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

Percentage Accurate: 96.8% → 99.6%

Time: 12.2s

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: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. sub-neg 96.5%

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

   2. +-commutative 96.5%

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

   3. associate-/r/ 99.6%

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

   4. distribute-lft-neg-in 99.6%

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

   5. fma-define 99.6%

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

   6. distribute-neg-frac2 99.6%

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

   7. distribute-neg-in 99.6%

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

   8. sub-neg 99.6%

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

   9. distribute-neg-in 99.6%

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

   10. remove-double-neg 99.6%

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

   11. +-commutative 99.6%

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

   12. sub-neg 99.6%

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

   13. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 2: 91.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+114} \lor \neg \left(t \leq 2.9 \cdot 10^{+69}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.5e+114) (not (<= t 2.9e+69)))
   (+ 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 <= -5.5e+114) || !(t <= 2.9e+69)) {
		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 <= (-5.5d+114)) .or. (.not. (t <= 2.9d+69))) 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 <= -5.5e+114) || !(t <= 2.9e+69)) {
		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 <= -5.5e+114) or not (t <= 2.9e+69):
		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 <= -5.5e+114) || !(t <= 2.9e+69))
		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 <= -5.5e+114) || ~((t <= 2.9e+69)))
		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[Or[LessEqual[t, -5.5e+114], N[Not[LessEqual[t, 2.9e+69]], $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 2 regimes

2. if t < -5.5000000000000001e114 or 2.8999999999999998e69 < t

   1. Initial program 97.5%

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

      1. associate-/r/ 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in t around inf 93.9%

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

   if -5.5000000000000001e114 < t < 2.8999999999999998e69

   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 t around 0 95.6%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+114} \lor \neg \left(t \leq 2.9 \cdot 10^{+69}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+81}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{a}{z} - \frac{a}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.1e+21)
   (+ x (/ (- y z) (/ z a)))
   (if (<= z 1.7e+81)
     (+ x (* a (/ y (- -1.0 t))))
     (+ x (* y (- (/ a z) (/ a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.1e+21) {
		tmp = x + ((y - z) / (z / a));
	} else if (z <= 1.7e+81) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x + (y * ((a / z) - (a / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.1d+21)) then
        tmp = x + ((y - z) / (z / a))
    else if (z <= 1.7d+81) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else
        tmp = x + (y * ((a / z) - (a / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.1e+21) {
		tmp = x + ((y - z) / (z / a));
	} else if (z <= 1.7e+81) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x + (y * ((a / z) - (a / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.1e+21:
		tmp = x + ((y - z) / (z / a))
	elif z <= 1.7e+81:
		tmp = x + (a * (y / (-1.0 - t)))
	else:
		tmp = x + (y * ((a / z) - (a / y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.1e+21)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(z / a)));
	elseif (z <= 1.7e+81)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(a / z) - Float64(a / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.1e+21)
		tmp = x + ((y - z) / (z / a));
	elseif (z <= 1.7e+81)
		tmp = x + (a * (y / (-1.0 - t)));
	else
		tmp = x + (y * ((a / z) - (a / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.1e+21], N[(x + N[(N[(y - z), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+81], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(a / z), $MachinePrecision] - N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1e21

   1. Initial program 92.1%

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

   3. Taylor expanded in z around inf 83.3%

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

      1. associate-*r/ 83.3%

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

      2. neg-mul-1 83.3%

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

   5. Simplified 83.3%

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

   if -2.1e21 < z < 1.70000000000000001e81

   1. Initial program 99.8%

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

      1. associate-/r/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 93.0%

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

   if 1.70000000000000001e81 < z

   1. Initial program 90.8%

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

   3. Taylor expanded in z around inf 88.1%

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

      1. associate-*r/ 88.1%

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

      2. neg-mul-1 88.1%

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

   5. Simplified 88.1%

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

   6. Taylor expanded in y around inf 89.3%

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

      1. mul-1-neg 89.3%

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

      2. +-commutative 89.3%

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

      3. unsub-neg 89.3%

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

   8. Simplified 89.3%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+81}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{a}{z} - \frac{a}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+21} \lor \neg \left(z \leq 3.6 \cdot 10^{+15}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.6e+21) (not (<= z 3.6e+15)))
   (+ 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 <= -1.6e+21) || !(z <= 3.6e+15)) {
		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 <= (-1.6d+21)) .or. (.not. (z <= 3.6d+15))) 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 <= -1.6e+21) || !(z <= 3.6e+15)) {
		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 <= -1.6e+21) or not (z <= 3.6e+15):
		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 <= -1.6e+21) || !(z <= 3.6e+15))
		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 <= -1.6e+21) || ~((z <= 3.6e+15)))
		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, -1.6e+21], N[Not[LessEqual[z, 3.6e+15]], $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 < -1.6e21 or 3.6e15 < z

   1. Initial program 92.4%

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

   3. Taylor expanded in z around inf 83.8%

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

      1. associate-*r/ 83.8%

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

      2. neg-mul-1 83.8%

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

   5. Simplified 83.8%

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

   if -1.6e21 < z < 3.6e15

   1. Initial program 99.8%

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

      1. associate-/r/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 95.1%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+21} \lor \neg \left(z \leq 3.6 \cdot 10^{+15}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+80} \lor \neg \left(z \leq 1.7 \cdot 10^{+81}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.5e+80) (not (<= z 1.7e+81)))
   (- 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 <= -9.5e+80) || !(z <= 1.7e+81)) {
		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 <= (-9.5d+80)) .or. (.not. (z <= 1.7d+81))) 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 <= -9.5e+80) || !(z <= 1.7e+81)) {
		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 <= -9.5e+80) or not (z <= 1.7e+81):
		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 <= -9.5e+80) || !(z <= 1.7e+81))
		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 <= -9.5e+80) || ~((z <= 1.7e+81)))
		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, -9.5e+80], N[Not[LessEqual[z, 1.7e+81]], $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 < -9.499999999999999e80 or 1.70000000000000001e81 < z

   1. Initial program 90.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 80.7%

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

   if -9.499999999999999e80 < z < 1.70000000000000001e81

   1. Initial program 99.8%

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

      1. associate-/r/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 92.2%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+80} \lor \neg \left(z \leq 1.7 \cdot 10^{+81}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+21} \lor \neg \left(z \leq 1.66 \cdot 10^{+109}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.02e+21) (not (<= z 1.66e+109))) (- x a) (- x (* a (/ y t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.02e+21) || !(z <= 1.66e+109)) {
		tmp = x - a;
	} else {
		tmp = x - (a * (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 ((z <= (-1.02d+21)) .or. (.not. (z <= 1.66d+109))) then
        tmp = x - a
    else
        tmp = x - (a * (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 ((z <= -1.02e+21) || !(z <= 1.66e+109)) {
		tmp = x - a;
	} else {
		tmp = x - (a * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.02e+21) or not (z <= 1.66e+109):
		tmp = x - a
	else:
		tmp = x - (a * (y / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.02e+21) || !(z <= 1.66e+109))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(a * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.02e+21) || ~((z <= 1.66e+109)))
		tmp = x - a;
	else
		tmp = x - (a * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.02e+21], N[Not[LessEqual[z, 1.66e+109]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.02e21 or 1.6599999999999999e109 < z

   1. Initial program 90.9%

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

      1. associate-/r/ 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 83.8%

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

   if -1.02e21 < z < 1.6599999999999999e109

   1. Initial program 99.8%

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

      1. associate-/r/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in t around inf 68.5%

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

   6. Taylor expanded in y around inf 66.9%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+21} \lor \neg \left(z \leq 1.66 \cdot 10^{+109}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+21} \lor \neg \left(z \leq 3400000000000\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9e+21) (not (<= z 3400000000000.0))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9e+21) || !(z <= 3400000000000.0)) {
		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 <= (-9d+21)) .or. (.not. (z <= 3400000000000.0d0))) 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 <= -9e+21) || !(z <= 3400000000000.0)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9e+21) or not (z <= 3400000000000.0):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9e+21) || !(z <= 3400000000000.0))
		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 <= -9e+21) || ~((z <= 3400000000000.0)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9e+21], N[Not[LessEqual[z, 3400000000000.0]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -9e21 or 3.4e12 < z

   1. Initial program 92.4%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 77.3%

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

   if -9e21 < z < 3.4e12

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-/r/ 99.3%

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

      4. distribute-lft-neg-in 99.3%

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

      5. fma-define 99.3%

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

      6. distribute-neg-frac2 99.3%

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

      7. distribute-neg-in 99.3%

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

      8. sub-neg 99.3%

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

      9. distribute-neg-in 99.3%

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

      10. remove-double-neg 99.3%

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

      11. +-commutative 99.3%

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

      12. sub-neg 99.3%

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

      13. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in t around inf 61.9%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+21} \lor \neg \left(z \leq 3400000000000\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 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 96.5%

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

   1. associate-/r/ 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 9: 54.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+202} \lor \neg \left(a \leq 1.28 \cdot 10^{+129}\right):\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.1e+202) (not (<= a 1.28e+129))) (- a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.1e+202) || !(a <= 1.28e+129)) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.1d+202)) .or. (.not. (a <= 1.28d+129))) then
        tmp = -a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.1e+202) || !(a <= 1.28e+129)) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.1e+202) or not (a <= 1.28e+129):
		tmp = -a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.1e+202) || !(a <= 1.28e+129))
		tmp = Float64(-a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.1e+202) || ~((a <= 1.28e+129)))
		tmp = -a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.1e+202], N[Not[LessEqual[a, 1.28e+129]], $MachinePrecision]], (-a), x]

Derivation

1. Split input into 2 regimes

2. if a < -3.09999999999999991e202 or 1.27999999999999994e129 < a

   1. Initial program 99.7%

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

      1. associate-/r/ 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in z around inf 34.3%

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

   6. Taylor expanded in x around 0 33.6%

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

      1. neg-mul-1 33.6%

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

   8. Simplified 33.6%

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

   if -3.09999999999999991e202 < a < 1.27999999999999994e129

   1. Initial program 95.8%

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

      1. sub-neg 95.8%

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

      2. +-commutative 95.8%

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

      3. associate-/r/ 99.9%

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

      4. distribute-lft-neg-in 99.9%

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

      5. fma-define 99.9%

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

      6. distribute-neg-frac2 99.9%

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

      7. distribute-neg-in 99.9%

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

      8. sub-neg 99.9%

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

      9. distribute-neg-in 99.9%

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

      10. remove-double-neg 99.9%

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

      11. +-commutative 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 64.9%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+202} \lor \neg \left(a \leq 1.28 \cdot 10^{+129}\right):\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.4% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. sub-neg 96.5%

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

   2. +-commutative 96.5%

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

   3. associate-/r/ 99.6%

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

   4. distribute-lft-neg-in 99.6%

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

   5. fma-define 99.6%

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

   6. distribute-neg-frac2 99.6%

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

   7. distribute-neg-in 99.6%

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

   8. sub-neg 99.6%

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

   9. distribute-neg-in 99.6%

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

   10. remove-double-neg 99.6%

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

   11. +-commutative 99.6%

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

   12. sub-neg 99.6%

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

   13. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in t around inf 55.0%

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

Developer Target 1: 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 2024146 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (- x (* (/ (- y z) (+ (- t z) 1)) a)))

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