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

Percentage Accurate: 97.1% → 99.5%

Time: 11.5s

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: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / (((t - z) + 1.0d0) / (z - y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

   1. associate-/r/ N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y - z}{\left(t - z\right) + 1} \cdot \color{blue}{a}\right)\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(a \cdot \color{blue}{\frac{y - z}{\left(t - z\right) + 1}}\right)\right) \]

   3. clear-num N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(a \cdot \frac{1}{\color{blue}{\frac{\left(t - z\right) + 1}{y - z}}}\right)\right) \]

   4. un-div-inv N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{a}{\color{blue}{\frac{\left(t - z\right) + 1}{y - z}}}\right)\right) \]

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \color{blue}{\left(\frac{\left(t - z\right) + 1}{y - z}\right)}\right)\right) \]

   6. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(\left(\left(t - z\right) + 1\right), \color{blue}{\left(y - z\right)}\right)\right)\right) \]

   7. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(t - z\right), 1\right), \left(\color{blue}{y} - z\right)\right)\right)\right) \]

   8. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(t, z\right), 1\right), \left(y - z\right)\right)\right)\right) \]

   9. --lowering--.f64 99.3%

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(t, z\right), 1\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

4. Applied egg-rr 99.3%

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

5. Final simplification 99.3%

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

Alternative 2: 91.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \frac{z - y}{t}\\ \mathbf{if}\;t \leq -4.7 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+121}:\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* a (/ (- z y) t)))))
   (if (<= t -4.7e+70)
     t_1
     (if (<= t 1.1e+121) (+ x (/ a (/ (- 1.0 z) (- z y)))) 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 <= -4.7e+70) {
		tmp = t_1;
	} else if (t <= 1.1e+121) {
		tmp = x + (a / ((1.0 - z) / (z - y)));
	} 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 <= (-4.7d+70)) then
        tmp = t_1
    else if (t <= 1.1d+121) then
        tmp = x + (a / ((1.0d0 - z) / (z - y)))
    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 <= -4.7e+70) {
		tmp = t_1;
	} else if (t <= 1.1e+121) {
		tmp = x + (a / ((1.0 - z) / (z - y)));
	} 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 <= -4.7e+70:
		tmp = t_1
	elif t <= 1.1e+121:
		tmp = x + (a / ((1.0 - z) / (z - y)))
	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 <= -4.7e+70)
		tmp = t_1;
	elseif (t <= 1.1e+121)
		tmp = Float64(x + Float64(a / Float64(Float64(1.0 - z) / Float64(z - y))));
	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 <= -4.7e+70)
		tmp = t_1;
	elseif (t <= 1.1e+121)
		tmp = x + (a / ((1.0 - z) / (z - y)));
	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, -4.7e+70], t$95$1, If[LessEqual[t, 1.1e+121], N[(x + N[(a / N[(N[(1.0 - z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.6999999999999998e70 or 1.10000000000000001e121 < t

   1. Initial program 95.8%

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

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 89.1%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 89.1%

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

      1. associate-/r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y - z}{t} \cdot \color{blue}{a}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y - z}{t}\right), \color{blue}{a}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), t\right), a\right)\right) \]

      4. --lowering--.f64 93.0%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), t\right), a\right)\right) \]

   7. Applied egg-rr 93.0%

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

   if -4.6999999999999998e70 < t < 1.10000000000000001e121

   1. Initial program 98.1%

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

      1. associate-/r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y - z}{\left(t - z\right) + 1} \cdot \color{blue}{a}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(a \cdot \color{blue}{\frac{y - z}{\left(t - z\right) + 1}}\right)\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(a \cdot \frac{1}{\color{blue}{\frac{\left(t - z\right) + 1}{y - z}}}\right)\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{a}{\color{blue}{\frac{\left(t - z\right) + 1}{y - z}}}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \color{blue}{\left(\frac{\left(t - z\right) + 1}{y - z}\right)}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(\left(\left(t - z\right) + 1\right), \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(t - z\right), 1\right), \left(\color{blue}{y} - z\right)\right)\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(t, z\right), 1\right), \left(y - z\right)\right)\right)\right) \]

      9. --lowering--.f64 99.9%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(t, z\right), 1\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \color{blue}{\left(\frac{1 - z}{y - z}\right)}\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(\left(1 - z\right), \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(1, z\right), \left(\color{blue}{y} - z\right)\right)\right)\right) \]

      3. --lowering--.f64 94.3%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(1, z\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   7. Simplified 94.3%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+70}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+121}:\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+51}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-223}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq 0.0011:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6e+51)
   (- x a)
   (if (<= z -2.2e-223)
     (- x (/ y (/ t a)))
     (if (<= z 0.0011) (- x (* a y)) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6e+51) {
		tmp = x - a;
	} else if (z <= -2.2e-223) {
		tmp = x - (y / (t / a));
	} else if (z <= 0.0011) {
		tmp = x - (a * y);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6d+51)) then
        tmp = x - a
    else if (z <= (-2.2d-223)) then
        tmp = x - (y / (t / a))
    else if (z <= 0.0011d0) then
        tmp = x - (a * y)
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6e+51) {
		tmp = x - a;
	} else if (z <= -2.2e-223) {
		tmp = x - (y / (t / a));
	} else if (z <= 0.0011) {
		tmp = x - (a * y);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6e+51:
		tmp = x - a
	elif z <= -2.2e-223:
		tmp = x - (y / (t / a))
	elif z <= 0.0011:
		tmp = x - (a * y)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6e+51)
		tmp = Float64(x - a);
	elseif (z <= -2.2e-223)
		tmp = Float64(x - Float64(y / Float64(t / a)));
	elseif (z <= 0.0011)
		tmp = Float64(x - Float64(a * y));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6e+51)
		tmp = x - a;
	elseif (z <= -2.2e-223)
		tmp = x - (y / (t / a));
	elseif (z <= 0.0011)
		tmp = x - (a * y);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6e+51], N[(x - a), $MachinePrecision], If[LessEqual[z, -2.2e-223], N[(x - N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0011], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6e51 or 0.00110000000000000007 < z

   1. Initial program 94.6%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x - a} \]
   4. Step-by-step derivation

      1. --lowering--.f64 78.4%

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{a}\right) \]

   5. Simplified 78.4%

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

   if -6e51 < z < -2.20000000000000009e-223

   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 inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 72.5%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 72.5%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{y}, \mathsf{/.f64}\left(t, a\right)\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 75.0%

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

   if -2.20000000000000009e-223 < z < 0.00110000000000000007

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot y}{1 + t}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(a \cdot y\right), \color{blue}{\left(1 + t\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, y\right), \left(\color{blue}{1} + t\right)\right)\right) \]

      3. +-lowering-+.f64 97.7%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, y\right), \mathsf{+.f64}\left(1, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 97.7%

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

   6. Taylor expanded in t around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(a \cdot y\right)}\right) \]

      2. *-lowering-*.f64 79.4%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{y}\right)\right) \]

   8. Simplified 79.4%

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

Alternative 4: 81.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+50}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1600000000000:\\ \;\;\;\;x + \frac{a \cdot y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7e+50)
   (- x a)
   (if (<= z 1600000000000.0) (+ x (/ (* a y) (- -1.0 t))) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7e+50) {
		tmp = x - a;
	} else if (z <= 1600000000000.0) {
		tmp = x + ((a * y) / (-1.0 - t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7d+50)) then
        tmp = x - a
    else if (z <= 1600000000000.0d0) then
        tmp = x + ((a * y) / ((-1.0d0) - t))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7e+50) {
		tmp = x - a;
	} else if (z <= 1600000000000.0) {
		tmp = x + ((a * y) / (-1.0 - t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7e+50:
		tmp = x - a
	elif z <= 1600000000000.0:
		tmp = x + ((a * y) / (-1.0 - t))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7e+50)
		tmp = Float64(x - a);
	elseif (z <= 1600000000000.0)
		tmp = Float64(x + Float64(Float64(a * y) / Float64(-1.0 - t)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7e+50)
		tmp = x - a;
	elseif (z <= 1600000000000.0)
		tmp = x + ((a * y) / (-1.0 - t));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7e+50], N[(x - a), $MachinePrecision], If[LessEqual[z, 1600000000000.0], N[(x + N[(N[(a * y), $MachinePrecision] / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.00000000000000012e50 or 1.6e12 < z

   1. Initial program 94.3%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x - a} \]
   4. Step-by-step derivation

      1. --lowering--.f64 78.3%

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{a}\right) \]

   5. Simplified 78.3%

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

   if -7.00000000000000012e50 < z < 1.6e12

   1. Initial program 99.3%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot y}{1 + t}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(a \cdot y\right), \color{blue}{\left(1 + t\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, y\right), \left(\color{blue}{1} + t\right)\right)\right) \]

      3. +-lowering-+.f64 92.9%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, y\right), \mathsf{+.f64}\left(1, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 92.9%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+50}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1600000000000:\\ \;\;\;\;x + \frac{a \cdot y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \frac{z - y}{t}\\ \mathbf{if}\;t \leq -4.3 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-18}:\\ \;\;\;\;x + a \cdot \frac{y}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* a (/ (- z y) t)))))
   (if (<= t -4.3e+70)
     t_1
     (if (<= t 3.1e-18) (+ x (* a (/ y (+ z -1.0)))) 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 <= -4.3e+70) {
		tmp = t_1;
	} else if (t <= 3.1e-18) {
		tmp = x + (a * (y / (z + -1.0)));
	} 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 <= (-4.3d+70)) then
        tmp = t_1
    else if (t <= 3.1d-18) then
        tmp = x + (a * (y / (z + (-1.0d0))))
    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 <= -4.3e+70) {
		tmp = t_1;
	} else if (t <= 3.1e-18) {
		tmp = x + (a * (y / (z + -1.0)));
	} 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 <= -4.3e+70:
		tmp = t_1
	elif t <= 3.1e-18:
		tmp = x + (a * (y / (z + -1.0)))
	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 <= -4.3e+70)
		tmp = t_1;
	elseif (t <= 3.1e-18)
		tmp = Float64(x + Float64(a * Float64(y / Float64(z + -1.0))));
	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 <= -4.3e+70)
		tmp = t_1;
	elseif (t <= 3.1e-18)
		tmp = x + (a * (y / (z + -1.0)));
	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, -4.3e+70], t$95$1, If[LessEqual[t, 3.1e-18], N[(x + N[(a * N[(y / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.3000000000000001e70 or 3.10000000000000007e-18 < t

   1. Initial program 96.6%

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

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 86.9%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 86.9%

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

      1. associate-/r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y - z}{t} \cdot \color{blue}{a}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y - z}{t}\right), \color{blue}{a}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), t\right), a\right)\right) \]

      4. --lowering--.f64 89.2%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), t\right), a\right)\right) \]

   7. Applied egg-rr 89.2%

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

   if -4.3000000000000001e70 < t < 3.10000000000000007e-18

   1. Initial program 97.8%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{y}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(t, z\right), 1\right), a\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 79.4%

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

   6. Taylor expanded in t around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot y}{1 - z}\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(a \cdot \color{blue}{\frac{y}{1 - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{y}{1 - z}\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(y, \color{blue}{\left(1 - z\right)}\right)\right)\right) \]

      5. --lowering--.f64 76.9%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 76.9%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+70}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-18}:\\ \;\;\;\;x + a \cdot \frac{y}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-18}:\\ \;\;\;\;x + a \cdot \frac{y}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a (/ y t)))))
   (if (<= t -2.6e+30)
     t_1
     (if (<= t 3.1e-18) (+ x (* a (/ y (+ z -1.0)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * (y / t));
	double tmp;
	if (t <= -2.6e+30) {
		tmp = t_1;
	} else if (t <= 3.1e-18) {
		tmp = x + (a * (y / (z + -1.0)));
	} 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 * (y / t))
    if (t <= (-2.6d+30)) then
        tmp = t_1
    else if (t <= 3.1d-18) then
        tmp = x + (a * (y / (z + (-1.0d0))))
    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 * (y / t));
	double tmp;
	if (t <= -2.6e+30) {
		tmp = t_1;
	} else if (t <= 3.1e-18) {
		tmp = x + (a * (y / (z + -1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a * (y / t))
	tmp = 0
	if t <= -2.6e+30:
		tmp = t_1
	elif t <= 3.1e-18:
		tmp = x + (a * (y / (z + -1.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * Float64(y / t)))
	tmp = 0.0
	if (t <= -2.6e+30)
		tmp = t_1;
	elseif (t <= 3.1e-18)
		tmp = Float64(x + Float64(a * Float64(y / Float64(z + -1.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a * (y / t));
	tmp = 0.0;
	if (t <= -2.6e+30)
		tmp = t_1;
	elseif (t <= 3.1e-18)
		tmp = x + (a * (y / (z + -1.0)));
	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[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.6e+30], t$95$1, If[LessEqual[t, 3.1e-18], N[(x + N[(a * N[(y / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.59999999999999988e30 or 3.10000000000000007e-18 < t

   1. Initial program 96.8%

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

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 84.7%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 84.7%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{y}, \mathsf{/.f64}\left(t, a\right)\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 80.6%

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

      1. associate-/r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{t} \cdot \color{blue}{a}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{t}\right), \color{blue}{a}\right)\right) \]

      3. /-lowering-/.f64 81.9%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), a\right)\right) \]

   10. Applied egg-rr 81.9%

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

   if -2.59999999999999988e30 < t < 3.10000000000000007e-18

   1. Initial program 97.7%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{y}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(t, z\right), 1\right), a\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 78.7%

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

   6. Taylor expanded in t around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot y}{1 - z}\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(a \cdot \color{blue}{\frac{y}{1 - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{y}{1 - z}\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(y, \color{blue}{\left(1 - z\right)}\right)\right)\right) \]

      5. --lowering--.f64 77.5%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 77.5%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+30}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-18}:\\ \;\;\;\;x + a \cdot \frac{y}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-18}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a (/ y t)))))
   (if (<= t -2.6e-24) t_1 (if (<= t 3.1e-18) (- x (* a y)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * (y / t));
	double tmp;
	if (t <= -2.6e-24) {
		tmp = t_1;
	} else if (t <= 3.1e-18) {
		tmp = x - (a * y);
	} 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 * (y / t))
    if (t <= (-2.6d-24)) then
        tmp = t_1
    else if (t <= 3.1d-18) then
        tmp = x - (a * y)
    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 * (y / t));
	double tmp;
	if (t <= -2.6e-24) {
		tmp = t_1;
	} else if (t <= 3.1e-18) {
		tmp = x - (a * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a * (y / t))
	tmp = 0
	if t <= -2.6e-24:
		tmp = t_1
	elif t <= 3.1e-18:
		tmp = x - (a * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * Float64(y / t)))
	tmp = 0.0
	if (t <= -2.6e-24)
		tmp = t_1;
	elseif (t <= 3.1e-18)
		tmp = Float64(x - Float64(a * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a * (y / t));
	tmp = 0.0;
	if (t <= -2.6e-24)
		tmp = t_1;
	elseif (t <= 3.1e-18)
		tmp = x - (a * y);
	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[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.6e-24], t$95$1, If[LessEqual[t, 3.1e-18], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.6e-24 or 3.10000000000000007e-18 < t

   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 inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 81.0%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 81.0%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{y}, \mathsf{/.f64}\left(t, a\right)\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 77.5%

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

      1. associate-/r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{t} \cdot \color{blue}{a}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{t}\right), \color{blue}{a}\right)\right) \]

      3. /-lowering-/.f64 78.7%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), a\right)\right) \]

   10. Applied egg-rr 78.7%

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

   if -2.6e-24 < t < 3.10000000000000007e-18

   1. Initial program 97.5%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot y}{1 + t}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(a \cdot y\right), \color{blue}{\left(1 + t\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, y\right), \left(\color{blue}{1} + t\right)\right)\right) \]

      3. +-lowering-+.f64 73.0%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, y\right), \mathsf{+.f64}\left(1, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 73.0%

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

   6. Taylor expanded in t around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(a \cdot y\right)}\right) \]

      2. *-lowering-*.f64 73.0%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{y}\right)\right) \]

   8. Simplified 73.0%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-24}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-18}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-21}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 0.0024:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8e-21) (- x a) (if (<= z 0.0024) (- x (* a y)) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e-21) {
		tmp = x - a;
	} else if (z <= 0.0024) {
		tmp = x - (a * y);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8d-21)) then
        tmp = x - a
    else if (z <= 0.0024d0) then
        tmp = x - (a * y)
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e-21) {
		tmp = x - a;
	} else if (z <= 0.0024) {
		tmp = x - (a * y);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8e-21:
		tmp = x - a
	elif z <= 0.0024:
		tmp = x - (a * y)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8e-21)
		tmp = Float64(x - a);
	elseif (z <= 0.0024)
		tmp = Float64(x - Float64(a * y));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8e-21)
		tmp = x - a;
	elseif (z <= 0.0024)
		tmp = x - (a * y);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8e-21], N[(x - a), $MachinePrecision], If[LessEqual[z, 0.0024], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.99999999999999926e-21 or 0.00239999999999999979 < z

   1. Initial program 95.3%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x - a} \]
   4. Step-by-step derivation

      1. --lowering--.f64 75.6%

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{a}\right) \]

   5. Simplified 75.6%

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

   if -7.99999999999999926e-21 < z < 0.00239999999999999979

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot y}{1 + t}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(a \cdot y\right), \color{blue}{\left(1 + t\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, y\right), \left(\color{blue}{1} + t\right)\right)\right) \]

      3. +-lowering-+.f64 95.3%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, y\right), \mathsf{+.f64}\left(1, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 95.3%

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

   6. Taylor expanded in t around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(a \cdot y\right)}\right) \]

      2. *-lowering-*.f64 74.9%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{y}\right)\right) \]

   8. Simplified 74.9%

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

Alternative 9: 65.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+16}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e+16) (- x a) (if (<= z 1.52e-33) x (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+16) {
		tmp = x - a;
	} else if (z <= 1.52e-33) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.8d+16)) then
        tmp = x - a
    else if (z <= 1.52d-33) then
        tmp = x
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+16) {
		tmp = x - a;
	} else if (z <= 1.52e-33) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.8e+16:
		tmp = x - a
	elif z <= 1.52e-33:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e+16)
		tmp = Float64(x - a);
	elseif (z <= 1.52e-33)
		tmp = x;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.8e+16)
		tmp = x - a;
	elseif (z <= 1.52e-33)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e+16], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.52e-33], x, N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e16 or 1.52e-33 < z

   1. Initial program 95.2%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x - a} \]
   4. Step-by-step derivation

      1. --lowering--.f64 76.0%

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{a}\right) \]

   5. Simplified 76.0%

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

   if -1.8e16 < z < 1.52e-33

   1. Initial program 99.2%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 65.0%

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

Alternative 10: 53.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+222}:\\ \;\;\;\;0 - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a -2.5e+222) (- 0.0 a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.5e+222) {
		tmp = 0.0 - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.5d+222)) then
        tmp = 0.0d0 - a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.5e+222) {
		tmp = 0.0 - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.5e+222:
		tmp = 0.0 - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.5e+222)
		tmp = Float64(0.0 - a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.5e+222)
		tmp = 0.0 - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.5e+222], N[(0.0 - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -2.50000000000000012e222

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x - a} \]
   4. Step-by-step derivation

      1. --lowering--.f64 41.3%

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{a}\right) \]

   5. Simplified 41.3%

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

   6. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(a\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{a} \]

      3. --lowering--.f64 42.0%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{a}\right) \]

   8. Simplified 42.0%

      \[\leadsto \color{blue}{0 - a} \]
   9. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(a\right) \]

      2. neg-lowering-neg.f64 42.0%

         \[\leadsto \mathsf{neg.f64}\left(a\right) \]

   10. Applied egg-rr 42.0%

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

   if -2.50000000000000012e222 < a

   1. Initial program 97.1%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 61.3%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+222}:\\ \;\;\;\;0 - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.9% 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 97.3%

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

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 58.2%

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

Developer Target 1: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024160 
(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))))