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

Percentage Accurate: 87.6% → 99.8%

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: 87.6% 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: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-288} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -2e-288) (not (<= t_0 0.0))) t_0 (* z (- -1.0 (/ x y))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -2e-288) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-2d-288)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = z * ((-1.0d0) - (x / 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 <= -2e-288) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -2e-288) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = z * (-1.0 - (x / 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 <= -2e-288) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(-1.0 - Float64(x / 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 <= -2e-288) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = z * (-1.0 - (x / 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, -2e-288], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -2.00000000000000012e-288 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 -2.00000000000000012e-288 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < 0.0

   1. Initial program 16.4%

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

      1. flip-- 4.6%

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

      2. associate-/r/ 1.9%

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

      3. metadata-eval 1.9%

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

      4. pow2 1.9%

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

   4. Applied egg-rr 1.9%

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

      1. associate-*l/ 4.6%

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

      2. +-commutative 4.6%

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

   6. Simplified 4.6%

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

      1. unpow2 4.6%

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

      2. clear-num 4.6%

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

      3. un-div-inv 4.6%

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

   8. Applied egg-rr 4.6%

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

   9. Taylor expanded in z around 0 90.0%

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

       1. mul-1-neg 90.0%

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

       2. associate-/l* 99.9%

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

       3. +-commutative 99.9%

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

       4. distribute-rgt-neg-in 99.9%

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

       5. neg-sub0 99.9%

          \[\leadsto z \cdot \color{blue}{\left(0 - \frac{y + x}{y}\right)} \]

       6. *-lft-identity 99.9%

          \[\leadsto z \cdot \left(0 - \color{blue}{1 \cdot \frac{y + x}{y}}\right) \]

       7. associate-*r/ 99.9%

          \[\leadsto z \cdot \left(0 - \color{blue}{\frac{1 \cdot \left(y + x\right)}{y}}\right) \]

       8. associate-*l/ 99.7%

          \[\leadsto z \cdot \left(0 - \color{blue}{\frac{1}{y} \cdot \left(y + x\right)}\right) \]

       9. distribute-rgt-in 99.7%

          \[\leadsto z \cdot \left(0 - \color{blue}{\left(y \cdot \frac{1}{y} + x \cdot \frac{1}{y}\right)}\right) \]

       10. rgt-mult-inverse 99.9%

           \[\leadsto z \cdot \left(0 - \left(\color{blue}{1} + x \cdot \frac{1}{y}\right)\right) \]

       11. associate--r+ 99.9%

           \[\leadsto z \cdot \color{blue}{\left(\left(0 - 1\right) - x \cdot \frac{1}{y}\right)} \]

       12. metadata-eval 99.9%

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

       13. associate-*r/ 99.9%

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

       14. *-rgt-identity 99.9%

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

   11. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-288} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+71} \lor \neg \left(y \leq 1.75 \cdot 10^{-31}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.5e+71) (not (<= y 1.75e-31)))
   (* z (- -1.0 (/ x y)))
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.5e+71) || !(y <= 1.75e-31)) {
		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 <= (-5.5d+71)) .or. (.not. (y <= 1.75d-31))) 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 <= -5.5e+71) || !(y <= 1.75e-31)) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.5e+71) or not (y <= 1.75e-31):
		tmp = z * (-1.0 - (x / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.5e+71) || !(y <= 1.75e-31))
		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 <= -5.5e+71) || ~((y <= 1.75e-31)))
		tmp = z * (-1.0 - (x / y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.5e+71], N[Not[LessEqual[y, 1.75e-31]], $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 < -5.5e71 or 1.74999999999999993e-31 < y

   1. Initial program 81.9%

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

      1. flip-- 55.5%

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

      2. associate-/r/ 55.5%

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

      3. metadata-eval 55.5%

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

      4. pow2 55.5%

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

   4. Applied egg-rr 55.5%

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

      1. associate-*l/ 43.0%

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

      2. +-commutative 43.0%

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

   6. Simplified 43.0%

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

      1. unpow2 43.0%

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

      2. clear-num 42.9%

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

      3. un-div-inv 43.0%

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

   8. Applied egg-rr 43.0%

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

   9. Taylor expanded in z around 0 50.7%

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

       1. mul-1-neg 50.7%

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

       2. associate-/l* 72.9%

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

       3. +-commutative 72.9%

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

       4. distribute-rgt-neg-in 72.9%

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

       5. neg-sub0 72.9%

          \[\leadsto z \cdot \color{blue}{\left(0 - \frac{y + x}{y}\right)} \]

       6. *-lft-identity 72.9%

          \[\leadsto z \cdot \left(0 - \color{blue}{1 \cdot \frac{y + x}{y}}\right) \]

       7. associate-*r/ 72.9%

          \[\leadsto z \cdot \left(0 - \color{blue}{\frac{1 \cdot \left(y + x\right)}{y}}\right) \]

       8. associate-*l/ 72.8%

          \[\leadsto z \cdot \left(0 - \color{blue}{\frac{1}{y} \cdot \left(y + x\right)}\right) \]

       9. distribute-rgt-in 72.8%

          \[\leadsto z \cdot \left(0 - \color{blue}{\left(y \cdot \frac{1}{y} + x \cdot \frac{1}{y}\right)}\right) \]

       10. rgt-mult-inverse 72.9%

           \[\leadsto z \cdot \left(0 - \left(\color{blue}{1} + x \cdot \frac{1}{y}\right)\right) \]

       11. associate--r+ 72.9%

           \[\leadsto z \cdot \color{blue}{\left(\left(0 - 1\right) - x \cdot \frac{1}{y}\right)} \]

       12. metadata-eval 72.9%

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

       13. associate-*r/ 72.9%

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

       14. *-rgt-identity 72.9%

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

   11. Simplified 72.9%

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

   if -5.5e71 < y < 1.74999999999999993e-31

   1. Initial program 99.3%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+71} \lor \neg \left(y \leq 1.75 \cdot 10^{-31}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 58.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+62}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-51}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.7e+62)
   (- z)
   (if (<= y -1.05e-51) y (if (<= y 1.8e-31) x (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e+62) {
		tmp = -z;
	} else if (y <= -1.05e-51) {
		tmp = y;
	} else if (y <= 1.8e-31) {
		tmp = x;
	} 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 <= (-2.7d+62)) then
        tmp = -z
    else if (y <= (-1.05d-51)) then
        tmp = y
    else if (y <= 1.8d-31) then
        tmp = x
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e+62) {
		tmp = -z;
	} else if (y <= -1.05e-51) {
		tmp = y;
	} else if (y <= 1.8e-31) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.7e+62:
		tmp = -z
	elif y <= -1.05e-51:
		tmp = y
	elif y <= 1.8e-31:
		tmp = x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.7e+62)
		tmp = Float64(-z);
	elseif (y <= -1.05e-51)
		tmp = y;
	elseif (y <= 1.8e-31)
		tmp = x;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.7e+62)
		tmp = -z;
	elseif (y <= -1.05e-51)
		tmp = y;
	elseif (y <= 1.8e-31)
		tmp = x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.7e+62], (-z), If[LessEqual[y, -1.05e-51], y, If[LessEqual[y, 1.8e-31], x, (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7e62 or 1.80000000000000002e-31 < y

   1. Initial program 82.5%

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

   3. Taylor expanded in y around inf 58.3%

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

      1. neg-mul-1 58.3%

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

   5. Simplified 58.3%

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

   if -2.7e62 < y < -1.05000000000000001e-51

   1. Initial program 96.5%

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

   3. Taylor expanded in z around inf 58.8%

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

      1. +-commutative 58.8%

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

   5. Simplified 58.8%

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

   6. Taylor expanded in y around inf 45.6%

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

   if -1.05000000000000001e-51 < y < 1.80000000000000002e-31

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.3%

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

Alternative 4: 66.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+62} \lor \neg \left(y \leq 4.8 \cdot 10^{+199}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.8e+62) (not (<= y 4.8e+199))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.8e+62) || !(y <= 4.8e+199)) {
		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 <= (-5.8d+62)) .or. (.not. (y <= 4.8d+199))) 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 <= -5.8e+62) || !(y <= 4.8e+199)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.8e+62) or not (y <= 4.8e+199):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.8e+62) || !(y <= 4.8e+199))
		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 <= -5.8e+62) || ~((y <= 4.8e+199)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.8e+62], N[Not[LessEqual[y, 4.8e+199]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.79999999999999968e62 or 4.8000000000000003e199 < y

   1. Initial program 76.6%

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

   3. Taylor expanded in y around inf 74.8%

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

      1. neg-mul-1 74.8%

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

   5. Simplified 74.8%

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

   if -5.79999999999999968e62 < y < 4.8000000000000003e199

   1. Initial program 96.8%

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

   3. Taylor expanded in z around inf 69.7%

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

      1. +-commutative 69.7%

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

   5. Simplified 69.7%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+62} \lor \neg \left(y \leq 4.8 \cdot 10^{+199}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 37.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-52}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.5e-52) y (if (<= y 1.8e-31) x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.5e-52) {
		tmp = y;
	} else if (y <= 1.8e-31) {
		tmp = x;
	} else {
		tmp = 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 <= (-1.5d-52)) then
        tmp = y
    else if (y <= 1.8d-31) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.5e-52) {
		tmp = y;
	} else if (y <= 1.8e-31) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.5e-52:
		tmp = y
	elif y <= 1.8e-31:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.5e-52)
		tmp = y;
	elseif (y <= 1.8e-31)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.5e-52)
		tmp = y;
	elseif (y <= 1.8e-31)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.5e-52], y, If[LessEqual[y, 1.8e-31], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5e-52 or 1.80000000000000002e-31 < y

   1. Initial program 85.1%

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

   3. Taylor expanded in z around inf 33.4%

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

      1. +-commutative 33.4%

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

   5. Simplified 33.4%

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

   6. Taylor expanded in y around inf 26.5%

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

   if -1.5e-52 < y < 1.80000000000000002e-31

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.3%

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

Alternative 6: 34.8% 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 91.1%

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

3. Taylor expanded in y around 0 36.3%

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

Developer Target 1: 93.9% 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 2024145 
(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))))