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

Percentage Accurate: 97.1% → 99.7%

Time: 9.5s

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: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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/ 99.3%

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

   4. distribute-lft-neg-in 99.3%

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

   5. fma-def 99.3%

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

   6. distribute-neg-frac 99.3%

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

   7. sub-neg 99.3%

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

   8. distribute-neg-in 99.3%

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

   9. remove-double-neg 99.3%

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

   10. +-commutative 99.3%

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

   11. sub-neg 99.3%

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

3. Simplified 99.3%

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

4. Final simplification 99.3%

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

Alternative 2: 90.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+140}:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+128}:\\ \;\;\;\;x - \frac{a}{\frac{1 - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.9e+140)
   (+ x (/ (- z y) (/ t a)))
   (if (<= t 1.12e+128)
     (- x (/ a (/ (- 1.0 z) (- y z))))
     (+ x (* a (/ (- z y) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.9e+140) {
		tmp = x + ((z - y) / (t / a));
	} else if (t <= 1.12e+128) {
		tmp = x - (a / ((1.0 - z) / (y - z)));
	} else {
		tmp = x + (a * ((z - y) / 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 (t <= (-1.9d+140)) then
        tmp = x + ((z - y) / (t / a))
    else if (t <= 1.12d+128) then
        tmp = x - (a / ((1.0d0 - z) / (y - z)))
    else
        tmp = x + (a * ((z - y) / 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 (t <= -1.9e+140) {
		tmp = x + ((z - y) / (t / a));
	} else if (t <= 1.12e+128) {
		tmp = x - (a / ((1.0 - z) / (y - z)));
	} else {
		tmp = x + (a * ((z - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.9e+140:
		tmp = x + ((z - y) / (t / a))
	elif t <= 1.12e+128:
		tmp = x - (a / ((1.0 - z) / (y - z)))
	else:
		tmp = x + (a * ((z - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.9e+140)
		tmp = Float64(x + Float64(Float64(z - y) / Float64(t / a)));
	elseif (t <= 1.12e+128)
		tmp = Float64(x - Float64(a / Float64(Float64(1.0 - z) / Float64(y - z))));
	else
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.9e+140)
		tmp = x + ((z - y) / (t / a));
	elseif (t <= 1.12e+128)
		tmp = x - (a / ((1.0 - z) / (y - z)));
	else
		tmp = x + (a * ((z - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.9e+140], N[(x + N[(N[(z - y), $MachinePrecision] / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.12e+128], N[(x - N[(a / N[(N[(1.0 - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9e140

   1. Initial program 95.0%

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

   2. Taylor expanded in t around inf 86.9%

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

   if -1.9e140 < t < 1.1200000000000001e128

   1. Initial program 97.7%

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

      1. associate-/r/ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 81.2%

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

      1. associate-/l* 96.0%

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

   6. Simplified 96.0%

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

   if 1.1200000000000001e128 < t

   1. Initial program 97.7%

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

      1. associate-/r/ 98.2%

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

      2. *-commutative 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in t around inf 87.4%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+140}:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+128}:\\ \;\;\;\;x - \frac{a}{\frac{1 - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \]

Alternative 3: 85.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -18000000000 \lor \neg \left(z \leq 7.8 \cdot 10^{+27}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot a}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -18000000000.0) (not (<= z 7.8e+27)))
   (+ x (/ (- z y) (/ (- z) a)))
   (- x (/ (* y a) (+ t 1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -18000000000.0) || !(z <= 7.8e+27)) {
		tmp = x + ((z - y) / (-z / 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 <= (-18000000000.0d0)) .or. (.not. (z <= 7.8d+27))) then
        tmp = x + ((z - y) / (-z / 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 <= -18000000000.0) || !(z <= 7.8e+27)) {
		tmp = x + ((z - y) / (-z / a));
	} else {
		tmp = x - ((y * a) / (t + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -18000000000.0) or not (z <= 7.8e+27):
		tmp = x + ((z - y) / (-z / a))
	else:
		tmp = x - ((y * a) / (t + 1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -18000000000.0) || !(z <= 7.8e+27))
		tmp = Float64(x + Float64(Float64(z - y) / Float64(Float64(-z) / 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 <= -18000000000.0) || ~((z <= 7.8e+27)))
		tmp = x + ((z - y) / (-z / 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, -18000000000.0], N[Not[LessEqual[z, 7.8e+27]], $MachinePrecision]], N[(x + N[(N[(z - y), $MachinePrecision] / N[((-z) / a), $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 < -1.8e10 or 7.7999999999999997e27 < z

   1. Initial program 96.1%

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

   2. Taylor expanded in z around inf 89.0%

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

      1. mul-1-neg 89.0%

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

      2. distribute-neg-frac 89.0%

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

   4. Simplified 89.0%

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

   if -1.8e10 < z < 7.7999999999999997e27

   1. Initial program 98.5%

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

      1. associate-/r/ 98.7%

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

      2. *-commutative 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in z around 0 87.6%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -18000000000 \lor \neg \left(z \leq 7.8 \cdot 10^{+27}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot a}{t + 1}\\ \end{array} \]

Alternative 4: 85.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-23}:\\ \;\;\;\;x + \frac{a}{\frac{\left(t - z\right) + 1}{z}}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+28}:\\ \;\;\;\;x - \frac{y \cdot a}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.7e-23)
   (+ x (/ a (/ (+ (- t z) 1.0) z)))
   (if (<= z 6.4e+28)
     (- 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 <= -1.7e-23) {
		tmp = x + (a / (((t - z) + 1.0) / z));
	} else if (z <= 6.4e+28) {
		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 <= (-1.7d-23)) then
        tmp = x + (a / (((t - z) + 1.0d0) / z))
    else if (z <= 6.4d+28) 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 <= -1.7e-23) {
		tmp = x + (a / (((t - z) + 1.0) / z));
	} else if (z <= 6.4e+28) {
		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 <= -1.7e-23:
		tmp = x + (a / (((t - z) + 1.0) / z))
	elif z <= 6.4e+28:
		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 <= -1.7e-23)
		tmp = Float64(x + Float64(a / Float64(Float64(Float64(t - z) + 1.0) / z)));
	elseif (z <= 6.4e+28)
		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 <= -1.7e-23)
		tmp = x + (a / (((t - z) + 1.0) / z));
	elseif (z <= 6.4e+28)
		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, -1.7e-23], N[(x + N[(a / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e+28], 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 < -1.7e-23

   1. Initial program 95.7%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-/r/ 95.7%

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

      3. div-inv 95.6%

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

      4. associate-/r* 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around 0 60.7%

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

      1. sub-neg 60.7%

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

      2. mul-1-neg 60.7%

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

      3. remove-double-neg 60.7%

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

      4. associate-/l* 88.4%

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

      5. associate--l+ 88.4%

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

   8. Simplified 88.4%

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

   if -1.7e-23 < z < 6.4000000000000001e28

   1. Initial program 99.1%

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

      1. associate-/r/ 98.6%

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

      2. *-commutative 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in z around 0 90.5%

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

   if 6.4000000000000001e28 < z

   1. Initial program 95.6%

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

   2. Taylor expanded in z around inf 92.1%

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

      1. mul-1-neg 92.1%

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

      2. distribute-neg-frac 92.1%

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

   4. Simplified 92.1%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-23}:\\ \;\;\;\;x + \frac{a}{\frac{\left(t - z\right) + 1}{z}}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+28}:\\ \;\;\;\;x - \frac{y \cdot a}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \end{array} \]

Alternative 5: 72.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-22}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-136}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{+35}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e-22)
   (- x a)
   (if (<= z 2.1e-136)
     (- x (* y a))
     (if (<= z 1.46e+35) (- x (/ a (/ t y))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e-22) {
		tmp = x - a;
	} else if (z <= 2.1e-136) {
		tmp = x - (y * a);
	} else if (z <= 1.46e+35) {
		tmp = x - (a / (t / y));
	} 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 <= (-2.4d-22)) then
        tmp = x - a
    else if (z <= 2.1d-136) then
        tmp = x - (y * a)
    else if (z <= 1.46d+35) then
        tmp = x - (a / (t / y))
    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 <= -2.4e-22) {
		tmp = x - a;
	} else if (z <= 2.1e-136) {
		tmp = x - (y * a);
	} else if (z <= 1.46e+35) {
		tmp = x - (a / (t / y));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e-22:
		tmp = x - a
	elif z <= 2.1e-136:
		tmp = x - (y * a)
	elif z <= 1.46e+35:
		tmp = x - (a / (t / y))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e-22)
		tmp = Float64(x - a);
	elseif (z <= 2.1e-136)
		tmp = Float64(x - Float64(y * a));
	elseif (z <= 1.46e+35)
		tmp = Float64(x - Float64(a / Float64(t / y)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.4e-22)
		tmp = x - a;
	elseif (z <= 2.1e-136)
		tmp = x - (y * a);
	elseif (z <= 1.46e+35)
		tmp = x - (a / (t / y));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e-22], N[(x - a), $MachinePrecision], If[LessEqual[z, 2.1e-136], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.46e+35], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.40000000000000002e-22 or 1.4599999999999999e35 < z

   1. Initial program 95.6%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 82.1%

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

   if -2.40000000000000002e-22 < z < 2.0999999999999999e-136

   1. Initial program 98.8%

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

   2. Taylor expanded in t around 0 77.6%

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

   3. Taylor expanded in z around 0 74.8%

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

   if 2.0999999999999999e-136 < z < 1.4599999999999999e35

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 73.8%

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

   3. Taylor expanded in y around inf 75.0%

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

      1. associate-/l* 78.0%

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

   5. Simplified 78.0%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-22}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-136}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{+35}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 6: 82.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-18}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+27}:\\ \;\;\;\;x - \frac{y \cdot a}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.6e-18)
   (- x a)
   (if (<= z 6.5e+27) (- x (/ (* y a) (+ t 1.0))) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.6e-18) {
		tmp = x - a;
	} else if (z <= 6.5e+27) {
		tmp = x - ((y * a) / (t + 1.0));
	} 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 <= (-4.6d-18)) then
        tmp = x - a
    else if (z <= 6.5d+27) then
        tmp = x - ((y * a) / (t + 1.0d0))
    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 <= -4.6e-18) {
		tmp = x - a;
	} else if (z <= 6.5e+27) {
		tmp = x - ((y * a) / (t + 1.0));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.6e-18:
		tmp = x - a
	elif z <= 6.5e+27:
		tmp = x - ((y * a) / (t + 1.0))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.6e-18)
		tmp = Float64(x - a);
	elseif (z <= 6.5e+27)
		tmp = Float64(x - Float64(Float64(y * a) / Float64(t + 1.0)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.6e-18)
		tmp = x - a;
	elseif (z <= 6.5e+27)
		tmp = x - ((y * a) / (t + 1.0));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.6e-18], N[(x - a), $MachinePrecision], If[LessEqual[z, 6.5e+27], N[(x - N[(N[(y * a), $MachinePrecision] / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.6000000000000002e-18 or 6.5000000000000005e27 < z

   1. Initial program 96.2%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 83.2%

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

   if -4.6000000000000002e-18 < z < 6.5000000000000005e27

   1. Initial program 98.4%

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

      1. associate-/r/ 98.6%

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

      2. *-commutative 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in z around 0 89.4%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-18}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+27}:\\ \;\;\;\;x - \frac{y \cdot a}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 7: 99.7% 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 97.3%

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

   1. associate-/r/ 99.3%

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

   2. *-commutative 99.3%

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

3. Simplified 99.3%

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

4. Final simplification 99.3%

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

Alternative 8: 66.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+36}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+29}:\\ \;\;\;\;x + z \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.35e+36) (- x a) (if (<= z 1.7e+29) (+ x (* z a)) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.35e+36) {
		tmp = x - a;
	} else if (z <= 1.7e+29) {
		tmp = x + (z * a);
	} 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 <= (-2.35d+36)) then
        tmp = x - a
    else if (z <= 1.7d+29) then
        tmp = x + (z * a)
    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 <= -2.35e+36) {
		tmp = x - a;
	} else if (z <= 1.7e+29) {
		tmp = x + (z * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.35e+36:
		tmp = x - a
	elif z <= 1.7e+29:
		tmp = x + (z * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.35e+36)
		tmp = Float64(x - a);
	elseif (z <= 1.7e+29)
		tmp = Float64(x + Float64(z * a));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.35e+36)
		tmp = x - a;
	elseif (z <= 1.7e+29)
		tmp = x + (z * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.35e+36], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.7e+29], N[(x + N[(z * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.34999999999999994e36 or 1.69999999999999991e29 < z

   1. Initial program 95.9%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 84.4%

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

   if -2.34999999999999994e36 < z < 1.69999999999999991e29

   1. Initial program 98.5%

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

      1. associate-/r/ 98.7%

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

      2. *-commutative 98.7%

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

   3. Simplified 98.7%

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

      1. *-commutative 98.7%

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

      2. associate-/r/ 98.5%

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

      3. div-inv 98.5%

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

      4. associate-/r* 98.6%

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

   5. Applied egg-rr 98.6%

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

   6. Taylor expanded in y around 0 69.9%

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

      1. sub-neg 69.9%

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

      2. mul-1-neg 69.9%

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

      3. remove-double-neg 69.9%

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

      4. associate-/l* 68.6%

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

      5. associate--l+ 68.6%

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

   8. Simplified 68.6%

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

   9. Taylor expanded in z around 0 69.9%

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

   10. Taylor expanded in t around 0 65.2%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+36}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+29}:\\ \;\;\;\;x + z \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 9: 73.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-22}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-5}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e-22) (- x a) (if (<= z 2.95e-5) (- x (* y a)) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e-22) {
		tmp = x - a;
	} else if (z <= 2.95e-5) {
		tmp = x - (y * a);
	} 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 <= (-2.4d-22)) then
        tmp = x - a
    else if (z <= 2.95d-5) then
        tmp = x - (y * a)
    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 <= -2.4e-22) {
		tmp = x - a;
	} else if (z <= 2.95e-5) {
		tmp = x - (y * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e-22:
		tmp = x - a
	elif z <= 2.95e-5:
		tmp = x - (y * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e-22)
		tmp = Float64(x - a);
	elseif (z <= 2.95e-5)
		tmp = Float64(x - Float64(y * a));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.4e-22)
		tmp = x - a;
	elseif (z <= 2.95e-5)
		tmp = x - (y * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e-22], N[(x - a), $MachinePrecision], If[LessEqual[z, 2.95e-5], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.40000000000000002e-22 or 2.9499999999999999e-5 < z

   1. Initial program 95.7%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 81.7%

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

   if -2.40000000000000002e-22 < z < 2.9499999999999999e-5

   1. Initial program 99.1%

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

   2. Taylor expanded in t around 0 75.2%

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

   3. Taylor expanded in z around 0 71.1%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-22}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-5}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 10: 66.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+33}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.85e+33) (- x a) (if (<= z 6.2e-70) x (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.85e+33) {
		tmp = x - a;
	} else if (z <= 6.2e-70) {
		tmp = x;
	} 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 <= (-1.85d+33)) then
        tmp = x - a
    else if (z <= 6.2d-70) then
        tmp = x
    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 <= -1.85e+33) {
		tmp = x - a;
	} else if (z <= 6.2e-70) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.85e+33:
		tmp = x - a
	elif z <= 6.2e-70:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.85e+33)
		tmp = Float64(x - a);
	elseif (z <= 6.2e-70)
		tmp = x;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.85e+33)
		tmp = x - a;
	elseif (z <= 6.2e-70)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.85e+33], N[(x - a), $MachinePrecision], If[LessEqual[z, 6.2e-70], x, N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8499999999999999e33 or 6.2e-70 < z

   1. Initial program 96.4%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 80.9%

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

   if -1.8499999999999999e33 < z < 6.2e-70

   1. Initial program 98.3%

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

      1. associate-/r/ 98.5%

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

      2. *-commutative 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in x around inf 63.2%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+33}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 11: 54.1% 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 97.3%

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

   1. associate-/r/ 99.3%

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

   2. *-commutative 99.3%

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

3. Simplified 99.3%

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

4. Taylor expanded in x around inf 58.1%

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

5. Final simplification 58.1%

   \[\leadsto x \]

Developer target: 99.7% 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 2023290 
(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))))