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

Percentage Accurate: 97.2% → 99.6%

Time: 8.7s

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: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% 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 98.0%

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

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

Alternative 2: 89.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+110}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y - z}}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+195}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.2e+110)
   (- x (/ a (/ t (- y z))))
   (if (<= t 3e+195)
     (+ x (* a (/ (- y z) (+ z -1.0))))
     (+ x (* a (/ (- z y) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.2e+110) {
		tmp = x - (a / (t / (y - z)));
	} else if (t <= 3e+195) {
		tmp = x + (a * ((y - z) / (z + -1.0)));
	} else {
		tmp = x + (a * ((z - y) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-6.2d+110)) then
        tmp = x - (a / (t / (y - z)))
    else if (t <= 3d+195) then
        tmp = x + (a * ((y - z) / (z + (-1.0d0))))
    else
        tmp = x + (a * ((z - y) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.2e+110) {
		tmp = x - (a / (t / (y - z)));
	} else if (t <= 3e+195) {
		tmp = x + (a * ((y - z) / (z + -1.0)));
	} else {
		tmp = x + (a * ((z - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.2e+110:
		tmp = x - (a / (t / (y - z)))
	elif t <= 3e+195:
		tmp = x + (a * ((y - z) / (z + -1.0)))
	else:
		tmp = x + (a * ((z - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.2e+110)
		tmp = Float64(x - Float64(a / Float64(t / Float64(y - z))));
	elseif (t <= 3e+195)
		tmp = Float64(x + Float64(a * Float64(Float64(y - z) / Float64(z + -1.0))));
	else
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.2e+110)
		tmp = x - (a / (t / (y - z)));
	elseif (t <= 3e+195)
		tmp = x + (a * ((y - z) / (z + -1.0)));
	else
		tmp = x + (a * ((z - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.2e+110], N[(x - N[(a / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+195], N[(x + N[(a * N[(N[(y - z), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.20000000000000035e110

   1. Initial program 97.0%

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

      1. associate-/r/ 99.8%

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

   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 99.7%

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

      3. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in t around inf 100.0%

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

   if -6.20000000000000035e110 < t < 3.0000000000000001e195

   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 t around 0 93.8%

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

   if 3.0000000000000001e195 < t

   1. Initial program 95.8%

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

      1. associate-/r/ 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 t around inf 95.2%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+110}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y - z}}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+195}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+19} \lor \neg \left(z \leq 1.2\right):\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.2e+19) (not (<= z 1.2)))
   (+ x (/ (- y z) (/ z a)))
   (+ x (* a (/ y (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.2e+19) || !(z <= 1.2)) {
		tmp = x + ((y - z) / (z / 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 <= (-5.2d+19)) .or. (.not. (z <= 1.2d0))) then
        tmp = x + ((y - z) / (z / 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 <= -5.2e+19) || !(z <= 1.2)) {
		tmp = x + ((y - z) / (z / a));
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.2e+19) or not (z <= 1.2):
		tmp = x + ((y - z) / (z / a))
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.2e+19) || !(z <= 1.2))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(z / 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 <= -5.2e+19) || ~((z <= 1.2)))
		tmp = x + ((y - z) / (z / 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, -5.2e+19], N[Not[LessEqual[z, 1.2]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $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 < -5.2e19 or 1.19999999999999996 < z

   1. Initial program 97.3%

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

   3. Taylor expanded in z around inf 90.7%

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

      1. mul-1-neg 90.7%

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

      2. distribute-neg-frac2 90.7%

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

   5. Simplified 90.7%

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

   if -5.2e19 < z < 1.19999999999999996

   1. Initial program 98.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 92.7%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+19} \lor \neg \left(z \leq 1.2\right):\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{-106} \lor \neg \left(z \leq 1.4 \cdot 10^{-47}\right):\\ \;\;\;\;x + z \cdot \frac{a}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.4e-106) (not (<= z 1.4e-47)))
   (+ x (* z (/ a (- 1.0 z))))
   (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.4e-106) || !(z <= 1.4e-47)) {
		tmp = x + (z * (a / (1.0 - z)));
	} 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 <= (-8.4d-106)) .or. (.not. (z <= 1.4d-47))) then
        tmp = x + (z * (a / (1.0d0 - z)))
    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 <= -8.4e-106) || !(z <= 1.4e-47)) {
		tmp = x + (z * (a / (1.0 - z)));
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.4e-106) or not (z <= 1.4e-47):
		tmp = x + (z * (a / (1.0 - z)))
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.4e-106) || !(z <= 1.4e-47))
		tmp = Float64(x + Float64(z * Float64(a / Float64(1.0 - z))));
	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 <= -8.4e-106) || ~((z <= 1.4e-47)))
		tmp = x + (z * (a / (1.0 - z)));
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.4e-106], N[Not[LessEqual[z, 1.4e-47]], $MachinePrecision]], N[(x + N[(z * N[(a / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.40000000000000013e-106 or 1.39999999999999996e-47 < z

   1. Initial program 97.1%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 70.8%

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

      1. mul-1-neg 70.8%

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

      2. *-commutative 70.8%

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

      3. associate--l+ 70.8%

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

      4. +-commutative 70.8%

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

      5. associate-*r/ 86.7%

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

      6. distribute-rgt-neg-in 86.7%

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

      7. distribute-neg-frac2 86.7%

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

      8. +-commutative 86.7%

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

      9. distribute-neg-in 86.7%

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

      10. metadata-eval 86.7%

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

      11. unsub-neg 86.7%

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

      12. associate--r- 86.7%

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

   7. Simplified 86.7%

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

   8. Taylor expanded in t around 0 82.0%

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

   if -8.40000000000000013e-106 < z < 1.39999999999999996e-47

   1. Initial program 99.7%

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

      1. associate-/r/ 99.9%

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

   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 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in t around 0 79.4%

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

   8. Taylor expanded in z around 0 78.6%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{-106} \lor \neg \left(z \leq 1.4 \cdot 10^{-47}\right):\\ \;\;\;\;x + z \cdot \frac{a}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-42}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t + 1\right) - z}\\ \mathbf{elif}\;z \leq 1.35:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.7e-42)
   (+ x (* a (/ z (- (+ t 1.0) z))))
   (if (<= z 1.35) (+ x (* a (/ y (- -1.0 t)))) (+ x (/ (- y z) (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.7e-42) {
		tmp = x + (a * (z / ((t + 1.0) - z)));
	} else if (z <= 1.35) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x + ((y - z) / (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.7d-42)) then
        tmp = x + (a * (z / ((t + 1.0d0) - z)))
    else if (z <= 1.35d0) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else
        tmp = x + ((y - z) / (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.7e-42) {
		tmp = x + (a * (z / ((t + 1.0) - z)));
	} else if (z <= 1.35) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x + ((y - z) / (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.7e-42:
		tmp = x + (a * (z / ((t + 1.0) - z)))
	elif z <= 1.35:
		tmp = x + (a * (y / (-1.0 - t)))
	else:
		tmp = x + ((y - z) / (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.7e-42)
		tmp = Float64(x + Float64(a * Float64(z / Float64(Float64(t + 1.0) - z))));
	elseif (z <= 1.35)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.7e-42)
		tmp = x + (a * (z / ((t + 1.0) - z)));
	elseif (z <= 1.35)
		tmp = x + (a * (y / (-1.0 - t)));
	else
		tmp = x + ((y - z) / (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.7e-42], N[(x + N[(a * N[(z / N[(N[(t + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.70000000000000011e-42

   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 y around 0 91.2%

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

      1. mul-1-neg 91.2%

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

      2. associate--l+ 91.2%

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

      3. +-commutative 91.2%

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

      4. distribute-neg-frac2 91.2%

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

      5. +-commutative 91.2%

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

      6. distribute-neg-in 91.2%

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

      7. metadata-eval 91.2%

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

      8. unsub-neg 91.2%

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

      9. associate--r- 91.2%

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

   7. Simplified 91.2%

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

   if -1.70000000000000011e-42 < z < 1.3500000000000001

   1. Initial program 98.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 94.7%

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

   if 1.3500000000000001 < z

   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 97.5%

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

      1. mul-1-neg 97.5%

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

      2. distribute-neg-frac2 97.5%

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

   5. Simplified 97.5%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-42}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t + 1\right) - z}\\ \mathbf{elif}\;z \leq 1.35:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-47}:\\ \;\;\;\;x - z \cdot \frac{a}{z + \left(-1 - t\right)}\\ \mathbf{elif}\;z \leq 1.95:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.35e-47)
   (- x (* z (/ a (+ z (- -1.0 t)))))
   (if (<= z 1.95) (+ x (* a (/ y (- -1.0 t)))) (+ x (/ (- y z) (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e-47) {
		tmp = x - (z * (a / (z + (-1.0 - t))));
	} else if (z <= 1.95) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x + ((y - z) / (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.35d-47)) then
        tmp = x - (z * (a / (z + ((-1.0d0) - t))))
    else if (z <= 1.95d0) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else
        tmp = x + ((y - z) / (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e-47) {
		tmp = x - (z * (a / (z + (-1.0 - t))));
	} else if (z <= 1.95) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x + ((y - z) / (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.35e-47:
		tmp = x - (z * (a / (z + (-1.0 - t))))
	elif z <= 1.95:
		tmp = x + (a * (y / (-1.0 - t)))
	else:
		tmp = x + ((y - z) / (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.35e-47)
		tmp = Float64(x - Float64(z * Float64(a / Float64(z + Float64(-1.0 - t)))));
	elseif (z <= 1.95)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.35e-47)
		tmp = x - (z * (a / (z + (-1.0 - t))));
	elseif (z <= 1.95)
		tmp = x + (a * (y / (-1.0 - t)));
	else
		tmp = x + ((y - z) / (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.35e-47], N[(x - N[(z * N[(a / N[(z + N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3499999999999999e-47

   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 y around 0 74.7%

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

      1. mul-1-neg 74.7%

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

      2. *-commutative 74.7%

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

      3. associate--l+ 74.7%

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

      4. +-commutative 74.7%

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

      5. associate-*r/ 88.4%

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

      6. distribute-rgt-neg-in 88.4%

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

      7. distribute-neg-frac2 88.4%

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

      8. +-commutative 88.4%

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

      9. distribute-neg-in 88.4%

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

      10. metadata-eval 88.4%

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

      11. unsub-neg 88.4%

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

      12. associate--r- 88.4%

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

   7. Simplified 88.4%

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

   if -1.3499999999999999e-47 < z < 1.94999999999999996

   1. Initial program 98.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 94.7%

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

   if 1.94999999999999996 < z

   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 97.5%

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

      1. mul-1-neg 97.5%

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

      2. distribute-neg-frac2 97.5%

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

   5. Simplified 97.5%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-47}:\\ \;\;\;\;x - z \cdot \frac{a}{z + \left(-1 - t\right)}\\ \mathbf{elif}\;z \leq 1.95:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+21}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-46}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{a}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.6e+21)
   (- x a)
   (if (<= z 6.5e-46)
     (+ x (* a (/ y (- -1.0 t))))
     (+ x (* z (/ a (- 1.0 z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.6e+21) {
		tmp = x - a;
	} else if (z <= 6.5e-46) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x + (z * (a / (1.0 - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.6d+21)) then
        tmp = x - a
    else if (z <= 6.5d-46) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else
        tmp = x + (z * (a / (1.0d0 - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.6e+21) {
		tmp = x - a;
	} else if (z <= 6.5e-46) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x + (z * (a / (1.0 - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.6e+21:
		tmp = x - a
	elif z <= 6.5e-46:
		tmp = x + (a * (y / (-1.0 - t)))
	else:
		tmp = x + (z * (a / (1.0 - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.6e+21)
		tmp = Float64(x - a);
	elseif (z <= 6.5e-46)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	else
		tmp = Float64(x + Float64(z * Float64(a / Float64(1.0 - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.6e+21)
		tmp = x - a;
	elseif (z <= 6.5e-46)
		tmp = x + (a * (y / (-1.0 - t)));
	else
		tmp = x + (z * (a / (1.0 - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.6e+21], N[(x - a), $MachinePrecision], If[LessEqual[z, 6.5e-46], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(a / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6e21

   1. Initial program 95.2%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 83.2%

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

   if -1.6e21 < z < 6.49999999999999966e-46

   1. Initial program 98.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 93.2%

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

   if 6.49999999999999966e-46 < z

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 y around 0 68.4%

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

      1. mul-1-neg 68.4%

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

      2. *-commutative 68.4%

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

      3. associate--l+ 68.4%

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

      4. +-commutative 68.4%

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

      5. associate-*r/ 88.5%

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

      6. distribute-rgt-neg-in 88.5%

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

      7. distribute-neg-frac2 88.5%

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

      8. +-commutative 88.5%

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

      9. distribute-neg-in 88.5%

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

      10. metadata-eval 88.5%

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

      11. unsub-neg 88.5%

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

      12. associate--r- 88.5%

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

   7. Simplified 88.5%

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

   8. Taylor expanded in t around 0 86.5%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+21}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-46}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{a}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-42} \lor \neg \left(z \leq 0.011\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.7e-42) (not (<= z 0.011))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.7e-42) || !(z <= 0.011)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.7d-42)) .or. (.not. (z <= 0.011d0))) then
        tmp = x - a
    else
        tmp = x - (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.7e-42) || !(z <= 0.011)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.7e-42) or not (z <= 0.011):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.7e-42) || !(z <= 0.011))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.7e-42) || ~((z <= 0.011)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.7e-42], N[Not[LessEqual[z, 0.011]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.70000000000000011e-42 or 0.010999999999999999 < z

   1. Initial program 97.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 83.0%

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

   if -1.70000000000000011e-42 < z < 0.010999999999999999

   1. Initial program 98.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. 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 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in t around 0 80.1%

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

   8. Taylor expanded in z around 0 76.5%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-42} \lor \neg \left(z \leq 0.011\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -850000000 \lor \neg \left(z \leq 2.35 \cdot 10^{-52}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -850000000.0) (not (<= z 2.35e-52))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -850000000.0) || !(z <= 2.35e-52)) {
		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 <= (-850000000.0d0)) .or. (.not. (z <= 2.35d-52))) 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 <= -850000000.0) || !(z <= 2.35e-52)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -850000000.0) or not (z <= 2.35e-52):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -850000000.0) || !(z <= 2.35e-52))
		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 <= -850000000.0) || ~((z <= 2.35e-52)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -850000000.0], N[Not[LessEqual[z, 2.35e-52]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -8.5e8 or 2.3499999999999999e-52 < z

   1. Initial program 97.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 83.1%

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

   if -8.5e8 < z < 2.3499999999999999e-52

   1. Initial program 98.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 t around inf 60.4%

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

   6. Taylor expanded in x around inf 54.6%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -850000000 \lor \neg \left(z \leq 2.35 \cdot 10^{-52}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.1% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x
end function

Java

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

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 98.0%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
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 inf 49.8%

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

6. Taylor expanded in x around inf 56.2%

   \[\leadsto \color{blue}{x} \]
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 2024100 
(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))))