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

Percentage Accurate: 96.9% → 99.7%

Time: 9.6s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

   1. associate-/r/ 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 90.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+185}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{+129}:\\ \;\;\;\;x - z \cdot \frac{a}{z + \left(-1 - t\right)}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{+35} \lor \neg \left(t \leq 0.0085\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.95e+185)
   (- x (/ a (/ t y)))
   (if (<= t -7.8e+129)
     (- x (* z (/ a (+ z (- -1.0 t)))))
     (if (or (<= t -4.2e+35) (not (<= t 0.0085)))
       (+ x (* a (/ (- z y) t)))
       (+ x (* a (/ (- y z) (+ z -1.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.95e+185) {
		tmp = x - (a / (t / y));
	} else if (t <= -7.8e+129) {
		tmp = x - (z * (a / (z + (-1.0 - t))));
	} else if ((t <= -4.2e+35) || !(t <= 0.0085)) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x + (a * ((y - z) / (z + -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 (t <= (-1.95d+185)) then
        tmp = x - (a / (t / y))
    else if (t <= (-7.8d+129)) then
        tmp = x - (z * (a / (z + ((-1.0d0) - t))))
    else if ((t <= (-4.2d+35)) .or. (.not. (t <= 0.0085d0))) then
        tmp = x + (a * ((z - y) / t))
    else
        tmp = x + (a * ((y - z) / (z + (-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 (t <= -1.95e+185) {
		tmp = x - (a / (t / y));
	} else if (t <= -7.8e+129) {
		tmp = x - (z * (a / (z + (-1.0 - t))));
	} else if ((t <= -4.2e+35) || !(t <= 0.0085)) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x + (a * ((y - z) / (z + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.95e+185:
		tmp = x - (a / (t / y))
	elif t <= -7.8e+129:
		tmp = x - (z * (a / (z + (-1.0 - t))))
	elif (t <= -4.2e+35) or not (t <= 0.0085):
		tmp = x + (a * ((z - y) / t))
	else:
		tmp = x + (a * ((y - z) / (z + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.95e+185)
		tmp = Float64(x - Float64(a / Float64(t / y)));
	elseif (t <= -7.8e+129)
		tmp = Float64(x - Float64(z * Float64(a / Float64(z + Float64(-1.0 - t)))));
	elseif ((t <= -4.2e+35) || !(t <= 0.0085))
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	else
		tmp = Float64(x + Float64(a * Float64(Float64(y - z) / Float64(z + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.95e+185)
		tmp = x - (a / (t / y));
	elseif (t <= -7.8e+129)
		tmp = x - (z * (a / (z + (-1.0 - t))));
	elseif ((t <= -4.2e+35) || ~((t <= 0.0085)))
		tmp = x + (a * ((z - y) / t));
	else
		tmp = x + (a * ((y - z) / (z + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.95e+185], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.8e+129], N[(x - N[(z * N[(a / N[(z + N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -4.2e+35], N[Not[LessEqual[t, 0.0085]], $MachinePrecision]], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(N[(y - z), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.9499999999999999e185

   1. Initial program 99.6%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 87.7%

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

      1. *-commutative 87.7%

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

      2. clear-num 87.6%

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

      3. un-div-inv 87.7%

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

   7. Applied egg-rr 87.7%

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

      1. associate-/r/ 87.8%

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

   9. Simplified 87.8%

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

   10. Taylor expanded in y around inf 68.2%

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

       1. associate-*l/ 93.8%

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

       2. associate-/r/ 93.8%

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

   12. Simplified 93.8%

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

   if -1.9499999999999999e185 < t < -7.7999999999999994e129

   1. Initial program 99.7%

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

      1. associate-/r/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 66.4%

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

      1. mul-1-neg 66.4%

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

      2. *-commutative 66.4%

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

      3. associate--l+ 66.4%

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

      4. +-commutative 66.4%

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

      5. associate-*r/ 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. distribute-neg-frac2 99.9%

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

      8. +-commutative 99.9%

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

      9. distribute-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

      11. unsub-neg 99.9%

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

      12. associate--r- 99.9%

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

   7. Simplified 99.9%

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

   if -7.7999999999999994e129 < t < -4.1999999999999998e35 or 0.0085000000000000006 < t

   1. Initial program 94.8%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 85.4%

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

   if -4.1999999999999998e35 < t < 0.0085000000000000006

   1. Initial program 98.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 t around 0 100.0%

      \[\leadsto x - \color{blue}{\frac{y - z}{1 - z}} \cdot a \]
3. Recombined 4 regimes into one program.

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+185}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{+129}:\\ \;\;\;\;x - z \cdot \frac{a}{z + \left(-1 - t\right)}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{+35} \lor \neg \left(t \leq 0.0085\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+45}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-127}:\\ \;\;\;\;x + z \cdot \frac{a}{t + 1}\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-281}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+17}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.4e+45)
   (- x a)
   (if (<= z -2.7e-127)
     (+ x (* z (/ a (+ t 1.0))))
     (if (<= z -2.35e-281)
       (- x (/ a (/ t y)))
       (if (<= z 4.2e+17) (- x (* y a)) (- x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.4e+45) {
		tmp = x - a;
	} else if (z <= -2.7e-127) {
		tmp = x + (z * (a / (t + 1.0)));
	} else if (z <= -2.35e-281) {
		tmp = x - (a / (t / y));
	} else if (z <= 4.2e+17) {
		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 <= (-4.4d+45)) then
        tmp = x - a
    else if (z <= (-2.7d-127)) then
        tmp = x + (z * (a / (t + 1.0d0)))
    else if (z <= (-2.35d-281)) then
        tmp = x - (a / (t / y))
    else if (z <= 4.2d+17) 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 <= -4.4e+45) {
		tmp = x - a;
	} else if (z <= -2.7e-127) {
		tmp = x + (z * (a / (t + 1.0)));
	} else if (z <= -2.35e-281) {
		tmp = x - (a / (t / y));
	} else if (z <= 4.2e+17) {
		tmp = x - (y * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.4e+45:
		tmp = x - a
	elif z <= -2.7e-127:
		tmp = x + (z * (a / (t + 1.0)))
	elif z <= -2.35e-281:
		tmp = x - (a / (t / y))
	elif z <= 4.2e+17:
		tmp = x - (y * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.4e+45)
		tmp = Float64(x - a);
	elseif (z <= -2.7e-127)
		tmp = Float64(x + Float64(z * Float64(a / Float64(t + 1.0))));
	elseif (z <= -2.35e-281)
		tmp = Float64(x - Float64(a / Float64(t / y)));
	elseif (z <= 4.2e+17)
		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 <= -4.4e+45)
		tmp = x - a;
	elseif (z <= -2.7e-127)
		tmp = x + (z * (a / (t + 1.0)));
	elseif (z <= -2.35e-281)
		tmp = x - (a / (t / y));
	elseif (z <= 4.2e+17)
		tmp = x - (y * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.4e+45], N[(x - a), $MachinePrecision], If[LessEqual[z, -2.7e-127], N[(x + N[(z * N[(a / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.35e-281], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+17], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.4000000000000001e45 or 4.2e17 < z

   1. Initial program 96.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 z around inf 82.8%

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

   if -4.4000000000000001e45 < z < -2.7e-127

   1. Initial program 99.8%

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

      1. associate-/r/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 74.5%

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

      1. mul-1-neg 74.5%

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

      2. *-commutative 74.5%

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

      3. associate--l+ 74.5%

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

      4. +-commutative 74.5%

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

      5. associate-*r/ 74.5%

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

      6. distribute-rgt-neg-in 74.5%

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

      7. distribute-neg-frac2 74.5%

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

      8. +-commutative 74.5%

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

      9. distribute-neg-in 74.5%

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

      10. metadata-eval 74.5%

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

      11. unsub-neg 74.5%

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

      12. associate--r- 74.5%

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

   7. Simplified 74.5%

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

   8. Taylor expanded in z around 0 71.8%

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

      1. mul-1-neg 71.8%

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

      2. *-commutative 71.8%

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

      3. associate-/l* 71.9%

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

      4. distribute-rgt-neg-out 71.9%

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

      5. distribute-neg-frac2 71.9%

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

      6. distribute-neg-in 71.9%

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

      7. metadata-eval 71.9%

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

      8. sub-neg 71.9%

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

   10. Simplified 71.9%

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

   if -2.7e-127 < z < -2.3500000000000001e-281

   1. Initial program 99.8%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 85.3%

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

      1. *-commutative 85.3%

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

      2. clear-num 85.3%

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

      3. un-div-inv 85.4%

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

   7. Applied egg-rr 85.4%

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

      1. associate-/r/ 85.3%

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

   9. Simplified 85.3%

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

   10. Taylor expanded in y around inf 85.5%

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

       1. associate-*l/ 85.3%

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

       2. associate-/r/ 85.5%

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

   12. Simplified 85.5%

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

   if -2.3500000000000001e-281 < z < 4.2e17

   1. Initial program 98.7%

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

      1. associate-/r/ 99.9%

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

   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. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0 75.1%

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

   8. Taylor expanded in z around 0 73.9%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+45}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-127}:\\ \;\;\;\;x + z \cdot \frac{a}{t + 1}\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-281}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+17}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+75}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 92000000000:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{a}{z + \left(-1 - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6e+75)
   (- x a)
   (if (<= z 92000000000.0)
     (+ x (* a (/ y (- -1.0 t))))
     (- x (* z (/ a (+ z (- -1.0 t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6e+75) {
		tmp = x - a;
	} else if (z <= 92000000000.0) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x - (z * (a / (z + (-1.0 - t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6d+75)) then
        tmp = x - a
    else if (z <= 92000000000.0d0) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else
        tmp = x - (z * (a / (z + ((-1.0d0) - t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6e+75) {
		tmp = x - a;
	} else if (z <= 92000000000.0) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x - (z * (a / (z + (-1.0 - t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6e+75:
		tmp = x - a
	elif z <= 92000000000.0:
		tmp = x + (a * (y / (-1.0 - t)))
	else:
		tmp = x - (z * (a / (z + (-1.0 - t))))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6e+75)
		tmp = Float64(x - a);
	elseif (z <= 92000000000.0)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	else
		tmp = Float64(x - Float64(z * Float64(a / Float64(z + Float64(-1.0 - t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6e+75)
		tmp = x - a;
	elseif (z <= 92000000000.0)
		tmp = x + (a * (y / (-1.0 - t)));
	else
		tmp = x - (z * (a / (z + (-1.0 - t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6e+75], N[(x - a), $MachinePrecision], If[LessEqual[z, 92000000000.0], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(a / N[(z + N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6e75

   1. Initial program 93.6%

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

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

   if -6e75 < z < 9.2e10

   1. Initial program 99.2%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 88.9%

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

   if 9.2e10 < z

   1. Initial program 98.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in y around 0 67.8%

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

      1. mul-1-neg 67.8%

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

      2. *-commutative 67.8%

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

      3. associate--l+ 67.8%

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

      4. +-commutative 67.8%

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

      5. associate-*r/ 83.8%

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

      6. distribute-rgt-neg-in 83.8%

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

      7. distribute-neg-frac2 83.8%

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

      8. +-commutative 83.8%

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

      9. distribute-neg-in 83.8%

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

      10. metadata-eval 83.8%

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

      11. unsub-neg 83.8%

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

      12. associate--r- 83.8%

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

   7. Simplified 83.8%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+75}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 92000000000:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{a}{z + \left(-1 - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+38}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-280}:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+17}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.05e+38)
   (- x a)
   (if (<= z -1e-280)
     (+ x (* (/ a t) (- z y)))
     (if (<= z 4.6e+17) (- x (* y a)) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+38) {
		tmp = x - a;
	} else if (z <= -1e-280) {
		tmp = x + ((a / t) * (z - y));
	} else if (z <= 4.6e+17) {
		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 <= (-1.05d+38)) then
        tmp = x - a
    else if (z <= (-1d-280)) then
        tmp = x + ((a / t) * (z - y))
    else if (z <= 4.6d+17) 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 <= -1.05e+38) {
		tmp = x - a;
	} else if (z <= -1e-280) {
		tmp = x + ((a / t) * (z - y));
	} else if (z <= 4.6e+17) {
		tmp = x - (y * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.05e+38:
		tmp = x - a
	elif z <= -1e-280:
		tmp = x + ((a / t) * (z - y))
	elif z <= 4.6e+17:
		tmp = x - (y * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.05e+38)
		tmp = Float64(x - a);
	elseif (z <= -1e-280)
		tmp = Float64(x + Float64(Float64(a / t) * Float64(z - y)));
	elseif (z <= 4.6e+17)
		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 <= -1.05e+38)
		tmp = x - a;
	elseif (z <= -1e-280)
		tmp = x + ((a / t) * (z - y));
	elseif (z <= 4.6e+17)
		tmp = x - (y * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.05e+38], N[(x - a), $MachinePrecision], If[LessEqual[z, -1e-280], N[(x + N[(N[(a / t), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+17], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05e38 or 4.6e17 < z

   1. Initial program 96.1%

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

   5. Taylor expanded in z around inf 83.1%

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

   if -1.05e38 < z < -9.9999999999999996e-281

   1. Initial program 99.8%

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

      1. associate-/r/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 71.3%

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

      1. *-commutative 71.3%

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

      2. clear-num 71.3%

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

      3. un-div-inv 71.4%

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

   7. Applied egg-rr 71.4%

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

      1. associate-/r/ 71.4%

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

   9. Simplified 71.4%

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

   if -9.9999999999999996e-281 < z < 4.6e17

   1. Initial program 98.7%

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

      1. associate-/r/ 99.9%

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

   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. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0 75.1%

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

   8. Taylor expanded in z around 0 73.9%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+38}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-280}:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+17}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+75} \lor \neg \left(z \leq 8.4 \cdot 10^{+17}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.8e+75) (not (<= z 8.4e+17)))
   (- x a)
   (+ x (* a (/ y (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.8e+75) || !(z <= 8.4e+17)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-6.8d+75)) .or. (.not. (z <= 8.4d+17))) then
        tmp = x - a
    else
        tmp = x + (a * (y / ((-1.0d0) - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.8e+75) || !(z <= 8.4e+17)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.8e+75) or not (z <= 8.4e+17):
		tmp = x - a
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.8e+75) || !(z <= 8.4e+17))
		tmp = Float64(x - a);
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.8e+75) || ~((z <= 8.4e+17)))
		tmp = x - a;
	else
		tmp = x + (a * (y / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.8e+75], N[Not[LessEqual[z, 8.4e+17]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.80000000000000022e75 or 8.4e17 < z

   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. Add Preprocessing

   5. Taylor expanded in z around inf 84.6%

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

   if -6.80000000000000022e75 < z < 8.4e17

   1. Initial program 99.2%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 88.4%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+75} \lor \neg \left(z \leq 8.4 \cdot 10^{+17}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+25} \lor \neg \left(z \leq 4.2 \cdot 10^{+17}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.5e+25) (not (<= z 4.2e+17))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.5e+25) || !(z <= 4.2e+17)) {
		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 <= (-5.5d+25)) .or. (.not. (z <= 4.2d+17))) 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 <= -5.5e+25) || !(z <= 4.2e+17)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.5e+25) or not (z <= 4.2e+17):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.5e+25) || !(z <= 4.2e+17))
		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 <= -5.5e+25) || ~((z <= 4.2e+17)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.5e+25], N[Not[LessEqual[z, 4.2e+17]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.50000000000000018e25 or 4.2e17 < z

   1. Initial program 96.1%

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

   5. Taylor expanded in z around inf 81.9%

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

   if -5.50000000000000018e25 < z < 4.2e17

   1. Initial program 99.1%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0 74.2%

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

   8. Taylor expanded in z around 0 70.6%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+25} \lor \neg \left(z \leq 4.2 \cdot 10^{+17}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-16} \lor \neg \left(z \leq 7.4 \cdot 10^{+28}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.2e-16) (not (<= z 7.4e+28))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.2e-16) || !(z <= 7.4e+28)) {
		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 <= (-1.2d-16)) .or. (.not. (z <= 7.4d+28))) 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 <= -1.2e-16) || !(z <= 7.4e+28)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.2e-16) or not (z <= 7.4e+28):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.2e-16) || !(z <= 7.4e+28))
		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 <= -1.2e-16) || ~((z <= 7.4e+28)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.2e-16], N[Not[LessEqual[z, 7.4e+28]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.20000000000000002e-16 or 7.3999999999999998e28 < z

   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. Add Preprocessing

   5. Taylor expanded in z around inf 80.9%

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

   if -1.20000000000000002e-16 < z < 7.3999999999999998e28

   1. Initial program 99.1%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 54.1%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-16} \lor \neg \left(z \leq 7.4 \cdot 10^{+28}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

   1. clear-num 97.6%

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

   2. associate-/r/ 97.6%

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

   3. clear-num 97.9%

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

4. Applied egg-rr 97.9%

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

5. Final simplification 97.9%

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

Alternative 10: 53.8% 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 97.7%

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

5. Taylor expanded in x around inf 52.9%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

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 2024091 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

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

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