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

Percentage Accurate: 97.3% → 99.5%

Time: 12.0s

Alternatives: 14

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: 97.3% 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: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) - (t - z))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.0%

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

   1. associate-/r/ 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 71.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y \cdot a}{t}\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+205}:\\ \;\;\;\;x + a \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -3.25:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-119}:\\ \;\;\;\;x - a \cdot \frac{z}{z + -1}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-18}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* y a) t))))
   (if (<= t -3.7e+205)
     (+ x (* a (/ z t)))
     (if (<= t -3.25)
       t_1
       (if (<= t 5e-119)
         (- x (* a (/ z (+ z -1.0))))
         (if (<= t 2.25e-18) (- x (* y a)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y * a) / t);
	double tmp;
	if (t <= -3.7e+205) {
		tmp = x + (a * (z / t));
	} else if (t <= -3.25) {
		tmp = t_1;
	} else if (t <= 5e-119) {
		tmp = x - (a * (z / (z + -1.0)));
	} else if (t <= 2.25e-18) {
		tmp = x - (y * a);
	} else {
		tmp = t_1;
	}
	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 - ((y * a) / t)
    if (t <= (-3.7d+205)) then
        tmp = x + (a * (z / t))
    else if (t <= (-3.25d0)) then
        tmp = t_1
    else if (t <= 5d-119) then
        tmp = x - (a * (z / (z + (-1.0d0))))
    else if (t <= 2.25d-18) then
        tmp = x - (y * a)
    else
        tmp = t_1
    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 - ((y * a) / t);
	double tmp;
	if (t <= -3.7e+205) {
		tmp = x + (a * (z / t));
	} else if (t <= -3.25) {
		tmp = t_1;
	} else if (t <= 5e-119) {
		tmp = x - (a * (z / (z + -1.0)));
	} else if (t <= 2.25e-18) {
		tmp = x - (y * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y * a) / t)
	tmp = 0
	if t <= -3.7e+205:
		tmp = x + (a * (z / t))
	elif t <= -3.25:
		tmp = t_1
	elif t <= 5e-119:
		tmp = x - (a * (z / (z + -1.0)))
	elif t <= 2.25e-18:
		tmp = x - (y * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y * a) / t))
	tmp = 0.0
	if (t <= -3.7e+205)
		tmp = Float64(x + Float64(a * Float64(z / t)));
	elseif (t <= -3.25)
		tmp = t_1;
	elseif (t <= 5e-119)
		tmp = Float64(x - Float64(a * Float64(z / Float64(z + -1.0))));
	elseif (t <= 2.25e-18)
		tmp = Float64(x - Float64(y * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y * a) / t);
	tmp = 0.0;
	if (t <= -3.7e+205)
		tmp = x + (a * (z / t));
	elseif (t <= -3.25)
		tmp = t_1;
	elseif (t <= 5e-119)
		tmp = x - (a * (z / (z + -1.0)));
	elseif (t <= 2.25e-18)
		tmp = x - (y * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.7e+205], N[(x + N[(a * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.25], t$95$1, If[LessEqual[t, 5e-119], N[(x - N[(a * N[(z / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.25e-18], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.69999999999999981e205

   1. Initial program 93.6%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 99.8%

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

   6. Taylor expanded in y around 0 78.4%

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

      1. neg-mul-1 78.4%

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

   8. Simplified 78.4%

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

   if -3.69999999999999981e205 < t < -3.25 or 2.24999999999999997e-18 < t

   1. Initial program 96.5%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 78.4%

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

   6. Taylor expanded in t around inf 77.5%

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

   if -3.25 < t < 4.99999999999999993e-119

   1. Initial program 98.0%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 99.4%

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

   6. Taylor expanded in y around 0 84.0%

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

      1. neg-mul-1 84.0%

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

      2. distribute-neg-frac2 84.0%

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

      3. sub-neg 84.0%

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

      4. distribute-neg-in 84.0%

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

      5. metadata-eval 84.0%

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

      6. remove-double-neg 84.0%

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

   8. Simplified 84.0%

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

   if 4.99999999999999993e-119 < t < 2.24999999999999997e-18

   1. Initial program 99.9%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 65.4%

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

   6. Taylor expanded in t around 0 65.4%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+205}:\\ \;\;\;\;x + a \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -3.25:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-119}:\\ \;\;\;\;x - a \cdot \frac{z}{z + -1}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-18}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{a}{\frac{t}{z - y}}\\ \mathbf{if}\;t \leq -92:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-119}:\\ \;\;\;\;x - a \cdot \frac{z}{z + -1}\\ \mathbf{elif}\;t \leq 2400:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ a (/ t (- z y))))))
   (if (<= t -92.0)
     t_1
     (if (<= t 2.4e-119)
       (- x (* a (/ z (+ z -1.0))))
       (if (<= t 2400.0) (- x (* y a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a / (t / (z - y)));
	double tmp;
	if (t <= -92.0) {
		tmp = t_1;
	} else if (t <= 2.4e-119) {
		tmp = x - (a * (z / (z + -1.0)));
	} else if (t <= 2400.0) {
		tmp = x - (y * a);
	} else {
		tmp = t_1;
	}
	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 + (a / (t / (z - y)))
    if (t <= (-92.0d0)) then
        tmp = t_1
    else if (t <= 2.4d-119) then
        tmp = x - (a * (z / (z + (-1.0d0))))
    else if (t <= 2400.0d0) then
        tmp = x - (y * a)
    else
        tmp = t_1
    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 / (t / (z - y)));
	double tmp;
	if (t <= -92.0) {
		tmp = t_1;
	} else if (t <= 2.4e-119) {
		tmp = x - (a * (z / (z + -1.0)));
	} else if (t <= 2400.0) {
		tmp = x - (y * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a / (t / (z - y)))
	tmp = 0
	if t <= -92.0:
		tmp = t_1
	elif t <= 2.4e-119:
		tmp = x - (a * (z / (z + -1.0)))
	elif t <= 2400.0:
		tmp = x - (y * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a / Float64(t / Float64(z - y))))
	tmp = 0.0
	if (t <= -92.0)
		tmp = t_1;
	elseif (t <= 2.4e-119)
		tmp = Float64(x - Float64(a * Float64(z / Float64(z + -1.0))));
	elseif (t <= 2400.0)
		tmp = Float64(x - Float64(y * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a / (t / (z - y)));
	tmp = 0.0;
	if (t <= -92.0)
		tmp = t_1;
	elseif (t <= 2.4e-119)
		tmp = x - (a * (z / (z + -1.0)));
	elseif (t <= 2400.0)
		tmp = x - (y * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(a / N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -92.0], t$95$1, If[LessEqual[t, 2.4e-119], N[(x - N[(a * N[(z / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2400.0], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -92 or 2400 < t

   1. Initial program 95.6%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in t around inf 89.7%

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

   if -92 < t < 2.40000000000000009e-119

   1. Initial program 98.0%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 99.4%

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

   6. Taylor expanded in y around 0 84.0%

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

      1. neg-mul-1 84.0%

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

      2. distribute-neg-frac2 84.0%

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

      3. sub-neg 84.0%

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

      4. distribute-neg-in 84.0%

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

      5. metadata-eval 84.0%

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

      6. remove-double-neg 84.0%

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

   8. Simplified 84.0%

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

   if 2.40000000000000009e-119 < t < 2400

   1. Initial program 99.9%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 68.4%

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

   6. Taylor expanded in t around 0 68.4%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -92:\\ \;\;\;\;x + \frac{a}{\frac{t}{z - y}}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-119}:\\ \;\;\;\;x - a \cdot \frac{z}{z + -1}\\ \mathbf{elif}\;t \leq 2400:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \frac{z - y}{t}\\ \mathbf{if}\;t \leq -95:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-120}:\\ \;\;\;\;x - a \cdot \frac{z}{z + -1}\\ \mathbf{elif}\;t \leq 520:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* a (/ (- z y) t)))))
   (if (<= t -95.0)
     t_1
     (if (<= t 2.9e-120)
       (- x (* a (/ z (+ z -1.0))))
       (if (<= t 520.0) (- x (* y a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * ((z - y) / t));
	double tmp;
	if (t <= -95.0) {
		tmp = t_1;
	} else if (t <= 2.9e-120) {
		tmp = x - (a * (z / (z + -1.0)));
	} else if (t <= 520.0) {
		tmp = x - (y * a);
	} else {
		tmp = t_1;
	}
	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 + (a * ((z - y) / t))
    if (t <= (-95.0d0)) then
        tmp = t_1
    else if (t <= 2.9d-120) then
        tmp = x - (a * (z / (z + (-1.0d0))))
    else if (t <= 520.0d0) then
        tmp = x - (y * a)
    else
        tmp = t_1
    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 * ((z - y) / t));
	double tmp;
	if (t <= -95.0) {
		tmp = t_1;
	} else if (t <= 2.9e-120) {
		tmp = x - (a * (z / (z + -1.0)));
	} else if (t <= 520.0) {
		tmp = x - (y * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a * ((z - y) / t))
	tmp = 0
	if t <= -95.0:
		tmp = t_1
	elif t <= 2.9e-120:
		tmp = x - (a * (z / (z + -1.0)))
	elif t <= 520.0:
		tmp = x - (y * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a * Float64(Float64(z - y) / t)))
	tmp = 0.0
	if (t <= -95.0)
		tmp = t_1;
	elseif (t <= 2.9e-120)
		tmp = Float64(x - Float64(a * Float64(z / Float64(z + -1.0))));
	elseif (t <= 520.0)
		tmp = Float64(x - Float64(y * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a * ((z - y) / t));
	tmp = 0.0;
	if (t <= -95.0)
		tmp = t_1;
	elseif (t <= 2.9e-120)
		tmp = x - (a * (z / (z + -1.0)));
	elseif (t <= 520.0)
		tmp = x - (y * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -95.0], t$95$1, If[LessEqual[t, 2.9e-120], N[(x - N[(a * N[(z / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 520.0], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -95 or 520 < t

   1. Initial program 95.6%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 89.7%

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

   if -95 < t < 2.9e-120

   1. Initial program 98.0%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 99.4%

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

   6. Taylor expanded in y around 0 84.0%

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

      1. neg-mul-1 84.0%

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

      2. distribute-neg-frac2 84.0%

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

      3. sub-neg 84.0%

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

      4. distribute-neg-in 84.0%

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

      5. metadata-eval 84.0%

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

      6. remove-double-neg 84.0%

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

   8. Simplified 84.0%

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

   if 2.9e-120 < t < 520

   1. Initial program 99.9%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 68.4%

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

   6. Taylor expanded in t around 0 68.4%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -95:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-120}:\\ \;\;\;\;x - a \cdot \frac{z}{z + -1}\\ \mathbf{elif}\;t \leq 520:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+24} \lor \neg \left(t \leq 5 \cdot 10^{+46}\right):\\ \;\;\;\;x - \frac{a}{\frac{t}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.9e+24) (not (<= t 5e+46)))
   (- x (/ a (/ t (- y z))))
   (+ x (* a (/ (- y z) (+ z -1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.9e+24) || !(t <= 5e+46)) {
		tmp = x - (a / (t / (y - z)));
	} else {
		tmp = x + (a * ((y - z) / (z + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.9d+24)) .or. (.not. (t <= 5d+46))) then
        tmp = x - (a / (t / (y - z)))
    else
        tmp = x + (a * ((y - z) / (z + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.9e+24) || !(t <= 5e+46)) {
		tmp = x - (a / (t / (y - z)));
	} else {
		tmp = x + (a * ((y - z) / (z + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.9e+24) or not (t <= 5e+46):
		tmp = x - (a / (t / (y - z)))
	else:
		tmp = x + (a * ((y - z) / (z + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.9e+24) || !(t <= 5e+46))
		tmp = Float64(x - Float64(a / Float64(t / Float64(y - z))));
	else
		tmp = Float64(x + Float64(a * Float64(Float64(y - z) / Float64(z + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.9e+24) || ~((t <= 5e+46)))
		tmp = x - (a / (t / (y - z)));
	else
		tmp = x + (a * ((y - z) / (z + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.9e+24], N[Not[LessEqual[t, 5e+46]], $MachinePrecision]], N[(x - N[(a / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(N[(y - z), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.89999999999999979e24 or 5.0000000000000002e46 < t

   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. Step-by-step derivation

      1. *-commutative 99.8%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in t around inf 92.4%

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

   if -2.89999999999999979e24 < t < 5.0000000000000002e46

   1. Initial program 98.4%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 97.5%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+24} \lor \neg \left(t \leq 5 \cdot 10^{+46}\right):\\ \;\;\;\;x - \frac{a}{\frac{t}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2400000000 \lor \neg \left(z \leq 5.8 \cdot 10^{-10}\right):\\ \;\;\;\;x - \frac{z - y}{\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot a}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2400000000.0) (not (<= z 5.8e-10)))
   (- x (/ (- z y) (/ z a)))
   (+ x (/ (* y a) (- -1.0 t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2400000000.0) || !(z <= 5.8e-10)) {
		tmp = x - ((z - y) / (z / a));
	} else {
		tmp = x + ((y * a) / (-1.0 - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2400000000.0d0)) .or. (.not. (z <= 5.8d-10))) then
        tmp = x - ((z - y) / (z / a))
    else
        tmp = x + ((y * a) / ((-1.0d0) - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2400000000.0) || !(z <= 5.8e-10)) {
		tmp = x - ((z - y) / (z / a));
	} else {
		tmp = x + ((y * a) / (-1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2400000000.0) or not (z <= 5.8e-10):
		tmp = x - ((z - y) / (z / a))
	else:
		tmp = x + ((y * a) / (-1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2400000000.0) || !(z <= 5.8e-10))
		tmp = Float64(x - Float64(Float64(z - y) / Float64(z / a)));
	else
		tmp = Float64(x + Float64(Float64(y * a) / Float64(-1.0 - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2400000000.0) || ~((z <= 5.8e-10)))
		tmp = x - ((z - y) / (z / a));
	else
		tmp = x + ((y * a) / (-1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2400000000.0], N[Not[LessEqual[z, 5.8e-10]], $MachinePrecision]], N[(x - N[(N[(z - y), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * a), $MachinePrecision] / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4e9 or 5.79999999999999962e-10 < z

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf 80.5%

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

      1. associate-*r/ 80.5%

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

      2. neg-mul-1 80.5%

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

   5. Simplified 80.5%

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

   if -2.4e9 < z < 5.79999999999999962e-10

   1. Initial program 98.4%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 90.4%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2400000000 \lor \neg \left(z \leq 5.8 \cdot 10^{-10}\right):\\ \;\;\;\;x - \frac{z - y}{\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot a}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2400000000:\\ \;\;\;\;x - \left(y + z\right) \cdot \frac{a}{z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{y \cdot a}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{a}{z}\right) - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2400000000.0)
   (- x (* (+ y z) (/ a z)))
   (if (<= z 5.8e-10) (+ x (/ (* y a) (- -1.0 t))) (- (- x (/ a z)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2400000000.0) {
		tmp = x - ((y + z) * (a / z));
	} else if (z <= 5.8e-10) {
		tmp = x + ((y * a) / (-1.0 - t));
	} else {
		tmp = (x - (a / z)) - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2400000000.0d0)) then
        tmp = x - ((y + z) * (a / z))
    else if (z <= 5.8d-10) then
        tmp = x + ((y * a) / ((-1.0d0) - t))
    else
        tmp = (x - (a / z)) - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2400000000.0) {
		tmp = x - ((y + z) * (a / z));
	} else if (z <= 5.8e-10) {
		tmp = x + ((y * a) / (-1.0 - t));
	} else {
		tmp = (x - (a / z)) - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2400000000.0:
		tmp = x - ((y + z) * (a / z))
	elif z <= 5.8e-10:
		tmp = x + ((y * a) / (-1.0 - t))
	else:
		tmp = (x - (a / z)) - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2400000000.0)
		tmp = Float64(x - Float64(Float64(y + z) * Float64(a / z)));
	elseif (z <= 5.8e-10)
		tmp = Float64(x + Float64(Float64(y * a) / Float64(-1.0 - t)));
	else
		tmp = Float64(Float64(x - Float64(a / z)) - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2400000000.0)
		tmp = x - ((y + z) * (a / z));
	elseif (z <= 5.8e-10)
		tmp = x + ((y * a) / (-1.0 - t));
	else
		tmp = (x - (a / z)) - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2400000000.0], N[(x - N[(N[(y + z), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-10], N[(x + N[(N[(y * a), $MachinePrecision] / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(a / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4e9

   1. Initial program 94.2%

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

   3. Taylor expanded in z around inf 73.5%

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

      1. associate-*r/ 73.5%

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

      2. neg-mul-1 73.5%

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

   5. Simplified 73.5%

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

      1. div-inv 73.4%

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

      2. sub-neg 73.4%

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

      3. add-sqr-sqrt 73.3%

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

      4. sqrt-unprod 29.8%

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

      5. sqr-neg 29.8%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 50.5%

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

      8. clear-num 50.6%

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

      9. add-sqr-sqrt 50.5%

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

      10. sqrt-unprod 48.9%

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

      11. sqr-neg 48.9%

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

      12. sqrt-unprod 0.0%

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

      13. add-sqr-sqrt 71.0%

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

   7. Applied egg-rr 71.0%

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

   if -2.4e9 < z < 5.79999999999999962e-10

   1. Initial program 98.4%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 90.4%

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

   if 5.79999999999999962e-10 < z

   1. Initial program 96.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 90.0%

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

   6. Taylor expanded in y around 0 84.6%

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

      1. neg-mul-1 84.6%

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

      2. distribute-neg-frac2 84.6%

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

      3. sub-neg 84.6%

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

      4. distribute-neg-in 84.6%

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

      5. metadata-eval 84.6%

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

      6. remove-double-neg 84.6%

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

   8. Simplified 84.6%

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

   9. Taylor expanded in z around inf 84.7%

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

       1. mul-1-neg 84.7%

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

       2. unsub-neg 84.7%

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

   11. Simplified 84.7%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2400000000:\\ \;\;\;\;x - \left(y + z\right) \cdot \frac{a}{z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{y \cdot a}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{a}{z}\right) - a\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2200000000 \lor \neg \left(z \leq 3.5 \cdot 10^{-12}\right):\\ \;\;\;\;\left(x - \frac{a}{z}\right) - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2200000000.0) (not (<= z 3.5e-12)))
   (- (- x (/ a z)) a)
   (- x (/ (* y a) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2200000000.0) || !(z <= 3.5e-12)) {
		tmp = (x - (a / z)) - a;
	} else {
		tmp = x - ((y * a) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2200000000.0d0)) .or. (.not. (z <= 3.5d-12))) then
        tmp = (x - (a / z)) - a
    else
        tmp = x - ((y * a) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2200000000.0) || !(z <= 3.5e-12)) {
		tmp = (x - (a / z)) - a;
	} else {
		tmp = x - ((y * a) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2200000000.0) or not (z <= 3.5e-12):
		tmp = (x - (a / z)) - a
	else:
		tmp = x - ((y * a) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2200000000.0) || !(z <= 3.5e-12))
		tmp = Float64(Float64(x - Float64(a / z)) - a);
	else
		tmp = Float64(x - Float64(Float64(y * a) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2200000000.0) || ~((z <= 3.5e-12)))
		tmp = (x - (a / z)) - a;
	else
		tmp = x - ((y * a) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2200000000.0], N[Not[LessEqual[z, 3.5e-12]], $MachinePrecision]], N[(N[(x - N[(a / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision], N[(x - N[(N[(y * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2e9 or 3.5e-12 < z

   1. Initial program 95.7%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 82.7%

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

   6. Taylor expanded in y around 0 78.1%

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

      1. neg-mul-1 78.1%

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

      2. distribute-neg-frac2 78.1%

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

      3. sub-neg 78.1%

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

      4. distribute-neg-in 78.1%

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

      5. metadata-eval 78.1%

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

      6. remove-double-neg 78.1%

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

   8. Simplified 78.1%

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

   9. Taylor expanded in z around inf 78.1%

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

       1. mul-1-neg 78.1%

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

       2. unsub-neg 78.1%

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

   11. Simplified 78.1%

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

   if -2.2e9 < z < 3.5e-12

   1. Initial program 98.4%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 90.4%

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

   6. Taylor expanded in t around inf 71.0%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2200000000 \lor \neg \left(z \leq 3.5 \cdot 10^{-12}\right):\\ \;\;\;\;\left(x - \frac{a}{z}\right) - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1500000000 \lor \neg \left(z \leq 5.8 \cdot 10^{-10}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1500000000.0) (not (<= z 5.8e-10)))
   (- x a)
   (- x (/ (* y a) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1500000000.0) || !(z <= 5.8e-10)) {
		tmp = x - a;
	} else {
		tmp = x - ((y * a) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1500000000.0d0)) .or. (.not. (z <= 5.8d-10))) then
        tmp = x - a
    else
        tmp = x - ((y * a) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1500000000.0) || !(z <= 5.8e-10)) {
		tmp = x - a;
	} else {
		tmp = x - ((y * a) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1500000000.0) or not (z <= 5.8e-10):
		tmp = x - a
	else:
		tmp = x - ((y * a) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1500000000.0) || !(z <= 5.8e-10))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(Float64(y * a) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1500000000.0) || ~((z <= 5.8e-10)))
		tmp = x - a;
	else
		tmp = x - ((y * a) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1500000000.0], N[Not[LessEqual[z, 5.8e-10]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(N[(y * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5e9 or 5.79999999999999962e-10 < z

   1. Initial program 95.7%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 77.9%

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

   if -1.5e9 < z < 5.79999999999999962e-10

   1. Initial program 98.4%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 90.4%

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

   6. Taylor expanded in t around inf 71.0%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1500000000 \lor \neg \left(z \leq 5.8 \cdot 10^{-10}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1600000000:\\ \;\;\;\;x - \left(y + z\right) \cdot \frac{a}{z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{a}{z}\right) - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1600000000.0)
   (- x (* (+ y z) (/ a z)))
   (if (<= z 5.8e-10) (- x (/ (* y a) t)) (- (- x (/ a z)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1600000000.0) {
		tmp = x - ((y + z) * (a / z));
	} else if (z <= 5.8e-10) {
		tmp = x - ((y * a) / t);
	} else {
		tmp = (x - (a / z)) - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1600000000.0d0)) then
        tmp = x - ((y + z) * (a / z))
    else if (z <= 5.8d-10) then
        tmp = x - ((y * a) / t)
    else
        tmp = (x - (a / z)) - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1600000000.0) {
		tmp = x - ((y + z) * (a / z));
	} else if (z <= 5.8e-10) {
		tmp = x - ((y * a) / t);
	} else {
		tmp = (x - (a / z)) - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1600000000.0:
		tmp = x - ((y + z) * (a / z))
	elif z <= 5.8e-10:
		tmp = x - ((y * a) / t)
	else:
		tmp = (x - (a / z)) - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1600000000.0)
		tmp = Float64(x - Float64(Float64(y + z) * Float64(a / z)));
	elseif (z <= 5.8e-10)
		tmp = Float64(x - Float64(Float64(y * a) / t));
	else
		tmp = Float64(Float64(x - Float64(a / z)) - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1600000000.0)
		tmp = x - ((y + z) * (a / z));
	elseif (z <= 5.8e-10)
		tmp = x - ((y * a) / t);
	else
		tmp = (x - (a / z)) - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1600000000.0], N[(x - N[(N[(y + z), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-10], N[(x - N[(N[(y * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(a / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6e9

   1. Initial program 94.2%

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

   3. Taylor expanded in z around inf 73.5%

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

      1. associate-*r/ 73.5%

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

      2. neg-mul-1 73.5%

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

   5. Simplified 73.5%

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

      1. div-inv 73.4%

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

      2. sub-neg 73.4%

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

      3. add-sqr-sqrt 73.3%

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

      4. sqrt-unprod 29.8%

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

      5. sqr-neg 29.8%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 50.5%

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

      8. clear-num 50.6%

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

      9. add-sqr-sqrt 50.5%

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

      10. sqrt-unprod 48.9%

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

      11. sqr-neg 48.9%

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

      12. sqrt-unprod 0.0%

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

      13. add-sqr-sqrt 71.0%

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

   7. Applied egg-rr 71.0%

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

   if -1.6e9 < z < 5.79999999999999962e-10

   1. Initial program 98.4%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 90.4%

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

   6. Taylor expanded in t around inf 71.0%

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

   if 5.79999999999999962e-10 < z

   1. Initial program 96.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 90.0%

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

   6. Taylor expanded in y around 0 84.6%

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

      1. neg-mul-1 84.6%

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

      2. distribute-neg-frac2 84.6%

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

      3. sub-neg 84.6%

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

      4. distribute-neg-in 84.6%

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

      5. metadata-eval 84.6%

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

      6. remove-double-neg 84.6%

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

   8. Simplified 84.6%

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

   9. Taylor expanded in z around inf 84.7%

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

       1. mul-1-neg 84.7%

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

       2. unsub-neg 84.7%

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

   11. Simplified 84.7%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1600000000:\\ \;\;\;\;x - \left(y + z\right) \cdot \frac{a}{z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{a}{z}\right) - a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 73.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -61000 \lor \neg \left(z \leq 2.25 \cdot 10^{-14}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -61000.0) (not (<= z 2.25e-14))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -61000.0) || !(z <= 2.25e-14)) {
		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 <= (-61000.0d0)) .or. (.not. (z <= 2.25d-14))) 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 <= -61000.0) || !(z <= 2.25e-14)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -61000.0) or not (z <= 2.25e-14):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -61000.0) || !(z <= 2.25e-14))
		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 <= -61000.0) || ~((z <= 2.25e-14)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -61000.0], N[Not[LessEqual[z, 2.25e-14]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -61000 or 2.2499999999999999e-14 < z

   1. Initial program 95.7%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 77.0%

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

   if -61000 < z < 2.2499999999999999e-14

   1. Initial program 98.4%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 90.2%

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

   6. Taylor expanded in t around 0 66.4%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -61000 \lor \neg \left(z \leq 2.25 \cdot 10^{-14}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1400000000 \lor \neg \left(z \leq 2.25 \cdot 10^{-14}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1400000000.0) (not (<= z 2.25e-14))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1400000000.0) || !(z <= 2.25e-14)) {
		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 <= (-1400000000.0d0)) .or. (.not. (z <= 2.25d-14))) 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 <= -1400000000.0) || !(z <= 2.25e-14)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1400000000.0) or not (z <= 2.25e-14):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1400000000.0) || !(z <= 2.25e-14))
		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 <= -1400000000.0) || ~((z <= 2.25e-14)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1400000000.0], N[Not[LessEqual[z, 2.25e-14]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e9 or 2.2499999999999999e-14 < z

   1. Initial program 95.7%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 77.4%

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

   if -1.4e9 < z < 2.2499999999999999e-14

   1. Initial program 98.4%

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

      1. sub-neg 98.4%

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

      2. +-commutative 98.4%

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

      3. associate-/r/ 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

      5. associate-*l/ 94.7%

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

      6. associate-/l* 98.4%

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

      7. fma-define 98.4%

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

      8. distribute-frac-neg 98.4%

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

      9. distribute-neg-frac2 98.4%

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

      10. distribute-neg-in 98.4%

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

      11. sub-neg 98.4%

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

      12. distribute-neg-in 98.4%

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

      13. remove-double-neg 98.4%

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

      14. +-commutative 98.4%

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

      15. sub-neg 98.4%

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

      16. metadata-eval 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in a around 0 61.0%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1400000000 \lor \neg \left(z \leq 2.25 \cdot 10^{-14}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.55 \cdot 10^{+120}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= z 2.55e+120) x (- a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 2.55e+120) {
		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 (z <= 2.55d+120) 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 (z <= 2.55e+120) {
		tmp = x;
	} else {
		tmp = -a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 2.55e+120:
		tmp = x
	else:
		tmp = -a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 2.55e+120)
		tmp = x;
	else
		tmp = Float64(-a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 2.55e+120)
		tmp = x;
	else
		tmp = -a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 2.55e+120], x, (-a)]

Derivation

1. Split input into 2 regimes

2. if z < 2.55000000000000014e120

   1. Initial program 97.4%

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

      1. sub-neg 97.4%

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

      2. +-commutative 97.4%

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

      3. associate-/r/ 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

      5. associate-*l/ 87.4%

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

      6. associate-/l* 97.5%

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

      7. fma-define 97.5%

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

      8. distribute-frac-neg 97.5%

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

      9. distribute-neg-frac2 97.5%

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

      10. distribute-neg-in 97.5%

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

      11. sub-neg 97.5%

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

      12. distribute-neg-in 97.5%

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

      13. remove-double-neg 97.5%

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

      14. +-commutative 97.5%

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

      15. sub-neg 97.5%

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

      16. metadata-eval 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in a around 0 56.3%

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

   if 2.55000000000000014e120 < 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/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 95.7%

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

   6. Taylor expanded in x around 0 59.0%

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

      1. neg-mul-1 59.0%

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

   8. Simplified 59.0%

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

Alternative 14: 54.1% 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 97.0%

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

   1. sub-neg 97.0%

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

   2. +-commutative 97.0%

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

   3. associate-/r/ 99.9%

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

   4. distribute-rgt-neg-in 99.9%

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

   5. associate-*l/ 83.0%

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

   6. associate-/l* 97.2%

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

   7. fma-define 97.2%

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

   8. distribute-frac-neg 97.2%

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

   9. distribute-neg-frac2 97.2%

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

   10. distribute-neg-in 97.2%

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

   11. sub-neg 97.2%

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

   12. distribute-neg-in 97.2%

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

   13. remove-double-neg 97.2%

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

   14. +-commutative 97.2%

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

   15. sub-neg 97.2%

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

   16. metadata-eval 97.2%

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

3. Simplified 97.2%

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

5. Taylor expanded in a around 0 52.9%

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

Developer Target 1: 99.5% 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 2024186 
(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))))