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

Percentage Accurate: 88.0% → 99.9%

Time: 7.1s

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: 88.0% 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: 99.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{-303}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\frac{z - y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (<= t_0 -4e-303)
     t_0
     (if (<= t_0 0.0) (* z (/ (+ x y) (- y))) (/ (+ x y) (/ (- 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 <= -4e-303) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = z * ((x + y) / -y);
	} else {
		tmp = (x + y) / ((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 <= (-4d-303)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = z * ((x + y) / -y)
    else
        tmp = (x + y) / ((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 <= -4e-303) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = z * ((x + y) / -y);
	} else {
		tmp = (x + y) / ((z - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if t_0 <= -4e-303:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = z * ((x + y) / -y)
	else:
		tmp = (x + y) / ((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 <= -4e-303)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(z * Float64(Float64(x + y) / Float64(-y)));
	else
		tmp = Float64(Float64(x + y) / Float64(Float64(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 <= -4e-303)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = z * ((x + y) / -y);
	else
		tmp = (x + y) / ((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[LessEqual[t$95$0, -4e-303], t$95$0, If[LessEqual[t$95$0, 0.0], N[(z * N[(N[(x + y), $MachinePrecision] / (-y)), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] / N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -3.99999999999999972e-303

   1. Initial program 99.9%

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

   if -3.99999999999999972e-303 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 5.5%

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

   3. Taylor expanded in z around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. associate-/l* 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. distribute-neg-frac2 100.0%

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

      5. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -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. Taylor expanded in z around 0 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -4 \cdot 10^{-303}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;\frac{x + y}{1 - \frac{y}{z}} \leq 0:\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\frac{z - y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{-303} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -4e-303) (not (<= t_0 0.0))) t_0 (* z (/ (+ x y) (- y))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -4e-303) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * ((x + y) / -y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-4d-303)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = z * ((x + y) / -y)
    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-303) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * ((x + y) / -y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -4e-303) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = z * ((x + y) / -y)
	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-303) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(Float64(x + y) / Float64(-y)));
	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-303) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = z * ((x + y) / -y);
	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-303], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(z * N[(N[(x + y), $MachinePrecision] / (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -3.99999999999999972e-303 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 -3.99999999999999972e-303 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 5.5%

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

   3. Taylor expanded in z around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. associate-/l* 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. distribute-neg-frac2 100.0%

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

      5. +-commutative 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -4 \cdot 10^{-303} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{-36} \lor \neg \left(y \leq 9.5 \cdot 10^{-43}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.95e-36) (not (<= y 9.5e-43)))
   (* z (- -1.0 (/ x y)))
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.95e-36) || !(y <= 9.5e-43)) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.95d-36)) .or. (.not. (y <= 9.5d-43))) then
        tmp = z * ((-1.0d0) - (x / y))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.95e-36) || !(y <= 9.5e-43)) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.95e-36) or not (y <= 9.5e-43):
		tmp = z * (-1.0 - (x / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.95e-36) || !(y <= 9.5e-43))
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.95e-36) || ~((y <= 9.5e-43)))
		tmp = z * (-1.0 - (x / y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.95e-36], N[Not[LessEqual[y, 9.5e-43]], $MachinePrecision]], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.94999999999999998e-36 or 9.50000000000000044e-43 < y

   1. Initial program 71.6%

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

   3. Taylor expanded in z around 0 65.6%

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

      1. mul-1-neg 65.6%

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

      2. associate-/l* 80.4%

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

      3. distribute-rgt-neg-in 80.4%

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

      4. distribute-neg-frac2 80.4%

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

      5. +-commutative 80.4%

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

   5. Simplified 80.4%

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

   6. Taylor expanded in z around 0 65.6%

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

      1. mul-1-neg 65.6%

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

      2. associate-/l* 80.4%

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

      3. +-commutative 80.4%

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

      4. distribute-rgt-neg-in 80.4%

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

      5. distribute-neg-frac 80.4%

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

      6. +-commutative 80.4%

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

      7. distribute-neg-in 80.4%

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

      8. mul-1-neg 80.4%

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

      9. unsub-neg 80.4%

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

      10. div-sub 80.4%

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

      11. associate-*r/ 80.4%

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

      12. *-rgt-identity 80.4%

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

      13. associate-*r/ 80.2%

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

      14. rgt-mult-inverse 80.4%

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

      15. sub-neg 80.4%

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

      16. metadata-eval 80.4%

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

      17. +-commutative 80.4%

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

      18. mul-1-neg 80.4%

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

      19. sub-neg 80.4%

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

   8. Simplified 80.4%

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

   if -2.94999999999999998e-36 < y < 9.50000000000000044e-43

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 82.5%

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

      1. +-commutative 82.5%

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

   5. Simplified 82.5%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{-36} \lor \neg \left(y \leq 9.5 \cdot 10^{-43}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+113} \lor \neg \left(y \leq 4.4 \cdot 10^{+65}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.4e+113) (not (<= y 4.4e+65))) (- z) (* x (/ z (- z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.4e+113) || !(y <= 4.4e+65)) {
		tmp = -z;
	} else {
		tmp = x * (z / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-5.4d+113)) .or. (.not. (y <= 4.4d+65))) then
        tmp = -z
    else
        tmp = x * (z / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.4e+113) || !(y <= 4.4e+65)) {
		tmp = -z;
	} else {
		tmp = x * (z / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.4e+113) or not (y <= 4.4e+65):
		tmp = -z
	else:
		tmp = x * (z / (z - y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.4e+113) || !(y <= 4.4e+65))
		tmp = Float64(-z);
	else
		tmp = Float64(x * Float64(z / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.4e+113) || ~((y <= 4.4e+65)))
		tmp = -z;
	else
		tmp = x * (z / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.4e+113], N[Not[LessEqual[y, 4.4e+65]], $MachinePrecision]], (-z), N[(x * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.40000000000000022e113 or 4.3999999999999997e65 < y

   1. Initial program 59.3%

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

   3. Taylor expanded in y around inf 78.3%

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

      1. neg-mul-1 78.3%

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

   5. Simplified 78.3%

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

   if -5.40000000000000022e113 < y < 4.3999999999999997e65

   1. Initial program 97.1%

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

   3. Taylor expanded in z around 0 97.1%

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

   4. Taylor expanded in x around inf 50.9%

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

      1. associate-/l* 69.6%

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

   6. Simplified 69.6%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+113} \lor \neg \left(y \leq 4.4 \cdot 10^{+65}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+29} \lor \neg \left(y \leq 3.5 \cdot 10^{-26}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.8e+29) (not (<= y 3.5e-26))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.8e+29) || !(y <= 3.5e-26)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-4.8d+29)) .or. (.not. (y <= 3.5d-26))) then
        tmp = -z
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.8e+29) || !(y <= 3.5e-26)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.8e+29) or not (y <= 3.5e-26):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.8e+29) || !(y <= 3.5e-26))
		tmp = Float64(-z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.8e+29) || ~((y <= 3.5e-26)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.8e+29], N[Not[LessEqual[y, 3.5e-26]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.8000000000000002e29 or 3.49999999999999985e-26 < y

   1. Initial program 68.9%

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

   3. Taylor expanded in y around inf 66.6%

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

      1. neg-mul-1 66.6%

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

   5. Simplified 66.6%

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

   if -4.8000000000000002e29 < y < 3.49999999999999985e-26

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 78.8%

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

      1. +-commutative 78.8%

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

   5. Simplified 78.8%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+29} \lor \neg \left(y \leq 3.5 \cdot 10^{-26}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+30} \lor \neg \left(y \leq 3.5 \cdot 10^{-42}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.6e+30) (not (<= y 3.5e-42))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.6e+30) || !(y <= 3.5e-42)) {
		tmp = -z;
	} else {
		tmp = 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 <= (-2.6d+30)) .or. (.not. (y <= 3.5d-42))) then
        tmp = -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.6e+30) || !(y <= 3.5e-42)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.6e+30) or not (y <= 3.5e-42):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.6e+30) || !(y <= 3.5e-42))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.6e+30) || ~((y <= 3.5e-42)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.6e+30], N[Not[LessEqual[y, 3.5e-42]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if y < -2.59999999999999988e30 or 3.5000000000000002e-42 < y

   1. Initial program 69.3%

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

   3. Taylor expanded in y around inf 65.7%

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

      1. neg-mul-1 65.7%

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

   5. Simplified 65.7%

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

   if -2.59999999999999988e30 < y < 3.5000000000000002e-42

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 65.1%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+30} \lor \neg \left(y \leq 3.5 \cdot 10^{-42}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 40.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.3 \cdot 10^{-197}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-122}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.3e-197) x (if (<= x 2.1e-122) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.3e-197) {
		tmp = x;
	} else if (x <= 2.1e-122) {
		tmp = y;
	} else {
		tmp = 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 (x <= (-5.3d-197)) then
        tmp = x
    else if (x <= 2.1d-122) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.3e-197) {
		tmp = x;
	} else if (x <= 2.1e-122) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.3e-197:
		tmp = x
	elif x <= 2.1e-122:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.3e-197)
		tmp = x;
	elseif (x <= 2.1e-122)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.3e-197)
		tmp = x;
	elseif (x <= 2.1e-122)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.3e-197], x, If[LessEqual[x, 2.1e-122], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.29999999999999972e-197 or 2.09999999999999992e-122 < x

   1. Initial program 85.1%

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

   3. Taylor expanded in y around 0 44.4%

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

   if -5.29999999999999972e-197 < x < 2.09999999999999992e-122

   1. Initial program 78.8%

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

   3. Taylor expanded in z around inf 48.1%

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

      1. +-commutative 48.1%

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

   5. Simplified 48.1%

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

   6. Taylor expanded in y around inf 41.5%

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

Alternative 8: 34.3% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 83.7%

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

3. Taylor expanded in y around 0 36.9%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer Target 1: 93.8% accurate, 0.5× 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 2024149 
(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))))