Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A

Percentage Accurate: 87.8% → 98.9%

Time: 5.8s

Alternatives: 6

Speedup: 0.3×

Specification

Math

\[\begin{array}{l} \\ \frac{x + y}{1 - \frac{y}{z}} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 87.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + y}{1 - \frac{y}{z}} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-222} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;\frac{x + y}{\frac{z - y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-1 - \frac{x}{y}\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -5e-222) (not (<= t_0 0.0)))
     (/ (+ x y) (/ (- z y) z))
     (* (- -1.0 (/ x y)) z))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -5e-222) || !(t_0 <= 0.0)) {
		tmp = (x + y) / ((z - y) / z);
	} else {
		tmp = (-1.0 - (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) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-5d-222)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = (x + y) / ((z - y) / z)
    else
        tmp = ((-1.0d0) - (x / y)) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -5e-222) || !(t_0 <= 0.0)) {
		tmp = (x + y) / ((z - y) / z);
	} else {
		tmp = (-1.0 - (x / y)) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -5e-222) or not (t_0 <= 0.0):
		tmp = (x + y) / ((z - y) / z)
	else:
		tmp = (-1.0 - (x / y)) * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -5e-222) || !(t_0 <= 0.0))
		tmp = Float64(Float64(x + y) / Float64(Float64(z - y) / z));
	else
		tmp = Float64(Float64(-1.0 - Float64(x / y)) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if ((t_0 <= -5e-222) || ~((t_0 <= 0.0)))
		tmp = (x + y) / ((z - y) / z);
	else
		tmp = (-1.0 - (x / y)) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -5e-222], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] / N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -5.00000000000000008e-222 or 0.0 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. div-inv N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. distribute-frac-neg2 N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in z around 0

      \[\leadsto \frac{x + y}{\color{blue}{\frac{z + -1 \cdot y}{z}}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. mul-1-neg N/A

         \[\leadsto \frac{x + y}{\frac{z + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}}{z}} \]

      3. unsub-neg N/A

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

      4. lower--.f64 99.9

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

   7. Applied rewrites 99.9%

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

   if -5.00000000000000008e-222 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < 0.0

   1. Initial program 16.2%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. +-commutative N/A

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

      7. distribute-lft-in N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

         \[\leadsto \frac{\color{blue}{-1 \cdot y - x}}{y} \cdot z \]

      10. div-sub N/A

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

      11. associate-*l/ N/A

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

      12. metadata-eval N/A

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

      13. distribute-neg-frac N/A

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

      14. distribute-lft-neg-out N/A

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

      15. lft-mult-inverse N/A

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

      16. metadata-eval N/A

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

      17. lower--.f64 N/A

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

      18. lower-/.f64 99.9

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

   5. Applied rewrites 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -5 \cdot 10^{-222} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{\frac{z - y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-1 - \frac{x}{y}\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-1 - \frac{x}{y}\right) \cdot z\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{+48}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -3400:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-84}:\\ \;\;\;\;\frac{z}{z - y} \cdot x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+101}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- -1.0 (/ x y)) z)))
   (if (<= y -1.85e+48)
     t_0
     (if (<= y -3400.0)
       (+ y x)
       (if (<= y 1.02e-84)
         (* (/ z (- z y)) x)
         (if (<= y 1.4e+101) (+ y x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (-1.0 - (x / y)) * z;
	double tmp;
	if (y <= -1.85e+48) {
		tmp = t_0;
	} else if (y <= -3400.0) {
		tmp = y + x;
	} else if (y <= 1.02e-84) {
		tmp = (z / (z - y)) * x;
	} else if (y <= 1.4e+101) {
		tmp = y + x;
	} 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 = ((-1.0d0) - (x / y)) * z
    if (y <= (-1.85d+48)) then
        tmp = t_0
    else if (y <= (-3400.0d0)) then
        tmp = y + x
    else if (y <= 1.02d-84) then
        tmp = (z / (z - y)) * x
    else if (y <= 1.4d+101) then
        tmp = y + x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (-1.0 - (x / y)) * z;
	double tmp;
	if (y <= -1.85e+48) {
		tmp = t_0;
	} else if (y <= -3400.0) {
		tmp = y + x;
	} else if (y <= 1.02e-84) {
		tmp = (z / (z - y)) * x;
	} else if (y <= 1.4e+101) {
		tmp = y + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (-1.0 - (x / y)) * z
	tmp = 0
	if y <= -1.85e+48:
		tmp = t_0
	elif y <= -3400.0:
		tmp = y + x
	elif y <= 1.02e-84:
		tmp = (z / (z - y)) * x
	elif y <= 1.4e+101:
		tmp = y + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-1.0 - Float64(x / y)) * z)
	tmp = 0.0
	if (y <= -1.85e+48)
		tmp = t_0;
	elseif (y <= -3400.0)
		tmp = Float64(y + x);
	elseif (y <= 1.02e-84)
		tmp = Float64(Float64(z / Float64(z - y)) * x);
	elseif (y <= 1.4e+101)
		tmp = Float64(y + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (-1.0 - (x / y)) * z;
	tmp = 0.0;
	if (y <= -1.85e+48)
		tmp = t_0;
	elseif (y <= -3400.0)
		tmp = y + x;
	elseif (y <= 1.02e-84)
		tmp = (z / (z - y)) * x;
	elseif (y <= 1.4e+101)
		tmp = y + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[y, -1.85e+48], t$95$0, If[LessEqual[y, -3400.0], N[(y + x), $MachinePrecision], If[LessEqual[y, 1.02e-84], N[(N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 1.4e+101], N[(y + x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.85e48 or 1.39999999999999991e101 < y

   1. Initial program 64.8%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. +-commutative N/A

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

      7. distribute-lft-in N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

         \[\leadsto \frac{\color{blue}{-1 \cdot y - x}}{y} \cdot z \]

      10. div-sub N/A

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

      11. associate-*l/ N/A

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

      12. metadata-eval N/A

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

      13. distribute-neg-frac N/A

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

      14. distribute-lft-neg-out N/A

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

      15. lft-mult-inverse N/A

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

      16. metadata-eval N/A

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

      17. lower--.f64 N/A

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

      18. lower-/.f64 83.4

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

   5. Applied rewrites 83.4%

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

   if -1.85e48 < y < -3400 or 1.02000000000000004e-84 < y < 1.39999999999999991e101

   1. Initial program 100.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{-1 \cdot \frac{\left(x \cdot z + \frac{z \cdot \left(x \cdot z - -1 \cdot {z}^{2}\right)}{y}\right) - -1 \cdot {z}^{2}}{y} + -1 \cdot z} \]

      2. mul-1-neg N/A

         \[\leadsto -1 \cdot \frac{\left(x \cdot z + \frac{z \cdot \left(x \cdot z - -1 \cdot {z}^{2}\right)}{y}\right) - -1 \cdot {z}^{2}}{y} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \]

      3. unsub-neg N/A

         \[\leadsto \color{blue}{-1 \cdot \frac{\left(x \cdot z + \frac{z \cdot \left(x \cdot z - -1 \cdot {z}^{2}\right)}{y}\right) - -1 \cdot {z}^{2}}{y} - z} \]

      4. lower--.f64 N/A

         \[\leadsto \color{blue}{-1 \cdot \frac{\left(x \cdot z + \frac{z \cdot \left(x \cdot z - -1 \cdot {z}^{2}\right)}{y}\right) - -1 \cdot {z}^{2}}{y} - z} \]

   5. Applied rewrites 27.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 27.6%

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

   9. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + y} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \color{blue}{y + x} \]

       2. lower-+.f64 74.1

          \[\leadsto \color{blue}{y + x} \]

   11. Applied rewrites 74.1%

       \[\leadsto \color{blue}{y + x} \]

   if -3400 < y < 1.02000000000000004e-84

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{1 - \frac{y}{z}}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 84.4

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

   5. Applied rewrites 84.4%

      \[\leadsto \color{blue}{\frac{x}{1 - \frac{y}{z}}} \]
   6. Step-by-step derivation

   7. Applied rewrites 84.4%

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

Alternative 3: 73.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+84} \lor \neg \left(z \leq 2.1 \cdot 10^{+26}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{-y} - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.55e+84) (not (<= z 2.1e+26)))
   (+ y x)
   (- (/ (* x z) (- y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.55e+84) || !(z <= 2.1e+26)) {
		tmp = y + x;
	} else {
		tmp = ((x * z) / -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 <= (-1.55d+84)) .or. (.not. (z <= 2.1d+26))) then
        tmp = y + x
    else
        tmp = ((x * z) / -y) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.55e+84) || !(z <= 2.1e+26)) {
		tmp = y + x;
	} else {
		tmp = ((x * z) / -y) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.55e+84) or not (z <= 2.1e+26):
		tmp = y + x
	else:
		tmp = ((x * z) / -y) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.55e+84) || !(z <= 2.1e+26))
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(Float64(x * z) / Float64(-y)) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.55e+84) || ~((z <= 2.1e+26)))
		tmp = y + x;
	else
		tmp = ((x * z) / -y) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.55e+84], N[Not[LessEqual[z, 2.1e+26]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(N[(N[(x * z), $MachinePrecision] / (-y)), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.55000000000000001e84 or 2.1000000000000001e26 < z

   1. Initial program 100.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{-1 \cdot \frac{\left(x \cdot z + \frac{z \cdot \left(x \cdot z - -1 \cdot {z}^{2}\right)}{y}\right) - -1 \cdot {z}^{2}}{y} + -1 \cdot z} \]

      2. mul-1-neg N/A

         \[\leadsto -1 \cdot \frac{\left(x \cdot z + \frac{z \cdot \left(x \cdot z - -1 \cdot {z}^{2}\right)}{y}\right) - -1 \cdot {z}^{2}}{y} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \]

      3. unsub-neg N/A

         \[\leadsto \color{blue}{-1 \cdot \frac{\left(x \cdot z + \frac{z \cdot \left(x \cdot z - -1 \cdot {z}^{2}\right)}{y}\right) - -1 \cdot {z}^{2}}{y} - z} \]

      4. lower--.f64 N/A

         \[\leadsto \color{blue}{-1 \cdot \frac{\left(x \cdot z + \frac{z \cdot \left(x \cdot z - -1 \cdot {z}^{2}\right)}{y}\right) - -1 \cdot {z}^{2}}{y} - z} \]

   5. Applied rewrites 9.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 13.5%

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

   9. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + y} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \color{blue}{y + x} \]

       2. lower-+.f64 85.5

          \[\leadsto \color{blue}{y + x} \]

   11. Applied rewrites 85.5%

       \[\leadsto \color{blue}{y + x} \]

   if -1.55000000000000001e84 < z < 2.1000000000000001e26

   1. Initial program 74.1%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{-1 \cdot \frac{\left(x \cdot z + \frac{z \cdot \left(x \cdot z - -1 \cdot {z}^{2}\right)}{y}\right) - -1 \cdot {z}^{2}}{y} + -1 \cdot z} \]

      2. mul-1-neg N/A

         \[\leadsto -1 \cdot \frac{\left(x \cdot z + \frac{z \cdot \left(x \cdot z - -1 \cdot {z}^{2}\right)}{y}\right) - -1 \cdot {z}^{2}}{y} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \]

      3. unsub-neg N/A

         \[\leadsto \color{blue}{-1 \cdot \frac{\left(x \cdot z + \frac{z \cdot \left(x \cdot z - -1 \cdot {z}^{2}\right)}{y}\right) - -1 \cdot {z}^{2}}{y} - z} \]

      4. lower--.f64 N/A

         \[\leadsto \color{blue}{-1 \cdot \frac{\left(x \cdot z + \frac{z \cdot \left(x \cdot z - -1 \cdot {z}^{2}\right)}{y}\right) - -1 \cdot {z}^{2}}{y} - z} \]

   5. Applied rewrites 76.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 76.7%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+84} \lor \neg \left(z \leq 2.1 \cdot 10^{+26}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{-y} - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+84} \lor \neg \left(z \leq 2.1 \cdot 10^{+26}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\left(-1 - \frac{x}{y}\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.6e+84) (not (<= z 2.1e+26))) (+ y x) (* (- -1.0 (/ x y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.6e+84) || !(z <= 2.1e+26)) {
		tmp = y + x;
	} else {
		tmp = (-1.0 - (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 <= (-1.6d+84)) .or. (.not. (z <= 2.1d+26))) then
        tmp = y + x
    else
        tmp = ((-1.0d0) - (x / y)) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.6e+84) || !(z <= 2.1e+26)) {
		tmp = y + x;
	} else {
		tmp = (-1.0 - (x / y)) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.6e+84) or not (z <= 2.1e+26):
		tmp = y + x
	else:
		tmp = (-1.0 - (x / y)) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.6e+84) || !(z <= 2.1e+26))
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(-1.0 - Float64(x / y)) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.6e+84) || ~((z <= 2.1e+26)))
		tmp = y + x;
	else
		tmp = (-1.0 - (x / y)) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.6e+84], N[Not[LessEqual[z, 2.1e+26]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.60000000000000005e84 or 2.1000000000000001e26 < z

   1. Initial program 100.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{-1 \cdot \frac{\left(x \cdot z + \frac{z \cdot \left(x \cdot z - -1 \cdot {z}^{2}\right)}{y}\right) - -1 \cdot {z}^{2}}{y} + -1 \cdot z} \]

      2. mul-1-neg N/A

         \[\leadsto -1 \cdot \frac{\left(x \cdot z + \frac{z \cdot \left(x \cdot z - -1 \cdot {z}^{2}\right)}{y}\right) - -1 \cdot {z}^{2}}{y} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \]

      3. unsub-neg N/A

         \[\leadsto \color{blue}{-1 \cdot \frac{\left(x \cdot z + \frac{z \cdot \left(x \cdot z - -1 \cdot {z}^{2}\right)}{y}\right) - -1 \cdot {z}^{2}}{y} - z} \]

      4. lower--.f64 N/A

         \[\leadsto \color{blue}{-1 \cdot \frac{\left(x \cdot z + \frac{z \cdot \left(x \cdot z - -1 \cdot {z}^{2}\right)}{y}\right) - -1 \cdot {z}^{2}}{y} - z} \]

   5. Applied rewrites 9.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 13.5%

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

   9. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + y} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \color{blue}{y + x} \]

       2. lower-+.f64 85.5

          \[\leadsto \color{blue}{y + x} \]

   11. Applied rewrites 85.5%

       \[\leadsto \color{blue}{y + x} \]

   if -1.60000000000000005e84 < z < 2.1000000000000001e26

   1. Initial program 74.1%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. +-commutative N/A

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

      7. distribute-lft-in N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

         \[\leadsto \frac{\color{blue}{-1 \cdot y - x}}{y} \cdot z \]

      10. div-sub N/A

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

      11. associate-*l/ N/A

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

      12. metadata-eval N/A

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

      13. distribute-neg-frac N/A

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

      14. distribute-lft-neg-out N/A

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

      15. lft-mult-inverse N/A

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

      16. metadata-eval N/A

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

      17. lower--.f64 N/A

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

      18. lower-/.f64 72.2

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

   5. Applied rewrites 72.2%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+84} \lor \neg \left(z \leq 2.1 \cdot 10^{+26}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\left(-1 - \frac{x}{y}\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.25 \cdot 10^{+49} \lor \neg \left(y \leq 5 \cdot 10^{+101}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.25e+49) (not (<= y 5e+101))) (- z) (+ y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.25e+49) || !(y <= 5e+101)) {
		tmp = -z;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-4.25d+49)) .or. (.not. (y <= 5d+101))) then
        tmp = -z
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.25e+49) || !(y <= 5e+101)) {
		tmp = -z;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.25e+49) or not (y <= 5e+101):
		tmp = -z
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.25e+49) || !(y <= 5e+101))
		tmp = Float64(-z);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.25e+49) || ~((y <= 5e+101)))
		tmp = -z;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.25e+49], N[Not[LessEqual[y, 5e+101]], $MachinePrecision]], (-z), N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2499999999999998e49 or 4.99999999999999989e101 < y

   1. Initial program 64.8%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

      2. lower-neg.f64 67.7

         \[\leadsto \color{blue}{-z} \]

   5. Applied rewrites 67.7%

      \[\leadsto \color{blue}{-z} \]

   if -4.2499999999999998e49 < y < 4.99999999999999989e101

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{-1 \cdot \frac{\left(x \cdot z + \frac{z \cdot \left(x \cdot z - -1 \cdot {z}^{2}\right)}{y}\right) - -1 \cdot {z}^{2}}{y} + -1 \cdot z} \]

      2. mul-1-neg N/A

         \[\leadsto -1 \cdot \frac{\left(x \cdot z + \frac{z \cdot \left(x \cdot z - -1 \cdot {z}^{2}\right)}{y}\right) - -1 \cdot {z}^{2}}{y} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \]

      3. unsub-neg N/A

         \[\leadsto \color{blue}{-1 \cdot \frac{\left(x \cdot z + \frac{z \cdot \left(x \cdot z - -1 \cdot {z}^{2}\right)}{y}\right) - -1 \cdot {z}^{2}}{y} - z} \]

      4. lower--.f64 N/A

         \[\leadsto \color{blue}{-1 \cdot \frac{\left(x \cdot z + \frac{z \cdot \left(x \cdot z - -1 \cdot {z}^{2}\right)}{y}\right) - -1 \cdot {z}^{2}}{y} - z} \]

   5. Applied rewrites 27.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 28.0%

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

   9. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + y} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \color{blue}{y + x} \]

       2. lower-+.f64 72.1

          \[\leadsto \color{blue}{y + x} \]

   11. Applied rewrites 72.1%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.25 \cdot 10^{+49} \lor \neg \left(y \leq 5 \cdot 10^{+101}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 34.4% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ -z \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return -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 = -z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := (-z)

Derivation

1. Initial program 84.8%

   \[\frac{x + y}{1 - \frac{y}{z}} \]
2. Add Preprocessing

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{-1 \cdot z} \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

   2. lower-neg.f64 35.8

      \[\leadsto \color{blue}{-z} \]

5. Applied rewrites 35.8%

   \[\leadsto \color{blue}{-z} \]
6. Add Preprocessing

Developer Target 1: 93.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y + x}{-y} \cdot z\\ \mathbf{if}\;y < -3.7429310762689856 \cdot 10^{+171}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y < 3.5534662456086734 \cdot 10^{+168}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ (+ y x) (- y)) z)))
   (if (< y -3.7429310762689856e+171)
     t_0
     (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1.0 (/ y z))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y + x) / -y) * z;
	double tmp;
	if (y < -3.7429310762689856e+171) {
		tmp = t_0;
	} else if (y < 3.5534662456086734e+168) {
		tmp = (x + y) / (1.0 - (y / z));
	} 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 = ((y + x) / -y) * z
    if (y < (-3.7429310762689856d+171)) then
        tmp = t_0
    else if (y < 3.5534662456086734d+168) then
        tmp = (x + y) / (1.0d0 - (y / z))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((y + x) / -y) * z;
	double tmp;
	if (y < -3.7429310762689856e+171) {
		tmp = t_0;
	} else if (y < 3.5534662456086734e+168) {
		tmp = (x + y) / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y + x) / -y) * z
	tmp = 0
	if y < -3.7429310762689856e+171:
		tmp = t_0
	elif y < 3.5534662456086734e+168:
		tmp = (x + y) / (1.0 - (y / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y + x) / Float64(-y)) * z)
	tmp = 0.0
	if (y < -3.7429310762689856e+171)
		tmp = t_0;
	elseif (y < 3.5534662456086734e+168)
		tmp = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y + x) / -y) * z;
	tmp = 0.0;
	if (y < -3.7429310762689856e+171)
		tmp = t_0;
	elseif (y < 3.5534662456086734e+168)
		tmp = (x + y) / (1.0 - (y / z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y + x), $MachinePrecision] / (-y)), $MachinePrecision] * z), $MachinePrecision]}, If[Less[y, -3.7429310762689856e+171], t$95$0, If[Less[y, 3.5534662456086734e+168], N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024317 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -3742931076268985600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* (/ (+ y x) (- y)) z) (if (< y 3553466245608673400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ x y) (- 1 (/ y z))) (* (/ (+ y x) (- y)) z))))

  (/ (+ x y) (- 1.0 (/ y z))))