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

Percentage Accurate: 96.9% → 99.6%

Time: 10.2s

Alternatives: 12

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: 96.9% 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

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

FPCore

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

C

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

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 * ((z - y) / ((t - z) + 1.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.0%

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

   1. associate-/r/ 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 86.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+17} \lor \neg \left(z \leq 5.2 \cdot 10^{-50}\right):\\ \;\;\;\;x + \frac{a}{\frac{t + 1}{z} + -1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot a}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.8e+17) (not (<= z 5.2e-50)))
   (+ x (/ a (+ (/ (+ t 1.0) z) -1.0)))
   (- x (/ (* y a) (+ t 1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.8e+17) || !(z <= 5.2e-50)) {
		tmp = x + (a / (((t + 1.0) / z) + -1.0));
	} else {
		tmp = x - ((y * a) / (t + 1.0));
	}
	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 <= (-1.8d+17)) .or. (.not. (z <= 5.2d-50))) then
        tmp = x + (a / (((t + 1.0d0) / z) + (-1.0d0)))
    else
        tmp = x - ((y * a) / (t + 1.0d0))
    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 <= -1.8e+17) || !(z <= 5.2e-50)) {
		tmp = x + (a / (((t + 1.0) / z) + -1.0));
	} else {
		tmp = x - ((y * a) / (t + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.8e+17) or not (z <= 5.2e-50):
		tmp = x + (a / (((t + 1.0) / z) + -1.0))
	else:
		tmp = x - ((y * a) / (t + 1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.8e+17) || !(z <= 5.2e-50))
		tmp = Float64(x + Float64(a / Float64(Float64(Float64(t + 1.0) / z) + -1.0)));
	else
		tmp = Float64(x - Float64(Float64(y * a) / Float64(t + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.8e+17) || ~((z <= 5.2e-50)))
		tmp = x + (a / (((t + 1.0) / z) + -1.0));
	else
		tmp = x - ((y * a) / (t + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.8e+17], N[Not[LessEqual[z, 5.2e-50]], $MachinePrecision]], N[(x + N[(a / N[(N[(N[(t + 1.0), $MachinePrecision] / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * a), $MachinePrecision] / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e17 or 5.2000000000000003e-50 < z

   1. Initial program 91.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in y around 0 65.4%

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

      1. sub-neg 65.4%

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

      2. mul-1-neg 65.4%

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

      3. *-commutative 65.4%

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

      4. associate--l+ 65.4%

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

      5. +-commutative 65.4%

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

      6. associate-*r/ 81.7%

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

      7. remove-double-neg 81.7%

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

      8. associate-*r/ 65.4%

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

      9. *-commutative 65.4%

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

      10. +-commutative 65.4%

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

      11. associate--l+ 65.4%

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

      12. associate-/l* 86.8%

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

      13. associate--l+ 86.8%

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

   6. Simplified 86.8%

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

   7. Taylor expanded in a around 0 65.4%

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

      1. associate-/l* 86.8%

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

      2. div-sub 86.8%

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

      3. sub-neg 86.8%

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

      4. *-inverses 86.8%

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

      5. metadata-eval 86.8%

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

   9. Simplified 86.8%

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

   if -1.8e17 < z < 5.2000000000000003e-50

   1. Initial program 98.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around 0 91.2%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+17} \lor \neg \left(z \leq 5.2 \cdot 10^{-50}\right):\\ \;\;\;\;x + \frac{a}{\frac{t + 1}{z} + -1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot a}{t + 1}\\ \end{array} \]

Alternative 3: 89.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+123} \lor \neg \left(t \leq 6.4 \cdot 10^{+187}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.6e+123) (not (<= t 6.4e+187)))
   (+ x (* a (/ (- z y) t)))
   (+ x (* a (/ (- z y) (- 1.0 z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.6e+123) || !(t <= 6.4e+187)) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x + (a * ((z - y) / (1.0 - 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 ((t <= (-4.6d+123)) .or. (.not. (t <= 6.4d+187))) then
        tmp = x + (a * ((z - y) / t))
    else
        tmp = x + (a * ((z - y) / (1.0d0 - 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 ((t <= -4.6e+123) || !(t <= 6.4e+187)) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x + (a * ((z - y) / (1.0 - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.6e+123) or not (t <= 6.4e+187):
		tmp = x + (a * ((z - y) / t))
	else:
		tmp = x + (a * ((z - y) / (1.0 - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.6e+123) || !(t <= 6.4e+187))
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	else
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / Float64(1.0 - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.6e+123) || ~((t <= 6.4e+187)))
		tmp = x + (a * ((z - y) / t));
	else
		tmp = x + (a * ((z - y) / (1.0 - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.6e+123], N[Not[LessEqual[t, 6.4e+187]], $MachinePrecision]], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.59999999999999981e123 or 6.39999999999999987e187 < t

   1. Initial program 93.0%

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

      1. associate-/r/ 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in t around inf 94.0%

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

   if -4.59999999999999981e123 < t < 6.39999999999999987e187

   1. Initial program 94.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in t around 0 93.0%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+123} \lor \neg \left(t \leq 6.4 \cdot 10^{+187}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \end{array} \]

Alternative 4: 84.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+49}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.25:\\ \;\;\;\;x - \frac{y \cdot a}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.2e+49)
   (- x a)
   (if (<= z 1.25) (- x (/ (* y a) (+ t 1.0))) (+ x (/ (- z y) (/ (- z) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.2e+49) {
		tmp = x - a;
	} else if (z <= 1.25) {
		tmp = x - ((y * a) / (t + 1.0));
	} else {
		tmp = x + ((z - y) / (-z / 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 <= (-9.2d+49)) then
        tmp = x - a
    else if (z <= 1.25d0) then
        tmp = x - ((y * a) / (t + 1.0d0))
    else
        tmp = x + ((z - y) / (-z / 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 <= -9.2e+49) {
		tmp = x - a;
	} else if (z <= 1.25) {
		tmp = x - ((y * a) / (t + 1.0));
	} else {
		tmp = x + ((z - y) / (-z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.2e+49:
		tmp = x - a
	elif z <= 1.25:
		tmp = x - ((y * a) / (t + 1.0))
	else:
		tmp = x + ((z - y) / (-z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.2e+49)
		tmp = Float64(x - a);
	elseif (z <= 1.25)
		tmp = Float64(x - Float64(Float64(y * a) / Float64(t + 1.0)));
	else
		tmp = Float64(x + Float64(Float64(z - y) / Float64(Float64(-z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.2e+49)
		tmp = x - a;
	elseif (z <= 1.25)
		tmp = x - ((y * a) / (t + 1.0));
	else
		tmp = x + ((z - y) / (-z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.2e+49], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.25], N[(x - N[(N[(y * a), $MachinePrecision] / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - y), $MachinePrecision] / N[((-z) / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.20000000000000008e49

   1. Initial program 89.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 85.1%

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

   if -9.20000000000000008e49 < z < 1.25

   1. Initial program 97.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around 0 88.3%

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

   if 1.25 < z

   1. Initial program 91.8%

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

   2. Taylor expanded in z around inf 84.6%

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

      1. mul-1-neg 84.6%

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

      2. distribute-neg-frac 84.6%

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

   4. Simplified 84.6%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+49}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.25:\\ \;\;\;\;x - \frac{y \cdot a}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \end{array} \]

Alternative 5: 72.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+16}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-62}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.9e+16)
   (- x a)
   (if (<= z 5.5e-62)
     (- x (* y a))
     (if (<= z 7e+22) (+ x (/ a (/ t z))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.9e+16) {
		tmp = x - a;
	} else if (z <= 5.5e-62) {
		tmp = x - (y * a);
	} else if (z <= 7e+22) {
		tmp = x + (a / (t / z));
	} else {
		tmp = x - 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 <= (-2.9d+16)) then
        tmp = x - a
    else if (z <= 5.5d-62) then
        tmp = x - (y * a)
    else if (z <= 7d+22) then
        tmp = x + (a / (t / z))
    else
        tmp = x - 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 <= -2.9e+16) {
		tmp = x - a;
	} else if (z <= 5.5e-62) {
		tmp = x - (y * a);
	} else if (z <= 7e+22) {
		tmp = x + (a / (t / z));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.9e+16:
		tmp = x - a
	elif z <= 5.5e-62:
		tmp = x - (y * a)
	elif z <= 7e+22:
		tmp = x + (a / (t / z))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.9e+16)
		tmp = Float64(x - a);
	elseif (z <= 5.5e-62)
		tmp = Float64(x - Float64(y * a));
	elseif (z <= 7e+22)
		tmp = Float64(x + Float64(a / Float64(t / z)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.9e+16)
		tmp = x - a;
	elseif (z <= 5.5e-62)
		tmp = x - (y * a);
	elseif (z <= 7e+22)
		tmp = x + (a / (t / z));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.9e+16], N[(x - a), $MachinePrecision], If[LessEqual[z, 5.5e-62], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+22], N[(x + N[(a / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9e16 or 7e22 < z

   1. Initial program 91.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 83.6%

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

   if -2.9e16 < z < 5.50000000000000022e-62

   1. Initial program 98.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in t around 0 76.0%

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

   5. Taylor expanded in z around 0 72.5%

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

   if 5.50000000000000022e-62 < z < 7e22

   1. Initial program 90.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in y around 0 64.1%

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

      1. sub-neg 64.1%

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

      2. mul-1-neg 64.1%

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

      3. *-commutative 64.1%

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

      4. associate--l+ 64.1%

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

      5. +-commutative 64.1%

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

      6. associate-*r/ 64.1%

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

      7. remove-double-neg 64.1%

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

      8. associate-*r/ 64.1%

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

      9. *-commutative 64.1%

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

      10. +-commutative 64.1%

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

      11. associate--l+ 64.1%

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

      12. associate-/l* 63.9%

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

      13. associate--l+ 63.9%

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

   6. Simplified 63.9%

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

   7. Taylor expanded in t around inf 74.7%

      \[\leadsto x + \color{blue}{\frac{a \cdot z}{t}} \]
   8. Step-by-step derivation

      1. associate-/l* 74.6%

         \[\leadsto x + \color{blue}{\frac{a}{\frac{t}{z}}} \]

   9. Simplified 74.6%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+16}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-62}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 6: 72.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+17}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-61}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{z \cdot a}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.06e+17)
   (- x a)
   (if (<= z 1.52e-61)
     (- x (* y a))
     (if (<= z 7.4e+22) (+ x (/ (* z a) t)) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.06e+17) {
		tmp = x - a;
	} else if (z <= 1.52e-61) {
		tmp = x - (y * a);
	} else if (z <= 7.4e+22) {
		tmp = x + ((z * a) / t);
	} else {
		tmp = x - 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 <= (-1.06d+17)) then
        tmp = x - a
    else if (z <= 1.52d-61) then
        tmp = x - (y * a)
    else if (z <= 7.4d+22) then
        tmp = x + ((z * a) / t)
    else
        tmp = x - 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 <= -1.06e+17) {
		tmp = x - a;
	} else if (z <= 1.52e-61) {
		tmp = x - (y * a);
	} else if (z <= 7.4e+22) {
		tmp = x + ((z * a) / t);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.06e+17:
		tmp = x - a
	elif z <= 1.52e-61:
		tmp = x - (y * a)
	elif z <= 7.4e+22:
		tmp = x + ((z * a) / t)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.06e+17)
		tmp = Float64(x - a);
	elseif (z <= 1.52e-61)
		tmp = Float64(x - Float64(y * a));
	elseif (z <= 7.4e+22)
		tmp = Float64(x + Float64(Float64(z * a) / t));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.06e+17)
		tmp = x - a;
	elseif (z <= 1.52e-61)
		tmp = x - (y * a);
	elseif (z <= 7.4e+22)
		tmp = x + ((z * a) / t);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.06e+17], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.52e-61], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.4e+22], N[(x + N[(N[(z * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.06e17 or 7.3999999999999996e22 < z

   1. Initial program 91.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 83.6%

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

   if -1.06e17 < z < 1.52000000000000003e-61

   1. Initial program 98.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in t around 0 76.0%

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

   5. Taylor expanded in z around 0 72.5%

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

   if 1.52000000000000003e-61 < z < 7.3999999999999996e22

   1. Initial program 90.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in y around 0 64.1%

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

      1. sub-neg 64.1%

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

      2. mul-1-neg 64.1%

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

      3. *-commutative 64.1%

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

      4. associate--l+ 64.1%

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

      5. +-commutative 64.1%

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

      6. associate-*r/ 64.1%

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

      7. remove-double-neg 64.1%

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

      8. associate-*r/ 64.1%

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

      9. *-commutative 64.1%

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

      10. +-commutative 64.1%

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

      11. associate--l+ 64.1%

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

      12. associate-/l* 63.9%

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

      13. associate--l+ 63.9%

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

   6. Simplified 63.9%

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

   7. Taylor expanded in t around inf 74.7%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+17}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-61}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{z \cdot a}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 7: 82.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{+45} \lor \neg \left(z \leq 9.8 \cdot 10^{+22}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot a}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.28e+45) (not (<= z 9.8e+22)))
   (- x a)
   (- x (/ (* y a) (+ t 1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.28e+45) || !(z <= 9.8e+22)) {
		tmp = x - a;
	} else {
		tmp = x - ((y * a) / (t + 1.0));
	}
	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 <= (-1.28d+45)) .or. (.not. (z <= 9.8d+22))) then
        tmp = x - a
    else
        tmp = x - ((y * a) / (t + 1.0d0))
    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 <= -1.28e+45) || !(z <= 9.8e+22)) {
		tmp = x - a;
	} else {
		tmp = x - ((y * a) / (t + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.28e+45) or not (z <= 9.8e+22):
		tmp = x - a
	else:
		tmp = x - ((y * a) / (t + 1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.28e+45) || !(z <= 9.8e+22))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(Float64(y * a) / Float64(t + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.28e+45) || ~((z <= 9.8e+22)))
		tmp = x - a;
	else
		tmp = x - ((y * a) / (t + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.28e+45], N[Not[LessEqual[z, 9.8e+22]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(N[(y * a), $MachinePrecision] / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.28000000000000002e45 or 9.79999999999999958e22 < z

   1. Initial program 90.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 84.5%

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

   if -1.28000000000000002e45 < z < 9.79999999999999958e22

   1. Initial program 97.1%

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

      1. associate-/r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 87.4%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{+45} \lor \neg \left(z \leq 9.8 \cdot 10^{+22}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot a}{t + 1}\\ \end{array} \]

Alternative 8: 70.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+44} \lor \neg \left(z \leq 7 \cdot 10^{+22}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.75e+44) (not (<= z 7e+22))) (- x a) (- x (/ a (/ t y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.75e+44) || !(z <= 7e+22)) {
		tmp = x - a;
	} else {
		tmp = x - (a / (t / y));
	}
	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 <= (-1.75d+44)) .or. (.not. (z <= 7d+22))) then
        tmp = x - a
    else
        tmp = x - (a / (t / y))
    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 <= -1.75e+44) || !(z <= 7e+22)) {
		tmp = x - a;
	} else {
		tmp = x - (a / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.75e+44) or not (z <= 7e+22):
		tmp = x - a
	else:
		tmp = x - (a / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.75e+44) || !(z <= 7e+22))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(a / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.75e+44) || ~((z <= 7e+22)))
		tmp = x - a;
	else
		tmp = x - (a / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.75e+44], N[Not[LessEqual[z, 7e+22]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.75e44 or 7e22 < z

   1. Initial program 90.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 84.5%

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

   if -1.75e44 < z < 7e22

   1. Initial program 97.1%

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

      1. associate-/r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 87.4%

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

   5. Taylor expanded in t around inf 70.7%

      \[\leadsto x - \color{blue}{\frac{a \cdot y}{t}} \]
   6. Step-by-step derivation

      1. associate-/l* 72.9%

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

   7. Simplified 72.9%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+44} \lor \neg \left(z \leq 7 \cdot 10^{+22}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \]

Alternative 9: 73.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+17} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.5e+17) (not (<= z 1.0))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.5e+17) || !(z <= 1.0)) {
		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 <= (-4.5d+17)) .or. (.not. (z <= 1.0d0))) 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 <= -4.5e+17) || !(z <= 1.0)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.5e+17) or not (z <= 1.0):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.5e+17) || !(z <= 1.0))
		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 <= -4.5e+17) || ~((z <= 1.0)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.5e+17], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5e17 or 1 < z

   1. Initial program 90.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 82.3%

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

   if -4.5e17 < z < 1

   1. Initial program 97.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in t around 0 74.2%

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

   5. Taylor expanded in z around 0 70.3%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+17} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]

Alternative 10: 65.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1750000 \lor \neg \left(z \leq 0.046\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1750000.0) (not (<= z 0.046))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1750000.0) || !(z <= 0.046)) {
		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 <= (-1750000.0d0)) .or. (.not. (z <= 0.046d0))) 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 <= -1750000.0) || !(z <= 0.046)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1750000.0) or not (z <= 0.046):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1750000.0) || !(z <= 0.046))
		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 <= -1750000.0) || ~((z <= 0.046)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1750000.0], N[Not[LessEqual[z, 0.046]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.75e6 or 0.045999999999999999 < z

   1. Initial program 91.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 81.0%

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

   if -1.75e6 < z < 0.045999999999999999

   1. Initial program 97.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in x around inf 60.2%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1750000 \lor \neg \left(z \leq 0.046\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 54.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+244} \lor \neg \left(a \leq 2.4 \cdot 10^{+158}\right):\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.6e+244) (not (<= a 2.4e+158))) (- a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.6e+244) || !(a <= 2.4e+158)) {
		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 <= (-1.6d+244)) .or. (.not. (a <= 2.4d+158))) 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 <= -1.6e+244) || !(a <= 2.4e+158)) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.6e+244) or not (a <= 2.4e+158):
		tmp = -a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.6e+244) || !(a <= 2.4e+158))
		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 <= -1.6e+244) || ~((a <= 2.4e+158)))
		tmp = -a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.6e+244], N[Not[LessEqual[a, 2.4e+158]], $MachinePrecision]], (-a), x]

Derivation

1. Split input into 2 regimes

2. if a < -1.6000000000000001e244 or 2.40000000000000008e158 < a

   1. Initial program 99.8%

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

      1. associate-/r/ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in t around 0 80.6%

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

   5. Taylor expanded in x around 0 29.9%

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

      1. mul-1-neg 29.9%

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

      2. associate-/l* 77.3%

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

      3. distribute-neg-frac 77.3%

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

   7. Simplified 77.3%

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

   8. Taylor expanded in z around inf 54.5%

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

      1. mul-1-neg 54.5%

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

   10. Simplified 54.5%

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

   if -1.6000000000000001e244 < a < 2.40000000000000008e158

   1. Initial program 93.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in x around inf 64.9%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+244} \lor \neg \left(a \leq 2.4 \cdot 10^{+158}\right):\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 53.5% 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 94.0%

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

   1. associate-/r/ 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in x around inf 55.6%

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

5. Final simplification 55.6%

   \[\leadsto x \]

Developer target: 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 2023318 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (- x (* (/ (- y z) (+ (- t z) 1.0)) a))

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