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

Percentage Accurate: 97.2% → 99.7%

Time: 11.0s

Alternatives: 14

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: 97.2% 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, 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 95.8%

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

   1. associate-/r/ 99.0%

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

3. Simplified 99.0%

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

4. Final simplification 99.0%

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

Alternative 2: 74.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{a}{\frac{z}{y}} - a\right)\\ t_2 := x + a \cdot \frac{z - y}{t}\\ t_3 := x - y \cdot a\\ \mathbf{if}\;t \leq -3.1 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-193}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-7}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- (/ a (/ z y)) a)))
        (t_2 (+ x (* a (/ (- z y) t))))
        (t_3 (- x (* y a))))
   (if (<= t -3.1e+32)
     t_2
     (if (<= t -7.6e-67)
       t_1
       (if (<= t -5e-193)
         t_3
         (if (<= t 2.7e-289) t_1 (if (<= t 1.12e-7) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((a / (z / y)) - a);
	double t_2 = x + (a * ((z - y) / t));
	double t_3 = x - (y * a);
	double tmp;
	if (t <= -3.1e+32) {
		tmp = t_2;
	} else if (t <= -7.6e-67) {
		tmp = t_1;
	} else if (t <= -5e-193) {
		tmp = t_3;
	} else if (t <= 2.7e-289) {
		tmp = t_1;
	} else if (t <= 1.12e-7) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + ((a / (z / y)) - a)
    t_2 = x + (a * ((z - y) / t))
    t_3 = x - (y * a)
    if (t <= (-3.1d+32)) then
        tmp = t_2
    else if (t <= (-7.6d-67)) then
        tmp = t_1
    else if (t <= (-5d-193)) then
        tmp = t_3
    else if (t <= 2.7d-289) then
        tmp = t_1
    else if (t <= 1.12d-7) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((a / (z / y)) - a);
	double t_2 = x + (a * ((z - y) / t));
	double t_3 = x - (y * a);
	double tmp;
	if (t <= -3.1e+32) {
		tmp = t_2;
	} else if (t <= -7.6e-67) {
		tmp = t_1;
	} else if (t <= -5e-193) {
		tmp = t_3;
	} else if (t <= 2.7e-289) {
		tmp = t_1;
	} else if (t <= 1.12e-7) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((a / (z / y)) - a)
	t_2 = x + (a * ((z - y) / t))
	t_3 = x - (y * a)
	tmp = 0
	if t <= -3.1e+32:
		tmp = t_2
	elif t <= -7.6e-67:
		tmp = t_1
	elif t <= -5e-193:
		tmp = t_3
	elif t <= 2.7e-289:
		tmp = t_1
	elif t <= 1.12e-7:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(a / Float64(z / y)) - a))
	t_2 = Float64(x + Float64(a * Float64(Float64(z - y) / t)))
	t_3 = Float64(x - Float64(y * a))
	tmp = 0.0
	if (t <= -3.1e+32)
		tmp = t_2;
	elseif (t <= -7.6e-67)
		tmp = t_1;
	elseif (t <= -5e-193)
		tmp = t_3;
	elseif (t <= 2.7e-289)
		tmp = t_1;
	elseif (t <= 1.12e-7)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((a / (z / y)) - a);
	t_2 = x + (a * ((z - y) / t));
	t_3 = x - (y * a);
	tmp = 0.0;
	if (t <= -3.1e+32)
		tmp = t_2;
	elseif (t <= -7.6e-67)
		tmp = t_1;
	elseif (t <= -5e-193)
		tmp = t_3;
	elseif (t <= 2.7e-289)
		tmp = t_1;
	elseif (t <= 1.12e-7)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(a / N[(z / y), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.1e+32], t$95$2, If[LessEqual[t, -7.6e-67], t$95$1, If[LessEqual[t, -5e-193], t$95$3, If[LessEqual[t, 2.7e-289], t$95$1, If[LessEqual[t, 1.12e-7], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.09999999999999993e32 or 1.12e-7 < t

   1. Initial program 95.7%

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

      1. associate-/r/ 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in t around inf 81.9%

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

   if -3.09999999999999993e32 < t < -7.59999999999999976e-67 or -5.0000000000000005e-193 < t < 2.7e-289

   1. Initial program 95.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 z around inf 81.3%

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

      1. mul-1-neg 81.3%

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

   6. Simplified 81.3%

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

   7. Taylor expanded in y around 0 79.1%

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

      1. mul-1-neg 79.1%

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

      2. unsub-neg 79.1%

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

      3. associate-/l* 83.6%

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

   9. Simplified 83.6%

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

   if -7.59999999999999976e-67 < t < -5.0000000000000005e-193 or 2.7e-289 < t < 1.12e-7

   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%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 84.2%

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

   5. Taylor expanded in t around 0 83.6%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+32}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-67}:\\ \;\;\;\;x + \left(\frac{a}{\frac{z}{y}} - a\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-193}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-289}:\\ \;\;\;\;x + \left(\frac{a}{\frac{z}{y}} - a\right)\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-7}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \]

Alternative 3: 90.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+109}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z} + -1}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+61}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{a}{\frac{z}{y}} - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.5e+109)
   (+ x (/ a (+ (/ t z) -1.0)))
   (if (<= z 2.9e+61)
     (+ x (* a (/ (- z y) (+ t 1.0))))
     (+ x (- (/ a (/ z y)) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.5e+109) {
		tmp = x + (a / ((t / z) + -1.0));
	} else if (z <= 2.9e+61) {
		tmp = x + (a * ((z - y) / (t + 1.0)));
	} else {
		tmp = x + ((a / (z / 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 <= (-3.5d+109)) then
        tmp = x + (a / ((t / z) + (-1.0d0)))
    else if (z <= 2.9d+61) then
        tmp = x + (a * ((z - y) / (t + 1.0d0)))
    else
        tmp = x + ((a / (z / 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 <= -3.5e+109) {
		tmp = x + (a / ((t / z) + -1.0));
	} else if (z <= 2.9e+61) {
		tmp = x + (a * ((z - y) / (t + 1.0)));
	} else {
		tmp = x + ((a / (z / y)) - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.5e+109:
		tmp = x + (a / ((t / z) + -1.0))
	elif z <= 2.9e+61:
		tmp = x + (a * ((z - y) / (t + 1.0)))
	else:
		tmp = x + ((a / (z / y)) - a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.5e+109)
		tmp = Float64(x + Float64(a / Float64(Float64(t / z) + -1.0)));
	elseif (z <= 2.9e+61)
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / Float64(t + 1.0))));
	else
		tmp = Float64(x + Float64(Float64(a / Float64(z / y)) - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.5e+109)
		tmp = x + (a / ((t / z) + -1.0));
	elseif (z <= 2.9e+61)
		tmp = x + (a * ((z - y) / (t + 1.0)));
	else
		tmp = x + ((a / (z / y)) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.5e+109], N[(x + N[(a / N[(N[(t / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+61], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a / N[(z / y), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.49999999999999983e109

   1. Initial program 89.2%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. clear-num 100.0%

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

      3. un-div-inv 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around 0 61.2%

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

      1. mul-1-neg 61.2%

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

      2. associate-/l* 91.4%

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

      3. distribute-neg-frac 91.4%

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

      4. div-sub 91.4%

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

      5. *-inverses 91.4%

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

      6. sub-neg 91.4%

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

      7. metadata-eval 91.4%

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

   8. Simplified 91.4%

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

   9. Taylor expanded in t around inf 91.4%

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

   if -3.49999999999999983e109 < z < 2.9000000000000001e61

   1. Initial program 98.6%

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

      1. associate-/r/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in z around 0 95.3%

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

   if 2.9000000000000001e61 < z

   1. Initial program 91.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 z around inf 89.8%

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

      1. mul-1-neg 89.8%

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

   6. Simplified 89.8%

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

   7. Taylor expanded in y around 0 82.9%

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

      1. mul-1-neg 82.9%

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

      2. unsub-neg 82.9%

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

      3. associate-/l* 89.8%

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

   9. Simplified 89.8%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+109}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z} + -1}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+61}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{a}{\frac{z}{y}} - a\right)\\ \end{array} \]

Alternative 4: 72.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+131}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+44}:\\ \;\;\;\;x + \frac{y \cdot a}{z}\\ \mathbf{elif}\;z \leq -63000000 \lor \neg \left(z \leq 3.95 \cdot 10^{+59}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.3e+131)
   (- x a)
   (if (<= z -1.2e+44)
     (+ x (/ (* y a) z))
     (if (or (<= z -63000000.0) (not (<= z 3.95e+59)))
       (- x a)
       (- x (* y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+131) {
		tmp = x - a;
	} else if (z <= -1.2e+44) {
		tmp = x + ((y * a) / z);
	} else if ((z <= -63000000.0) || !(z <= 3.95e+59)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.3d+131)) then
        tmp = x - a
    else if (z <= (-1.2d+44)) then
        tmp = x + ((y * a) / z)
    else if ((z <= (-63000000.0d0)) .or. (.not. (z <= 3.95d+59))) then
        tmp = x - a
    else
        tmp = x - (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+131) {
		tmp = x - a;
	} else if (z <= -1.2e+44) {
		tmp = x + ((y * a) / z);
	} else if ((z <= -63000000.0) || !(z <= 3.95e+59)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.3e+131:
		tmp = x - a
	elif z <= -1.2e+44:
		tmp = x + ((y * a) / z)
	elif (z <= -63000000.0) or not (z <= 3.95e+59):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.3e+131)
		tmp = Float64(x - a);
	elseif (z <= -1.2e+44)
		tmp = Float64(x + Float64(Float64(y * a) / z));
	elseif ((z <= -63000000.0) || !(z <= 3.95e+59))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.3e+131)
		tmp = x - a;
	elseif (z <= -1.2e+44)
		tmp = x + ((y * a) / z);
	elseif ((z <= -63000000.0) || ~((z <= 3.95e+59)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.3e+131], N[(x - a), $MachinePrecision], If[LessEqual[z, -1.2e+44], N[(x + N[(N[(y * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -63000000.0], N[Not[LessEqual[z, 3.95e+59]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3e131 or -1.20000000000000007e44 < z < -6.3e7 or 3.95e59 < 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 79.9%

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

   if -1.3e131 < z < -1.20000000000000007e44

   1. Initial program 94.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 z around inf 83.8%

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

      1. mul-1-neg 83.8%

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

   6. Simplified 83.8%

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

   7. Taylor expanded in y around inf 89.1%

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

      1. associate-*r/ 89.1%

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

      2. neg-mul-1 89.1%

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

   9. Simplified 89.1%

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

   10. Taylor expanded in x around 0 84.0%

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

   if -6.3e7 < z < 3.95e59

   1. Initial program 99.1%

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

      1. associate-/r/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in z around 0 87.1%

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

   5. Taylor expanded in t around 0 70.4%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+131}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+44}:\\ \;\;\;\;x + \frac{y \cdot a}{z}\\ \mathbf{elif}\;z \leq -63000000 \lor \neg \left(z \leq 3.95 \cdot 10^{+59}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]

Alternative 5: 70.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{a}{\frac{t}{y}}\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-60}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 0.96:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ a (/ t y)))))
   (if (<= t -1.05e+129)
     t_1
     (if (<= t -4.4e-60) (- x a) (if (<= t 0.96) (- x (* y a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a / (t / y));
	double tmp;
	if (t <= -1.05e+129) {
		tmp = t_1;
	} else if (t <= -4.4e-60) {
		tmp = x - a;
	} else if (t <= 0.96) {
		tmp = x - (y * a);
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = x - (a / (t / y))
    if (t <= (-1.05d+129)) then
        tmp = t_1
    else if (t <= (-4.4d-60)) then
        tmp = x - a
    else if (t <= 0.96d0) then
        tmp = x - (y * a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a / (t / y));
	double tmp;
	if (t <= -1.05e+129) {
		tmp = t_1;
	} else if (t <= -4.4e-60) {
		tmp = x - a;
	} else if (t <= 0.96) {
		tmp = x - (y * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a / (t / y))
	tmp = 0
	if t <= -1.05e+129:
		tmp = t_1
	elif t <= -4.4e-60:
		tmp = x - a
	elif t <= 0.96:
		tmp = x - (y * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a / Float64(t / y)))
	tmp = 0.0
	if (t <= -1.05e+129)
		tmp = t_1;
	elseif (t <= -4.4e-60)
		tmp = Float64(x - a);
	elseif (t <= 0.96)
		tmp = Float64(x - Float64(y * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a / (t / y));
	tmp = 0.0;
	if (t <= -1.05e+129)
		tmp = t_1;
	elseif (t <= -4.4e-60)
		tmp = x - a;
	elseif (t <= 0.96)
		tmp = x - (y * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e+129], t$95$1, If[LessEqual[t, -4.4e-60], N[(x - a), $MachinePrecision], If[LessEqual[t, 0.96], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.04999999999999998e129 or 0.95999999999999996 < t

   1. Initial program 95.8%

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

      1. associate-/r/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in z around 0 77.5%

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

   5. Taylor expanded in t around inf 76.9%

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

      1. associate-/l* 82.0%

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

   7. Simplified 82.0%

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

   if -1.04999999999999998e129 < t < -4.3999999999999998e-60

   1. Initial program 97.1%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 74.6%

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

   if -4.3999999999999998e-60 < t < 0.95999999999999996

   1. Initial program 95.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 76.3%

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

   5. Taylor expanded in t around 0 75.9%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+129}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-60}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 0.96:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \]

Alternative 6: 73.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+28} \lor \neg \left(t \leq 1.12 \cdot 10^{-7}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.4e+28) (not (<= t 1.12e-7)))
   (+ x (* a (/ (- z y) t)))
   (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.4e+28) || !(t <= 1.12e-7)) {
		tmp = x + (a * ((z - y) / t));
	} 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 ((t <= (-2.4d+28)) .or. (.not. (t <= 1.12d-7))) then
        tmp = x + (a * ((z - y) / t))
    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 ((t <= -2.4e+28) || !(t <= 1.12e-7)) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.4e+28) or not (t <= 1.12e-7):
		tmp = x + (a * ((z - y) / t))
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.4e+28) || !(t <= 1.12e-7))
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	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 ((t <= -2.4e+28) || ~((t <= 1.12e-7)))
		tmp = x + (a * ((z - y) / t));
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.4e+28], N[Not[LessEqual[t, 1.12e-7]], $MachinePrecision]], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.39999999999999981e28 or 1.12e-7 < t

   1. Initial program 95.8%

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

      1. associate-/r/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in t around inf 81.6%

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

   if -2.39999999999999981e28 < t < 1.12e-7

   1. Initial program 95.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 74.7%

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

   5. Taylor expanded in t around 0 75.3%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+28} \lor \neg \left(t \leq 1.12 \cdot 10^{-7}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]

Alternative 7: 87.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+109} \lor \neg \left(z \leq 8 \cdot 10^{+59}\right):\\ \;\;\;\;x + \left(\frac{a}{\frac{z}{y}} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.3e+109) (not (<= z 8e+59)))
   (+ x (- (/ a (/ z y)) a))
   (- x (/ a (/ (+ t 1.0) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.3e+109) || !(z <= 8e+59)) {
		tmp = x + ((a / (z / y)) - a);
	} else {
		tmp = x - (a / ((t + 1.0) / 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 <= (-3.3d+109)) .or. (.not. (z <= 8d+59))) then
        tmp = x + ((a / (z / y)) - a)
    else
        tmp = x - (a / ((t + 1.0d0) / 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 <= -3.3e+109) || !(z <= 8e+59)) {
		tmp = x + ((a / (z / y)) - a);
	} else {
		tmp = x - (a / ((t + 1.0) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.3e+109) or not (z <= 8e+59):
		tmp = x + ((a / (z / y)) - a)
	else:
		tmp = x - (a / ((t + 1.0) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.3e+109) || !(z <= 8e+59))
		tmp = Float64(x + Float64(Float64(a / Float64(z / y)) - a));
	else
		tmp = Float64(x - Float64(a / Float64(Float64(t + 1.0) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.3e+109) || ~((z <= 8e+59)))
		tmp = x + ((a / (z / y)) - a);
	else
		tmp = x - (a / ((t + 1.0) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.3e+109], N[Not[LessEqual[z, 8e+59]], $MachinePrecision]], N[(x + N[(N[(a / N[(z / y), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(x - N[(a / N[(N[(t + 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2999999999999999e109 or 7.99999999999999977e59 < z

   1. Initial program 90.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 90.5%

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

      1. mul-1-neg 90.5%

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

   6. Simplified 90.5%

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

   7. Taylor expanded in y around 0 87.0%

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

      1. mul-1-neg 87.0%

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

      2. unsub-neg 87.0%

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

      3. associate-/l* 90.5%

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

   9. Simplified 90.5%

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

   if -3.2999999999999999e109 < z < 7.99999999999999977e59

   1. Initial program 98.6%

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

      1. associate-/r/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in z around 0 84.9%

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

      1. associate-/l* 88.3%

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

   6. Simplified 88.3%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+109} \lor \neg \left(z \leq 8 \cdot 10^{+59}\right):\\ \;\;\;\;x + \left(\frac{a}{\frac{z}{y}} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \end{array} \]

Alternative 8: 87.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+109}:\\ \;\;\;\;x - a \cdot \frac{y - z}{-z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+59}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{a}{\frac{z}{y}} - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.3e+109)
   (- x (* a (/ (- y z) (- z))))
   (if (<= z 4e+59) (- x (/ a (/ (+ t 1.0) y))) (+ x (- (/ a (/ z y)) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e+109) {
		tmp = x - (a * ((y - z) / -z));
	} else if (z <= 4e+59) {
		tmp = x - (a / ((t + 1.0) / y));
	} else {
		tmp = x + ((a / (z / 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 <= (-3.3d+109)) then
        tmp = x - (a * ((y - z) / -z))
    else if (z <= 4d+59) then
        tmp = x - (a / ((t + 1.0d0) / y))
    else
        tmp = x + ((a / (z / 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 <= -3.3e+109) {
		tmp = x - (a * ((y - z) / -z));
	} else if (z <= 4e+59) {
		tmp = x - (a / ((t + 1.0) / y));
	} else {
		tmp = x + ((a / (z / y)) - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.3e+109:
		tmp = x - (a * ((y - z) / -z))
	elif z <= 4e+59:
		tmp = x - (a / ((t + 1.0) / y))
	else:
		tmp = x + ((a / (z / y)) - a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.3e+109)
		tmp = Float64(x - Float64(a * Float64(Float64(y - z) / Float64(-z))));
	elseif (z <= 4e+59)
		tmp = Float64(x - Float64(a / Float64(Float64(t + 1.0) / y)));
	else
		tmp = Float64(x + Float64(Float64(a / Float64(z / y)) - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.3e+109)
		tmp = x - (a * ((y - z) / -z));
	elseif (z <= 4e+59)
		tmp = x - (a / ((t + 1.0) / y));
	else
		tmp = x + ((a / (z / y)) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.3e+109], N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+59], N[(x - N[(a / N[(N[(t + 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a / N[(z / y), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2999999999999999e109

   1. Initial program 89.2%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 91.2%

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

      1. mul-1-neg 91.2%

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

   6. Simplified 91.2%

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

   if -3.2999999999999999e109 < z < 3.99999999999999989e59

   1. Initial program 98.6%

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

      1. associate-/r/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in z around 0 84.9%

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

      1. associate-/l* 88.3%

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

   6. Simplified 88.3%

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

   if 3.99999999999999989e59 < z

   1. Initial program 91.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 z around inf 89.8%

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

      1. mul-1-neg 89.8%

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

   6. Simplified 89.8%

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

   7. Taylor expanded in y around 0 82.9%

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

      1. mul-1-neg 82.9%

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

      2. unsub-neg 82.9%

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

      3. associate-/l* 89.8%

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

   9. Simplified 89.8%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+109}:\\ \;\;\;\;x - a \cdot \frac{y - z}{-z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+59}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{a}{\frac{z}{y}} - a\right)\\ \end{array} \]

Alternative 9: 86.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+109}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z} + -1}\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+60}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{a}{\frac{z}{y}} - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.8e+109)
   (+ x (/ a (+ (/ t z) -1.0)))
   (if (<= z 1.36e+60) (- x (/ a (/ (+ t 1.0) y))) (+ x (- (/ a (/ z y)) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.8e+109) {
		tmp = x + (a / ((t / z) + -1.0));
	} else if (z <= 1.36e+60) {
		tmp = x - (a / ((t + 1.0) / y));
	} else {
		tmp = x + ((a / (z / 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 <= (-3.8d+109)) then
        tmp = x + (a / ((t / z) + (-1.0d0)))
    else if (z <= 1.36d+60) then
        tmp = x - (a / ((t + 1.0d0) / y))
    else
        tmp = x + ((a / (z / 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 <= -3.8e+109) {
		tmp = x + (a / ((t / z) + -1.0));
	} else if (z <= 1.36e+60) {
		tmp = x - (a / ((t + 1.0) / y));
	} else {
		tmp = x + ((a / (z / y)) - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.8e+109:
		tmp = x + (a / ((t / z) + -1.0))
	elif z <= 1.36e+60:
		tmp = x - (a / ((t + 1.0) / y))
	else:
		tmp = x + ((a / (z / y)) - a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.8e+109)
		tmp = Float64(x + Float64(a / Float64(Float64(t / z) + -1.0)));
	elseif (z <= 1.36e+60)
		tmp = Float64(x - Float64(a / Float64(Float64(t + 1.0) / y)));
	else
		tmp = Float64(x + Float64(Float64(a / Float64(z / y)) - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.8e+109)
		tmp = x + (a / ((t / z) + -1.0));
	elseif (z <= 1.36e+60)
		tmp = x - (a / ((t + 1.0) / y));
	else
		tmp = x + ((a / (z / y)) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.8e+109], N[(x + N[(a / N[(N[(t / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.36e+60], N[(x - N[(a / N[(N[(t + 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a / N[(z / y), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.80000000000000039e109

   1. Initial program 89.2%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. clear-num 100.0%

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

      3. un-div-inv 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around 0 61.2%

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

      1. mul-1-neg 61.2%

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

      2. associate-/l* 91.4%

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

      3. distribute-neg-frac 91.4%

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

      4. div-sub 91.4%

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

      5. *-inverses 91.4%

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

      6. sub-neg 91.4%

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

      7. metadata-eval 91.4%

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

   8. Simplified 91.4%

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

   9. Taylor expanded in t around inf 91.4%

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

   if -3.80000000000000039e109 < z < 1.36000000000000002e60

   1. Initial program 98.6%

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

      1. associate-/r/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in z around 0 84.9%

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

      1. associate-/l* 88.3%

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

   6. Simplified 88.3%

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

   if 1.36000000000000002e60 < z

   1. Initial program 91.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 z around inf 89.8%

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

      1. mul-1-neg 89.8%

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

   6. Simplified 89.8%

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

   7. Taylor expanded in y around 0 82.9%

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

      1. mul-1-neg 82.9%

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

      2. unsub-neg 82.9%

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

      3. associate-/l* 89.8%

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

   9. Simplified 89.8%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+109}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z} + -1}\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+60}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{a}{\frac{z}{y}} - a\right)\\ \end{array} \]

Alternative 10: 97.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.8%

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

   1. clear-num 95.7%

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

   2. associate-/r/ 95.8%

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

   3. clear-num 96.3%

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

3. Applied egg-rr 96.3%

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

4. Final simplification 96.3%

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

Alternative 11: 63.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+131}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-165}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-225}:\\ \;\;\;\;y \cdot \left(-a\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.55e+131)
   (- x a)
   (if (<= z -1.02e-165)
     x
     (if (<= z -1e-225) (* y (- a)) (if (<= z 3.2e+75) x (- x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.55e+131) {
		tmp = x - a;
	} else if (z <= -1.02e-165) {
		tmp = x;
	} else if (z <= -1e-225) {
		tmp = y * -a;
	} else if (z <= 3.2e+75) {
		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 <= (-1.55d+131)) then
        tmp = x - a
    else if (z <= (-1.02d-165)) then
        tmp = x
    else if (z <= (-1d-225)) then
        tmp = y * -a
    else if (z <= 3.2d+75) 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 <= -1.55e+131) {
		tmp = x - a;
	} else if (z <= -1.02e-165) {
		tmp = x;
	} else if (z <= -1e-225) {
		tmp = y * -a;
	} else if (z <= 3.2e+75) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.55e+131:
		tmp = x - a
	elif z <= -1.02e-165:
		tmp = x
	elif z <= -1e-225:
		tmp = y * -a
	elif z <= 3.2e+75:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.55e+131)
		tmp = Float64(x - a);
	elseif (z <= -1.02e-165)
		tmp = x;
	elseif (z <= -1e-225)
		tmp = Float64(y * Float64(-a));
	elseif (z <= 3.2e+75)
		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 <= -1.55e+131)
		tmp = x - a;
	elseif (z <= -1.02e-165)
		tmp = x;
	elseif (z <= -1e-225)
		tmp = y * -a;
	elseif (z <= 3.2e+75)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.55e+131], N[(x - a), $MachinePrecision], If[LessEqual[z, -1.02e-165], x, If[LessEqual[z, -1e-225], N[(y * (-a)), $MachinePrecision], If[LessEqual[z, 3.2e+75], x, N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55000000000000008e131 or 3.19999999999999985e75 < z

   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 z around inf 82.7%

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

   if -1.55000000000000008e131 < z < -1.02e-165 or -9.9999999999999996e-226 < z < 3.19999999999999985e75

   1. Initial program 98.1%

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

      1. associate-/r/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in z around 0 83.1%

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

   5. Taylor expanded in x around inf 59.7%

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

   if -1.02e-165 < z < -9.9999999999999996e-226

   1. Initial program 99.8%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 100.0%

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

   5. Taylor expanded in t around 0 87.6%

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

   6. Taylor expanded in x around 0 83.9%

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

      1. mul-1-neg 83.9%

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

      2. distribute-rgt-neg-in 83.9%

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

   8. Simplified 83.9%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+131}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-165}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-225}:\\ \;\;\;\;y \cdot \left(-a\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 12: 72.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -132000000 \lor \neg \left(z \leq 4 \cdot 10^{+59}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -132000000.0) (not (<= z 4e+59))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -132000000.0) || !(z <= 4e+59)) {
		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 <= (-132000000.0d0)) .or. (.not. (z <= 4d+59))) 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 <= -132000000.0) || !(z <= 4e+59)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -132000000.0) or not (z <= 4e+59):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -132000000.0) || !(z <= 4e+59))
		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 <= -132000000.0) || ~((z <= 4e+59)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -132000000.0], N[Not[LessEqual[z, 4e+59]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.32e8 or 3.99999999999999989e59 < z

   1. Initial program 91.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 76.4%

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

   if -1.32e8 < z < 3.99999999999999989e59

   1. Initial program 99.1%

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

      1. associate-/r/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in z around 0 87.1%

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

   5. Taylor expanded in t around 0 70.4%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -132000000 \lor \neg \left(z \leq 4 \cdot 10^{+59}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]

Alternative 13: 64.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+131} \lor \neg \left(z \leq 4.8 \cdot 10^{+74}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.55e+131) (not (<= z 4.8e+74))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.55e+131) || !(z <= 4.8e+74)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.55d+131)) .or. (.not. (z <= 4.8d+74))) then
        tmp = x - a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.55e+131) || !(z <= 4.8e+74)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.55e+131) or not (z <= 4.8e+74):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.55e+131) || !(z <= 4.8e+74))
		tmp = Float64(x - a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.55e+131) || ~((z <= 4.8e+74)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.55e+131], N[Not[LessEqual[z, 4.8e+74]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.55000000000000008e131 or 4.80000000000000017e74 < z

   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 z around inf 82.7%

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

   if -1.55000000000000008e131 < z < 4.80000000000000017e74

   1. Initial program 98.2%

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

      1. associate-/r/ 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in z around 0 83.8%

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

   5. Taylor expanded in x around inf 57.4%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+131} \lor \neg \left(z \leq 4.8 \cdot 10^{+74}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 53.9% 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 95.8%

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

   1. associate-/r/ 99.0%

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

3. Simplified 99.0%

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

4. Taylor expanded in z around 0 73.9%

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

5. Taylor expanded in x around inf 57.2%

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

6. Final simplification 57.2%

   \[\leadsto x \]

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 2023339 
(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))))