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

Percentage Accurate: 96.8% → 99.6%

Time: 13.6s

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: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. sub-neg 97.2%

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

   2. +-commutative 97.2%

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

   3. associate-/r/ 99.6%

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

   4. distribute-lft-neg-in 99.6%

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

   5. fma-def 99.6%

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

   6. distribute-neg-frac 99.6%

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

   7. sub-neg 99.6%

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

   8. distribute-neg-in 99.6%

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

   9. remove-double-neg 99.6%

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

   10. +-commutative 99.6%

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

   11. sub-neg 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 2: 73.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{a}{\frac{1 - z}{z}}\\ t_2 := x - \frac{a}{\frac{t}{y}}\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-235}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ a (/ (- 1.0 z) z)))) (t_2 (- x (/ a (/ t y)))))
   (if (<= t -1.9e+38)
     t_2
     (if (<= t -1.55e-106)
       t_1
       (if (<= t 2.8e-235) (- x (* y a)) (if (<= t 1.9e+97) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a / ((1.0 - z) / z));
	double t_2 = x - (a / (t / y));
	double tmp;
	if (t <= -1.9e+38) {
		tmp = t_2;
	} else if (t <= -1.55e-106) {
		tmp = t_1;
	} else if (t <= 2.8e-235) {
		tmp = x - (y * a);
	} else if (t <= 1.9e+97) {
		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 / ((1.0d0 - z) / z))
    t_2 = x - (a / (t / y))
    if (t <= (-1.9d+38)) then
        tmp = t_2
    else if (t <= (-1.55d-106)) then
        tmp = t_1
    else if (t <= 2.8d-235) then
        tmp = x - (y * a)
    else if (t <= 1.9d+97) 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 / ((1.0 - z) / z));
	double t_2 = x - (a / (t / y));
	double tmp;
	if (t <= -1.9e+38) {
		tmp = t_2;
	} else if (t <= -1.55e-106) {
		tmp = t_1;
	} else if (t <= 2.8e-235) {
		tmp = x - (y * a);
	} else if (t <= 1.9e+97) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a / ((1.0 - z) / z))
	t_2 = x - (a / (t / y))
	tmp = 0
	if t <= -1.9e+38:
		tmp = t_2
	elif t <= -1.55e-106:
		tmp = t_1
	elif t <= 2.8e-235:
		tmp = x - (y * a)
	elif t <= 1.9e+97:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a / Float64(Float64(1.0 - z) / z)))
	t_2 = Float64(x - Float64(a / Float64(t / y)))
	tmp = 0.0
	if (t <= -1.9e+38)
		tmp = t_2;
	elseif (t <= -1.55e-106)
		tmp = t_1;
	elseif (t <= 2.8e-235)
		tmp = Float64(x - Float64(y * a));
	elseif (t <= 1.9e+97)
		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 / ((1.0 - z) / z));
	t_2 = x - (a / (t / y));
	tmp = 0.0;
	if (t <= -1.9e+38)
		tmp = t_2;
	elseif (t <= -1.55e-106)
		tmp = t_1;
	elseif (t <= 2.8e-235)
		tmp = x - (y * a);
	elseif (t <= 1.9e+97)
		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[(N[(1.0 - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.9e+38], t$95$2, If[LessEqual[t, -1.55e-106], t$95$1, If[LessEqual[t, 2.8e-235], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e+97], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.8999999999999999e38 or 1.90000000000000018e97 < t

   1. Initial program 95.1%

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

   5. Taylor expanded in z around 0 78.6%

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

      1. associate-/l* 82.5%

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

   7. Simplified 82.5%

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

   8. Taylor expanded in t around inf 78.6%

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

      1. associate-/l* 82.5%

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

   10. Simplified 82.5%

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

   if -1.8999999999999999e38 < t < -1.54999999999999993e-106 or 2.79999999999999995e-235 < t < 1.90000000000000018e97

   1. Initial program 98.8%

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

   3. Taylor expanded in t around 0 96.5%

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

   4. Taylor expanded in y around 0 71.6%

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

      1. sub-neg 71.6%

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

      2. mul-1-neg 71.6%

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

      3. remove-double-neg 71.6%

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

      4. associate-/l* 88.1%

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

   6. Simplified 88.1%

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

   if -1.54999999999999993e-106 < t < 2.79999999999999995e-235

   1. Initial program 98.4%

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

   5. Taylor expanded in z around 0 73.5%

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

      1. associate-/l* 73.4%

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

   7. Simplified 73.4%

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

   8. Taylor expanded in t around 0 73.5%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+38}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-106}:\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-235}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+97}:\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{a}{\frac{t}{y}}\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-105}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{-202}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+17}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ a (/ t y)))))
   (if (<= t -8.2e+37)
     t_1
     (if (<= t -4.4e-105)
       (- x a)
       (if (<= t 1.56e-202) (- x (* y a)) (if (<= t 5.5e+17) (- x 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 <= -8.2e+37) {
		tmp = t_1;
	} else if (t <= -4.4e-105) {
		tmp = x - a;
	} else if (t <= 1.56e-202) {
		tmp = x - (y * a);
	} else if (t <= 5.5e+17) {
		tmp = x - 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 <= (-8.2d+37)) then
        tmp = t_1
    else if (t <= (-4.4d-105)) then
        tmp = x - a
    else if (t <= 1.56d-202) then
        tmp = x - (y * a)
    else if (t <= 5.5d+17) then
        tmp = x - 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 <= -8.2e+37) {
		tmp = t_1;
	} else if (t <= -4.4e-105) {
		tmp = x - a;
	} else if (t <= 1.56e-202) {
		tmp = x - (y * a);
	} else if (t <= 5.5e+17) {
		tmp = x - 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 <= -8.2e+37:
		tmp = t_1
	elif t <= -4.4e-105:
		tmp = x - a
	elif t <= 1.56e-202:
		tmp = x - (y * a)
	elif t <= 5.5e+17:
		tmp = x - 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 <= -8.2e+37)
		tmp = t_1;
	elseif (t <= -4.4e-105)
		tmp = Float64(x - a);
	elseif (t <= 1.56e-202)
		tmp = Float64(x - Float64(y * a));
	elseif (t <= 5.5e+17)
		tmp = Float64(x - 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 <= -8.2e+37)
		tmp = t_1;
	elseif (t <= -4.4e-105)
		tmp = x - a;
	elseif (t <= 1.56e-202)
		tmp = x - (y * a);
	elseif (t <= 5.5e+17)
		tmp = x - 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, -8.2e+37], t$95$1, If[LessEqual[t, -4.4e-105], N[(x - a), $MachinePrecision], If[LessEqual[t, 1.56e-202], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+17], N[(x - a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.1999999999999996e37 or 5.5e17 < t

   1. Initial program 95.6%

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

      1. associate-/r/ 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in z around 0 80.2%

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

      1. associate-/l* 83.6%

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

   7. Simplified 83.6%

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

   8. Taylor expanded in t around inf 80.2%

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

      1. associate-/l* 83.6%

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

   10. Simplified 83.6%

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

   if -8.1999999999999996e37 < t < -4.40000000000000008e-105 or 1.56e-202 < t < 5.5e17

   1. Initial program 98.4%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 81.8%

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

   if -4.40000000000000008e-105 < t < 1.56e-202

   1. Initial program 98.6%

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

   5. Taylor expanded in z around 0 73.1%

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

      1. associate-/l* 73.0%

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

   7. Simplified 73.0%

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

   8. Taylor expanded in t around 0 73.1%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+37}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-105}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{-202}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+17}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+44} \lor \neg \left(z \leq 0.014\right):\\ \;\;\;\;x + \frac{a}{\frac{\left(t + 1\right) - z}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.2e+44) (not (<= z 0.014)))
   (+ x (/ a (/ (- (+ t 1.0) z) z)))
   (- x (* a (/ y (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.2e+44) || !(z <= 0.014)) {
		tmp = x + (a / (((t + 1.0) - z) / z));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-7.2d+44)) .or. (.not. (z <= 0.014d0))) then
        tmp = x + (a / (((t + 1.0d0) - z) / z))
    else
        tmp = x - (a * (y / (t + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.2e+44) || !(z <= 0.014)) {
		tmp = x + (a / (((t + 1.0) - z) / z));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.2e+44) or not (z <= 0.014):
		tmp = x + (a / (((t + 1.0) - z) / z))
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.2e+44) || !(z <= 0.014))
		tmp = Float64(x + Float64(a / Float64(Float64(Float64(t + 1.0) - z) / z)));
	else
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.2e+44) || ~((z <= 0.014)))
		tmp = x + (a / (((t + 1.0) - z) / z));
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.2e+44], N[Not[LessEqual[z, 0.014]], $MachinePrecision]], N[(x + N[(a / N[(N[(N[(t + 1.0), $MachinePrecision] - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.2e44 or 0.0140000000000000003 < z

   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. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 99.9%

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

      2. associate-/r/ 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 62.3%

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

      1. sub-neg 62.3%

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

      2. mul-1-neg 62.3%

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

      3. remove-double-neg 62.3%

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

      4. associate-/l* 89.7%

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

   9. Simplified 89.7%

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

   if -7.2e44 < z < 0.0140000000000000003

   1. Initial program 99.1%

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

      1. associate-/r/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around 0 91.7%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+44} \lor \neg \left(z \leq 0.014\right):\\ \;\;\;\;x + \frac{a}{\frac{\left(t + 1\right) - z}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + 1\right) - z\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+45} \lor \neg \left(z \leq 900000000000\right):\\ \;\;\;\;x + \frac{a}{\frac{t_1}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot a}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ t 1.0) z)))
   (if (or (<= z -1.8e+45) (not (<= z 900000000000.0)))
     (+ x (/ a (/ t_1 z)))
     (- x (/ (* y a) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t + 1.0) - z;
	double tmp;
	if ((z <= -1.8e+45) || !(z <= 900000000000.0)) {
		tmp = x + (a / (t_1 / z));
	} else {
		tmp = x - ((y * a) / 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 = (t + 1.0d0) - z
    if ((z <= (-1.8d+45)) .or. (.not. (z <= 900000000000.0d0))) then
        tmp = x + (a / (t_1 / z))
    else
        tmp = x - ((y * a) / 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 = (t + 1.0) - z;
	double tmp;
	if ((z <= -1.8e+45) || !(z <= 900000000000.0)) {
		tmp = x + (a / (t_1 / z));
	} else {
		tmp = x - ((y * a) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t + 1.0) - z
	tmp = 0
	if (z <= -1.8e+45) or not (z <= 900000000000.0):
		tmp = x + (a / (t_1 / z))
	else:
		tmp = x - ((y * a) / t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t + 1.0) - z)
	tmp = 0.0
	if ((z <= -1.8e+45) || !(z <= 900000000000.0))
		tmp = Float64(x + Float64(a / Float64(t_1 / z)));
	else
		tmp = Float64(x - Float64(Float64(y * a) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t + 1.0) - z;
	tmp = 0.0;
	if ((z <= -1.8e+45) || ~((z <= 900000000000.0)))
		tmp = x + (a / (t_1 / z));
	else
		tmp = x - ((y * a) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t + 1.0), $MachinePrecision] - z), $MachinePrecision]}, If[Or[LessEqual[z, -1.8e+45], N[Not[LessEqual[z, 900000000000.0]], $MachinePrecision]], N[(x + N[(a / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * a), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e45 or 9e11 < z

   1. Initial program 95.1%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 61.6%

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

      1. sub-neg 61.6%

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

      2. mul-1-neg 61.6%

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

      3. remove-double-neg 61.6%

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

      4. associate-/l* 90.0%

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

   9. Simplified 90.0%

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

   if -1.8e45 < z < 9e11

   1. Initial program 99.2%

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

      1. associate-/r/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around inf 92.0%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+45} \lor \neg \left(z \leq 900000000000\right):\\ \;\;\;\;x + \frac{a}{\frac{\left(t + 1\right) - z}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot a}{\left(t + 1\right) - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.9 \cdot 10^{+90} \lor \neg \left(t \leq 1.5 \cdot 10^{+95}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{\frac{1 - z}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7.9e+90) (not (<= t 1.5e+95)))
   (+ x (* a (/ (- z y) t)))
   (- x (/ (- y z) (/ (- 1.0 z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.9e+90) || !(t <= 1.5e+95)) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x - ((y - z) / ((1.0 - z) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-7.9d+90)) .or. (.not. (t <= 1.5d+95))) then
        tmp = x + (a * ((z - y) / t))
    else
        tmp = x - ((y - z) / ((1.0d0 - z) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.9e+90) || !(t <= 1.5e+95)) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x - ((y - z) / ((1.0 - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7.9e+90) or not (t <= 1.5e+95):
		tmp = x + (a * ((z - y) / t))
	else:
		tmp = x - ((y - z) / ((1.0 - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7.9e+90) || !(t <= 1.5e+95))
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	else
		tmp = Float64(x - Float64(Float64(y - z) / Float64(Float64(1.0 - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7.9e+90) || ~((t <= 1.5e+95)))
		tmp = x + (a * ((z - y) / t));
	else
		tmp = x - ((y - z) / ((1.0 - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7.9e+90], N[Not[LessEqual[t, 1.5e+95]], $MachinePrecision]], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(1.0 - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.8999999999999996e90 or 1.49999999999999996e95 < t

   1. Initial program 94.4%

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

      1. associate-/r/ 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in t around inf 86.6%

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

   if -7.8999999999999996e90 < t < 1.49999999999999996e95

   1. Initial program 98.7%

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

   3. Taylor expanded in t around 0 95.7%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.9 \cdot 10^{+90} \lor \neg \left(t \leq 1.5 \cdot 10^{+95}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{\frac{1 - z}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+16}:\\ \;\;\;\;x - \left(a - y \cdot \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+128}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.5e+16)
   (- x (- a (* y (/ a z))))
   (if (<= z 1.1e+128)
     (- x (* a (/ y (+ t 1.0))))
     (+ x (/ (- z y) (/ (- z) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.5e+16) {
		tmp = x - (a - (y * (a / z)));
	} else if (z <= 1.1e+128) {
		tmp = x - (a * (y / (t + 1.0)));
	} else {
		tmp = x + ((z - y) / (-z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.5d+16)) then
        tmp = x - (a - (y * (a / z)))
    else if (z <= 1.1d+128) then
        tmp = x - (a * (y / (t + 1.0d0)))
    else
        tmp = x + ((z - y) / (-z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.5e+16) {
		tmp = x - (a - (y * (a / z)));
	} else if (z <= 1.1e+128) {
		tmp = x - (a * (y / (t + 1.0)));
	} else {
		tmp = x + ((z - y) / (-z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.5e+16:
		tmp = x - (a - (y * (a / z)))
	elif z <= 1.1e+128:
		tmp = x - (a * (y / (t + 1.0)))
	else:
		tmp = x + ((z - y) / (-z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.5e+16)
		tmp = Float64(x - Float64(a - Float64(y * Float64(a / z))));
	elseif (z <= 1.1e+128)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	else
		tmp = Float64(x + Float64(Float64(z - y) / Float64(Float64(-z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.5e+16)
		tmp = x - (a - (y * (a / z)));
	elseif (z <= 1.1e+128)
		tmp = x - (a * (y / (t + 1.0)));
	else
		tmp = x + ((z - y) / (-z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.5e+16], N[(x - N[(a - N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+128], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - y), $MachinePrecision] / N[((-z) / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5e16

   1. Initial program 93.9%

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

   3. Taylor expanded in z around inf 82.5%

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

      1. mul-1-neg 82.5%

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

      2. distribute-neg-frac 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in y around 0 77.5%

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

      1. mul-1-neg 77.5%

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

      2. unsub-neg 77.5%

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

      3. *-commutative 77.5%

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

      4. associate-*l/ 85.1%

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

      5. associate-/r/ 84.2%

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

      6. *-rgt-identity 84.2%

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

      7. associate-*r/ 84.3%

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

      8. associate-/r/ 84.3%

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

      9. associate-*l/ 84.3%

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

      10. *-lft-identity 84.3%

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

   8. Simplified 84.3%

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

   if -3.5e16 < z < 1.10000000000000008e128

   1. Initial program 99.2%

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

      1. associate-/r/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 90.0%

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

   if 1.10000000000000008e128 < z

   1. Initial program 95.4%

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

   3. Taylor expanded in z around inf 91.2%

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

      1. mul-1-neg 91.2%

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

      2. distribute-neg-frac 91.2%

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

   5. Simplified 91.2%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+16}:\\ \;\;\;\;x - \left(a - y \cdot \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+128}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+45} \lor \neg \left(z \leq 2.5 \cdot 10^{+158}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.6e+45) (not (<= z 2.5e+158)))
   (- x a)
   (- x (* a (/ y (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.6e+45) || !(z <= 2.5e+158)) {
		tmp = x - a;
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.6d+45)) .or. (.not. (z <= 2.5d+158))) then
        tmp = x - a
    else
        tmp = x - (a * (y / (t + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.6e+45) || !(z <= 2.5e+158)) {
		tmp = x - a;
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.6e+45) or not (z <= 2.5e+158):
		tmp = x - a
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.6e+45) || !(z <= 2.5e+158))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.6e+45) || ~((z <= 2.5e+158)))
		tmp = x - a;
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.6e+45], N[Not[LessEqual[z, 2.5e+158]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6000000000000001e45 or 2.4999999999999998e158 < z

   1. Initial program 94.9%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 85.7%

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

   if -1.6000000000000001e45 < z < 2.4999999999999998e158

   1. Initial program 98.7%

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

      1. associate-/r/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 87.6%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+45} \lor \neg \left(z \leq 2.5 \cdot 10^{+158}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1150000000000 \lor \neg \left(z \leq 1.1 \cdot 10^{+128}\right):\\ \;\;\;\;x + \left(y \cdot \frac{a}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1150000000000.0) (not (<= z 1.1e+128)))
   (+ x (- (* y (/ a z)) a))
   (- x (* a (/ y (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1150000000000.0) || !(z <= 1.1e+128)) {
		tmp = x + ((y * (a / z)) - a);
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1150000000000.0d0)) .or. (.not. (z <= 1.1d+128))) then
        tmp = x + ((y * (a / z)) - a)
    else
        tmp = x - (a * (y / (t + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1150000000000.0) || !(z <= 1.1e+128)) {
		tmp = x + ((y * (a / z)) - a);
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1150000000000.0) or not (z <= 1.1e+128):
		tmp = x + ((y * (a / z)) - a)
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1150000000000.0) || !(z <= 1.1e+128))
		tmp = Float64(x + Float64(Float64(y * Float64(a / z)) - a));
	else
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1150000000000.0) || ~((z <= 1.1e+128)))
		tmp = x + ((y * (a / z)) - a);
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1150000000000.0], N[Not[LessEqual[z, 1.1e+128]], $MachinePrecision]], N[(x + N[(N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e12 or 1.10000000000000008e128 < z

   1. Initial program 94.5%

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

   3. Taylor expanded in z around inf 85.9%

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

      1. mul-1-neg 85.9%

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

      2. distribute-neg-frac 85.9%

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

   5. Simplified 85.9%

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

   6. Taylor expanded in y around 0 80.5%

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

      1. mul-1-neg 80.5%

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

      2. unsub-neg 80.5%

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

      3. *-commutative 80.5%

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

      4. associate-*l/ 87.6%

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

      5. associate-/r/ 86.2%

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

      6. *-rgt-identity 86.2%

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

      7. associate-*r/ 86.2%

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

      8. associate-/r/ 86.7%

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

      9. associate-*l/ 86.7%

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

      10. *-lft-identity 86.7%

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

   8. Simplified 86.7%

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

   if -1.15e12 < z < 1.10000000000000008e128

   1. Initial program 99.2%

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

      1. associate-/r/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 90.0%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1150000000000 \lor \neg \left(z \leq 1.1 \cdot 10^{+128}\right):\\ \;\;\;\;x + \left(y \cdot \frac{a}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-37} \lor \neg \left(z \leq 12500000000000\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.6e-37) (not (<= z 12500000000000.0))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e-37) || !(z <= 12500000000000.0)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.6d-37)) .or. (.not. (z <= 12500000000000.0d0))) then
        tmp = x - a
    else
        tmp = x - (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e-37) || !(z <= 12500000000000.0)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.6e-37) or not (z <= 12500000000000.0):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.6e-37) || !(z <= 12500000000000.0))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.6e-37) || ~((z <= 12500000000000.0)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.6e-37], N[Not[LessEqual[z, 12500000000000.0]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5999999999999998e-37 or 1.25e13 < z

   1. Initial program 95.4%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 80.6%

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

   if -2.5999999999999998e-37 < z < 1.25e13

   1. Initial program 99.1%

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

      1. associate-/r/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around 0 90.6%

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

      1. associate-/l* 91.2%

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

   7. Simplified 91.2%

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

   8. Taylor expanded in t around 0 72.7%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-37} \lor \neg \left(z \leq 12500000000000\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+21} \lor \neg \left(z \leq 9.5 \cdot 10^{+14}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.05e+21) (not (<= z 9.5e+14))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.05e+21) || !(z <= 9.5e+14)) {
		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 <= (-1.05d+21)) .or. (.not. (z <= 9.5d+14))) 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 <= -1.05e+21) || !(z <= 9.5e+14)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.05e+21) or not (z <= 9.5e+14):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.05e+21) || !(z <= 9.5e+14))
		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 <= -1.05e+21) || ~((z <= 9.5e+14)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.05e+21], N[Not[LessEqual[z, 9.5e+14]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e21 or 9.5e14 < z

   1. Initial program 95.3%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 81.4%

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

   if -1.05e21 < z < 9.5e14

   1. Initial program 99.1%

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

      1. associate-/r/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around inf 63.2%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+21} \lor \neg \left(z \leq 9.5 \cdot 10^{+14}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. associate-/r/ 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 13: 55.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+257} \lor \neg \left(a \leq 2.9 \cdot 10^{+239}\right):\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.2e+257) (not (<= a 2.9e+239))) (- a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.2e+257) || !(a <= 2.9e+239)) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.2d+257)) .or. (.not. (a <= 2.9d+239))) then
        tmp = -a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.2e+257) || !(a <= 2.9e+239)) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.2e+257) or not (a <= 2.9e+239):
		tmp = -a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.2e+257) || !(a <= 2.9e+239))
		tmp = Float64(-a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.2e+257) || ~((a <= 2.9e+239)))
		tmp = -a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.2e+257], N[Not[LessEqual[a, 2.9e+239]], $MachinePrecision]], (-a), x]

Derivation

1. Split input into 2 regimes

2. if a < -2.1999999999999999e257 or 2.9000000000000002e239 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 66.7%

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

      1. mul-1-neg 66.7%

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

      2. distribute-neg-frac 66.7%

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

   5. Simplified 66.7%

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

   6. Taylor expanded in x around 0 11.4%

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

   7. Taylor expanded in y around 0 58.8%

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

      1. mul-1-neg 58.8%

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

   9. Simplified 58.8%

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

   if -2.1999999999999999e257 < a < 2.9000000000000002e239

   1. Initial program 97.0%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 64.6%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+257} \lor \neg \left(a \leq 2.9 \cdot 10^{+239}\right):\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

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 97.2%

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

   1. associate-/r/ 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in x around inf 59.0%

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

6. Final simplification 59.0%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024020 
(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))))