Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3

Percentage Accurate: 97.1% → 99.6%

Time: 11.0s

Alternatives: 11

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x - ((y - z) / (((t - z) + 1.0d0) / a))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

Python

def code(x, y, z, t, a):
	return x - ((y - z) / (((t - z) + 1.0) / a))

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(y - z) / Float64(Float64(Float64(t - z) + 1.0) / a)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - ((y - z) / (((t - z) + 1.0) / a));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 97.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x - ((y - z) / (((t - z) + 1.0d0) / a))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

Python

def code(x, y, z, t, a):
	return x - ((y - z) / (((t - z) + 1.0) / a))

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(y - z) / Float64(Float64(Float64(t - z) + 1.0) / a)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - ((y - z) / (((t - z) + 1.0) / a));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + a \cdot \frac{y - z}{-1 + \left(z - t\right)} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ x (* a (/ (- y z) (+ -1.0 (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (a * ((y - z) / (-1.0 + (z - t))));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (a * ((y - z) / ((-1.0d0) + (z - t))))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (a * ((y - z) / (-1.0 + (z - t))));
}

Python

def code(x, y, z, t, a):
	return x + (a * ((y - z) / (-1.0 + (z - t))))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(a * Float64(Float64(y - z) / Float64(-1.0 + Float64(z - t)))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (a * ((y - z) / (-1.0 + (z - t))));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(a * N[(N[(y - z), $MachinePrecision] / N[(-1.0 + N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.0%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
2. Step-by-step derivation

   1. associate-/r/ 99.6%

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

3. Simplified 99.6%

   \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
4. Add Preprocessing

5. Final simplification 99.6%

   \[\leadsto x + a \cdot \frac{y - z}{-1 + \left(z - t\right)} \]
6. Add Preprocessing

Alternative 2: 87.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+72} \lor \neg \left(z \leq 1.6 \cdot 10^{-29}\right):\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.1e+72) (not (<= z 1.6e-29)))
   (+ x (* a (/ z (+ (- t z) 1.0))))
   (+ x (* a (/ y (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.1e+72) || !(z <= 1.6e-29)) {
		tmp = x + (a * (z / ((t - z) + 1.0)));
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.1d+72)) .or. (.not. (z <= 1.6d-29))) then
        tmp = x + (a * (z / ((t - z) + 1.0d0)))
    else
        tmp = x + (a * (y / ((-1.0d0) - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.1e+72) || !(z <= 1.6e-29)) {
		tmp = x + (a * (z / ((t - z) + 1.0)));
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.1e+72) or not (z <= 1.6e-29):
		tmp = x + (a * (z / ((t - z) + 1.0)))
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.1e+72) || !(z <= 1.6e-29))
		tmp = Float64(x + Float64(a * Float64(z / Float64(Float64(t - z) + 1.0))));
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.1e+72) || ~((z <= 1.6e-29)))
		tmp = x + (a * (z / ((t - z) + 1.0)));
	else
		tmp = x + (a * (y / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.1e+72], N[Not[LessEqual[z, 1.6e-29]], $MachinePrecision]], N[(x + N[(a * N[(z / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.09999999999999988e72 or 1.6e-29 < z

   1. Initial program 96.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. sub-neg 96.5%

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

      2. +-commutative 96.5%

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

      3. associate-/r/ 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. associate-*l/ 81.1%

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

      6. associate-/l* 96.5%

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

      7. fma-define 96.5%

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

      8. distribute-frac-neg 96.5%

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

      9. distribute-neg-frac2 96.5%

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

      10. distribute-neg-in 96.5%

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

      11. sub-neg 96.5%

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

      12. distribute-neg-in 96.5%

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

      13. remove-double-neg 96.5%

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

      14. +-commutative 96.5%

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

      15. sub-neg 96.5%

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

      16. metadata-eval 96.5%

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

   3. Simplified 96.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{a}{\left(z - t\right) + -1}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 76.0%

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

      1. mul-1-neg 76.0%

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

      2. unsub-neg 76.0%

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

      3. associate-/l* 92.7%

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

      4. associate--r+ 92.7%

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

      5. sub-neg 92.7%

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

      6. metadata-eval 92.7%

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

      7. +-commutative 92.7%

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

      8. associate--l+ 92.7%

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

   7. Simplified 92.7%

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

   if -3.09999999999999988e72 < z < 1.6e-29

   1. Initial program 99.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.3%

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

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 92.9%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+72} \lor \neg \left(z \leq 1.6 \cdot 10^{-29}\right):\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+27} \lor \neg \left(z \leq 20000000000000\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.7e+27) (not (<= z 20000000000000.0)))
   (+ x (* (- y z) (/ a z)))
   (+ x (* a (/ y (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.7e+27) || !(z <= 20000000000000.0)) {
		tmp = x + ((y - z) * (a / z));
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.7d+27)) .or. (.not. (z <= 20000000000000.0d0))) then
        tmp = x + ((y - z) * (a / z))
    else
        tmp = x + (a * (y / ((-1.0d0) - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.7e+27) || !(z <= 20000000000000.0)) {
		tmp = x + ((y - z) * (a / z));
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.7e+27) or not (z <= 20000000000000.0):
		tmp = x + ((y - z) * (a / z))
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.7e+27) || !(z <= 20000000000000.0))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(a / z)));
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.7e+27) || ~((z <= 20000000000000.0)))
		tmp = x + ((y - z) * (a / z));
	else
		tmp = x + (a * (y / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.7e+27], N[Not[LessEqual[z, 20000000000000.0]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e27 or 2e13 < z

   1. Initial program 96.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 96.5%

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

      2. associate-/r/ 96.4%

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

      3. clear-num 96.5%

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

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in z around inf 89.8%

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

      1. associate-*r/ 89.8%

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

      2. neg-mul-1 89.8%

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

   7. Simplified 89.8%

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

   if -1.7e27 < z < 2e13

   1. Initial program 99.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.2%

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

   3. Simplified 99.2%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 94.9%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+27} \lor \neg \left(z \leq 20000000000000\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+72} \lor \neg \left(z \leq 2.8 \cdot 10^{+16}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3e+72) (not (<= z 2.8e+16)))
   (- x a)
   (+ x (* a (/ y (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3e+72) || !(z <= 2.8e+16)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3d+72)) .or. (.not. (z <= 2.8d+16))) then
        tmp = x - a
    else
        tmp = x + (a * (y / ((-1.0d0) - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3e+72) || !(z <= 2.8e+16)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3e+72) or not (z <= 2.8e+16):
		tmp = x - a
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3e+72) || !(z <= 2.8e+16))
		tmp = Float64(x - a);
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3e+72) || ~((z <= 2.8e+16)))
		tmp = x - a;
	else
		tmp = x + (a * (y / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3e+72], N[Not[LessEqual[z, 2.8e+16]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.00000000000000003e72 or 2.8e16 < z

   1. Initial program 96.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 87.7%

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

   if -3.00000000000000003e72 < z < 2.8e16

   1. Initial program 99.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.3%

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

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 91.9%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+72} \lor \neg \left(z \leq 2.8 \cdot 10^{+16}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+27}:\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+16}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.5e+27)
   (+ x (/ (- y z) (/ z a)))
   (if (<= z 8e+16) (+ x (* a (/ y (- -1.0 t)))) (+ x (* (- y z) (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+27) {
		tmp = x + ((y - z) / (z / a));
	} else if (z <= 8e+16) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x + ((y - z) * (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.5d+27)) then
        tmp = x + ((y - z) / (z / a))
    else if (z <= 8d+16) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else
        tmp = x + ((y - z) * (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+27) {
		tmp = x + ((y - z) / (z / a));
	} else if (z <= 8e+16) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x + ((y - z) * (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.5e+27:
		tmp = x + ((y - z) / (z / a))
	elif z <= 8e+16:
		tmp = x + (a * (y / (-1.0 - t)))
	else:
		tmp = x + ((y - z) * (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.5e+27)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(z / a)));
	elseif (z <= 8e+16)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	else
		tmp = Float64(x + Float64(Float64(y - z) * Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.5e+27)
		tmp = x + ((y - z) / (z / a));
	elseif (z <= 8e+16)
		tmp = x + (a * (y / (-1.0 - t)));
	else
		tmp = x + ((y - z) * (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.5e+27], N[(x + N[(N[(y - z), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+16], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.49999999999999988e27

   1. Initial program 96.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 89.5%

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

      1. associate-*r/ 89.5%

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

      2. neg-mul-1 89.5%

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

   5. Simplified 89.5%

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

   if -1.49999999999999988e27 < z < 8e16

   1. Initial program 99.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.2%

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

   3. Simplified 99.2%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 94.9%

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

   if 8e16 < z

   1. Initial program 97.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 97.0%

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

      2. associate-/r/ 97.0%

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

      3. clear-num 97.1%

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

   4. Applied egg-rr 97.1%

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

   5. Taylor expanded in z around inf 90.1%

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

      1. associate-*r/ 90.1%

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

      2. neg-mul-1 90.1%

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

   7. Simplified 90.1%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+27}:\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+16}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-50} \lor \neg \left(z \leq 1.9 \cdot 10^{-71}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.95e-50) (not (<= z 1.9e-71))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.95e-50) || !(z <= 1.9e-71)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.95d-50)) .or. (.not. (z <= 1.9d-71))) then
        tmp = x - a
    else
        tmp = x - (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.95e-50) || !(z <= 1.9e-71)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.95e-50) or not (z <= 1.9e-71):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.95e-50) || !(z <= 1.9e-71))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.95e-50) || ~((z <= 1.9e-71)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.95e-50], N[Not[LessEqual[z, 1.9e-71]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9500000000000001e-50 or 1.89999999999999996e-71 < z

   1. Initial program 97.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 81.0%

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

   if -1.9500000000000001e-50 < z < 1.89999999999999996e-71

   1. Initial program 99.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.3%

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

      2. associate-/r/ 99.3%

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

      3. clear-num 99.4%

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

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in z around 0 94.7%

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

   6. Taylor expanded in t around 0 78.3%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-50} \lor \neg \left(z \leq 1.9 \cdot 10^{-71}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+38} \lor \neg \left(z \leq 9.5 \cdot 10^{-79}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.1e+38) (not (<= z 9.5e-79))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.1e+38) || !(z <= 9.5e-79)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.1d+38)) .or. (.not. (z <= 9.5d-79))) then
        tmp = x - a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.1e+38) || !(z <= 9.5e-79)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.1e+38) or not (z <= 9.5e-79):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.1e+38) || !(z <= 9.5e-79))
		tmp = Float64(x - a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.1e+38) || ~((z <= 9.5e-79)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.1e+38], N[Not[LessEqual[z, 9.5e-79]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.10000000000000003e38 or 9.4999999999999997e-79 < z

   1. Initial program 96.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 82.9%

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

   if -1.10000000000000003e38 < z < 9.4999999999999997e-79

   1. Initial program 99.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. sub-neg 99.4%

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

      2. +-commutative 99.4%

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

      3. associate-/r/ 99.2%

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

      4. distribute-rgt-neg-in 99.2%

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

      5. associate-*l/ 96.8%

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

      6. associate-/l* 99.4%

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

      7. fma-define 99.4%

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

      8. distribute-frac-neg 99.4%

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

      9. distribute-neg-frac2 99.4%

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

      10. distribute-neg-in 99.4%

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

      11. sub-neg 99.4%

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

      12. distribute-neg-in 99.4%

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

      13. remove-double-neg 99.4%

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

      14. +-commutative 99.4%

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

      15. sub-neg 99.4%

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

      16. metadata-eval 99.4%

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

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{a}{\left(z - t\right) + -1}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 62.9%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+38} \lor \neg \left(z \leq 9.5 \cdot 10^{-79}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(y - z\right) \cdot \frac{a}{-1 + \left(z - t\right)} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ x (* (- y z) (/ a (+ -1.0 (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	return x + ((y - z) * (a / (-1.0 + (z - t))));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + ((y - z) * (a / ((-1.0d0) + (z - t))))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + ((y - z) * (a / (-1.0 + (z - t))));
}

Python

def code(x, y, z, t, a):
	return x + ((y - z) * (a / (-1.0 + (z - t))))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(y - z) * Float64(a / Float64(-1.0 + Float64(z - t)))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + ((y - z) * (a / (-1.0 + (z - t))));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(y - z), $MachinePrecision] * N[(a / N[(-1.0 + N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.0%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. clear-num 97.9%

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

   2. associate-/r/ 97.9%

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

   3. clear-num 98.0%

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

4. Applied egg-rr 98.0%

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

5. Final simplification 98.0%

   \[\leadsto x + \left(y - z\right) \cdot \frac{a}{-1 + \left(z - t\right)} \]
6. Add Preprocessing

Alternative 9: 53.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+128} \lor \neg \left(a \leq 1.08 \cdot 10^{+82}\right):\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.55e+128) (not (<= a 1.08e+82))) (- a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.55e+128) || !(a <= 1.08e+82)) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.55d+128)) .or. (.not. (a <= 1.08d+82))) then
        tmp = -a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.55e+128) || !(a <= 1.08e+82)) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.55e+128) or not (a <= 1.08e+82):
		tmp = -a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.55e+128) || !(a <= 1.08e+82))
		tmp = Float64(-a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.55e+128) || ~((a <= 1.08e+82)))
		tmp = -a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.55e+128], N[Not[LessEqual[a, 1.08e+82]], $MachinePrecision]], (-a), x]

Derivation

1. Split input into 2 regimes

2. if a < -1.55000000000000002e128 or 1.08e82 < a

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 48.5%

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

   6. Taylor expanded in x around 0 40.1%

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

      1. neg-mul-1 40.1%

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

   8. Simplified 40.1%

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

   if -1.55000000000000002e128 < a < 1.08e82

   1. Initial program 97.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. sub-neg 97.3%

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

      2. +-commutative 97.3%

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

      3. associate-/r/ 99.5%

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

      4. distribute-rgt-neg-in 99.5%

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

      5. associate-*l/ 96.7%

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

      6. associate-/l* 97.3%

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

      7. fma-define 97.3%

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

      8. distribute-frac-neg 97.3%

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

      9. distribute-neg-frac2 97.3%

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

      10. distribute-neg-in 97.3%

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

      11. sub-neg 97.3%

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

      12. distribute-neg-in 97.3%

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

      13. remove-double-neg 97.3%

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

      14. +-commutative 97.3%

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

      15. sub-neg 97.3%

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

      16. metadata-eval 97.3%

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

   3. Simplified 97.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{a}{\left(z - t\right) + -1}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 74.9%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+128} \lor \neg \left(a \leq 1.08 \cdot 10^{+82}\right):\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.7% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 98.0%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
2. Step-by-step derivation

   1. sub-neg 98.0%

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

   2. +-commutative 98.0%

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

   3. associate-/r/ 99.6%

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

   4. distribute-rgt-neg-in 99.6%

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

   5. associate-*l/ 88.6%

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

   6. associate-/l* 98.0%

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

   7. fma-define 98.0%

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

   8. distribute-frac-neg 98.0%

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

   9. distribute-neg-frac2 98.0%

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

   10. distribute-neg-in 98.0%

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

   11. sub-neg 98.0%

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

   12. distribute-neg-in 98.0%

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

   13. remove-double-neg 98.0%

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

   14. +-commutative 98.0%

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

   15. sub-neg 98.0%

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

   16. metadata-eval 98.0%

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

3. Simplified 98.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{a}{\left(z - t\right) + -1}, x\right)} \]
4. Add Preprocessing

5. Taylor expanded in a around 0 58.3%

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

Alternative 11: 3.2% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := a

Derivation

1. Initial program 98.0%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
2. Step-by-step derivation

   1. associate-/r/ 99.6%

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

3. Simplified 99.6%

   \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 66.8%

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

6. Taylor expanded in x around 0 18.8%

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

   1. neg-mul-1 18.8%

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

8. Simplified 18.8%

   \[\leadsto \color{blue}{-a} \]
9. Step-by-step derivation

   1. neg-sub0 18.8%

      \[\leadsto \color{blue}{0 - a} \]

   2. sub-neg 18.8%

      \[\leadsto \color{blue}{0 + \left(-a\right)} \]

   3. add-sqr-sqrt 8.2%

      \[\leadsto 0 + \color{blue}{\sqrt{-a} \cdot \sqrt{-a}} \]

   4. sqrt-unprod 9.4%

      \[\leadsto 0 + \color{blue}{\sqrt{\left(-a\right) \cdot \left(-a\right)}} \]

   5. sqr-neg 9.4%

      \[\leadsto 0 + \sqrt{\color{blue}{a \cdot a}} \]

   6. sqrt-unprod 1.6%

      \[\leadsto 0 + \color{blue}{\sqrt{a} \cdot \sqrt{a}} \]

   7. add-sqr-sqrt 3.1%

      \[\leadsto 0 + \color{blue}{a} \]

10. Applied egg-rr 3.1%

    \[\leadsto \color{blue}{0 + a} \]
11. Step-by-step derivation

    1. +-lft-identity 3.1%

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

12. Simplified 3.1%

    \[\leadsto \color{blue}{a} \]
13. Add Preprocessing

Developer Target 1: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\left(t - z\right) + 1} \cdot a \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (* (/ (- y z) (+ (- t z) 1.0)) a)))

C

double code(double x, double y, double z, double t, double a) {
	return x - (((y - z) / ((t - z) + 1.0)) * a);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x - (((y - z) / ((t - z) + 1.0d0)) * a)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - (((y - z) / ((t - z) + 1.0)) * a);
}

Python

def code(x, y, z, t, a):
	return x - (((y - z) / ((t - z) + 1.0)) * a)

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(Float64(y - z) / Float64(Float64(t - z) + 1.0)) * a))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - (((y - z) / ((t - z) + 1.0)) * a);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(N[(y - z), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024181 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (- x (* (/ (- y z) (+ (- t z) 1)) a)))

  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))