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

Percentage Accurate: 97.1% → 99.7%

Time: 13.1s

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: 97.1% 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

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

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 97.6%

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

   1. sub-neg 97.6%

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

   2. +-commutative 97.6%

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

   3. associate-/r/ 99.1%

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

   4. distribute-lft-neg-in 99.1%

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

   5. fma-define 99.2%

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

   6. distribute-neg-frac2 99.2%

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

   7. distribute-neg-in 99.2%

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

   8. sub-neg 99.2%

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

   9. distribute-neg-in 99.2%

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

   10. remove-double-neg 99.2%

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

   11. +-commutative 99.2%

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

   12. sub-neg 99.2%

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

   13. metadata-eval 99.2%

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

3. Simplified 99.2%

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

5. Final simplification 99.2%

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

Alternative 2: 88.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{a}{\left(t + 1\right) - z}\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-32}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(-1 + \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ a (- (+ t 1.0) z))))))
   (if (<= z -7.8e-10)
     t_1
     (if (<= z 1.06e-32)
       (- x (* a (/ y (+ t 1.0))))
       (if (<= z 2.6e+45) t_1 (+ x (* a (+ -1.0 (/ y z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (a / ((t + 1.0) - z)));
	double tmp;
	if (z <= -7.8e-10) {
		tmp = t_1;
	} else if (z <= 1.06e-32) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if (z <= 2.6e+45) {
		tmp = t_1;
	} else {
		tmp = x + (a * (-1.0 + (y / 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) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (a / ((t + 1.0d0) - z)))
    if (z <= (-7.8d-10)) then
        tmp = t_1
    else if (z <= 1.06d-32) then
        tmp = x - (a * (y / (t + 1.0d0)))
    else if (z <= 2.6d+45) then
        tmp = t_1
    else
        tmp = x + (a * ((-1.0d0) + (y / z)))
    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 + (z * (a / ((t + 1.0) - z)));
	double tmp;
	if (z <= -7.8e-10) {
		tmp = t_1;
	} else if (z <= 1.06e-32) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if (z <= 2.6e+45) {
		tmp = t_1;
	} else {
		tmp = x + (a * (-1.0 + (y / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (a / ((t + 1.0) - z)))
	tmp = 0
	if z <= -7.8e-10:
		tmp = t_1
	elif z <= 1.06e-32:
		tmp = x - (a * (y / (t + 1.0)))
	elif z <= 2.6e+45:
		tmp = t_1
	else:
		tmp = x + (a * (-1.0 + (y / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(a / Float64(Float64(t + 1.0) - z))))
	tmp = 0.0
	if (z <= -7.8e-10)
		tmp = t_1;
	elseif (z <= 1.06e-32)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	elseif (z <= 2.6e+45)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(a * Float64(-1.0 + Float64(y / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (a / ((t + 1.0) - z)));
	tmp = 0.0;
	if (z <= -7.8e-10)
		tmp = t_1;
	elseif (z <= 1.06e-32)
		tmp = x - (a * (y / (t + 1.0)));
	elseif (z <= 2.6e+45)
		tmp = t_1;
	else
		tmp = x + (a * (-1.0 + (y / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(a / N[(N[(t + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e-10], t$95$1, If[LessEqual[z, 1.06e-32], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+45], t$95$1, N[(x + N[(a * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.7999999999999999e-10 or 1.05999999999999994e-32 < z < 2.60000000000000007e45

   1. Initial program 94.9%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 75.9%

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

      1. mul-1-neg 75.9%

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

      2. *-commutative 75.9%

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

      3. associate--l+ 75.9%

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

      4. +-commutative 75.9%

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

      5. associate-*r/ 86.9%

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

      6. distribute-rgt-neg-in 86.9%

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

      7. distribute-neg-frac 86.9%

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

      8. +-commutative 86.9%

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

      9. associate--l+ 86.9%

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

   7. Simplified 86.9%

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

   if -7.7999999999999999e-10 < z < 1.05999999999999994e-32

   1. Initial program 99.8%

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

      1. associate-/r/ 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in z around 0 94.5%

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

   if 2.60000000000000007e45 < z

   1. Initial program 96.5%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 87.7%

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

      1. associate--l+ 87.7%

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

      2. associate-*r/ 87.7%

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

      3. associate-*r/ 87.7%

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

      4. mul-1-neg 87.7%

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

      5. div-sub 87.7%

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

      6. mul-1-neg 87.7%

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

      7. distribute-lft-out-- 87.7%

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

      8. associate-*r/ 87.7%

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

      9. mul-1-neg 87.7%

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

      10. unsub-neg 87.7%

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

      11. sub-neg 87.7%

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

      12. mul-1-neg 87.7%

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

      13. distribute-lft-in 87.7%

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

      14. metadata-eval 87.7%

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

      15. mul-1-neg 87.7%

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

      16. unsub-neg 87.7%

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

   7. Simplified 87.7%

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

   8. Taylor expanded in y around inf 90.3%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;x + z \cdot \frac{a}{\left(t + 1\right) - z}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-32}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+45}:\\ \;\;\;\;x + z \cdot \frac{a}{\left(t + 1\right) - z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(-1 + \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+66}:\\ \;\;\;\;x - \frac{y - z}{\frac{t}{a}}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-11}:\\ \;\;\;\;x + a \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+34}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot a}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.2e+66)
   (- x (/ (- y z) (/ t a)))
   (if (<= t -6.5e-11)
     (+ x (* a (+ -1.0 (/ y z))))
     (if (<= t 3.1e+34)
       (+ x (/ (* (- y z) a) (+ z -1.0)))
       (+ x (* (/ a t) (- z y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.2e+66) {
		tmp = x - ((y - z) / (t / a));
	} else if (t <= -6.5e-11) {
		tmp = x + (a * (-1.0 + (y / z)));
	} else if (t <= 3.1e+34) {
		tmp = x + (((y - z) * a) / (z + -1.0));
	} else {
		tmp = x + ((a / t) * (z - 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 (t <= (-1.2d+66)) then
        tmp = x - ((y - z) / (t / a))
    else if (t <= (-6.5d-11)) then
        tmp = x + (a * ((-1.0d0) + (y / z)))
    else if (t <= 3.1d+34) then
        tmp = x + (((y - z) * a) / (z + (-1.0d0)))
    else
        tmp = x + ((a / t) * (z - 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 (t <= -1.2e+66) {
		tmp = x - ((y - z) / (t / a));
	} else if (t <= -6.5e-11) {
		tmp = x + (a * (-1.0 + (y / z)));
	} else if (t <= 3.1e+34) {
		tmp = x + (((y - z) * a) / (z + -1.0));
	} else {
		tmp = x + ((a / t) * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.2e+66:
		tmp = x - ((y - z) / (t / a))
	elif t <= -6.5e-11:
		tmp = x + (a * (-1.0 + (y / z)))
	elif t <= 3.1e+34:
		tmp = x + (((y - z) * a) / (z + -1.0))
	else:
		tmp = x + ((a / t) * (z - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.2e+66)
		tmp = Float64(x - Float64(Float64(y - z) / Float64(t / a)));
	elseif (t <= -6.5e-11)
		tmp = Float64(x + Float64(a * Float64(-1.0 + Float64(y / z))));
	elseif (t <= 3.1e+34)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * a) / Float64(z + -1.0)));
	else
		tmp = Float64(x + Float64(Float64(a / t) * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.2e+66)
		tmp = x - ((y - z) / (t / a));
	elseif (t <= -6.5e-11)
		tmp = x + (a * (-1.0 + (y / z)));
	elseif (t <= 3.1e+34)
		tmp = x + (((y - z) * a) / (z + -1.0));
	else
		tmp = x + ((a / t) * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.2e+66], N[(x - N[(N[(y - z), $MachinePrecision] / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.5e-11], N[(x + N[(a * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e+34], N[(x + N[(N[(N[(y - z), $MachinePrecision] * a), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a / t), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.2000000000000001e66

   1. Initial program 95.6%

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

   3. Taylor expanded in t around inf 88.2%

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

   if -1.2000000000000001e66 < t < -6.49999999999999953e-11

   1. Initial program 94.3%

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

      1. associate-/r/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 82.3%

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

      1. associate--l+ 82.3%

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

      2. associate-*r/ 82.3%

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

      3. associate-*r/ 82.3%

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

      4. mul-1-neg 82.3%

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

      5. div-sub 82.3%

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

      6. mul-1-neg 82.3%

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

      7. distribute-lft-out-- 82.3%

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

      8. associate-*r/ 82.3%

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

      9. mul-1-neg 82.3%

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

      10. unsub-neg 82.3%

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

      11. sub-neg 82.3%

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

      12. mul-1-neg 82.3%

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

      13. distribute-lft-in 82.3%

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

      14. metadata-eval 82.3%

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

      15. mul-1-neg 82.3%

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

      16. unsub-neg 82.3%

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

   7. Simplified 82.3%

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

   8. Taylor expanded in y around inf 82.8%

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

   if -6.49999999999999953e-11 < t < 3.09999999999999977e34

   1. Initial program 98.6%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 91.0%

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

   if 3.09999999999999977e34 < t

   1. Initial program 97.7%

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

      1. associate-/r/ 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in t around inf 79.7%

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

      1. *-commutative 79.7%

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

      2. *-un-lft-identity 79.7%

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

      3. times-frac 87.8%

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

   7. Applied egg-rr 87.8%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+66}:\\ \;\;\;\;x - \frac{y - z}{\frac{t}{a}}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-11}:\\ \;\;\;\;x + a \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+34}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot a}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -14.2 \lor \neg \left(z \leq 2.4 \cdot 10^{-5}\right):\\ \;\;\;\;x + a \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -14.2) (not (<= z 2.4e-5)))
   (+ x (* a (+ -1.0 (/ y z))))
   (- x (* a (/ y (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -14.2) || !(z <= 2.4e-5)) {
		tmp = x + (a * (-1.0 + (y / z)));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-14.2d0)) .or. (.not. (z <= 2.4d-5))) then
        tmp = x + (a * ((-1.0d0) + (y / z)))
    else
        tmp = x - (a * (y / (t + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -14.2) || !(z <= 2.4e-5)) {
		tmp = x + (a * (-1.0 + (y / z)));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -14.2) or not (z <= 2.4e-5):
		tmp = x + (a * (-1.0 + (y / z)))
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -14.2) || !(z <= 2.4e-5))
		tmp = Float64(x + Float64(a * Float64(-1.0 + Float64(y / z))));
	else
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -14.2) || ~((z <= 2.4e-5)))
		tmp = x + (a * (-1.0 + (y / z)));
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -14.2], N[Not[LessEqual[z, 2.4e-5]], $MachinePrecision]], N[(x + N[(a * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -14.199999999999999 or 2.4000000000000001e-5 < z

   1. Initial program 95.3%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 80.7%

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

      1. associate--l+ 80.7%

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

      2. associate-*r/ 80.7%

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

      3. associate-*r/ 80.7%

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

      4. mul-1-neg 80.7%

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

      5. div-sub 80.7%

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

      6. mul-1-neg 80.7%

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

      7. distribute-lft-out-- 80.7%

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

      8. associate-*r/ 80.7%

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

      9. mul-1-neg 80.7%

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

      10. unsub-neg 80.7%

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

      11. sub-neg 80.7%

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

      12. mul-1-neg 80.7%

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

      13. distribute-lft-in 80.7%

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

      14. metadata-eval 80.7%

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

      15. mul-1-neg 80.7%

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

      16. unsub-neg 80.7%

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

   7. Simplified 80.7%

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

   8. Taylor expanded in y around inf 82.1%

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

   if -14.199999999999999 < z < 2.4000000000000001e-5

   1. Initial program 99.8%

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

      1. associate-/r/ 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in z around 0 93.2%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -14.2 \lor \neg \left(z \leq 2.4 \cdot 10^{-5}\right):\\ \;\;\;\;x + a \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-25} \lor \neg \left(z \leq 2.4 \cdot 10^{-5}\right):\\ \;\;\;\;x + a \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.5e-25) (not (<= z 2.4e-5)))
   (+ x (* a (+ -1.0 (/ y z))))
   (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.5e-25) || !(z <= 2.4e-5)) {
		tmp = x + (a * (-1.0 + (y / 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 <= (-6.5d-25)) .or. (.not. (z <= 2.4d-5))) then
        tmp = x + (a * ((-1.0d0) + (y / 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 <= -6.5e-25) || !(z <= 2.4e-5)) {
		tmp = x + (a * (-1.0 + (y / z)));
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.5e-25) or not (z <= 2.4e-5):
		tmp = x + (a * (-1.0 + (y / z)))
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.5e-25) || !(z <= 2.4e-5))
		tmp = Float64(x + Float64(a * Float64(-1.0 + Float64(y / 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 <= -6.5e-25) || ~((z <= 2.4e-5)))
		tmp = x + (a * (-1.0 + (y / z)));
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.5e-25], N[Not[LessEqual[z, 2.4e-5]], $MachinePrecision]], N[(x + N[(a * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5e-25 or 2.4000000000000001e-5 < z

   1. Initial program 95.5%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 79.2%

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

      1. associate--l+ 79.2%

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

      2. associate-*r/ 79.2%

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

      3. associate-*r/ 79.2%

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

      4. mul-1-neg 79.2%

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

      5. div-sub 79.2%

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

      6. mul-1-neg 79.2%

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

      7. distribute-lft-out-- 79.2%

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

      8. associate-*r/ 79.2%

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

      9. mul-1-neg 79.2%

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

      10. unsub-neg 79.2%

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

      11. sub-neg 79.2%

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

      12. mul-1-neg 79.2%

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

      13. distribute-lft-in 79.2%

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

      14. metadata-eval 79.2%

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

      15. mul-1-neg 79.2%

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

      16. unsub-neg 79.2%

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

   7. Simplified 79.2%

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

   8. Taylor expanded in y around inf 80.7%

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

   if -6.5e-25 < z < 2.4000000000000001e-5

   1. Initial program 99.8%

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

      1. associate-/r/ 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in t around 0 79.1%

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

   6. Taylor expanded in z around 0 76.2%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-25} \lor \neg \left(z \leq 2.4 \cdot 10^{-5}\right):\\ \;\;\;\;x + a \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-9} \lor \neg \left(z \leq 2.4 \cdot 10^{-5}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.5e-9) (not (<= z 2.4e-5))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.5e-9) || !(z <= 2.4e-5)) {
		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 <= (-7.5d-9)) .or. (.not. (z <= 2.4d-5))) 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 <= -7.5e-9) || !(z <= 2.4e-5)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.5e-9) or not (z <= 2.4e-5):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.5e-9) || !(z <= 2.4e-5))
		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 <= -7.5e-9) || ~((z <= 2.4e-5)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.5e-9], N[Not[LessEqual[z, 2.4e-5]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.49999999999999933e-9 or 2.4000000000000001e-5 < z

   1. Initial program 95.4%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 72.8%

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

   if -7.49999999999999933e-9 < z < 2.4000000000000001e-5

   1. Initial program 99.8%

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

      1. associate-/r/ 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in t around 0 79.6%

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

   6. Taylor expanded in z around 0 76.0%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-9} \lor \neg \left(z \leq 2.4 \cdot 10^{-5}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{-26} \lor \neg \left(z \leq 2.4 \cdot 10^{-5}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.4e-26) (not (<= z 2.4e-5))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.4e-26) || !(z <= 2.4e-5)) {
		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 <= (-9.4d-26)) .or. (.not. (z <= 2.4d-5))) 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 <= -9.4e-26) || !(z <= 2.4e-5)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.4e-26) or not (z <= 2.4e-5):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.4e-26) || !(z <= 2.4e-5))
		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 <= -9.4e-26) || ~((z <= 2.4e-5)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.4e-26], N[Not[LessEqual[z, 2.4e-5]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -9.39999999999999979e-26 or 2.4000000000000001e-5 < z

   1. Initial program 95.5%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 72.0%

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

   if -9.39999999999999979e-26 < z < 2.4000000000000001e-5

   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/ 98.4%

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

      4. distribute-lft-neg-in 98.4%

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

      5. fma-define 98.4%

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

      6. distribute-neg-frac2 98.4%

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

      7. distribute-neg-in 98.4%

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

      8. sub-neg 98.4%

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

      9. distribute-neg-in 98.4%

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

      10. remove-double-neg 98.4%

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

      11. +-commutative 98.4%

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

      12. sub-neg 98.4%

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

      13. metadata-eval 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in t around inf 50.2%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{-26} \lor \neg \left(z \leq 2.4 \cdot 10^{-5}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. associate-/r/ 99.1%

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

3. Simplified 99.1%

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

5. Final simplification 99.1%

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

Alternative 9: 56.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-237}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-175}:\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -3.8e-237) x (if (<= x 4.3e-175) (- a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.8e-237) {
		tmp = x;
	} else if (x <= 4.3e-175) {
		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 (x <= (-3.8d-237)) then
        tmp = x
    else if (x <= 4.3d-175) 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 (x <= -3.8e-237) {
		tmp = x;
	} else if (x <= 4.3e-175) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -3.8e-237:
		tmp = x
	elif x <= 4.3e-175:
		tmp = -a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -3.8e-237)
		tmp = x;
	elseif (x <= 4.3e-175)
		tmp = Float64(-a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -3.8e-237)
		tmp = x;
	elseif (x <= 4.3e-175)
		tmp = -a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -3.8e-237], x, If[LessEqual[x, 4.3e-175], (-a), x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.80000000000000024e-237 or 4.29999999999999998e-175 < x

   1. Initial program 98.9%

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

      1. sub-neg 98.9%

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

      2. +-commutative 98.9%

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

      3. associate-/r/ 99.5%

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

      4. distribute-lft-neg-in 99.5%

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

      5. fma-define 99.5%

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

      6. distribute-neg-frac2 99.5%

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

      7. distribute-neg-in 99.5%

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

      8. sub-neg 99.5%

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

      9. distribute-neg-in 99.5%

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

      10. remove-double-neg 99.5%

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

      11. +-commutative 99.5%

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

      12. sub-neg 99.5%

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

      13. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in t around inf 58.5%

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

   if -3.80000000000000024e-237 < x < 4.29999999999999998e-175

   1. Initial program 92.2%

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

      1. sub-neg 92.2%

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

      2. +-commutative 92.2%

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

      3. associate-/r/ 97.9%

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

      4. distribute-lft-neg-in 97.9%

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

      5. fma-define 97.9%

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

      6. distribute-neg-frac2 97.9%

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

      7. distribute-neg-in 97.9%

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

      8. sub-neg 97.9%

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

      9. distribute-neg-in 97.9%

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

      10. remove-double-neg 97.9%

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

      11. +-commutative 97.9%

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

      12. sub-neg 97.9%

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

      13. metadata-eval 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in a around inf 94.3%

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

      1. div-sub 94.3%

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

   7. Simplified 94.3%

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

   8. Taylor expanded in z around inf 36.8%

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

      1. neg-mul-1 36.8%

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

   10. Simplified 36.8%

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

Alternative 10: 54.3% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. sub-neg 97.6%

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

   2. +-commutative 97.6%

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

   3. associate-/r/ 99.1%

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

   4. distribute-lft-neg-in 99.1%

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

   5. fma-define 99.2%

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

   6. distribute-neg-frac2 99.2%

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

   7. distribute-neg-in 99.2%

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

   8. sub-neg 99.2%

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

   9. distribute-neg-in 99.2%

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

   10. remove-double-neg 99.2%

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

   11. +-commutative 99.2%

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

   12. sub-neg 99.2%

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

   13. metadata-eval 99.2%

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

3. Simplified 99.2%

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

5. Taylor expanded in t around inf 48.3%

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

Developer Target 1: 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 2024137 
(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))))