right)\right) \cdot \frac{x}{y}\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x}{y} + \left(-1 \cdot z\right) \cdot \frac{x}{y}\right)\right) \]

      9. distribute-rgt1-in N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\left(-1 \cdot z + 1\right) \cdot \frac{x}{y}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x}{y} \cdot \left(-1 \cdot z + 1\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\left(\frac{x}{y}\right), \left(-1 \cdot z + 1\right)\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(-1 \cdot z + 1\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(1 + -1 \cdot z\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(1 + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(1 - z\right)\right)\right) \]

      16. --lowering--.f64 76.9%

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{\_.f64}\left(1, z\right)\right)\right) \]

   7. Simplified 76.9%

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

   if -0.00730000000000000007 < z < 7.00000000000000005e70

   1. Initial program 95.9%

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

      1. fabs-lowering-fabs.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x + 4}{y} - \frac{x}{y} \cdot z\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x + 4}{y} + \left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) + \frac{x + 4}{y}\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\left(0 - \frac{x}{y} \cdot z\right) + \frac{x + 4}{y}\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(0 - \left(\frac{x}{y} \cdot z - \frac{x + 4}{y}\right)\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\mathsf{neg}\left(\left(\frac{x}{y} \cdot z - \frac{x + 4}{y}\right)\right)\right)\right) \]

      7. neg-mul-1 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(-1 \cdot \left(\frac{x}{y} \cdot z - \frac{x + 4}{y}\right)\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\frac{x}{y} \cdot z\right) \cdot -1 - \frac{x + 4}{y} \cdot -1\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(-1 \cdot \left(\frac{x}{y} \cdot z\right) - \frac{x + 4}{y} \cdot -1\right)\right) \]

      10. neg-mul-1 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{x + 4}{y} \cdot -1\right)\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\left(x + 4\right) \cdot -1}{y}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{-1 \cdot \left(x + 4\right)}{y}\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\mathsf{neg}\left(\left(x + 4\right)\right)}{y}\right)\right) \]

      14. distribute-neg-in N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\left(\mathsf{neg}\left(x\right)\right) + \left(\mathsf{neg}\left(4\right)\right)}{y}\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\left(\mathsf{neg}\left(x\right)\right) - 4}{y}\right)\right) \]

      16. div-sub N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\frac{\mathsf{neg}\left(x\right)}{y} - \frac{4}{y}\right)\right)\right) \]

      17. distribute-neg-frac N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\left(\mathsf{neg}\left(\frac{x}{y}\right)\right) - \frac{4}{y}\right)\right)\right) \]

      18. associate--r- N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right) + \frac{4}{y}\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{4}{y} + \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\left(\frac{4}{y}\right), \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

      21. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(4, y\right), \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

      22. sub-neg N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(4, y\right), \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{fabs.f64}\left(\color{blue}{\left(4 \cdot \frac{1}{y} + \frac{x}{y}\right)}\right) \]
   6. Step-by-step derivation

      1. *-rgt-identity N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(4 \cdot \frac{1}{y} + \frac{x \cdot 1}{y}\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(4 \cdot \frac{1}{y} + x \cdot \frac{1}{y}\right)\right) \]

      3. distribute-rgt-out N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{1}{y} \cdot \left(4 + x\right)\right)\right) \]

      4. associate-*l/ N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{1 \cdot \left(4 + x\right)}{y}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{\left(\mathsf{neg}\left(-1\right)\right) \cdot \left(4 + x\right)}{y}\right)\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{\mathsf{neg}\left(-1 \cdot \left(4 + x\right)\right)}{y}\right)\right) \]

      7. distribute-frac-neg N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\mathsf{neg}\left(\frac{-1 \cdot \left(4 + x\right)}{y}\right)\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\mathsf{neg}\left(\frac{\mathsf{neg}\left(\left(4 + x\right)\right)}{y}\right)\right)\right) \]

      9. distribute-frac-neg N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{4 + x}{y}\right)\right)\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{4 + x}{y}\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{/.f64}\left(\left(4 + x\right), y\right)\right) \]

      12. +-lowering-+.f64 98.1%

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(4, x\right), y\right)\right) \]

   7. Simplified 98.1%

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

   if 7.00000000000000005e70 < z

   1. Initial program 86.4%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \left(z \cdot \frac{x}{y}\right)\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \left(z \cdot \frac{1}{\frac{y}{x}}\right)\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \left(\frac{z}{\frac{y}{x}}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \mathsf{/.f64}\left(z, \left(\frac{y}{x}\right)\right)\right)\right) \]

      5. /-lowering-/.f64 86.3%

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(y, x\right)\right)\right)\right) \]

   4. Applied egg-rr 86.3%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{fabs.f64}\left(\color{blue}{\left(-1 \cdot \frac{x \cdot z}{y}\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\mathsf{neg}\left(\frac{x \cdot z}{y}\right)\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\mathsf{neg}\left(x \cdot \frac{z}{y}\right)\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(x \cdot \left(\mathsf{neg}\left(\frac{z}{y}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\frac{z}{y}\right)\right)\right)\right) \]

      5. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{z}{\mathsf{neg}\left(y\right)}\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(z, \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      7. neg-sub0 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(z, \left(0 - y\right)\right)\right)\right) \]

      8. --lowering--.f64 87.0%

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(z, \mathsf{\_.f64}\left(0, y\right)\right)\right)\right) \]

   7. Simplified 87.0%

      \[\leadsto \left|\color{blue}{x \cdot \frac{z}{0 - y}}\right| \]
   8. Step-by-step derivation

      1. neg-fabs N/A

         \[\leadsto \left|\mathsf{neg}\left(x \cdot \frac{z}{0 - y}\right)\right| \]

      2. sub0-neg N/A

         \[\leadsto \left|\mathsf{neg}\left(x \cdot \frac{z}{\mathsf{neg}\left(y\right)}\right)\right| \]

      3. associate-*r/ N/A

         \[\leadsto \left|\mathsf{neg}\left(\frac{x \cdot z}{\mathsf{neg}\left(y\right)}\right)\right| \]

      4. distribute-neg-frac2 N/A

         \[\leadsto \left|\frac{x \cdot z}{\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)}\right| \]

      5. remove-double-neg N/A

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

      6. associate-*l/ N/A

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

      7. associate-/r/ N/A

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

      8. fabs-lowering-fabs.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x}{\frac{y}{z}}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{/.f64}\left(x, \left(\frac{y}{z}\right)\right)\right) \]

      10. /-lowering-/.f64 86.9%

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, z\right)\right)\right) \]

   9. Applied egg-rr 86.9%

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

       1. associate-/r/ N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x}{y} \cdot z\right)\right) \]

       2. clear-num N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{1}{\frac{y}{x}} \cdot z\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{\frac{y}{x}}\right), z\right)\right) \]

       4. clear-num N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\left(\frac{x}{y}\right), z\right)\right) \]

       5. /-lowering-/.f64 89.4%

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), z\right)\right) \]

   11. Applied egg-rr 89.4%

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

Alternative 5: 85.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1600:\\ \;\;\;\;\left|\frac{x}{\frac{y}{z}}\right|\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+71}:\\ \;\;\;\;\left|\frac{4 + x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x}{y} \cdot z\right|\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1600.0)
   (fabs (/ x (/ y z)))
   (if (<= z 8.5e+71) (fabs (/ (+ 4.0 x) y)) (fabs (* (/ x y) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1600.0) {
		tmp = fabs((x / (y / z)));
	} else if (z <= 8.5e+71) {
		tmp = fabs(((4.0 + x) / y));
	} else {
		tmp = fabs(((x / y) * z));
	}
	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 <= (-1600.0d0)) then
        tmp = abs((x / (y / z)))
    else if (z <= 8.5d+71) then
        tmp = abs(((4.0d0 + x) / y))
    else
        tmp = abs(((x / y) * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1600.0) {
		tmp = Math.abs((x / (y / z)));
	} else if (z <= 8.5e+71) {
		tmp = Math.abs(((4.0 + x) / y));
	} else {
		tmp = Math.abs(((x / y) * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1600.0:
		tmp = math.fabs((x / (y / z)))
	elif z <= 8.5e+71:
		tmp = math.fabs(((4.0 + x) / y))
	else:
		tmp = math.fabs(((x / y) * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1600.0)
		tmp = abs(Float64(x / Float64(y / z)));
	elseif (z <= 8.5e+71)
		tmp = abs(Float64(Float64(4.0 + x) / y));
	else
		tmp = abs(Float64(Float64(x / y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1600.0)
		tmp = abs((x / (y / z)));
	elseif (z <= 8.5e+71)
		tmp = abs(((4.0 + x) / y));
	else
		tmp = abs(((x / y) * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1600.0], N[Abs[N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[z, 8.5e+71], N[Abs[N[(N[(4.0 + x), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision], N[Abs[N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1600

   1. Initial program 96.8%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \left(z \cdot \frac{x}{y}\right)\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \left(z \cdot \frac{1}{\frac{y}{x}}\right)\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \left(\frac{z}{\frac{y}{x}}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \mathsf{/.f64}\left(z, \left(\frac{y}{x}\right)\right)\right)\right) \]

      5. /-lowering-/.f64 96.8%

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(y, x\right)\right)\right)\right) \]

   4. Applied egg-rr 96.8%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{fabs.f64}\left(\color{blue}{\left(-1 \cdot \frac{x \cdot z}{y}\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\mathsf{neg}\left(\frac{x \cdot z}{y}\right)\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\mathsf{neg}\left(x \cdot \frac{z}{y}\right)\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(x \cdot \left(\mathsf{neg}\left(\frac{z}{y}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\frac{z}{y}\right)\right)\right)\right) \]

      5. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{z}{\mathsf{neg}\left(y\right)}\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(z, \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      7. neg-sub0 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(z, \left(0 - y\right)\right)\right)\right) \]

      8. --lowering--.f64 72.9%

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(z, \mathsf{\_.f64}\left(0, y\right)\right)\right)\right) \]

   7. Simplified 72.9%

      \[\leadsto \left|\color{blue}{x \cdot \frac{z}{0 - y}}\right| \]
   8. Step-by-step derivation

      1. neg-fabs N/A

         \[\leadsto \left|\mathsf{neg}\left(x \cdot \frac{z}{0 - y}\right)\right| \]

      2. sub0-neg N/A

         \[\leadsto \left|\mathsf{neg}\left(x \cdot \frac{z}{\mathsf{neg}\left(y\right)}\right)\right| \]

      3. associate-*r/ N/A

         \[\leadsto \left|\mathsf{neg}\left(\frac{x \cdot z}{\mathsf{neg}\left(y\right)}\right)\right| \]

      4. distribute-neg-frac2 N/A

         \[\leadsto \left|\frac{x \cdot z}{\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)}\right| \]

      5. remove-double-neg N/A

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

      6. associate-*l/ N/A

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

      7. associate-/r/ N/A

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

      8. fabs-lowering-fabs.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x}{\frac{y}{z}}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{/.f64}\left(x, \left(\frac{y}{z}\right)\right)\right) \]

      10. /-lowering-/.f64 74.3%

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, z\right)\right)\right) \]

   9. Applied egg-rr 74.3%

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

   if -1600 < z < 8.4999999999999996e71

   1. Initial program 95.9%

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

      1. fabs-lowering-fabs.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x + 4}{y} - \frac{x}{y} \cdot z\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x + 4}{y} + \left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) + \frac{x + 4}{y}\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\left(0 - \frac{x}{y} \cdot z\right) + \frac{x + 4}{y}\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(0 - \left(\frac{x}{y} \cdot z - \frac{x + 4}{y}\right)\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\mathsf{neg}\left(\left(\frac{x}{y} \cdot z - \frac{x + 4}{y}\right)\right)\right)\right) \]

      7. neg-mul-1 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(-1 \cdot \left(\frac{x}{y} \cdot z - \frac{x + 4}{y}\right)\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\frac{x}{y} \cdot z\right) \cdot -1 - \frac{x + 4}{y} \cdot -1\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(-1 \cdot \left(\frac{x}{y} \cdot z\right) - \frac{x + 4}{y} \cdot -1\right)\right) \]

      10. neg-mul-1 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{x + 4}{y} \cdot -1\right)\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\left(x + 4\right) \cdot -1}{y}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{-1 \cdot \left(x + 4\right)}{y}\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\mathsf{neg}\left(\left(x + 4\right)\right)}{y}\right)\right) \]

      14. distribute-neg-in N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\left(\mathsf{neg}\left(x\right)\right) + \left(\mathsf{neg}\left(4\right)\right)}{y}\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\left(\mathsf{neg}\left(x\right)\right) - 4}{y}\right)\right) \]

      16. div-sub N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\frac{\mathsf{neg}\left(x\right)}{y} - \frac{4}{y}\right)\right)\right) \]

      17. distribute-neg-frac N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\left(\mathsf{neg}\left(\frac{x}{y}\right)\right) - \frac{4}{y}\right)\right)\right) \]

      18. associate--r- N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right) + \frac{4}{y}\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{4}{y} + \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\left(\frac{4}{y}\right), \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

      21. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(4, y\right), \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

      22. sub-neg N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(4, y\right), \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{fabs.f64}\left(\color{blue}{\left(4 \cdot \frac{1}{y} + \frac{x}{y}\right)}\right) \]
   6. Step-by-step derivation

      1. *-rgt-identity N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(4 \cdot \frac{1}{y} + \frac{x \cdot 1}{y}\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(4 \cdot \frac{1}{y} + x \cdot \frac{1}{y}\right)\right) \]

      3. distribute-rgt-out N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{1}{y} \cdot \left(4 + x\right)\right)\right) \]

      4. associate-*l/ N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{1 \cdot \left(4 + x\right)}{y}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{\left(\mathsf{neg}\left(-1\right)\right) \cdot \left(4 + x\right)}{y}\right)\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{\mathsf{neg}\left(-1 \cdot \left(4 + x\right)\right)}{y}\right)\right) \]

      7. distribute-frac-neg N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\mathsf{neg}\left(\frac{-1 \cdot \left(4 + x\right)}{y}\right)\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\mathsf{neg}\left(\frac{\mathsf{neg}\left(\left(4 + x\right)\right)}{y}\right)\right)\right) \]

      9. distribute-frac-neg N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{4 + x}{y}\right)\right)\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{4 + x}{y}\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{/.f64}\left(\left(4 + x\right), y\right)\right) \]

      12. +-lowering-+.f64 97.1%

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(4, x\right), y\right)\right) \]

   7. Simplified 97.1%

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

   if 8.4999999999999996e71 < z

   1. Initial program 86.4%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \left(z \cdot \frac{x}{y}\right)\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \left(z \cdot \frac{1}{\frac{y}{x}}\right)\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \left(\frac{z}{\frac{y}{x}}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \mathsf{/.f64}\left(z, \left(\frac{y}{x}\right)\right)\right)\right) \]

      5. /-lowering-/.f64 86.3%

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(x, 4\right), y\right), \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(y, x\right)\right)\right)\right) \]

   4. Applied egg-rr 86.3%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{fabs.f64}\left(\color{blue}{\left(-1 \cdot \frac{x \cdot z}{y}\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\mathsf{neg}\left(\frac{x \cdot z}{y}\right)\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\mathsf{neg}\left(x \cdot \frac{z}{y}\right)\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(x \cdot \left(\mathsf{neg}\left(\frac{z}{y}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\frac{z}{y}\right)\right)\right)\right) \]

      5. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{z}{\mathsf{neg}\left(y\right)}\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(z, \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      7. neg-sub0 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(z, \left(0 - y\right)\right)\right)\right) \]

      8. --lowering--.f64 87.0%

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(z, \mathsf{\_.f64}\left(0, y\right)\right)\right)\right) \]

   7. Simplified 87.0%

      \[\leadsto \left|\color{blue}{x \cdot \frac{z}{0 - y}}\right| \]
   8. Step-by-step derivation

      1. neg-fabs N/A

         \[\leadsto \left|\mathsf{neg}\left(x \cdot \frac{z}{0 - y}\right)\right| \]

      2. sub0-neg N/A

         \[\leadsto \left|\mathsf{neg}\left(x \cdot \frac{z}{\mathsf{neg}\left(y\right)}\right)\right| \]

      3. associate-*r/ N/A

         \[\leadsto \left|\mathsf{neg}\left(\frac{x \cdot z}{\mathsf{neg}\left(y\right)}\right)\right| \]

      4. distribute-neg-frac2 N/A

         \[\leadsto \left|\frac{x \cdot z}{\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)}\right| \]

      5. remove-double-neg N/A

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

      6. associate-*l/ N/A

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

      7. associate-/r/ N/A

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

      8. fabs-lowering-fabs.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x}{\frac{y}{z}}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{/.f64}\left(x, \left(\frac{y}{z}\right)\right)\right) \]

      10. /-lowering-/.f64 86.9%

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, z\right)\right)\right) \]

   9. Applied egg-rr 86.9%

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

       1. associate-/r/ N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x}{y} \cdot z\right)\right) \]

       2. clear-num N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{1}{\frac{y}{x}} \cdot z\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{\frac{y}{x}}\right), z\right)\right) \]

       4. clear-num N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\left(\frac{x}{y}\right), z\right)\right) \]

       5. /-lowering-/.f64 89.4%

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), z\right)\right) \]

   11. Applied egg-rr 89.4%

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

Alternative 6: 68.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\frac{x}{y}\right|\\ \mathbf{if}\;x \leq -1.52:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fabs (/ x y))))
   (if (<= x -1.52) t_0 (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 <= -1.52) {
		tmp = t_0;
	} 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 <= (-1.52d0)) then
        tmp = t_0
    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 <= -1.52) {
		tmp = t_0;
	} 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 <= -1.52:
		tmp = t_0
	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 <= -1.52)
		tmp = t_0;
	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 <= -1.52)
		tmp = t_0;
	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, -1.52], t$95$0, If[LessEqual[x, 4.0], N[Abs[N[(4.0 / y), $MachinePrecision]], $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.52 or 4 < x

   1. Initial program 91.5%

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

      1. fabs-lowering-fabs.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x + 4}{y} - \frac{x}{y} \cdot z\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x + 4}{y} + \left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) + \frac{x + 4}{y}\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\left(0 - \frac{x}{y} \cdot z\right) + \frac{x + 4}{y}\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(0 - \left(\frac{x}{y} \cdot z - \frac{x + 4}{y}\right)\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\mathsf{neg}\left(\left(\frac{x}{y} \cdot z - \frac{x + 4}{y}\right)\right)\right)\right) \]

      7. neg-mul-1 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(-1 \cdot \left(\frac{x}{y} \cdot z - \frac{x + 4}{y}\right)\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\frac{x}{y} \cdot z\right) \cdot -1 - \frac{x + 4}{y} \cdot -1\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(-1 \cdot \left(\frac{x}{y} \cdot z\right) - \frac{x + 4}{y} \cdot -1\right)\right) \]

      10. neg-mul-1 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{x + 4}{y} \cdot -1\right)\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\left(x + 4\right) \cdot -1}{y}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{-1 \cdot \left(x + 4\right)}{y}\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\mathsf{neg}\left(\left(x + 4\right)\right)}{y}\right)\right) \]

      14. distribute-neg-in N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\left(\mathsf{neg}\left(x\right)\right) + \left(\mathsf{neg}\left(4\right)\right)}{y}\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\left(\mathsf{neg}\left(x\right)\right) - 4}{y}\right)\right) \]

      16. div-sub N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\frac{\mathsf{neg}\left(x\right)}{y} - \frac{4}{y}\right)\right)\right) \]

      17. distribute-neg-frac N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\left(\mathsf{neg}\left(\frac{x}{y}\right)\right) - \frac{4}{y}\right)\right)\right) \]

      18. associate--r- N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right) + \frac{4}{y}\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{4}{y} + \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\left(\frac{4}{y}\right), \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

      21. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(4, y\right), \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

      22. sub-neg N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(4, y\right), \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(4, y\right), \color{blue}{\left(\frac{x}{y}\right)}\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 60.6%

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(4, y\right), \mathsf{/.f64}\left(x, y\right)\right)\right) \]

   7. Simplified 60.6%

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

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{fabs.f64}\left(\color{blue}{\left(\frac{x}{y}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 59.6%

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{/.f64}\left(x, y\right)\right) \]

   10. Simplified 59.6%

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

   if -1.52 < x < 4

   1. Initial program 97.7%

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

      1. fabs-lowering-fabs.f64 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x + 4}{y} - \frac{x}{y} \cdot z\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x + 4}{y} + \left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) + \frac{x + 4}{y}\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\left(0 - \frac{x}{y} \cdot z\right) + \frac{x + 4}{y}\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(0 - \left(\frac{x}{y} \cdot z - \frac{x + 4}{y}\right)\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\mathsf{neg}\left(\left(\frac{x}{y} \cdot z - \frac{x + 4}{y}\right)\right)\right)\right) \]

      7. neg-mul-1 N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(-1 \cdot \left(\frac{x}{y} \cdot z - \frac{x + 4}{y}\right)\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\frac{x}{y} \cdot z\right) \cdot -1 - \frac{x + 4}{y} \cdot -1\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fabs.f64}\left(\left(-1 \cdot \left(\frac{x}{y} \cdot z\right) - \frac{x + 4}{y} \cdot -1\right)\right) \]

      10. neg-mul-1 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{x + 4}{y} \cdot -1\right)\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\left(x + 4\right) \cdot -1}{y}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{-1 \cdot \left(x + 4\right)}{y}\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\mathsf{neg}\left(\left(x + 4\right)\right)}{y}\right)\right) \]

      14. distribute-neg-in N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\left(\mathsf{neg}\left(x\right)\right) + \left(\mathsf{neg}\left(4\right)\right)}{y}\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\left(\mathsf{neg}\left(x\right)\right) - 4}{y}\right)\right) \]

      16. div-sub N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\frac{\mathsf{neg}\left(x\right)}{y} - \frac{4}{y}\right)\right)\right) \]

      17. distribute-neg-frac N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\left(\mathsf{neg}\left(\frac{x}{y}\right)\right) - \frac{4}{y}\right)\right)\right) \]

      18. associate--r- N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right) + \frac{4}{y}\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{4}{y} + \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\left(\frac{4}{y}\right), \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

      21. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(4, y\right), \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

      22. sub-neg N/A

          \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(4, y\right), \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 97.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fabs.f64}\left(\color{blue}{\left(\frac{4}{y}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 75.9%

         \[\leadsto \mathsf{fabs.f64}\left(\mathsf{/.f64}\left(4, y\right)\right) \]

   7. Simplified 75.9%

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

Alternative 7: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return fabs(((4.0 / y) + ((x / y) * (1.0 - 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(((4.0d0 / y) + ((x / y) * (1.0d0 - z))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.5%

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

   1. fabs-lowering-fabs.f64 N/A

      \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x + 4}{y} - \frac{x}{y} \cdot z\right)\right) \]

   2. sub-neg N/A

      \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x + 4}{y} + \left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right)\right)\right) \]

   3. +-commutative N/A

      \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) + \frac{x + 4}{y}\right)\right) \]

   4. neg-sub0 N/A

      \[\leadsto \mathsf{fabs.f64}\left(\left(\left(0 - \frac{x}{y} \cdot z\right) + \frac{x + 4}{y}\right)\right) \]

   5. associate-+l- N/A

      \[\leadsto \mathsf{fabs.f64}\left(\left(0 - \left(\frac{x}{y} \cdot z - \frac{x + 4}{y}\right)\right)\right) \]

   6. sub0-neg N/A

      \[\leadsto \mathsf{fabs.f64}\left(\left(\mathsf{neg}\left(\left(\frac{x}{y} \cdot z - \frac{x + 4}{y}\right)\right)\right)\right) \]

   7. neg-mul-1 N/A

      \[\leadsto \mathsf{fabs.f64}\left(\left(-1 \cdot \left(\frac{x}{y} \cdot z - \frac{x + 4}{y}\right)\right)\right) \]

   8. distribute-rgt-out-- N/A

      \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\frac{x}{y} \cdot z\right) \cdot -1 - \frac{x + 4}{y} \cdot -1\right)\right) \]

   9. *-commutative N/A

      \[\leadsto \mathsf{fabs.f64}\left(\left(-1 \cdot \left(\frac{x}{y} \cdot z\right) - \frac{x + 4}{y} \cdot -1\right)\right) \]

   10. neg-mul-1 N/A

       \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{x + 4}{y} \cdot -1\right)\right) \]

   11. associate-*l/ N/A

       \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\left(x + 4\right) \cdot -1}{y}\right)\right) \]

   12. *-commutative N/A

       \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{-1 \cdot \left(x + 4\right)}{y}\right)\right) \]

   13. neg-mul-1 N/A

       \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\mathsf{neg}\left(\left(x + 4\right)\right)}{y}\right)\right) \]

   14. distribute-neg-in N/A

       \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\left(\mathsf{neg}\left(x\right)\right) + \left(\mathsf{neg}\left(4\right)\right)}{y}\right)\right) \]

   15. sub-neg N/A

       \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\left(\mathsf{neg}\left(x\right)\right) - 4}{y}\right)\right) \]

   16. div-sub N/A

       \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\frac{\mathsf{neg}\left(x\right)}{y} - \frac{4}{y}\right)\right)\right) \]

   17. distribute-neg-frac N/A

       \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\left(\mathsf{neg}\left(\frac{x}{y}\right)\right) - \frac{4}{y}\right)\right)\right) \]

   18. associate--r- N/A

       \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right) + \frac{4}{y}\right)\right) \]

   19. +-commutative N/A

       \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{4}{y} + \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

   20. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\left(\frac{4}{y}\right), \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

   21. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(4, y\right), \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

   22. sub-neg N/A

       \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(4, y\right), \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right)\right)\right) \]

3. Simplified 98.8%

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

Alternative 8: 40.0% 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 94.5%

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

   1. fabs-lowering-fabs.f64 N/A

      \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x + 4}{y} - \frac{x}{y} \cdot z\right)\right) \]

   2. sub-neg N/A

      \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{x + 4}{y} + \left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right)\right)\right) \]

   3. +-commutative N/A

      \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) + \frac{x + 4}{y}\right)\right) \]

   4. neg-sub0 N/A

      \[\leadsto \mathsf{fabs.f64}\left(\left(\left(0 - \frac{x}{y} \cdot z\right) + \frac{x + 4}{y}\right)\right) \]

   5. associate-+l- N/A

      \[\leadsto \mathsf{fabs.f64}\left(\left(0 - \left(\frac{x}{y} \cdot z - \frac{x + 4}{y}\right)\right)\right) \]

   6. sub0-neg N/A

      \[\leadsto \mathsf{fabs.f64}\left(\left(\mathsf{neg}\left(\left(\frac{x}{y} \cdot z - \frac{x + 4}{y}\right)\right)\right)\right) \]

   7. neg-mul-1 N/A

      \[\leadsto \mathsf{fabs.f64}\left(\left(-1 \cdot \left(\frac{x}{y} \cdot z - \frac{x + 4}{y}\right)\right)\right) \]

   8. distribute-rgt-out-- N/A

      \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\frac{x}{y} \cdot z\right) \cdot -1 - \frac{x + 4}{y} \cdot -1\right)\right) \]

   9. *-commutative N/A

      \[\leadsto \mathsf{fabs.f64}\left(\left(-1 \cdot \left(\frac{x}{y} \cdot z\right) - \frac{x + 4}{y} \cdot -1\right)\right) \]

   10. neg-mul-1 N/A

       \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{x + 4}{y} \cdot -1\right)\right) \]

   11. associate-*l/ N/A

       \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\left(x + 4\right) \cdot -1}{y}\right)\right) \]

   12. *-commutative N/A

       \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{-1 \cdot \left(x + 4\right)}{y}\right)\right) \]

   13. neg-mul-1 N/A

       \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\mathsf{neg}\left(\left(x + 4\right)\right)}{y}\right)\right) \]

   14. distribute-neg-in N/A

       \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\left(\mathsf{neg}\left(x\right)\right) + \left(\mathsf{neg}\left(4\right)\right)}{y}\right)\right) \]

   15. sub-neg N/A

       \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \frac{\left(\mathsf{neg}\left(x\right)\right) - 4}{y}\right)\right) \]

   16. div-sub N/A

       \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\frac{\mathsf{neg}\left(x\right)}{y} - \frac{4}{y}\right)\right)\right) \]

   17. distribute-neg-frac N/A

       \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\left(\mathsf{neg}\left(\frac{x}{y}\right)\right) - \frac{4}{y}\right)\right)\right) \]

   18. associate--r- N/A

       \[\leadsto \mathsf{fabs.f64}\left(\left(\left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right) + \frac{4}{y}\right)\right) \]

   19. +-commutative N/A

       \[\leadsto \mathsf{fabs.f64}\left(\left(\frac{4}{y} + \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

   20. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\left(\frac{4}{y}\right), \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

   21. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(4, y\right), \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

   22. sub-neg N/A

       \[\leadsto \mathsf{fabs.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(4, y\right), \left(\left(\mathsf{neg}\left(\frac{x}{y} \cdot z\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right)\right)\right) \]

3. Simplified 98.8%

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

5. Taylor expanded in x around 0

   \[\leadsto \mathsf{fabs.f64}\left(\color{blue}{\left(\frac{4}{y}\right)}\right) \]
6. Step-by-step derivation

   1. /-lowering-/.f64 39.7%

      \[\leadsto \mathsf{fabs.f64}\left(\mathsf{/.f64}\left(4, y\right)\right) \]

7. Simplified 39.7%

   \[\leadsto \left|\color{blue}{\frac{4}{y}}\right| \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024141 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4.0) y) (* (/ x y) z))))