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

Percentage Accurate: 88.1% → 98.5%

Time: 5.7s

Alternatives: 8

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: 88.1% 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: 98.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-208} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-\left(\frac{z \cdot \left(\left(\frac{z \cdot \left(x + z\right)}{y} + x\right) + z\right)}{y} + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -2e-208) (not (<= t_0 0.0)))
     t_0
     (- (+ (/ (* z (+ (+ (/ (* z (+ x z)) y) x) z)) 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 <= -2e-208) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -(((z * ((((z * (x + z)) / y) + 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) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-2d-208)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = -(((z * ((((z * (x + z)) / y) + x) + z)) / 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 <= -2e-208) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -(((z * ((((z * (x + z)) / y) + x) + z)) / y) + z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -2e-208) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = -(((z * ((((z * (x + z)) / y) + x) + z)) / 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 <= -2e-208) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(-Float64(Float64(Float64(z * Float64(Float64(Float64(Float64(z * Float64(x + z)) / y) + x) + z)) / 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 <= -2e-208) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = -(((z * ((((z * (x + z)) / y) + x) + z)) / 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, -2e-208], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, (-N[(N[(N[(z * N[(N[(N[(N[(z * N[(x + z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + z), $MachinePrecision])]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -2.0000000000000002e-208 or 0.0 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.8%

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

   if -2.0000000000000002e-208 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < 0.0

   1. Initial program 13.5%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-208} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-\left(\frac{z \cdot \left(\left(\frac{z \cdot \left(x + z\right)}{y} + x\right) + z\right)}{y} + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-208} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-x}{y}, z, -z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -2e-208) (not (<= t_0 0.0)))
     t_0
     (fma (/ (- x) y) z (- z)))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -2e-208) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = fma((-x / y), z, -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 <= -2e-208) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = fma(Float64(Float64(-x) / y), z, Float64(-z));
	end
	return 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, -2e-208], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(N[((-x) / y), $MachinePrecision] * z + (-z)), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -2.0000000000000002e-208 or 0.0 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.8%

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

   if -2.0000000000000002e-208 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < 0.0

   1. Initial program 13.5%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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%

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

   7. Applied rewrites 100.0%

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

   9. Applied rewrites 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-208} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-x}{y}, z, -z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+59}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 47000000000000:\\ \;\;\;\;\frac{x + y}{1}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+87}:\\ \;\;\;\;\frac{\left(-z\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(-1 - \frac{z}{y}\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.3e+59)
   (- z)
   (if (<= y 47000000000000.0)
     (/ (+ x y) 1.0)
     (if (<= y 7.6e+87) (/ (* (- z) x) y) (* (- -1.0 (/ z y)) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.3e+59) {
		tmp = -z;
	} else if (y <= 47000000000000.0) {
		tmp = (x + y) / 1.0;
	} else if (y <= 7.6e+87) {
		tmp = (-z * x) / y;
	} else {
		tmp = (-1.0 - (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 (y <= (-2.3d+59)) then
        tmp = -z
    else if (y <= 47000000000000.0d0) then
        tmp = (x + y) / 1.0d0
    else if (y <= 7.6d+87) then
        tmp = (-z * x) / y
    else
        tmp = ((-1.0d0) - (z / y)) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.3e+59) {
		tmp = -z;
	} else if (y <= 47000000000000.0) {
		tmp = (x + y) / 1.0;
	} else if (y <= 7.6e+87) {
		tmp = (-z * x) / y;
	} else {
		tmp = (-1.0 - (z / y)) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.3e+59:
		tmp = -z
	elif y <= 47000000000000.0:
		tmp = (x + y) / 1.0
	elif y <= 7.6e+87:
		tmp = (-z * x) / y
	else:
		tmp = (-1.0 - (z / y)) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.3e+59)
		tmp = Float64(-z);
	elseif (y <= 47000000000000.0)
		tmp = Float64(Float64(x + y) / 1.0);
	elseif (y <= 7.6e+87)
		tmp = Float64(Float64(Float64(-z) * x) / y);
	else
		tmp = Float64(Float64(-1.0 - Float64(z / y)) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.3e+59)
		tmp = -z;
	elseif (y <= 47000000000000.0)
		tmp = (x + y) / 1.0;
	elseif (y <= 7.6e+87)
		tmp = (-z * x) / y;
	else
		tmp = (-1.0 - (z / y)) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.3e+59], (-z), If[LessEqual[y, 47000000000000.0], N[(N[(x + y), $MachinePrecision] / 1.0), $MachinePrecision], If[LessEqual[y, 7.6e+87], N[(N[((-z) * x), $MachinePrecision] / y), $MachinePrecision], N[(N[(-1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.30000000000000008e59

   1. Initial program 69.5%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 72.5

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

   5. Applied rewrites 72.5%

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

   if -2.30000000000000008e59 < y < 4.7e13

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 72.2%

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

   if 4.7e13 < y < 7.60000000000000022e87

   1. Initial program 72.7%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 99.6

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

   5. Applied rewrites 99.6%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 72.4%

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

   10. Applied rewrites 86.4%

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

   if 7.60000000000000022e87 < y

   1. Initial program 73.9%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 62.2

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

   5. Applied rewrites 62.2%

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

   6. Taylor expanded in y around inf

      \[\leadsto -1 \cdot z + \color{blue}{-1 \cdot \frac{{z}^{2}}{y}} \]
   7. Step-by-step derivation

   8. Applied rewrites 75.8%

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

Alternative 4: 67.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+59}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 47000000000000:\\ \;\;\;\;\frac{x + y}{1}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+87}:\\ \;\;\;\;\frac{\left(-z\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.3e+59)
   (- z)
   (if (<= y 47000000000000.0)
     (/ (+ x y) 1.0)
     (if (<= y 7.6e+87) (/ (* (- z) x) y) (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.3e+59) {
		tmp = -z;
	} else if (y <= 47000000000000.0) {
		tmp = (x + y) / 1.0;
	} else if (y <= 7.6e+87) {
		tmp = (-z * x) / y;
	} else {
		tmp = -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 (y <= (-2.3d+59)) then
        tmp = -z
    else if (y <= 47000000000000.0d0) then
        tmp = (x + y) / 1.0d0
    else if (y <= 7.6d+87) then
        tmp = (-z * x) / y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.3e+59) {
		tmp = -z;
	} else if (y <= 47000000000000.0) {
		tmp = (x + y) / 1.0;
	} else if (y <= 7.6e+87) {
		tmp = (-z * x) / y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.3e+59:
		tmp = -z
	elif y <= 47000000000000.0:
		tmp = (x + y) / 1.0
	elif y <= 7.6e+87:
		tmp = (-z * x) / y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.3e+59)
		tmp = Float64(-z);
	elseif (y <= 47000000000000.0)
		tmp = Float64(Float64(x + y) / 1.0);
	elseif (y <= 7.6e+87)
		tmp = Float64(Float64(Float64(-z) * x) / y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.3e+59)
		tmp = -z;
	elseif (y <= 47000000000000.0)
		tmp = (x + y) / 1.0;
	elseif (y <= 7.6e+87)
		tmp = (-z * x) / y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.3e+59], (-z), If[LessEqual[y, 47000000000000.0], N[(N[(x + y), $MachinePrecision] / 1.0), $MachinePrecision], If[LessEqual[y, 7.6e+87], N[(N[((-z) * x), $MachinePrecision] / y), $MachinePrecision], (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.30000000000000008e59 or 7.60000000000000022e87 < y

   1. Initial program 71.2%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 73.6

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

   5. Applied rewrites 73.6%

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

   if -2.30000000000000008e59 < y < 4.7e13

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 72.2%

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

   if 4.7e13 < y < 7.60000000000000022e87

   1. Initial program 72.7%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 99.6

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

   5. Applied rewrites 99.6%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 72.4%

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

   10. Applied rewrites 86.4%

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

Alternative 5: 74.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-27} \lor \neg \left(y \leq 4.7 \cdot 10^{-51}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{-x}{y}, z, -z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.3e-27) (not (<= y 4.7e-51)))
   (fma (/ (- x) y) z (- z))
   (/ (+ x y) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.3e-27) || !(y <= 4.7e-51)) {
		tmp = fma((-x / y), z, -z);
	} else {
		tmp = (x + y) / 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.3e-27) || !(y <= 4.7e-51))
		tmp = fma(Float64(Float64(-x) / y), z, Float64(-z));
	else
		tmp = Float64(Float64(x + y) / 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.3e-27], N[Not[LessEqual[y, 4.7e-51]], $MachinePrecision]], N[(N[((-x) / y), $MachinePrecision] * z + (-z)), $MachinePrecision], N[(N[(x + y), $MachinePrecision] / 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2999999999999999e-27 or 4.6999999999999997e-51 < y

   1. Initial program 77.4%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 78.6

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

   5. Applied rewrites 78.6%

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

   7. Applied rewrites 78.6%

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

   9. Applied rewrites 78.6%

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

   if -2.2999999999999999e-27 < y < 4.6999999999999997e-51

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 80.3%

      \[\leadsto \frac{x + y}{\color{blue}{1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-27} \lor \neg \left(y \leq 4.7 \cdot 10^{-51}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{-x}{y}, z, -z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-27} \lor \neg \left(y \leq 4.7 \cdot 10^{-51}\right):\\ \;\;\;\;\left(-1 - \frac{x}{y}\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.3e-27) (not (<= y 4.7e-51)))
   (* (- -1.0 (/ x y)) z)
   (/ (+ x y) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.3e-27) || !(y <= 4.7e-51)) {
		tmp = (-1.0 - (x / y)) * z;
	} else {
		tmp = (x + y) / 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.3d-27)) .or. (.not. (y <= 4.7d-51))) then
        tmp = ((-1.0d0) - (x / y)) * z
    else
        tmp = (x + y) / 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.3e-27) || !(y <= 4.7e-51)) {
		tmp = (-1.0 - (x / y)) * z;
	} else {
		tmp = (x + y) / 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.3e-27) or not (y <= 4.7e-51):
		tmp = (-1.0 - (x / y)) * z
	else:
		tmp = (x + y) / 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.3e-27) || !(y <= 4.7e-51))
		tmp = Float64(Float64(-1.0 - Float64(x / y)) * z);
	else
		tmp = Float64(Float64(x + y) / 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.3e-27) || ~((y <= 4.7e-51)))
		tmp = (-1.0 - (x / y)) * z;
	else
		tmp = (x + y) / 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.3e-27], N[Not[LessEqual[y, 4.7e-51]], $MachinePrecision]], N[(N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(N[(x + y), $MachinePrecision] / 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2999999999999999e-27 or 4.6999999999999997e-51 < y

   1. Initial program 77.4%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 78.6

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

   5. Applied rewrites 78.6%

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

   if -2.2999999999999999e-27 < y < 4.6999999999999997e-51

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 80.3%

      \[\leadsto \frac{x + y}{\color{blue}{1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-27} \lor \neg \left(y \leq 4.7 \cdot 10^{-51}\right):\\ \;\;\;\;\left(-1 - \frac{x}{y}\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+59} \lor \neg \left(y \leq 1.55 \cdot 10^{+37}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.3e+59) (not (<= y 1.55e+37))) (- z) (/ (+ x y) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.3e+59) || !(y <= 1.55e+37)) {
		tmp = -z;
	} else {
		tmp = (x + y) / 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.3d+59)) .or. (.not. (y <= 1.55d+37))) then
        tmp = -z
    else
        tmp = (x + y) / 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.3e+59) || !(y <= 1.55e+37)) {
		tmp = -z;
	} else {
		tmp = (x + y) / 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.3e+59) or not (y <= 1.55e+37):
		tmp = -z
	else:
		tmp = (x + y) / 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.3e+59) || !(y <= 1.55e+37))
		tmp = Float64(-z);
	else
		tmp = Float64(Float64(x + y) / 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.3e+59) || ~((y <= 1.55e+37)))
		tmp = -z;
	else
		tmp = (x + y) / 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.3e+59], N[Not[LessEqual[y, 1.55e+37]], $MachinePrecision]], (-z), N[(N[(x + y), $MachinePrecision] / 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.30000000000000008e59 or 1.5500000000000001e37 < y

   1. Initial program 71.1%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 70.8

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

   5. Applied rewrites 70.8%

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

   if -2.30000000000000008e59 < y < 1.5500000000000001e37

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 71.7%

      \[\leadsto \frac{x + y}{\color{blue}{1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+59} \lor \neg \left(y \leq 1.55 \cdot 10^{+37}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 35.3% 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 86.7%

   \[\frac{x + y}{1 - \frac{y}{z}} \]
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 38.2

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

5. Applied rewrites 38.2%

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

Developer Target 1: 93.8% 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 2024307 
(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))))