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

Percentage Accurate: 88.3% → 99.8%

Time: 5.6s

Alternatives: 7

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: 88.3% 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

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-285} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(-1 - \frac{x}{y}\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -2e-285) (not (<= t_0 0.0))) t_0 (* (- -1.0 (/ x y)) z))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -2e-285) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = (-1.0 - (x / y)) * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-2d-285)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = ((-1.0d0) - (x / y)) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -2e-285) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = (-1.0 - (x / y)) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -2e-285) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = (-1.0 - (x / y)) * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -2e-285) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(-1.0 - Float64(x / y)) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if ((t_0 <= -2e-285) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = (-1.0 - (x / y)) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -2e-285], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -2.00000000000000015e-285 or 0.0 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.8%

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

   if -2.00000000000000015e-285 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < 0.0

   1. Initial program 9.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. +-commutative N/A

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

      7. distribute-lft-in N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. div-sub N/A

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

      11. associate-*l/ N/A

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

      12. metadata-eval N/A

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

      13. distribute-neg-frac N/A

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

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

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

      15. lft-mult-inverse N/A

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

      16. metadata-eval N/A

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

      17. lower--.f64 N/A

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

      18. lower-/.f64 100.0

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

   5. Applied rewrites 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-285} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-1 - \frac{x}{y}\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-55} \lor \neg \left(y \leq 6.2 \cdot 10^{-38}\right):\\ \;\;\;\;\left(-1 - \frac{x}{y}\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.15e-55) (not (<= y 6.2e-38)))
   (* (- -1.0 (/ x y)) z)
   (/ x (- 1.0 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.15e-55) || !(y <= 6.2e-38)) {
		tmp = (-1.0 - (x / y)) * z;
	} else {
		tmp = x / (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.15d-55)) .or. (.not. (y <= 6.2d-38))) then
        tmp = ((-1.0d0) - (x / y)) * z
    else
        tmp = x / (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.15e-55) || !(y <= 6.2e-38)) {
		tmp = (-1.0 - (x / y)) * z;
	} else {
		tmp = x / (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.15e-55) or not (y <= 6.2e-38):
		tmp = (-1.0 - (x / y)) * z
	else:
		tmp = x / (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.15e-55) || !(y <= 6.2e-38))
		tmp = Float64(Float64(-1.0 - Float64(x / y)) * z);
	else
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.15e-55) || ~((y <= 6.2e-38)))
		tmp = (-1.0 - (x / y)) * z;
	else
		tmp = x / (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.15e-55], N[Not[LessEqual[y, 6.2e-38]], $MachinePrecision]], N[(N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15000000000000006e-55 or 6.19999999999999966e-38 < y

   1. Initial program 83.4%

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

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. +-commutative N/A

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

      7. distribute-lft-in N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. div-sub N/A

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

      11. associate-*l/ N/A

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

      12. metadata-eval N/A

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

      13. distribute-neg-frac N/A

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

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

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

      15. lft-mult-inverse N/A

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

      16. metadata-eval N/A

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

      17. lower--.f64 N/A

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

      18. lower-/.f64 77.7

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

   5. Applied rewrites 77.7%

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

   if -1.15000000000000006e-55 < y < 6.19999999999999966e-38

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 82.5

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

   5. Applied rewrites 82.5%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-55} \lor \neg \left(y \leq 6.2 \cdot 10^{-38}\right):\\ \;\;\;\;\left(-1 - \frac{x}{y}\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-75} \lor \neg \left(y \leq 6.2 \cdot 10^{-38}\right):\\ \;\;\;\;\left(-1 - \frac{x}{y}\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.3e-75) (not (<= y 6.2e-38)))
   (* (- -1.0 (/ x y)) z)
   (/ (+ x y) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.3e-75) || !(y <= 6.2e-38)) {
		tmp = (-1.0 - (x / y)) * z;
	} else {
		tmp = (x + y) / 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-3.3d-75)) .or. (.not. (y <= 6.2d-38))) then
        tmp = ((-1.0d0) - (x / y)) * z
    else
        tmp = (x + y) / 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.3e-75) || !(y <= 6.2e-38)) {
		tmp = (-1.0 - (x / y)) * z;
	} else {
		tmp = (x + y) / 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.3e-75) or not (y <= 6.2e-38):
		tmp = (-1.0 - (x / y)) * z
	else:
		tmp = (x + y) / 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.3e-75) || !(y <= 6.2e-38))
		tmp = Float64(Float64(-1.0 - Float64(x / y)) * z);
	else
		tmp = Float64(Float64(x + y) / 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.3e-75) || ~((y <= 6.2e-38)))
		tmp = (-1.0 - (x / y)) * z;
	else
		tmp = (x + y) / 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.3e-75], N[Not[LessEqual[y, 6.2e-38]], $MachinePrecision]], N[(N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(N[(x + y), $MachinePrecision] / 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3e-75 or 6.19999999999999966e-38 < y

   1. Initial program 83.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. +-commutative N/A

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

      7. distribute-lft-in N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. div-sub N/A

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

      11. associate-*l/ N/A

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

      12. metadata-eval N/A

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

      13. distribute-neg-frac N/A

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

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

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

      15. lft-mult-inverse N/A

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

      16. metadata-eval N/A

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

      17. lower--.f64 N/A

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

      18. lower-/.f64 77.2

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

   5. Applied rewrites 77.2%

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

   if -3.3e-75 < y < 6.19999999999999966e-38

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 83.1%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-75} \lor \neg \left(y \leq 6.2 \cdot 10^{-38}\right):\\ \;\;\;\;\left(-1 - \frac{x}{y}\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+15} \lor \neg \left(y \leq 6.2 \cdot 10^{-38}\right):\\ \;\;\;\;\left(-1 - \frac{z}{y}\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.35e+15) (not (<= y 6.2e-38)))
   (* (- -1.0 (/ z y)) z)
   (/ (+ x y) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.35e+15) || !(y <= 6.2e-38)) {
		tmp = (-1.0 - (z / y)) * z;
	} else {
		tmp = (x + y) / 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.35d+15)) .or. (.not. (y <= 6.2d-38))) then
        tmp = ((-1.0d0) - (z / y)) * z
    else
        tmp = (x + y) / 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.35e+15) || !(y <= 6.2e-38)) {
		tmp = (-1.0 - (z / y)) * z;
	} else {
		tmp = (x + y) / 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.35e+15) or not (y <= 6.2e-38):
		tmp = (-1.0 - (z / y)) * z
	else:
		tmp = (x + y) / 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.35e+15) || !(y <= 6.2e-38))
		tmp = Float64(Float64(-1.0 - Float64(z / y)) * z);
	else
		tmp = Float64(Float64(x + y) / 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.35e+15) || ~((y <= 6.2e-38)))
		tmp = (-1.0 - (z / y)) * z;
	else
		tmp = (x + y) / 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.35e+15], N[Not[LessEqual[y, 6.2e-38]], $MachinePrecision]], N[(N[(-1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(N[(x + y), $MachinePrecision] / 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35e15 or 6.19999999999999966e-38 < y

   1. Initial program 81.2%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 66.9

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

   5. Applied rewrites 66.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 66.8%

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

   if -1.35e15 < y < 6.19999999999999966e-38

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 73.3%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+15} \lor \neg \left(y \leq 6.2 \cdot 10^{-38}\right):\\ \;\;\;\;\left(-1 - \frac{z}{y}\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-75}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{y}, \left(-x\right) - z, -z\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-38}:\\ \;\;\;\;\frac{x + y}{1}\\ \mathbf{else}:\\ \;\;\;\;\left(-1 - \frac{x}{y}\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.3e-75)
   (fma (/ z y) (- (- x) z) (- z))
   (if (<= y 6.2e-38) (/ (+ x y) 1.0) (* (- -1.0 (/ x y)) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.3e-75) {
		tmp = fma((z / y), (-x - z), -z);
	} else if (y <= 6.2e-38) {
		tmp = (x + y) / 1.0;
	} else {
		tmp = (-1.0 - (x / y)) * z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.3e-75)
		tmp = fma(Float64(z / y), Float64(Float64(-x) - z), Float64(-z));
	elseif (y <= 6.2e-38)
		tmp = Float64(Float64(x + y) / 1.0);
	else
		tmp = Float64(Float64(-1.0 - Float64(x / y)) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.3e-75], N[(N[(z / y), $MachinePrecision] * N[((-x) - z), $MachinePrecision] + (-z)), $MachinePrecision], If[LessEqual[y, 6.2e-38], N[(N[(x + y), $MachinePrecision] / 1.0), $MachinePrecision], N[(N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.3e-75

   1. Initial program 82.6%

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

   3. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. associate-*r* N/A

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

      5. unpow2 N/A

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

      6. associate-/l* N/A

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

      7. distribute-rgt-out-- N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 N/A

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

      13. mul-1-neg N/A

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

      14. lower-neg.f64 78.5

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

   5. Applied rewrites 78.5%

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

   if -3.3e-75 < y < 6.19999999999999966e-38

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 83.1%

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

   if 6.19999999999999966e-38 < y

   1. Initial program 85.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. +-commutative N/A

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

      7. distribute-lft-in N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. div-sub N/A

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

      11. associate-*l/ N/A

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

      12. metadata-eval N/A

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

      13. distribute-neg-frac N/A

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

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

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

      15. lft-mult-inverse N/A

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

      16. metadata-eval N/A

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

      17. lower--.f64 N/A

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

      18. lower-/.f64 75.5

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

   5. Applied rewrites 75.5%

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

Alternative 6: 65.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+15} \lor \neg \left(y \leq 6.2 \cdot 10^{-38}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.35e+15) (not (<= y 6.2e-38))) (- z) (/ (+ x y) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.35e+15) || !(y <= 6.2e-38)) {
		tmp = -z;
	} else {
		tmp = (x + y) / 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.35d+15)) .or. (.not. (y <= 6.2d-38))) then
        tmp = -z
    else
        tmp = (x + y) / 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.35e+15) || !(y <= 6.2e-38)) {
		tmp = -z;
	} else {
		tmp = (x + y) / 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.35e+15) or not (y <= 6.2e-38):
		tmp = -z
	else:
		tmp = (x + y) / 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.35e+15) || !(y <= 6.2e-38))
		tmp = Float64(-z);
	else
		tmp = Float64(Float64(x + y) / 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.35e+15) || ~((y <= 6.2e-38)))
		tmp = -z;
	else
		tmp = (x + y) / 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.35e+15], N[Not[LessEqual[y, 6.2e-38]], $MachinePrecision]], (-z), N[(N[(x + y), $MachinePrecision] / 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35e15 or 6.19999999999999966e-38 < y

   1. Initial program 81.2%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 66.5

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

   5. Applied rewrites 66.5%

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

   if -1.35e15 < y < 6.19999999999999966e-38

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 73.3%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+15} \lor \neg \left(y \leq 6.2 \cdot 10^{-38}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 34.1% 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 89.7%

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

3. Taylor expanded in y around inf

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

   1. mul-1-neg N/A

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

   2. lower-neg.f64 41.7

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

5. Applied rewrites 41.7%

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

Developer Target 1: 93.5% 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 2024324 
(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))))