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

Percentage Accurate: 97.2% → 99.7%

Time: 9.7s

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: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. sub-neg 98.0%

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

   2. +-commutative 98.0%

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

   3. associate-/r/ 99.5%

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

   4. *-commutative 99.5%

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

   5. distribute-rgt-neg-in 99.5%

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

   6. fma-def 99.5%

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

   7. div-sub 99.5%

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

   8. sub-neg 99.5%

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

   9. +-commutative 99.5%

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

   10. distribute-neg-in 99.5%

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

   11. remove-double-neg 99.5%

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

   12. sub-neg 99.5%

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

   13. div-sub 99.5%

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

3. Simplified 99.5%

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

4. Final simplification 99.5%

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

Alternative 2: 63.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-a\right)\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+19}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-225}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-297}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-223}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- a))))
   (if (<= z -9.5e+19)
     (- x a)
     (if (<= z -3.3e-225)
       x
       (if (<= z 2.25e-297)
         t_1
         (if (<= z 3e-223)
           x
           (if (<= z 2.1e-198) t_1 (if (<= z 2.7e-12) x (- x a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * -a;
	double tmp;
	if (z <= -9.5e+19) {
		tmp = x - a;
	} else if (z <= -3.3e-225) {
		tmp = x;
	} else if (z <= 2.25e-297) {
		tmp = t_1;
	} else if (z <= 3e-223) {
		tmp = x;
	} else if (z <= 2.1e-198) {
		tmp = t_1;
	} else if (z <= 2.7e-12) {
		tmp = x;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * -a
    if (z <= (-9.5d+19)) then
        tmp = x - a
    else if (z <= (-3.3d-225)) then
        tmp = x
    else if (z <= 2.25d-297) then
        tmp = t_1
    else if (z <= 3d-223) then
        tmp = x
    else if (z <= 2.1d-198) then
        tmp = t_1
    else if (z <= 2.7d-12) then
        tmp = x
    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 t_1 = y * -a;
	double tmp;
	if (z <= -9.5e+19) {
		tmp = x - a;
	} else if (z <= -3.3e-225) {
		tmp = x;
	} else if (z <= 2.25e-297) {
		tmp = t_1;
	} else if (z <= 3e-223) {
		tmp = x;
	} else if (z <= 2.1e-198) {
		tmp = t_1;
	} else if (z <= 2.7e-12) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * -a
	tmp = 0
	if z <= -9.5e+19:
		tmp = x - a
	elif z <= -3.3e-225:
		tmp = x
	elif z <= 2.25e-297:
		tmp = t_1
	elif z <= 3e-223:
		tmp = x
	elif z <= 2.1e-198:
		tmp = t_1
	elif z <= 2.7e-12:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(-a))
	tmp = 0.0
	if (z <= -9.5e+19)
		tmp = Float64(x - a);
	elseif (z <= -3.3e-225)
		tmp = x;
	elseif (z <= 2.25e-297)
		tmp = t_1;
	elseif (z <= 3e-223)
		tmp = x;
	elseif (z <= 2.1e-198)
		tmp = t_1;
	elseif (z <= 2.7e-12)
		tmp = x;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * -a;
	tmp = 0.0;
	if (z <= -9.5e+19)
		tmp = x - a;
	elseif (z <= -3.3e-225)
		tmp = x;
	elseif (z <= 2.25e-297)
		tmp = t_1;
	elseif (z <= 3e-223)
		tmp = x;
	elseif (z <= 2.1e-198)
		tmp = t_1;
	elseif (z <= 2.7e-12)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * (-a)), $MachinePrecision]}, If[LessEqual[z, -9.5e+19], N[(x - a), $MachinePrecision], If[LessEqual[z, -3.3e-225], x, If[LessEqual[z, 2.25e-297], t$95$1, If[LessEqual[z, 3e-223], x, If[LessEqual[z, 2.1e-198], t$95$1, If[LessEqual[z, 2.7e-12], x, N[(x - a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5e19 or 2.6999999999999998e-12 < z

   1. Initial program 95.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 76.8%

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

   if -9.5e19 < z < -3.3000000000000001e-225 or 2.24999999999999988e-297 < z < 2.99999999999999991e-223 or 2.09999999999999993e-198 < z < 2.6999999999999998e-12

   1. Initial program 99.8%

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

      1. associate-/r/ 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in x around inf 63.3%

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

   if -3.3000000000000001e-225 < z < 2.24999999999999988e-297 or 2.99999999999999991e-223 < z < 2.09999999999999993e-198

   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. Taylor expanded in z around 0 100.0%

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

   5. Taylor expanded in x around 0 78.8%

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

      1. associate-*r/ 78.8%

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

      2. *-commutative 78.8%

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

      3. associate-*r/ 78.8%

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

      4. mul-1-neg 78.8%

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

      5. associate-*r/ 78.8%

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

      6. *-commutative 78.8%

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

      7. distribute-rgt-neg-in 78.8%

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

   7. Simplified 78.8%

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

   8. Taylor expanded in t around 0 65.1%

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

      1. associate-*r* 65.1%

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

      2. mul-1-neg 65.1%

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

   10. Simplified 65.1%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+19}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-225}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-297}:\\ \;\;\;\;y \cdot \left(-a\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-223}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-198}:\\ \;\;\;\;y \cdot \left(-a\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 3: 71.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot y\\ t_2 := x - \frac{a}{\frac{t}{y}}\\ \mathbf{if}\;t \leq -19.5:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-294}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a y))) (t_2 (- x (/ a (/ t y)))))
   (if (<= t -19.5)
     t_2
     (if (<= t -4.5e-166)
       t_1
       (if (<= t -2.5e-294) (- x a) (if (<= t 2.85e-5) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * y);
	double t_2 = x - (a / (t / y));
	double tmp;
	if (t <= -19.5) {
		tmp = t_2;
	} else if (t <= -4.5e-166) {
		tmp = t_1;
	} else if (t <= -2.5e-294) {
		tmp = x - a;
	} else if (t <= 2.85e-5) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (a * y)
    t_2 = x - (a / (t / y))
    if (t <= (-19.5d0)) then
        tmp = t_2
    else if (t <= (-4.5d-166)) then
        tmp = t_1
    else if (t <= (-2.5d-294)) then
        tmp = x - a
    else if (t <= 2.85d-5) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * y);
	double t_2 = x - (a / (t / y));
	double tmp;
	if (t <= -19.5) {
		tmp = t_2;
	} else if (t <= -4.5e-166) {
		tmp = t_1;
	} else if (t <= -2.5e-294) {
		tmp = x - a;
	} else if (t <= 2.85e-5) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a * y)
	t_2 = x - (a / (t / y))
	tmp = 0
	if t <= -19.5:
		tmp = t_2
	elif t <= -4.5e-166:
		tmp = t_1
	elif t <= -2.5e-294:
		tmp = x - a
	elif t <= 2.85e-5:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * y))
	t_2 = Float64(x - Float64(a / Float64(t / y)))
	tmp = 0.0
	if (t <= -19.5)
		tmp = t_2;
	elseif (t <= -4.5e-166)
		tmp = t_1;
	elseif (t <= -2.5e-294)
		tmp = Float64(x - a);
	elseif (t <= 2.85e-5)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a * y);
	t_2 = x - (a / (t / y));
	tmp = 0.0;
	if (t <= -19.5)
		tmp = t_2;
	elseif (t <= -4.5e-166)
		tmp = t_1;
	elseif (t <= -2.5e-294)
		tmp = x - a;
	elseif (t <= 2.85e-5)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -19.5], t$95$2, If[LessEqual[t, -4.5e-166], t$95$1, If[LessEqual[t, -2.5e-294], N[(x - a), $MachinePrecision], If[LessEqual[t, 2.85e-5], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -19.5 or 2.8500000000000002e-5 < t

   1. Initial program 99.1%

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

      1. associate-/r/ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around 0 75.6%

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

   5. Taylor expanded in t around inf 75.4%

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

      1. *-commutative 75.4%

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

      2. associate-/l* 84.2%

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

   7. Simplified 84.2%

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

   if -19.5 < t < -4.4999999999999998e-166 or -2.5000000000000001e-294 < t < 2.8500000000000002e-5

   1. Initial program 96.7%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 79.2%

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

   5. Taylor expanded in t around 0 78.7%

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

   if -4.4999999999999998e-166 < t < -2.5000000000000001e-294

   1. Initial program 97.1%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 71.9%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -19.5:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-166}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-294}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{-5}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \]

Alternative 4: 88.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+24} \lor \neg \left(z \leq 15000000000\right):\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.2e+24) (not (<= z 15000000000.0)))
   (+ x (/ (- z y) (/ (- z) a)))
   (- x (/ a (/ (+ t 1.0) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.2e+24) || !(z <= 15000000000.0)) {
		tmp = x + ((z - y) / (-z / a));
	} else {
		tmp = x - (a / ((t + 1.0) / 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 <= (-3.2d+24)) .or. (.not. (z <= 15000000000.0d0))) then
        tmp = x + ((z - y) / (-z / a))
    else
        tmp = x - (a / ((t + 1.0d0) / 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 <= -3.2e+24) || !(z <= 15000000000.0)) {
		tmp = x + ((z - y) / (-z / a));
	} else {
		tmp = x - (a / ((t + 1.0) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.2e+24) or not (z <= 15000000000.0):
		tmp = x + ((z - y) / (-z / a))
	else:
		tmp = x - (a / ((t + 1.0) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.2e+24) || !(z <= 15000000000.0))
		tmp = Float64(x + Float64(Float64(z - y) / Float64(Float64(-z) / a)));
	else
		tmp = Float64(x - Float64(a / Float64(Float64(t + 1.0) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.2e+24) || ~((z <= 15000000000.0)))
		tmp = x + ((z - y) / (-z / a));
	else
		tmp = x - (a / ((t + 1.0) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.2e+24], N[Not[LessEqual[z, 15000000000.0]], $MachinePrecision]], N[(x + N[(N[(z - y), $MachinePrecision] / N[((-z) / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a / N[(N[(t + 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1999999999999997e24 or 1.5e10 < z

   1. Initial program 95.8%

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

   2. Taylor expanded in z around inf 83.0%

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

      1. mul-1-neg 83.0%

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

      2. distribute-neg-frac 83.0%

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

   4. Simplified 83.0%

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

   if -3.1999999999999997e24 < z < 1.5e10

   1. Initial program 99.8%

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

      1. associate-/r/ 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in z around 0 91.9%

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

      1. associate-/l* 96.5%

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

   6. Simplified 96.5%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+24} \lor \neg \left(z \leq 15000000000\right):\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \end{array} \]

Alternative 5: 83.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+98} \lor \neg \left(z \leq 8.6 \cdot 10^{+145}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.8e+98) (not (<= z 8.6e+145)))
   (- x a)
   (- x (/ a (/ (+ t 1.0) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.8e+98) || !(z <= 8.6e+145)) {
		tmp = x - a;
	} else {
		tmp = x - (a / ((t + 1.0) / 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 <= (-1.8d+98)) .or. (.not. (z <= 8.6d+145))) then
        tmp = x - a
    else
        tmp = x - (a / ((t + 1.0d0) / 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 <= -1.8e+98) || !(z <= 8.6e+145)) {
		tmp = x - a;
	} else {
		tmp = x - (a / ((t + 1.0) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.8e+98) or not (z <= 8.6e+145):
		tmp = x - a
	else:
		tmp = x - (a / ((t + 1.0) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.8e+98) || !(z <= 8.6e+145))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(a / Float64(Float64(t + 1.0) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.8e+98) || ~((z <= 8.6e+145)))
		tmp = x - a;
	else
		tmp = x - (a / ((t + 1.0) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.8e+98], N[Not[LessEqual[z, 8.6e+145]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(a / N[(N[(t + 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7999999999999999e98 or 8.59999999999999996e145 < z

   1. Initial program 95.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 84.8%

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

   if -1.7999999999999999e98 < z < 8.59999999999999996e145

   1. Initial program 99.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around 0 85.2%

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

      1. associate-/l* 90.9%

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

   6. Simplified 90.9%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+98} \lor \neg \left(z \leq 8.6 \cdot 10^{+145}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \end{array} \]

Alternative 6: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. associate-/r/ 99.5%

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

3. Simplified 99.5%

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

4. Final simplification 99.5%

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

Alternative 7: 73.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -80000 \lor \neg \left(z \leq 3 \cdot 10^{-12}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -80000.0) (not (<= z 3e-12))) (- x a) (- x (* a y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -80000.0) || !(z <= 3e-12)) {
		tmp = x - a;
	} else {
		tmp = x - (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 <= (-80000.0d0)) .or. (.not. (z <= 3d-12))) then
        tmp = x - a
    else
        tmp = x - (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 <= -80000.0) || !(z <= 3e-12)) {
		tmp = x - a;
	} else {
		tmp = x - (a * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -80000.0) or not (z <= 3e-12):
		tmp = x - a
	else:
		tmp = x - (a * y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -80000.0) || !(z <= 3e-12))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(a * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -80000.0) || ~((z <= 3e-12)))
		tmp = x - a;
	else
		tmp = x - (a * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -80000.0], N[Not[LessEqual[z, 3e-12]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8e4 or 3.0000000000000001e-12 < 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. Taylor expanded in z around inf 76.0%

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

   if -8e4 < z < 3.0000000000000001e-12

   1. Initial program 99.8%

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

      1. associate-/r/ 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in z around 0 93.5%

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

   5. Taylor expanded in t around 0 74.5%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -80000 \lor \neg \left(z \leq 3 \cdot 10^{-12}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot y\\ \end{array} \]

Alternative 8: 66.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+19}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e+19) (- x a) (if (<= z 1.85e-12) x (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+19) {
		tmp = x - a;
	} else if (z <= 1.85e-12) {
		tmp = x;
	} 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 <= (-2d+19)) then
        tmp = x - a
    else if (z <= 1.85d-12) then
        tmp = x
    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 <= -2e+19) {
		tmp = x - a;
	} else if (z <= 1.85e-12) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2e+19:
		tmp = x - a
	elif z <= 1.85e-12:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e+19)
		tmp = Float64(x - a);
	elseif (z <= 1.85e-12)
		tmp = x;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2e+19)
		tmp = x - a;
	elseif (z <= 1.85e-12)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e+19], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.85e-12], x, N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2e19 or 1.84999999999999999e-12 < z

   1. Initial program 95.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 76.8%

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

   if -2e19 < z < 1.84999999999999999e-12

   1. Initial program 99.8%

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

      1. associate-/r/ 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in x around inf 54.3%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+19}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 9: 54.2% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.25 \cdot 10^{+176}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a 2.25e+176) x (- a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 2.25e+176) {
		tmp = x;
	} else {
		tmp = -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 (a <= 2.25d+176) then
        tmp = x
    else
        tmp = -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 (a <= 2.25e+176) {
		tmp = x;
	} else {
		tmp = -a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 2.25e+176:
		tmp = x
	else:
		tmp = -a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 2.25e+176)
		tmp = x;
	else
		tmp = Float64(-a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= 2.25e+176)
		tmp = x;
	else
		tmp = -a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 2.25e+176], x, (-a)]

Derivation

1. Split input into 2 regimes

2. if a < 2.25000000000000002e176

   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. Taylor expanded in x around inf 58.8%

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

   if 2.25000000000000002e176 < a

   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/ 96.8%

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

      4. *-commutative 96.8%

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

      5. distribute-rgt-neg-in 96.8%

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

      6. fma-def 96.8%

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

      7. div-sub 96.8%

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

      8. sub-neg 96.8%

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

      9. +-commutative 96.8%

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

      10. distribute-neg-in 96.8%

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

      11. remove-double-neg 96.8%

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

      12. sub-neg 96.8%

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

      13. div-sub 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in a around -inf 47.0%

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

      1. associate-/l* 83.1%

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

      2. associate-/r/ 86.1%

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

      3. associate--l+ 86.1%

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

   6. Simplified 86.1%

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

   7. Taylor expanded in z around inf 32.8%

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

      1. mul-1-neg 32.8%

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

   9. Simplified 32.8%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.25 \cdot 10^{+176}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-a\\ \end{array} \]

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/ 99.5%

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

3. Simplified 99.5%

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

4. Taylor expanded in x around inf 53.2%

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

5. Final simplification 53.2%

   \[\leadsto x \]

Developer target: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023240 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

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

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