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

Percentage Accurate: 97.1% → 99.7%

Time: 11.4s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 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, 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]

Derivation

1. Initial program 96.7%

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

   1. associate-/r/ 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 2: 76.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \frac{y}{1 - z}\\ t_2 := x - a \cdot \frac{y - z}{t}\\ t_3 := x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{if}\;t \leq -52000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-179}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 0.6:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a (/ y (- 1.0 z)))))
        (t_2 (- x (* a (/ (- y z) t))))
        (t_3 (+ x (- (* a (/ y z)) a))))
   (if (<= t -52000000000.0)
     t_2
     (if (<= t -1.6e-160)
       t_1
       (if (<= t 6e-179)
         t_3
         (if (<= t 1.02e-79) t_1 (if (<= t 0.6) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * (y / (1.0 - z)));
	double t_2 = x - (a * ((y - z) / t));
	double t_3 = x + ((a * (y / z)) - a);
	double tmp;
	if (t <= -52000000000.0) {
		tmp = t_2;
	} else if (t <= -1.6e-160) {
		tmp = t_1;
	} else if (t <= 6e-179) {
		tmp = t_3;
	} else if (t <= 1.02e-79) {
		tmp = t_1;
	} else if (t <= 0.6) {
		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 * (y / (1.0d0 - z)))
    t_2 = x - (a * ((y - z) / t))
    t_3 = x + ((a * (y / z)) - a)
    if (t <= (-52000000000.0d0)) then
        tmp = t_2
    else if (t <= (-1.6d-160)) then
        tmp = t_1
    else if (t <= 6d-179) then
        tmp = t_3
    else if (t <= 1.02d-79) then
        tmp = t_1
    else if (t <= 0.6d0) 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 * (y / (1.0 - z)));
	double t_2 = x - (a * ((y - z) / t));
	double t_3 = x + ((a * (y / z)) - a);
	double tmp;
	if (t <= -52000000000.0) {
		tmp = t_2;
	} else if (t <= -1.6e-160) {
		tmp = t_1;
	} else if (t <= 6e-179) {
		tmp = t_3;
	} else if (t <= 1.02e-79) {
		tmp = t_1;
	} else if (t <= 0.6) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a * (y / (1.0 - z)))
	t_2 = x - (a * ((y - z) / t))
	t_3 = x + ((a * (y / z)) - a)
	tmp = 0
	if t <= -52000000000.0:
		tmp = t_2
	elif t <= -1.6e-160:
		tmp = t_1
	elif t <= 6e-179:
		tmp = t_3
	elif t <= 1.02e-79:
		tmp = t_1
	elif t <= 0.6:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * Float64(y / Float64(1.0 - z))))
	t_2 = Float64(x - Float64(a * Float64(Float64(y - z) / t)))
	t_3 = Float64(x + Float64(Float64(a * Float64(y / z)) - a))
	tmp = 0.0
	if (t <= -52000000000.0)
		tmp = t_2;
	elseif (t <= -1.6e-160)
		tmp = t_1;
	elseif (t <= 6e-179)
		tmp = t_3;
	elseif (t <= 1.02e-79)
		tmp = t_1;
	elseif (t <= 0.6)
		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 * (y / (1.0 - z)));
	t_2 = x - (a * ((y - z) / t));
	t_3 = x + ((a * (y / z)) - a);
	tmp = 0.0;
	if (t <= -52000000000.0)
		tmp = t_2;
	elseif (t <= -1.6e-160)
		tmp = t_1;
	elseif (t <= 6e-179)
		tmp = t_3;
	elseif (t <= 1.02e-79)
		tmp = t_1;
	elseif (t <= 0.6)
		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[(a * N[(y / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -52000000000.0], t$95$2, If[LessEqual[t, -1.6e-160], t$95$1, If[LessEqual[t, 6e-179], t$95$3, If[LessEqual[t, 1.02e-79], t$95$1, If[LessEqual[t, 0.6], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.2e10 or 0.599999999999999978 < t

   1. Initial program 98.3%

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

      1. associate-/r/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in t around inf 90.2%

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

   if -5.2e10 < t < -1.60000000000000004e-160 or 6.00000000000000012e-179 < t < 1.02000000000000002e-79

   1. Initial program 96.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 t around 0 99.0%

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

   5. Taylor expanded in y around inf 83.0%

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

   if -1.60000000000000004e-160 < t < 6.00000000000000012e-179 or 1.02000000000000002e-79 < t < 0.599999999999999978

   1. Initial program 94.7%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 83.5%

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

      1. mul-1-neg 83.5%

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

   6. Simplified 83.5%

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

   7. Taylor expanded in y around 0 76.6%

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

      1. mul-1-neg 76.6%

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

      2. unsub-neg 76.6%

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

      3. *-lft-identity 76.6%

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

      4. times-frac 83.5%

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

      5. /-rgt-identity 83.5%

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

   9. Simplified 83.5%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -52000000000:\\ \;\;\;\;x - a \cdot \frac{y - z}{t}\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-160}:\\ \;\;\;\;x - a \cdot \frac{y}{1 - z}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-179}:\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-79}:\\ \;\;\;\;x - a \cdot \frac{y}{1 - z}\\ \mathbf{elif}\;t \leq 0.6:\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 3: 76.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \frac{y}{1 - z}\\ t_2 := x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{if}\;t \leq -900:\\ \;\;\;\;x - \frac{a}{\frac{t}{y - z}}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-178}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.45:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a (/ y (- 1.0 z))))) (t_2 (+ x (- (* a (/ y z)) a))))
   (if (<= t -900.0)
     (- x (/ a (/ t (- y z))))
     (if (<= t -1.7e-159)
       t_1
       (if (<= t 1.25e-178)
         t_2
         (if (<= t 2.05e-78)
           t_1
           (if (<= t 3.45) t_2 (- x (* a (/ (- y z) t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * (y / (1.0 - z)));
	double t_2 = x + ((a * (y / z)) - a);
	double tmp;
	if (t <= -900.0) {
		tmp = x - (a / (t / (y - z)));
	} else if (t <= -1.7e-159) {
		tmp = t_1;
	} else if (t <= 1.25e-178) {
		tmp = t_2;
	} else if (t <= 2.05e-78) {
		tmp = t_1;
	} else if (t <= 3.45) {
		tmp = t_2;
	} else {
		tmp = x - (a * ((y - z) / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (a * (y / (1.0d0 - z)))
    t_2 = x + ((a * (y / z)) - a)
    if (t <= (-900.0d0)) then
        tmp = x - (a / (t / (y - z)))
    else if (t <= (-1.7d-159)) then
        tmp = t_1
    else if (t <= 1.25d-178) then
        tmp = t_2
    else if (t <= 2.05d-78) then
        tmp = t_1
    else if (t <= 3.45d0) then
        tmp = t_2
    else
        tmp = x - (a * ((y - z) / t))
    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 * (y / (1.0 - z)));
	double t_2 = x + ((a * (y / z)) - a);
	double tmp;
	if (t <= -900.0) {
		tmp = x - (a / (t / (y - z)));
	} else if (t <= -1.7e-159) {
		tmp = t_1;
	} else if (t <= 1.25e-178) {
		tmp = t_2;
	} else if (t <= 2.05e-78) {
		tmp = t_1;
	} else if (t <= 3.45) {
		tmp = t_2;
	} else {
		tmp = x - (a * ((y - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a * (y / (1.0 - z)))
	t_2 = x + ((a * (y / z)) - a)
	tmp = 0
	if t <= -900.0:
		tmp = x - (a / (t / (y - z)))
	elif t <= -1.7e-159:
		tmp = t_1
	elif t <= 1.25e-178:
		tmp = t_2
	elif t <= 2.05e-78:
		tmp = t_1
	elif t <= 3.45:
		tmp = t_2
	else:
		tmp = x - (a * ((y - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * Float64(y / Float64(1.0 - z))))
	t_2 = Float64(x + Float64(Float64(a * Float64(y / z)) - a))
	tmp = 0.0
	if (t <= -900.0)
		tmp = Float64(x - Float64(a / Float64(t / Float64(y - z))));
	elseif (t <= -1.7e-159)
		tmp = t_1;
	elseif (t <= 1.25e-178)
		tmp = t_2;
	elseif (t <= 2.05e-78)
		tmp = t_1;
	elseif (t <= 3.45)
		tmp = t_2;
	else
		tmp = Float64(x - Float64(a * Float64(Float64(y - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a * (y / (1.0 - z)));
	t_2 = x + ((a * (y / z)) - a);
	tmp = 0.0;
	if (t <= -900.0)
		tmp = x - (a / (t / (y - z)));
	elseif (t <= -1.7e-159)
		tmp = t_1;
	elseif (t <= 1.25e-178)
		tmp = t_2;
	elseif (t <= 2.05e-78)
		tmp = t_1;
	elseif (t <= 3.45)
		tmp = t_2;
	else
		tmp = x - (a * ((y - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(a * N[(y / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -900.0], N[(x - N[(a / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.7e-159], t$95$1, If[LessEqual[t, 1.25e-178], t$95$2, If[LessEqual[t, 2.05e-78], t$95$1, If[LessEqual[t, 3.45], t$95$2, N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -900

   1. Initial program 98.0%

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

      1. associate-/r/ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in t around inf 79.4%

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

      1. associate-/l* 93.2%

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

   6. Simplified 93.2%

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

   if -900 < t < -1.69999999999999992e-159 or 1.24999999999999994e-178 < t < 2.0499999999999999e-78

   1. Initial program 96.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 t around 0 99.0%

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

   5. Taylor expanded in y around inf 83.0%

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

   if -1.69999999999999992e-159 < t < 1.24999999999999994e-178 or 2.0499999999999999e-78 < t < 3.4500000000000002

   1. Initial program 94.7%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 83.5%

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

      1. mul-1-neg 83.5%

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

   6. Simplified 83.5%

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

   7. Taylor expanded in y around 0 76.6%

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

      1. mul-1-neg 76.6%

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

      2. unsub-neg 76.6%

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

      3. *-lft-identity 76.6%

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

      4. times-frac 83.5%

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

      5. /-rgt-identity 83.5%

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

   9. Simplified 83.5%

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

   if 3.4500000000000002 < t

   1. Initial program 98.5%

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

      1. associate-/r/ 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in t around inf 88.1%

      \[\leadsto x - \color{blue}{\frac{y - z}{t}} \cdot a \]
3. Recombined 4 regimes into one program.

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -900:\\ \;\;\;\;x - \frac{a}{\frac{t}{y - z}}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-159}:\\ \;\;\;\;x - a \cdot \frac{y}{1 - z}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-178}:\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-78}:\\ \;\;\;\;x - a \cdot \frac{y}{1 - z}\\ \mathbf{elif}\;t \leq 3.45:\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 4: 70.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ t_2 := x - \frac{a}{\frac{t}{y}}\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-214}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.22:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))) (t_2 (- x (/ a (/ t y)))))
   (if (<= t -1.6e+16)
     t_2
     (if (<= t -1.9e-163)
       t_1
       (if (<= t 3.6e-214)
         (- x a)
         (if (<= t 2e-78) t_1 (if (<= t 1.22) (- x a) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double t_2 = x - (a / (t / y));
	double tmp;
	if (t <= -1.6e+16) {
		tmp = t_2;
	} else if (t <= -1.9e-163) {
		tmp = t_1;
	} else if (t <= 3.6e-214) {
		tmp = x - a;
	} else if (t <= 2e-78) {
		tmp = t_1;
	} else if (t <= 1.22) {
		tmp = x - a;
	} 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) :: tmp
    t_1 = x - (y * a)
    t_2 = x - (a / (t / y))
    if (t <= (-1.6d+16)) then
        tmp = t_2
    else if (t <= (-1.9d-163)) then
        tmp = t_1
    else if (t <= 3.6d-214) then
        tmp = x - a
    else if (t <= 2d-78) then
        tmp = t_1
    else if (t <= 1.22d0) then
        tmp = x - a
    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 - (y * a);
	double t_2 = x - (a / (t / y));
	double tmp;
	if (t <= -1.6e+16) {
		tmp = t_2;
	} else if (t <= -1.9e-163) {
		tmp = t_1;
	} else if (t <= 3.6e-214) {
		tmp = x - a;
	} else if (t <= 2e-78) {
		tmp = t_1;
	} else if (t <= 1.22) {
		tmp = x - a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * a)
	t_2 = x - (a / (t / y))
	tmp = 0
	if t <= -1.6e+16:
		tmp = t_2
	elif t <= -1.9e-163:
		tmp = t_1
	elif t <= 3.6e-214:
		tmp = x - a
	elif t <= 2e-78:
		tmp = t_1
	elif t <= 1.22:
		tmp = x - a
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * a))
	t_2 = Float64(x - Float64(a / Float64(t / y)))
	tmp = 0.0
	if (t <= -1.6e+16)
		tmp = t_2;
	elseif (t <= -1.9e-163)
		tmp = t_1;
	elseif (t <= 3.6e-214)
		tmp = Float64(x - a);
	elseif (t <= 2e-78)
		tmp = t_1;
	elseif (t <= 1.22)
		tmp = Float64(x - a);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * a);
	t_2 = x - (a / (t / y));
	tmp = 0.0;
	if (t <= -1.6e+16)
		tmp = t_2;
	elseif (t <= -1.9e-163)
		tmp = t_1;
	elseif (t <= 3.6e-214)
		tmp = x - a;
	elseif (t <= 2e-78)
		tmp = t_1;
	elseif (t <= 1.22)
		tmp = x - a;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e+16], t$95$2, If[LessEqual[t, -1.9e-163], t$95$1, If[LessEqual[t, 3.6e-214], N[(x - a), $MachinePrecision], If[LessEqual[t, 2e-78], t$95$1, If[LessEqual[t, 1.22], N[(x - a), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6e16 or 1.21999999999999997 < t

   1. Initial program 98.3%

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

      1. associate-/r/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in t around inf 74.9%

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

      1. associate-/l* 90.1%

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

   6. Simplified 90.1%

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

   7. Taylor expanded in y around inf 86.9%

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

   if -1.6e16 < t < -1.9e-163 or 3.6e-214 < t < 2e-78

   1. Initial program 96.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 75.0%

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

   5. Taylor expanded in t around 0 74.3%

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

   if -1.9e-163 < t < 3.6e-214 or 2e-78 < t < 1.21999999999999997

   1. Initial program 94.2%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 75.4%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+16}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-163}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-214}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-78}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 1.22:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \]

Alternative 5: 76.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \frac{y}{1 - z}\\ t_2 := x - \frac{a}{\frac{t}{y}}\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-262}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-215}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 3.75 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a (/ y (- 1.0 z))))) (t_2 (- x (/ a (/ t y)))))
   (if (<= t -1.6e+16)
     t_2
     (if (<= t 2.2e-262)
       t_1
       (if (<= t 8.5e-215) (- x a) (if (<= t 3.75e+17) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * (y / (1.0 - z)));
	double t_2 = x - (a / (t / y));
	double tmp;
	if (t <= -1.6e+16) {
		tmp = t_2;
	} else if (t <= 2.2e-262) {
		tmp = t_1;
	} else if (t <= 8.5e-215) {
		tmp = x - a;
	} else if (t <= 3.75e+17) {
		tmp = t_1;
	} 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) :: tmp
    t_1 = x - (a * (y / (1.0d0 - z)))
    t_2 = x - (a / (t / y))
    if (t <= (-1.6d+16)) then
        tmp = t_2
    else if (t <= 2.2d-262) then
        tmp = t_1
    else if (t <= 8.5d-215) then
        tmp = x - a
    else if (t <= 3.75d+17) then
        tmp = t_1
    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 * (y / (1.0 - z)));
	double t_2 = x - (a / (t / y));
	double tmp;
	if (t <= -1.6e+16) {
		tmp = t_2;
	} else if (t <= 2.2e-262) {
		tmp = t_1;
	} else if (t <= 8.5e-215) {
		tmp = x - a;
	} else if (t <= 3.75e+17) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a * (y / (1.0 - z)))
	t_2 = x - (a / (t / y))
	tmp = 0
	if t <= -1.6e+16:
		tmp = t_2
	elif t <= 2.2e-262:
		tmp = t_1
	elif t <= 8.5e-215:
		tmp = x - a
	elif t <= 3.75e+17:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * Float64(y / Float64(1.0 - z))))
	t_2 = Float64(x - Float64(a / Float64(t / y)))
	tmp = 0.0
	if (t <= -1.6e+16)
		tmp = t_2;
	elseif (t <= 2.2e-262)
		tmp = t_1;
	elseif (t <= 8.5e-215)
		tmp = Float64(x - a);
	elseif (t <= 3.75e+17)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a * (y / (1.0 - z)));
	t_2 = x - (a / (t / y));
	tmp = 0.0;
	if (t <= -1.6e+16)
		tmp = t_2;
	elseif (t <= 2.2e-262)
		tmp = t_1;
	elseif (t <= 8.5e-215)
		tmp = x - a;
	elseif (t <= 3.75e+17)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(a * N[(y / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e+16], t$95$2, If[LessEqual[t, 2.2e-262], t$95$1, If[LessEqual[t, 8.5e-215], N[(x - a), $MachinePrecision], If[LessEqual[t, 3.75e+17], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6e16 or 3.75e17 < t

   1. Initial program 98.2%

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

      1. associate-/r/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in t around inf 74.4%

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

      1. associate-/l* 90.4%

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

   6. Simplified 90.4%

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

   7. Taylor expanded in y around inf 87.1%

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

   if -1.6e16 < t < 2.19999999999999989e-262 or 8.4999999999999998e-215 < t < 3.75e17

   1. Initial program 95.9%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 98.8%

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

   5. Taylor expanded in y around inf 76.3%

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

   if 2.19999999999999989e-262 < t < 8.4999999999999998e-215

   1. Initial program 92.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 85.5%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+16}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-262}:\\ \;\;\;\;x - a \cdot \frac{y}{1 - z}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-215}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 3.75 \cdot 10^{+17}:\\ \;\;\;\;x - a \cdot \frac{y}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \]

Alternative 6: 78.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \frac{y}{1 - z}\\ t_2 := x - a \cdot \frac{y - z}{t}\\ \mathbf{if}\;t \leq -44:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-214}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a (/ y (- 1.0 z))))) (t_2 (- x (* a (/ (- y z) t)))))
   (if (<= t -44.0)
     t_2
     (if (<= t 7.5e-264)
       t_1
       (if (<= t 1.35e-214) (- x a) (if (<= t 7.8e+17) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * (y / (1.0 - z)));
	double t_2 = x - (a * ((y - z) / t));
	double tmp;
	if (t <= -44.0) {
		tmp = t_2;
	} else if (t <= 7.5e-264) {
		tmp = t_1;
	} else if (t <= 1.35e-214) {
		tmp = x - a;
	} else if (t <= 7.8e+17) {
		tmp = t_1;
	} 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) :: tmp
    t_1 = x - (a * (y / (1.0d0 - z)))
    t_2 = x - (a * ((y - z) / t))
    if (t <= (-44.0d0)) then
        tmp = t_2
    else if (t <= 7.5d-264) then
        tmp = t_1
    else if (t <= 1.35d-214) then
        tmp = x - a
    else if (t <= 7.8d+17) then
        tmp = t_1
    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 * (y / (1.0 - z)));
	double t_2 = x - (a * ((y - z) / t));
	double tmp;
	if (t <= -44.0) {
		tmp = t_2;
	} else if (t <= 7.5e-264) {
		tmp = t_1;
	} else if (t <= 1.35e-214) {
		tmp = x - a;
	} else if (t <= 7.8e+17) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a * (y / (1.0 - z)))
	t_2 = x - (a * ((y - z) / t))
	tmp = 0
	if t <= -44.0:
		tmp = t_2
	elif t <= 7.5e-264:
		tmp = t_1
	elif t <= 1.35e-214:
		tmp = x - a
	elif t <= 7.8e+17:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * Float64(y / Float64(1.0 - z))))
	t_2 = Float64(x - Float64(a * Float64(Float64(y - z) / t)))
	tmp = 0.0
	if (t <= -44.0)
		tmp = t_2;
	elseif (t <= 7.5e-264)
		tmp = t_1;
	elseif (t <= 1.35e-214)
		tmp = Float64(x - a);
	elseif (t <= 7.8e+17)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a * (y / (1.0 - z)));
	t_2 = x - (a * ((y - z) / t));
	tmp = 0.0;
	if (t <= -44.0)
		tmp = t_2;
	elseif (t <= 7.5e-264)
		tmp = t_1;
	elseif (t <= 1.35e-214)
		tmp = x - a;
	elseif (t <= 7.8e+17)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(a * N[(y / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -44.0], t$95$2, If[LessEqual[t, 7.5e-264], t$95$1, If[LessEqual[t, 1.35e-214], N[(x - a), $MachinePrecision], If[LessEqual[t, 7.8e+17], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -44 or 7.8e17 < t

   1. Initial program 98.2%

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

      1. associate-/r/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in t around inf 90.5%

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

   if -44 < t < 7.5000000000000001e-264 or 1.35e-214 < t < 7.8e17

   1. Initial program 95.9%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 99.6%

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

   5. Taylor expanded in y around inf 76.8%

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

   if 7.5000000000000001e-264 < t < 1.35e-214

   1. Initial program 92.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 85.5%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -44:\\ \;\;\;\;x - a \cdot \frac{y - z}{t}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-264}:\\ \;\;\;\;x - a \cdot \frac{y}{1 - z}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-214}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+17}:\\ \;\;\;\;x - a \cdot \frac{y}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 7: 91.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -26000000000000 \lor \neg \left(t \leq 8.6 \cdot 10^{+61}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -26000000000000.0) (not (<= t 8.6e+61)))
   (+ x (/ (- z y) (/ t a)))
   (+ x (* a (/ (- z y) (- 1.0 z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -26000000000000.0) || !(t <= 8.6e+61)) {
		tmp = x + ((z - y) / (t / a));
	} else {
		tmp = x + (a * ((z - y) / (1.0 - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-26000000000000.0d0)) .or. (.not. (t <= 8.6d+61))) then
        tmp = x + ((z - y) / (t / a))
    else
        tmp = x + (a * ((z - y) / (1.0d0 - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -26000000000000.0) || !(t <= 8.6e+61)) {
		tmp = x + ((z - y) / (t / a));
	} else {
		tmp = x + (a * ((z - y) / (1.0 - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -26000000000000.0) or not (t <= 8.6e+61):
		tmp = x + ((z - y) / (t / a))
	else:
		tmp = x + (a * ((z - y) / (1.0 - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -26000000000000.0) || !(t <= 8.6e+61))
		tmp = Float64(x + Float64(Float64(z - y) / Float64(t / a)));
	else
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / Float64(1.0 - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -26000000000000.0) || ~((t <= 8.6e+61)))
		tmp = x + ((z - y) / (t / a));
	else
		tmp = x + (a * ((z - y) / (1.0 - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -26000000000000.0], N[Not[LessEqual[t, 8.6e+61]], $MachinePrecision]], N[(x + N[(N[(z - y), $MachinePrecision] / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.6e13 or 8.6000000000000003e61 < t

   1. Initial program 98.0%

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

   2. Taylor expanded in t around inf 95.0%

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

   if -2.6e13 < t < 8.6000000000000003e61

   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 t around 0 98.4%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -26000000000000 \lor \neg \left(t \leq 8.6 \cdot 10^{+61}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \end{array} \]

Alternative 8: 89.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-11} \lor \neg \left(z \leq 9 \cdot 10^{+30}\right):\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t + 1}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.4e-11) (not (<= z 9e+30)))
   (+ x (- (* a (/ y z)) a))
   (- x (/ y (/ (+ t 1.0) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.4e-11) || !(z <= 9e+30)) {
		tmp = x + ((a * (y / z)) - a);
	} else {
		tmp = x - (y / ((t + 1.0) / 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-11)) .or. (.not. (z <= 9d+30))) then
        tmp = x + ((a * (y / z)) - a)
    else
        tmp = x - (y / ((t + 1.0d0) / 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-11) || !(z <= 9e+30)) {
		tmp = x + ((a * (y / z)) - a);
	} else {
		tmp = x - (y / ((t + 1.0) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.4e-11) or not (z <= 9e+30):
		tmp = x + ((a * (y / z)) - a)
	else:
		tmp = x - (y / ((t + 1.0) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.4e-11) || !(z <= 9e+30))
		tmp = Float64(x + Float64(Float64(a * Float64(y / z)) - a));
	else
		tmp = Float64(x - Float64(y / Float64(Float64(t + 1.0) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.4e-11) || ~((z <= 9e+30)))
		tmp = x + ((a * (y / z)) - a);
	else
		tmp = x - (y / ((t + 1.0) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.4e-11], N[Not[LessEqual[z, 9e+30]], $MachinePrecision]], N[(x + N[(N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(N[(t + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4000000000000001e-11 or 8.9999999999999999e30 < z

   1. Initial program 93.1%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 87.4%

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

      1. mul-1-neg 87.4%

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

   6. Simplified 87.4%

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

   7. Taylor expanded in y around 0 81.0%

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

      1. mul-1-neg 81.0%

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

      2. unsub-neg 81.0%

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

      3. *-lft-identity 81.0%

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

      4. times-frac 87.4%

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

      5. /-rgt-identity 87.4%

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

   9. Simplified 87.4%

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

   if -2.4000000000000001e-11 < z < 8.9999999999999999e30

   1. Initial program 99.9%

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

      1. associate-/r/ 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in z around 0 86.2%

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

      1. *-commutative 86.2%

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

      2. associate-/l* 93.7%

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

   6. Simplified 93.7%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-11} \lor \neg \left(z \leq 9 \cdot 10^{+30}\right):\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t + 1}{a}}\\ \end{array} \]

Alternative 9: 89.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-11} \lor \neg \left(z \leq 1.85 \cdot 10^{+35}\right):\\ \;\;\;\;x + \frac{a}{\frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t + 1}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.4e-11) (not (<= z 1.85e+35)))
   (+ x (/ a (/ z (- y z))))
   (- x (/ y (/ (+ t 1.0) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.4e-11) || !(z <= 1.85e+35)) {
		tmp = x + (a / (z / (y - z)));
	} else {
		tmp = x - (y / ((t + 1.0) / 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-11)) .or. (.not. (z <= 1.85d+35))) then
        tmp = x + (a / (z / (y - z)))
    else
        tmp = x - (y / ((t + 1.0d0) / 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-11) || !(z <= 1.85e+35)) {
		tmp = x + (a / (z / (y - z)));
	} else {
		tmp = x - (y / ((t + 1.0) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.4e-11) or not (z <= 1.85e+35):
		tmp = x + (a / (z / (y - z)))
	else:
		tmp = x - (y / ((t + 1.0) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.4e-11) || !(z <= 1.85e+35))
		tmp = Float64(x + Float64(a / Float64(z / Float64(y - z))));
	else
		tmp = Float64(x - Float64(y / Float64(Float64(t + 1.0) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.4e-11) || ~((z <= 1.85e+35)))
		tmp = x + (a / (z / (y - z)));
	else
		tmp = x - (y / ((t + 1.0) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.4e-11], N[Not[LessEqual[z, 1.85e+35]], $MachinePrecision]], N[(x + N[(a / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(N[(t + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4000000000000001e-11 or 1.85e35 < z

   1. Initial program 93.1%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 87.4%

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

      1. mul-1-neg 87.4%

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

   6. Simplified 87.4%

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

   7. Taylor expanded in a around 0 68.4%

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

      1. mul-1-neg 68.4%

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

      2. associate-/l* 87.4%

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

      3. distribute-neg-frac 87.4%

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

   9. Simplified 87.4%

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

   if -2.4000000000000001e-11 < z < 1.85e35

   1. Initial program 99.9%

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

      1. associate-/r/ 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in z around 0 86.2%

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

      1. *-commutative 86.2%

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

      2. associate-/l* 93.7%

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

   6. Simplified 93.7%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-11} \lor \neg \left(z \leq 1.85 \cdot 10^{+35}\right):\\ \;\;\;\;x + \frac{a}{\frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t + 1}{a}}\\ \end{array} \]

Alternative 10: 73.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+47}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+30}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.9e+47) (- x a) (if (<= z 7.2e+30) (- x (* y a)) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.9e+47) {
		tmp = x - a;
	} else if (z <= 7.2e+30) {
		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 <= (-3.9d+47)) then
        tmp = x - a
    else if (z <= 7.2d+30) 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 <= -3.9e+47) {
		tmp = x - a;
	} else if (z <= 7.2e+30) {
		tmp = x - (y * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.9e+47:
		tmp = x - a
	elif z <= 7.2e+30:
		tmp = x - (y * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.9e+47)
		tmp = Float64(x - a);
	elseif (z <= 7.2e+30)
		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 <= -3.9e+47)
		tmp = x - a;
	elseif (z <= 7.2e+30)
		tmp = x - (y * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.9e+47], N[(x - a), $MachinePrecision], If[LessEqual[z, 7.2e+30], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.90000000000000025e47 or 7.2000000000000004e30 < z

   1. Initial program 92.6%

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

      1. associate-/r/ 99.9%

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

   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 78.4%

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

   if -3.90000000000000025e47 < z < 7.2000000000000004e30

   1. Initial program 99.9%

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

      1. associate-/r/ 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in z around 0 85.7%

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

   5. Taylor expanded in t around 0 69.0%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+47}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+30}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 11: 61.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-61}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+112}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2e-61) x (if (<= t 5.4e+112) (- x a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2e-61) {
		tmp = x;
	} else if (t <= 5.4e+112) {
		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 (t <= (-2d-61)) then
        tmp = x
    else if (t <= 5.4d+112) 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 (t <= -2e-61) {
		tmp = x;
	} else if (t <= 5.4e+112) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2e-61:
		tmp = x
	elif t <= 5.4e+112:
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2e-61)
		tmp = x;
	elseif (t <= 5.4e+112)
		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 (t <= -2e-61)
		tmp = x;
	elseif (t <= 5.4e+112)
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2e-61], x, If[LessEqual[t, 5.4e+112], N[(x - a), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -2.0000000000000001e-61 or 5.4000000000000002e112 < t

   1. Initial program 98.9%

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

      1. associate-/r/ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in x around inf 71.1%

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

   if -2.0000000000000001e-61 < t < 5.4000000000000002e112

   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 inf 63.9%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-61}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+112}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 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 96.7%

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

   1. associate-/r/ 99.2%

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

3. Simplified 99.2%

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

4. Taylor expanded in x around inf 55.1%

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

5. Final simplification 55.1%

   \[\leadsto x \]

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 2023200 
(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))))