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

Percentage Accurate: 88.4% → 99.4%

Time: 7.0s

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: 88.4% 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: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{-248} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{-y} - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -4e-248) (not (<= t_0 0.0))) t_0 (- (/ (* z 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 <= -4e-248) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = ((z * 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 <= (-4d-248)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = ((z * 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 <= -4e-248) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = ((z * x) / -y) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -4e-248) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = ((z * 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 <= -4e-248) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(z * x) / Float64(-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 <= -4e-248) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = ((z * 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, -4e-248], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(N[(N[(z * x), $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))) < -3.99999999999999992e-248 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

   if -3.99999999999999992e-248 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 15.0%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -4 \cdot 10^{-248} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{-y} - z\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+22} \lor \neg \left(y \leq 7.2 \cdot 10^{-54}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(y + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.6e+22) (not (<= y 7.2e-54)))
   (* z (- -1.0 (/ x y)))
   (* 1.0 (+ y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.6e+22) || !(y <= 7.2e-54)) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = 1.0 * (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 <= (-3.6d+22)) .or. (.not. (y <= 7.2d-54))) then
        tmp = z * ((-1.0d0) - (x / y))
    else
        tmp = 1.0d0 * (y + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.6e+22) || !(y <= 7.2e-54)) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = 1.0 * (y + x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.6e+22) or not (y <= 7.2e-54):
		tmp = z * (-1.0 - (x / y))
	else:
		tmp = 1.0 * (y + x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.6e+22) || !(y <= 7.2e-54))
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	else
		tmp = Float64(1.0 * Float64(y + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.6e+22) || ~((y <= 7.2e-54)))
		tmp = z * (-1.0 - (x / y));
	else
		tmp = 1.0 * (y + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.6e+22], N[Not[LessEqual[y, 7.2e-54]], $MachinePrecision]], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 * N[(y + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.6e22 or 7.19999999999999953e-54 < y

   1. Initial program 75.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. div-add N/A

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

      5. distribute-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. *-inverses N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. *-commutative N/A

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

      11. mul-1-neg N/A

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

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

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

      13. associate-/l* N/A

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

      14. *-commutative N/A

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

      15. mul-1-neg N/A

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

      16. +-commutative N/A

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

      17. fp-cancel-sign-sub-inv N/A

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. *-commutative N/A

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

      21. *-commutative N/A

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

      22. associate-/l* N/A

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

   5. Applied rewrites 79.8%

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

   if -3.6e22 < y < 7.19999999999999953e-54

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. lower-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower-/.f64 76.2

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

   5. Applied rewrites 76.2%

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

   7. Applied rewrites 76.2%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 76.2%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+22} \lor \neg \left(y \leq 7.2 \cdot 10^{-54}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(y + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+22}:\\ \;\;\;\;-\mathsf{fma}\left(\frac{z + x}{y}, z, z\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-54}:\\ \;\;\;\;1 \cdot \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.6e+22)
   (- (fma (/ (+ z x) y) z z))
   (if (<= y 7.2e-54) (* 1.0 (+ y x)) (* z (- -1.0 (/ x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.6e+22) {
		tmp = -fma(((z + x) / y), z, z);
	} else if (y <= 7.2e-54) {
		tmp = 1.0 * (y + x);
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.6e+22)
		tmp = Float64(-fma(Float64(Float64(z + x) / y), z, z));
	elseif (y <= 7.2e-54)
		tmp = Float64(1.0 * Float64(y + x));
	else
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.6e+22], (-N[(N[(N[(z + x), $MachinePrecision] / y), $MachinePrecision] * z + z), $MachinePrecision]), If[LessEqual[y, 7.2e-54], N[(1.0 * N[(y + x), $MachinePrecision]), $MachinePrecision], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6e22

   1. Initial program 71.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. div-add N/A

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

      5. distribute-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. *-inverses N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. *-commutative N/A

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

      11. mul-1-neg N/A

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

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

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

      13. associate-/l* N/A

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

      14. *-commutative N/A

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

      15. mul-1-neg N/A

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

      16. +-commutative N/A

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

      17. fp-cancel-sign-sub-inv N/A

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. *-commutative N/A

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

      21. *-commutative N/A

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

      22. associate-/l* N/A

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

   5. Applied rewrites 73.8%

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

   6. Taylor expanded in y around inf

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. associate--l- N/A

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

      5. div-add N/A

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

      6. unpow2 N/A

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

      7. distribute-rgt-in N/A

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

      8. associate-/l* N/A

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

      9. div-add-rev N/A

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

      10. mul-1-neg N/A

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

      11. *-rgt-identity N/A

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

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

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

      13. mul-1-neg N/A

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

      14. fp-cancel-sub-sign N/A

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

      15. mul-1-neg N/A

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

      16. distribute-lft-in N/A

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

      17. mul-1-neg N/A

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

   8. Applied rewrites 73.8%

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

   if -3.6e22 < y < 7.19999999999999953e-54

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. lower-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower-/.f64 76.2

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

   5. Applied rewrites 76.2%

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

   7. Applied rewrites 76.2%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 76.2%

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

   if 7.19999999999999953e-54 < y

   1. Initial program 77.3%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. div-add N/A

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

      5. distribute-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. *-inverses N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. *-commutative N/A

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

      11. mul-1-neg N/A

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

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

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

      13. associate-/l* N/A

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

      14. *-commutative N/A

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

      15. mul-1-neg N/A

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

      16. +-commutative N/A

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

      17. fp-cancel-sign-sub-inv N/A

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. *-commutative N/A

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

      21. *-commutative N/A

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

      22. associate-/l* N/A

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

   5. Applied rewrites 84.4%

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

Alternative 4: 66.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+57}:\\ \;\;\;\;-\mathsf{fma}\left(\frac{z}{y}, z, z\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+24}:\\ \;\;\;\;1 \cdot \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.42e+57)
   (- (fma (/ z y) z z))
   (if (<= y 3.1e+24) (* 1.0 (+ y x)) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.42e+57) {
		tmp = -fma((z / y), z, z);
	} else if (y <= 3.1e+24) {
		tmp = 1.0 * (y + x);
	} else {
		tmp = -z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.42e+57)
		tmp = Float64(-fma(Float64(z / y), z, z));
	elseif (y <= 3.1e+24)
		tmp = Float64(1.0 * Float64(y + x));
	else
		tmp = Float64(-z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.42e+57], (-N[(N[(z / y), $MachinePrecision] * z + z), $MachinePrecision]), If[LessEqual[y, 3.1e+24], N[(1.0 * N[(y + x), $MachinePrecision]), $MachinePrecision], (-z)]]

Derivation

1. Split input into 3 regimes

2. if y < -1.42e57

   1. Initial program 66.3%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. div-add N/A

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

      5. distribute-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. *-inverses N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. *-commutative N/A

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

      11. mul-1-neg N/A

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

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

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

      13. associate-/l* N/A

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

      14. *-commutative N/A

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

      15. mul-1-neg N/A

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

      16. +-commutative N/A

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

      17. fp-cancel-sign-sub-inv N/A

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. *-commutative N/A

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

      21. *-commutative N/A

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

      22. associate-/l* N/A

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

   5. Applied rewrites 77.1%

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

   6. Taylor expanded in y around inf

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. associate--l- N/A

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

      5. div-add N/A

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

      6. unpow2 N/A

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

      7. distribute-rgt-in N/A

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

      8. associate-/l* N/A

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

      9. div-add-rev N/A

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

      10. mul-1-neg N/A

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

      11. *-rgt-identity N/A

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

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

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

      13. mul-1-neg N/A

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

      14. fp-cancel-sub-sign N/A

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

      15. mul-1-neg N/A

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

      16. distribute-lft-in N/A

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

      17. mul-1-neg N/A

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

   8. Applied rewrites 77.1%

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

   9. Taylor expanded in x around 0

      \[\leadsto -\mathsf{fma}\left(\frac{z}{y}, z, z\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 61.9%

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

   if -1.42e57 < y < 3.10000000000000011e24

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. lower-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower-/.f64 68.4

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

   5. Applied rewrites 68.4%

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

   7. Applied rewrites 68.4%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 68.5%

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

   if 3.10000000000000011e24 < y

   1. Initial program 73.4%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 68.3

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

   5. Applied rewrites 68.3%

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

Alternative 5: 67.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+57} \lor \neg \left(y \leq 3.1 \cdot 10^{+24}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(y + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.4e+57) (not (<= y 3.1e+24))) (- z) (* 1.0 (+ y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.4e+57) || !(y <= 3.1e+24)) {
		tmp = -z;
	} else {
		tmp = 1.0 * (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 <= (-1.4d+57)) .or. (.not. (y <= 3.1d+24))) then
        tmp = -z
    else
        tmp = 1.0d0 * (y + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.4e+57) || !(y <= 3.1e+24)) {
		tmp = -z;
	} else {
		tmp = 1.0 * (y + x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.4e+57) or not (y <= 3.1e+24):
		tmp = -z
	else:
		tmp = 1.0 * (y + x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.4e+57) || !(y <= 3.1e+24))
		tmp = Float64(-z);
	else
		tmp = Float64(1.0 * Float64(y + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.4e+57) || ~((y <= 3.1e+24)))
		tmp = -z;
	else
		tmp = 1.0 * (y + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.4e+57], N[Not[LessEqual[y, 3.1e+24]], $MachinePrecision]], (-z), N[(1.0 * N[(y + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e57 or 3.10000000000000011e24 < y

   1. Initial program 70.4%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 65.6

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

   5. Applied rewrites 65.6%

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

   if -1.4e57 < y < 3.10000000000000011e24

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. lower-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower-/.f64 68.4

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

   5. Applied rewrites 68.4%

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

   7. Applied rewrites 68.4%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 68.5%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+57} \lor \neg \left(y \leq 3.1 \cdot 10^{+24}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(y + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 34.9% 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 86.3%

   \[\frac{x + y}{1 - \frac{y}{z}} \]
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 39.2

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

5. Applied rewrites 39.2%

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

Developer Target 1: 94.0% 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 2024338 
(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))))