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

Percentage Accurate: 97.3% → 99.7%

Time: 11.2s

Alternatives: 11

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: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. associate-/r/ 99.5%

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

3. Simplified 99.5%

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

5. Final simplification 99.5%

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

Alternative 2: 70.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ t_2 := x - \frac{a}{\frac{t}{y}}\\ \mathbf{if}\;t \leq -600:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -5.7 \cdot 10^{-196}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-190}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 10^{-44}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))) (t_2 (- x (/ a (/ t y)))))
   (if (<= t -600.0)
     t_2
     (if (<= t -5.7e-196)
       (- x a)
       (if (<= t 2.4e-190)
         t_1
         (if (<= t 1e-44) (- x a) (if (<= t 1.05e-32) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double t_2 = x - (a / (t / y));
	double tmp;
	if (t <= -600.0) {
		tmp = t_2;
	} else if (t <= -5.7e-196) {
		tmp = x - a;
	} else if (t <= 2.4e-190) {
		tmp = t_1;
	} else if (t <= 1e-44) {
		tmp = x - a;
	} else if (t <= 1.05e-32) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (y * a)
    t_2 = x - (a / (t / y))
    if (t <= (-600.0d0)) then
        tmp = t_2
    else if (t <= (-5.7d-196)) then
        tmp = x - a
    else if (t <= 2.4d-190) then
        tmp = t_1
    else if (t <= 1d-44) then
        tmp = x - a
    else if (t <= 1.05d-32) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double t_2 = x - (a / (t / y));
	double tmp;
	if (t <= -600.0) {
		tmp = t_2;
	} else if (t <= -5.7e-196) {
		tmp = x - a;
	} else if (t <= 2.4e-190) {
		tmp = t_1;
	} else if (t <= 1e-44) {
		tmp = x - a;
	} else if (t <= 1.05e-32) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * a)
	t_2 = x - (a / (t / y))
	tmp = 0
	if t <= -600.0:
		tmp = t_2
	elif t <= -5.7e-196:
		tmp = x - a
	elif t <= 2.4e-190:
		tmp = t_1
	elif t <= 1e-44:
		tmp = x - a
	elif t <= 1.05e-32:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * a))
	t_2 = Float64(x - Float64(a / Float64(t / y)))
	tmp = 0.0
	if (t <= -600.0)
		tmp = t_2;
	elseif (t <= -5.7e-196)
		tmp = Float64(x - a);
	elseif (t <= 2.4e-190)
		tmp = t_1;
	elseif (t <= 1e-44)
		tmp = Float64(x - a);
	elseif (t <= 1.05e-32)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * a);
	t_2 = x - (a / (t / y));
	tmp = 0.0;
	if (t <= -600.0)
		tmp = t_2;
	elseif (t <= -5.7e-196)
		tmp = x - a;
	elseif (t <= 2.4e-190)
		tmp = t_1;
	elseif (t <= 1e-44)
		tmp = x - a;
	elseif (t <= 1.05e-32)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -600.0], t$95$2, If[LessEqual[t, -5.7e-196], N[(x - a), $MachinePrecision], If[LessEqual[t, 2.4e-190], t$95$1, If[LessEqual[t, 1e-44], N[(x - a), $MachinePrecision], If[LessEqual[t, 1.05e-32], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -600 or 1.05e-32 < t

   1. Initial program 95.2%

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

      1. associate-/r/ 99.2%

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

   3. Simplified 99.2%

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

      1. *-commutative 99.2%

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

      2. clear-num 99.2%

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

      3. un-div-inv 99.2%

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

   6. Applied egg-rr 99.2%

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

   7. Taylor expanded in z around 0 87.9%

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

   8. Taylor expanded in t around inf 87.2%

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

   if -600 < t < -5.7000000000000002e-196 or 2.4e-190 < t < 9.99999999999999953e-45

   1. Initial program 98.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 68.2%

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

   if -5.7000000000000002e-196 < t < 2.4e-190 or 9.99999999999999953e-45 < t < 1.05e-32

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 99.9%

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

   4. Taylor expanded in z around 0 82.4%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -600:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -5.7 \cdot 10^{-196}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-190}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 10^{-44}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-32}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \frac{z}{1 - z}\\ t_2 := x - \frac{a}{\frac{t}{y}}\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-197}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-190}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* a (/ z (- 1.0 z))))) (t_2 (- x (/ a (/ t y)))))
   (if (<= t -4.4e+34)
     t_2
     (if (<= t -1.95e-197)
       t_1
       (if (<= t 3.7e-190) (- x (* y a)) (if (<= t 2.8e-37) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * (z / (1.0 - z)));
	double t_2 = x - (a / (t / y));
	double tmp;
	if (t <= -4.4e+34) {
		tmp = t_2;
	} else if (t <= -1.95e-197) {
		tmp = t_1;
	} else if (t <= 3.7e-190) {
		tmp = x - (y * a);
	} else if (t <= 2.8e-37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (a * (z / (1.0d0 - z)))
    t_2 = x - (a / (t / y))
    if (t <= (-4.4d+34)) then
        tmp = t_2
    else if (t <= (-1.95d-197)) then
        tmp = t_1
    else if (t <= 3.7d-190) then
        tmp = x - (y * a)
    else if (t <= 2.8d-37) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * (z / (1.0 - z)));
	double t_2 = x - (a / (t / y));
	double tmp;
	if (t <= -4.4e+34) {
		tmp = t_2;
	} else if (t <= -1.95e-197) {
		tmp = t_1;
	} else if (t <= 3.7e-190) {
		tmp = x - (y * a);
	} else if (t <= 2.8e-37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a * (z / (1.0 - z)))
	t_2 = x - (a / (t / y))
	tmp = 0
	if t <= -4.4e+34:
		tmp = t_2
	elif t <= -1.95e-197:
		tmp = t_1
	elif t <= 3.7e-190:
		tmp = x - (y * a)
	elif t <= 2.8e-37:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a * Float64(z / Float64(1.0 - z))))
	t_2 = Float64(x - Float64(a / Float64(t / y)))
	tmp = 0.0
	if (t <= -4.4e+34)
		tmp = t_2;
	elseif (t <= -1.95e-197)
		tmp = t_1;
	elseif (t <= 3.7e-190)
		tmp = Float64(x - Float64(y * a));
	elseif (t <= 2.8e-37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a * (z / (1.0 - z)));
	t_2 = x - (a / (t / y));
	tmp = 0.0;
	if (t <= -4.4e+34)
		tmp = t_2;
	elseif (t <= -1.95e-197)
		tmp = t_1;
	elseif (t <= 3.7e-190)
		tmp = x - (y * a);
	elseif (t <= 2.8e-37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(a * N[(z / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.4e+34], t$95$2, If[LessEqual[t, -1.95e-197], t$95$1, If[LessEqual[t, 3.7e-190], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e-37], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.4000000000000005e34 or 2.8000000000000001e-37 < 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/ 99.2%

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

   3. Simplified 99.2%

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

      1. *-commutative 99.2%

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

      2. clear-num 99.2%

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

      3. un-div-inv 99.2%

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

   6. Applied egg-rr 99.2%

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

   7. Taylor expanded in z around 0 88.7%

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

   8. Taylor expanded in t around inf 87.8%

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

   if -4.4000000000000005e34 < t < -1.95e-197 or 3.7000000000000002e-190 < t < 2.8000000000000001e-37

   1. Initial program 97.1%

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

   3. Taylor expanded in t around 0 95.7%

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

   4. Taylor expanded in y around 0 67.7%

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

      1. sub-neg 67.7%

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

      2. mul-1-neg 67.7%

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

      3. remove-double-neg 67.7%

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

      4. associate-/l* 79.5%

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

   6. Simplified 79.5%

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

   if -1.95e-197 < t < 3.7000000000000002e-190

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 99.9%

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

   4. Taylor expanded in z around 0 81.1%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+34}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-197}:\\ \;\;\;\;x + a \cdot \frac{z}{1 - z}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-190}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-37}:\\ \;\;\;\;x + a \cdot \frac{z}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+38} \lor \neg \left(t \leq 11500000000\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{1 - z}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.3e+38) (not (<= t 11500000000.0)))
   (+ x (* a (/ (- z y) t)))
   (+ x (/ (- z y) (/ (- 1.0 z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.3e+38) || !(t <= 11500000000.0)) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x + ((z - y) / ((1.0 - 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 ((t <= (-2.3d+38)) .or. (.not. (t <= 11500000000.0d0))) then
        tmp = x + (a * ((z - y) / t))
    else
        tmp = x + ((z - y) / ((1.0d0 - 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 ((t <= -2.3e+38) || !(t <= 11500000000.0)) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x + ((z - y) / ((1.0 - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.3e+38) or not (t <= 11500000000.0):
		tmp = x + (a * ((z - y) / t))
	else:
		tmp = x + ((z - y) / ((1.0 - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.3e+38) || !(t <= 11500000000.0))
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	else
		tmp = Float64(x + Float64(Float64(z - y) / Float64(Float64(1.0 - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.3e+38) || ~((t <= 11500000000.0)))
		tmp = x + (a * ((z - y) / t));
	else
		tmp = x + ((z - y) / ((1.0 - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.3e+38], N[Not[LessEqual[t, 11500000000.0]], $MachinePrecision]], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - y), $MachinePrecision] / N[(N[(1.0 - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.3000000000000001e38 or 1.15e10 < t

   1. Initial program 95.3%

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

      1. associate-/r/ 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in t around inf 92.1%

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

   if -2.3000000000000001e38 < t < 1.15e10

   1. Initial program 98.4%

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

   3. Taylor expanded in t around 0 97.7%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+38} \lor \neg \left(t \leq 11500000000\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{1 - z}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+44} \lor \neg \left(z \leq 1.1 \cdot 10^{+14}\right):\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.3e+44) (not (<= z 1.1e+14)))
   (+ x (- (* a (/ y z)) a))
   (+ x (* a (/ y (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.3e+44) || !(z <= 1.1e+14)) {
		tmp = x + ((a * (y / z)) - a);
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.3d+44)) .or. (.not. (z <= 1.1d+14))) then
        tmp = x + ((a * (y / z)) - a)
    else
        tmp = x + (a * (y / ((-1.0d0) - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.3e+44) || !(z <= 1.1e+14)) {
		tmp = x + ((a * (y / z)) - a);
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.3e+44) or not (z <= 1.1e+14):
		tmp = x + ((a * (y / z)) - a)
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.3e+44) || !(z <= 1.1e+14))
		tmp = Float64(x + Float64(Float64(a * Float64(y / z)) - a));
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.3e+44) || ~((z <= 1.1e+14)))
		tmp = x + ((a * (y / z)) - a);
	else
		tmp = x + (a * (y / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.3e+44], N[Not[LessEqual[z, 1.1e+14]], $MachinePrecision]], N[(x + N[(N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e44 or 1.1e14 < z

   1. Initial program 94.2%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 94.8%

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

      1. mul-1-neg 94.8%

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

   7. Simplified 94.8%

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

   8. Taylor expanded in y around 0 88.3%

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

      1. mul-1-neg 88.3%

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

      2. unsub-neg 88.3%

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

      3. associate-/l* 94.8%

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

   10. Simplified 94.8%

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

   if -1.3e44 < z < 1.1e14

   1. Initial program 99.1%

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

      1. associate-/r/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around 0 92.3%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+44} \lor \neg \left(z \leq 1.1 \cdot 10^{+14}\right):\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+43} \lor \neg \left(z \leq 440000000000\right):\\ \;\;\;\;x + \left(\frac{a}{\frac{z}{y}} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.1e+43) (not (<= z 440000000000.0)))
   (+ x (- (/ a (/ z y)) a))
   (+ x (* a (/ y (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.1e+43) || !(z <= 440000000000.0)) {
		tmp = x + ((a / (z / y)) - a);
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.1d+43)) .or. (.not. (z <= 440000000000.0d0))) then
        tmp = x + ((a / (z / y)) - a)
    else
        tmp = x + (a * (y / ((-1.0d0) - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.1e+43) || !(z <= 440000000000.0)) {
		tmp = x + ((a / (z / y)) - a);
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.1e+43) or not (z <= 440000000000.0):
		tmp = x + ((a / (z / y)) - a)
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.1e+43) || !(z <= 440000000000.0))
		tmp = Float64(x + Float64(Float64(a / Float64(z / y)) - a));
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.1e+43) || ~((z <= 440000000000.0)))
		tmp = x + ((a / (z / y)) - a);
	else
		tmp = x + (a * (y / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.1e+43], N[Not[LessEqual[z, 440000000000.0]], $MachinePrecision]], N[(x + N[(N[(a / N[(z / y), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.10000000000000002e43 or 4.4e11 < z

   1. Initial program 94.2%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 94.8%

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

      1. mul-1-neg 94.8%

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

   7. Simplified 94.8%

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

   8. Taylor expanded in y around 0 88.3%

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

      1. mul-1-neg 88.3%

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

      2. unsub-neg 88.3%

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

      3. associate-/l* 94.8%

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

   10. Simplified 94.8%

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

   11. Taylor expanded in a around 0 88.3%

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

       1. associate-*l/ 94.3%

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

       2. associate-/r/ 94.8%

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

   13. Simplified 94.8%

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

   if -2.10000000000000002e43 < z < 4.4e11

   1. Initial program 99.1%

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

      1. associate-/r/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around 0 92.3%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+43} \lor \neg \left(z \leq 440000000000\right):\\ \;\;\;\;x + \left(\frac{a}{\frac{z}{y}} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+121}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-11}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.2e+121)
   (- x a)
   (if (<= z 1.95e-11)
     (+ x (* a (/ y (- -1.0 t))))
     (+ x (* a (/ z (- 1.0 z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e+121) {
		tmp = x - a;
	} else if (z <= 1.95e-11) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x + (a * (z / (1.0 - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.2d+121)) then
        tmp = x - a
    else if (z <= 1.95d-11) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else
        tmp = x + (a * (z / (1.0d0 - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e+121) {
		tmp = x - a;
	} else if (z <= 1.95e-11) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x + (a * (z / (1.0 - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.2e+121:
		tmp = x - a
	elif z <= 1.95e-11:
		tmp = x + (a * (y / (-1.0 - t)))
	else:
		tmp = x + (a * (z / (1.0 - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.2e+121)
		tmp = Float64(x - a);
	elseif (z <= 1.95e-11)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	else
		tmp = Float64(x + Float64(a * Float64(z / Float64(1.0 - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.2e+121)
		tmp = x - a;
	elseif (z <= 1.95e-11)
		tmp = x + (a * (y / (-1.0 - t)));
	else
		tmp = x + (a * (z / (1.0 - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.2e+121], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.95e-11], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(z / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.1999999999999998e121

   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 inf 94.4%

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

   if -5.1999999999999998e121 < z < 1.95000000000000005e-11

   1. Initial program 99.2%

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

      1. associate-/r/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 91.4%

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

   if 1.95000000000000005e-11 < z

   1. Initial program 92.1%

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

   3. Taylor expanded in t around 0 90.4%

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

   4. Taylor expanded in y around 0 68.9%

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

      1. sub-neg 68.9%

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

      2. mul-1-neg 68.9%

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

      3. remove-double-neg 68.9%

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

      4. associate-/l* 83.9%

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

   6. Simplified 83.9%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+121}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-11}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+33} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.1e+33) (not (<= z 1.0))) (- x a) (+ x (* z a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.1e+33) || !(z <= 1.0)) {
		tmp = x - a;
	} else {
		tmp = x + (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 <= (-3.1d+33)) .or. (.not. (z <= 1.0d0))) then
        tmp = x - a
    else
        tmp = x + (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 <= -3.1e+33) || !(z <= 1.0)) {
		tmp = x - a;
	} else {
		tmp = x + (z * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.1e+33) or not (z <= 1.0):
		tmp = x - a
	else:
		tmp = x + (z * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.1e+33) || !(z <= 1.0))
		tmp = Float64(x - a);
	else
		tmp = Float64(x + Float64(z * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.1e+33) || ~((z <= 1.0)))
		tmp = x - a;
	else
		tmp = x + (z * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.1e+33], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x + N[(z * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1e33 or 1 < z

   1. Initial program 94.4%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 82.0%

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

   if -3.1e33 < z < 1

   1. Initial program 99.1%

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

   3. Taylor expanded in t around 0 73.1%

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

   4. Taylor expanded in y around 0 63.7%

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

      1. sub-neg 63.7%

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

      2. mul-1-neg 63.7%

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

      3. remove-double-neg 63.7%

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

      4. associate-/l* 63.0%

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

   6. Simplified 63.0%

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

   7. Taylor expanded in z around 0 63.1%

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

      1. +-commutative 63.1%

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

   9. Simplified 63.1%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+33} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+121} \lor \neg \left(z \leq 3.6 \cdot 10^{-5}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.3e+121) (not (<= z 3.6e-5))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.3e+121) || !(z <= 3.6e-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 <= (-3.3d+121)) .or. (.not. (z <= 3.6d-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 <= -3.3e+121) || !(z <= 3.6e-5)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.3e+121) or not (z <= 3.6e-5):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.3e+121) || !(z <= 3.6e-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 <= -3.3e+121) || ~((z <= 3.6e-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, -3.3e+121], N[Not[LessEqual[z, 3.6e-5]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.29999999999999979e121 or 3.60000000000000009e-5 < z

   1. Initial program 93.2%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 86.7%

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

   if -3.29999999999999979e121 < z < 3.60000000000000009e-5

   1. Initial program 99.2%

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

   3. Taylor expanded in t around 0 74.7%

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

   4. Taylor expanded in z around 0 68.8%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+121} \lor \neg \left(z \leq 3.6 \cdot 10^{-5}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+66} \lor \neg \left(z \leq 54\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5e+66) (not (<= z 54.0))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5e+66) || !(z <= 54.0)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5d+66)) .or. (.not. (z <= 54.0d0))) then
        tmp = x - a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5e+66) || !(z <= 54.0)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5e+66) or not (z <= 54.0):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5e+66) || !(z <= 54.0))
		tmp = Float64(x - a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5e+66) || ~((z <= 54.0)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5e+66], N[Not[LessEqual[z, 54.0]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.99999999999999991e66 or 54 < z

   1. Initial program 93.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 84.5%

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

   if -4.99999999999999991e66 < z < 54

   1. Initial program 99.1%

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

      1. associate-/r/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around inf 60.7%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+66} \lor \neg \left(z \leq 54\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.5% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. associate-/r/ 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in x around inf 60.2%

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

6. Final simplification 60.2%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024039 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

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

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