Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B

Percentage Accurate: 85.6% → 99.4%

Time: 9.8s

Alternatives: 15

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+246}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- z t) y) (- a t))))
   (if (<= t_1 (- INFINITY))
     (+ x (/ (- z t) (/ (- a t) y)))
     (if (<= t_1 5e+246) (+ x t_1) (fma (/ y (- a t)) (- z t) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / (a - t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + ((z - t) / ((a - t) / y));
	} else if (t_1 <= 5e+246) {
		tmp = x + t_1;
	} else {
		tmp = fma((y / (a - t)), (z - t), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(z - t) * y) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(a - t) / y)));
	elseif (t_1 <= 5e+246)
		tmp = Float64(x + t_1);
	else
		tmp = fma(Float64(y / Float64(a - t)), Float64(z - t), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+246], N[(x + t$95$1), $MachinePrecision], N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < -inf.0

   1. Initial program 31.9%

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

      1. *-commutative 31.9%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < 4.99999999999999976e246

   1. Initial program 99.8%

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

   if 4.99999999999999976e246 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

   1. Initial program 50.6%

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

      1. +-commutative 50.6%

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

      2. associate-*l/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{a - t} \leq -\infty:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{a - t} \leq 5 \cdot 10^{+246}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)\\ \end{array} \]

Alternative 2: 98.2% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 87.3%

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

   1. +-commutative 87.3%

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

   2. *-commutative 87.3%

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

   3. associate-*l/ 98.0%

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

   4. fma-def 98.0%

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

3. Simplified 98.0%

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

4. Final simplification 98.0%

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

Alternative 3: 99.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+246}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{1}{\frac{y}{a - t}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- z t) y) (- a t))))
   (if (<= t_1 (- INFINITY))
     (+ x (/ (- z t) (/ (- a t) y)))
     (if (<= t_1 5e+246) (+ x t_1) (+ x (/ (- z t) (/ 1.0 (/ y (- a t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / (a - t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + ((z - t) / ((a - t) / y));
	} else if (t_1 <= 5e+246) {
		tmp = x + t_1;
	} else {
		tmp = x + ((z - t) / (1.0 / (y / (a - t))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / (a - t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + ((z - t) / ((a - t) / y));
	} else if (t_1 <= 5e+246) {
		tmp = x + t_1;
	} else {
		tmp = x + ((z - t) / (1.0 / (y / (a - t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((z - t) * y) / (a - t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + ((z - t) / ((a - t) / y))
	elif t_1 <= 5e+246:
		tmp = x + t_1
	else:
		tmp = x + ((z - t) / (1.0 / (y / (a - t))))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(z - t) * y) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(a - t) / y)));
	elseif (t_1 <= 5e+246)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(1.0 / Float64(y / Float64(a - t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((z - t) * y) / (a - t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + ((z - t) / ((a - t) / y));
	elseif (t_1 <= 5e+246)
		tmp = x + t_1;
	else
		tmp = x + ((z - t) / (1.0 / (y / (a - t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+246], N[(x + t$95$1), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] / N[(1.0 / N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < -inf.0

   1. Initial program 31.9%

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

      1. *-commutative 31.9%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < 4.99999999999999976e246

   1. Initial program 99.8%

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

   if 4.99999999999999976e246 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

   1. Initial program 50.6%

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

      1. *-commutative 50.6%

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

      2. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.8%

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

      2. inv-pow 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. unpow-1 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{a - t} \leq -\infty:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{a - t} \leq 5 \cdot 10^{+246}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{1}{\frac{y}{a - t}}}\\ \end{array} \]

Alternative 4: 99.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+289}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- z t) y) (- a t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+289)))
     (+ x (/ (- z t) (/ (- a t) y)))
     (+ x t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / (a - t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+289)) {
		tmp = x + ((z - t) / ((a - t) / y));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / (a - t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+289)) {
		tmp = x + ((z - t) / ((a - t) / y));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((z - t) * y) / (a - t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+289):
		tmp = x + ((z - t) / ((a - t) / y))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(z - t) * y) / Float64(a - t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+289))
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(a - t) / y)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((z - t) * y) / (a - t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+289)))
		tmp = x + ((z - t) / ((a - t) / y));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+289]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < -inf.0 or 2.0000000000000001e289 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

   1. Initial program 38.1%

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

      1. *-commutative 38.1%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < 2.0000000000000001e289

   1. Initial program 99.8%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{a - t} \leq -\infty \lor \neg \left(\frac{\left(z - t\right) \cdot y}{a - t} \leq 2 \cdot 10^{+289}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a - t}\\ \end{array} \]

Alternative 5: 76.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+32}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-89}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-103} \lor \neg \left(t \leq 1.7 \cdot 10^{-52}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.5e+32)
   (+ y x)
   (if (<= t -9.8e-89)
     (- x (/ y (/ t z)))
     (if (or (<= t -2.05e-103) (not (<= t 1.7e-52)))
       (+ y x)
       (+ x (/ y (/ a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.5e+32) {
		tmp = y + x;
	} else if (t <= -9.8e-89) {
		tmp = x - (y / (t / z));
	} else if ((t <= -2.05e-103) || !(t <= 1.7e-52)) {
		tmp = y + x;
	} else {
		tmp = x + (y / (a / 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 (t <= (-3.5d+32)) then
        tmp = y + x
    else if (t <= (-9.8d-89)) then
        tmp = x - (y / (t / z))
    else if ((t <= (-2.05d-103)) .or. (.not. (t <= 1.7d-52))) then
        tmp = y + x
    else
        tmp = x + (y / (a / 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 (t <= -3.5e+32) {
		tmp = y + x;
	} else if (t <= -9.8e-89) {
		tmp = x - (y / (t / z));
	} else if ((t <= -2.05e-103) || !(t <= 1.7e-52)) {
		tmp = y + x;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.5e+32:
		tmp = y + x
	elif t <= -9.8e-89:
		tmp = x - (y / (t / z))
	elif (t <= -2.05e-103) or not (t <= 1.7e-52):
		tmp = y + x
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.5e+32)
		tmp = Float64(y + x);
	elseif (t <= -9.8e-89)
		tmp = Float64(x - Float64(y / Float64(t / z)));
	elseif ((t <= -2.05e-103) || !(t <= 1.7e-52))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.5e+32)
		tmp = y + x;
	elseif (t <= -9.8e-89)
		tmp = x - (y / (t / z));
	elseif ((t <= -2.05e-103) || ~((t <= 1.7e-52)))
		tmp = y + x;
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.5e+32], N[(y + x), $MachinePrecision], If[LessEqual[t, -9.8e-89], N[(x - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -2.05e-103], N[Not[LessEqual[t, 1.7e-52]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.5000000000000001e32 or -9.8e-89 < t < -2.04999999999999998e-103 or 1.70000000000000009e-52 < t

   1. Initial program 81.4%

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

   2. Taylor expanded in t around inf 78.2%

      \[\leadsto \color{blue}{x + y} \]
   3. Step-by-step derivation

      1. +-commutative 78.2%

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

   4. Simplified 78.2%

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

   if -3.5000000000000001e32 < t < -9.8e-89

   1. Initial program 93.7%

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

   2. Taylor expanded in z around inf 81.9%

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

      1. associate-*l/ 85.0%

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

      2. *-commutative 85.0%

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

   4. Simplified 85.0%

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

   5. Taylor expanded in a around 0 69.7%

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

      1. mul-1-neg 69.7%

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

      2. unsub-neg 69.7%

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

      3. associate-/l* 69.7%

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

   7. Simplified 69.7%

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

   if -2.04999999999999998e-103 < t < 1.70000000000000009e-52

   1. Initial program 94.3%

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

   2. Taylor expanded in t around 0 80.1%

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

      1. +-commutative 80.1%

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

      2. associate-/l* 83.7%

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

   4. Simplified 83.7%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+32}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-89}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-103} \lor \neg \left(t \leq 1.7 \cdot 10^{-52}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 6: 76.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+31}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-89}:\\ \;\;\;\;x - \frac{z \cdot y}{t}\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-103}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-51}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.3e+31)
   (+ y x)
   (if (<= t -1.4e-89)
     (- x (/ (* z y) t))
     (if (<= t -2.05e-103)
       (+ y x)
       (if (<= t 3.2e-51) (+ x (/ y (/ a z))) (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.3e+31) {
		tmp = y + x;
	} else if (t <= -1.4e-89) {
		tmp = x - ((z * y) / t);
	} else if (t <= -2.05e-103) {
		tmp = y + x;
	} else if (t <= 3.2e-51) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y + 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 (t <= (-2.3d+31)) then
        tmp = y + x
    else if (t <= (-1.4d-89)) then
        tmp = x - ((z * y) / t)
    else if (t <= (-2.05d-103)) then
        tmp = y + x
    else if (t <= 3.2d-51) then
        tmp = x + (y / (a / z))
    else
        tmp = y + 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 (t <= -2.3e+31) {
		tmp = y + x;
	} else if (t <= -1.4e-89) {
		tmp = x - ((z * y) / t);
	} else if (t <= -2.05e-103) {
		tmp = y + x;
	} else if (t <= 3.2e-51) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.3e+31:
		tmp = y + x
	elif t <= -1.4e-89:
		tmp = x - ((z * y) / t)
	elif t <= -2.05e-103:
		tmp = y + x
	elif t <= 3.2e-51:
		tmp = x + (y / (a / z))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.3e+31)
		tmp = Float64(y + x);
	elseif (t <= -1.4e-89)
		tmp = Float64(x - Float64(Float64(z * y) / t));
	elseif (t <= -2.05e-103)
		tmp = Float64(y + x);
	elseif (t <= 3.2e-51)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.3e+31)
		tmp = y + x;
	elseif (t <= -1.4e-89)
		tmp = x - ((z * y) / t);
	elseif (t <= -2.05e-103)
		tmp = y + x;
	elseif (t <= 3.2e-51)
		tmp = x + (y / (a / z));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.3e+31], N[(y + x), $MachinePrecision], If[LessEqual[t, -1.4e-89], N[(x - N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.05e-103], N[(y + x), $MachinePrecision], If[LessEqual[t, 3.2e-51], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.3e31 or -1.3999999999999999e-89 < t < -2.04999999999999998e-103 or 3.2e-51 < t

   1. Initial program 81.4%

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

   2. Taylor expanded in t around inf 78.2%

      \[\leadsto \color{blue}{x + y} \]
   3. Step-by-step derivation

      1. +-commutative 78.2%

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

   4. Simplified 78.2%

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

   if -2.3e31 < t < -1.3999999999999999e-89

   1. Initial program 93.7%

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

   2. Taylor expanded in a around 0 81.4%

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

      1. mul-1-neg 81.4%

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

      2. unsub-neg 81.4%

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

      3. associate-/l* 81.4%

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

   4. Simplified 81.4%

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

   5. Taylor expanded in t around 0 69.7%

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

   if -2.04999999999999998e-103 < t < 3.2e-51

   1. Initial program 94.3%

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

   2. Taylor expanded in t around 0 80.1%

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

      1. +-commutative 80.1%

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

      2. associate-/l* 83.7%

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

   4. Simplified 83.7%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+31}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-89}:\\ \;\;\;\;x - \frac{z \cdot y}{t}\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-103}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-51}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 7: 76.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+31}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-89}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-103}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.5e+31)
   (+ y x)
   (if (<= t -8.5e-89)
     (- x (* z (/ y t)))
     (if (<= t -2e-103)
       (+ y x)
       (if (<= t 3.4e-49) (+ x (/ y (/ a z))) (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.5e+31) {
		tmp = y + x;
	} else if (t <= -8.5e-89) {
		tmp = x - (z * (y / t));
	} else if (t <= -2e-103) {
		tmp = y + x;
	} else if (t <= 3.4e-49) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y + 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 (t <= (-6.5d+31)) then
        tmp = y + x
    else if (t <= (-8.5d-89)) then
        tmp = x - (z * (y / t))
    else if (t <= (-2d-103)) then
        tmp = y + x
    else if (t <= 3.4d-49) then
        tmp = x + (y / (a / z))
    else
        tmp = y + 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 (t <= -6.5e+31) {
		tmp = y + x;
	} else if (t <= -8.5e-89) {
		tmp = x - (z * (y / t));
	} else if (t <= -2e-103) {
		tmp = y + x;
	} else if (t <= 3.4e-49) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.5e+31:
		tmp = y + x
	elif t <= -8.5e-89:
		tmp = x - (z * (y / t))
	elif t <= -2e-103:
		tmp = y + x
	elif t <= 3.4e-49:
		tmp = x + (y / (a / z))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.5e+31)
		tmp = Float64(y + x);
	elseif (t <= -8.5e-89)
		tmp = Float64(x - Float64(z * Float64(y / t)));
	elseif (t <= -2e-103)
		tmp = Float64(y + x);
	elseif (t <= 3.4e-49)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.5e+31)
		tmp = y + x;
	elseif (t <= -8.5e-89)
		tmp = x - (z * (y / t));
	elseif (t <= -2e-103)
		tmp = y + x;
	elseif (t <= 3.4e-49)
		tmp = x + (y / (a / z));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.5e+31], N[(y + x), $MachinePrecision], If[LessEqual[t, -8.5e-89], N[(x - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2e-103], N[(y + x), $MachinePrecision], If[LessEqual[t, 3.4e-49], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.5000000000000004e31 or -8.49999999999999937e-89 < t < -1.99999999999999992e-103 or 3.40000000000000005e-49 < t

   1. Initial program 81.4%

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

   2. Taylor expanded in t around inf 78.2%

      \[\leadsto \color{blue}{x + y} \]
   3. Step-by-step derivation

      1. +-commutative 78.2%

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

   4. Simplified 78.2%

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

   if -6.5000000000000004e31 < t < -8.49999999999999937e-89

   1. Initial program 93.7%

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

   2. Taylor expanded in z around inf 81.9%

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

      1. associate-*l/ 85.0%

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

      2. *-commutative 85.0%

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

   4. Simplified 85.0%

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

   5. Taylor expanded in a around 0 69.8%

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

      1. associate-*r/ 69.8%

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

      2. neg-mul-1 69.8%

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

   7. Simplified 69.8%

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

   if -1.99999999999999992e-103 < t < 3.40000000000000005e-49

   1. Initial program 94.3%

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

   2. Taylor expanded in t around 0 80.1%

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

      1. +-commutative 80.1%

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

      2. associate-/l* 83.7%

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

   4. Simplified 83.7%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+31}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-89}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-103}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 8: 92.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.82 \cdot 10^{+155} \lor \neg \left(t \leq 8.4 \cdot 10^{+71}\right):\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.82e+155) (not (<= t 8.4e+71)))
   (- x (* y (/ t (- a t))))
   (+ x (/ (* (- z t) y) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.82e+155) || !(t <= 8.4e+71)) {
		tmp = x - (y * (t / (a - t)));
	} else {
		tmp = x + (((z - t) * y) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.82d+155)) .or. (.not. (t <= 8.4d+71))) then
        tmp = x - (y * (t / (a - t)))
    else
        tmp = x + (((z - t) * y) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.82e+155) || !(t <= 8.4e+71)) {
		tmp = x - (y * (t / (a - t)));
	} else {
		tmp = x + (((z - t) * y) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.82e+155) or not (t <= 8.4e+71):
		tmp = x - (y * (t / (a - t)))
	else:
		tmp = x + (((z - t) * y) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.82e+155) || !(t <= 8.4e+71))
		tmp = Float64(x - Float64(y * Float64(t / Float64(a - t))));
	else
		tmp = Float64(x + Float64(Float64(Float64(z - t) * y) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.82e+155) || ~((t <= 8.4e+71)))
		tmp = x - (y * (t / (a - t)));
	else
		tmp = x + (((z - t) * y) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.82e+155], N[Not[LessEqual[t, 8.4e+71]], $MachinePrecision]], N[(x - N[(y * N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.81999999999999989e155 or 8.39999999999999957e71 < t

   1. Initial program 74.8%

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

   2. Taylor expanded in z around 0 71.7%

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

      1. mul-1-neg 71.7%

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

      2. associate-*l/ 95.0%

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

      3. unsub-neg 95.0%

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

      4. *-commutative 95.0%

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

   4. Simplified 95.0%

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

   if -1.81999999999999989e155 < t < 8.39999999999999957e71

   1. Initial program 93.7%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.82 \cdot 10^{+155} \lor \neg \left(t \leq 8.4 \cdot 10^{+71}\right):\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a - t}\\ \end{array} \]

Alternative 9: 84.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{+156} \lor \neg \left(t \leq 6 \cdot 10^{+204}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.75e+156) (not (<= t 6e+204)))
   (+ y x)
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.75e+156) || !(t <= 6e+204)) {
		tmp = y + x;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.75d+156)) .or. (.not. (t <= 6d+204))) then
        tmp = y + x
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.75e+156) || !(t <= 6e+204)) {
		tmp = y + x;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.75e+156) or not (t <= 6e+204):
		tmp = y + x
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.75e+156) || !(t <= 6e+204))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.75e+156) || ~((t <= 6e+204)))
		tmp = y + x;
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.75e+156], N[Not[LessEqual[t, 6e+204]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.7500000000000001e156 or 5.99999999999999965e204 < t

   1. Initial program 69.8%

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

   2. Taylor expanded in t around inf 92.3%

      \[\leadsto \color{blue}{x + y} \]
   3. Step-by-step derivation

      1. +-commutative 92.3%

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

   4. Simplified 92.3%

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

   if -2.7500000000000001e156 < t < 5.99999999999999965e204

   1. Initial program 92.3%

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

   2. Taylor expanded in z around inf 79.9%

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

      1. associate-*l/ 83.4%

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

      2. *-commutative 83.4%

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

   4. Simplified 83.4%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{+156} \lor \neg \left(t \leq 6 \cdot 10^{+204}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 10: 88.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-32} \lor \neg \left(z \leq 12500000000\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.6e-32) (not (<= z 12500000000.0)))
   (+ x (* z (/ y (- a t))))
   (- x (* y (/ t (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.6e-32) || !(z <= 12500000000.0)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (y * (t / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-6.6d-32)) .or. (.not. (z <= 12500000000.0d0))) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x - (y * (t / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.6e-32) || !(z <= 12500000000.0)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (y * (t / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.6e-32) or not (z <= 12500000000.0):
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x - (y * (t / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.6e-32) || !(z <= 12500000000.0))
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x - Float64(y * Float64(t / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.6e-32) || ~((z <= 12500000000.0)))
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x - (y * (t / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.6e-32], N[Not[LessEqual[z, 12500000000.0]], $MachinePrecision]], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.60000000000000051e-32 or 1.25e10 < z

   1. Initial program 83.9%

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

   2. Taylor expanded in z around inf 81.8%

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

      1. associate-*l/ 90.2%

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

      2. *-commutative 90.2%

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

   4. Simplified 90.2%

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

   if -6.60000000000000051e-32 < z < 1.25e10

   1. Initial program 90.2%

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

   2. Taylor expanded in z around 0 83.6%

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

      1. mul-1-neg 83.6%

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

      2. associate-*l/ 93.2%

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

      3. unsub-neg 93.2%

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

      4. *-commutative 93.2%

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

   4. Simplified 93.2%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-32} \lor \neg \left(z \leq 12500000000\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \end{array} \]

Alternative 11: 74.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-103} \lor \neg \left(t \leq 2.6 \cdot 10^{-56}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.5e-103) (not (<= t 2.6e-56))) (+ y x) (+ x (/ (* z y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.5e-103) || !(t <= 2.6e-56)) {
		tmp = y + x;
	} else {
		tmp = x + ((z * 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 ((t <= (-1.5d-103)) .or. (.not. (t <= 2.6d-56))) then
        tmp = y + x
    else
        tmp = x + ((z * 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 ((t <= -1.5e-103) || !(t <= 2.6e-56)) {
		tmp = y + x;
	} else {
		tmp = x + ((z * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.5e-103) or not (t <= 2.6e-56):
		tmp = y + x
	else:
		tmp = x + ((z * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.5e-103) || !(t <= 2.6e-56))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(Float64(z * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.5e-103) || ~((t <= 2.6e-56)))
		tmp = y + x;
	else
		tmp = x + ((z * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.5e-103], N[Not[LessEqual[t, 2.6e-56]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.5e-103 or 2.59999999999999997e-56 < t

   1. Initial program 83.7%

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

   2. Taylor expanded in t around inf 73.8%

      \[\leadsto \color{blue}{x + y} \]
   3. Step-by-step derivation

      1. +-commutative 73.8%

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

   4. Simplified 73.8%

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

   if -1.5e-103 < t < 2.59999999999999997e-56

   1. Initial program 94.3%

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

   2. Taylor expanded in t around 0 80.1%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-103} \lor \neg \left(t \leq 2.6 \cdot 10^{-56}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \]

Alternative 12: 75.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{-104} \lor \neg \left(t \leq 3.25 \cdot 10^{-49}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.25e-104) (not (<= t 3.25e-49))) (+ y x) (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.25e-104) || !(t <= 3.25e-49)) {
		tmp = y + x;
	} else {
		tmp = x + (z * (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 ((t <= (-2.25d-104)) .or. (.not. (t <= 3.25d-49))) then
        tmp = y + x
    else
        tmp = x + (z * (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 ((t <= -2.25e-104) || !(t <= 3.25e-49)) {
		tmp = y + x;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.25e-104) or not (t <= 3.25e-49):
		tmp = y + x
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.25e-104) || !(t <= 3.25e-49))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.25e-104) || ~((t <= 3.25e-49)))
		tmp = y + x;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.25e-104], N[Not[LessEqual[t, 3.25e-49]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2499999999999999e-104 or 3.24999999999999984e-49 < t

   1. Initial program 83.7%

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

   2. Taylor expanded in t around inf 73.8%

      \[\leadsto \color{blue}{x + y} \]
   3. Step-by-step derivation

      1. +-commutative 73.8%

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

   4. Simplified 73.8%

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

   if -2.2499999999999999e-104 < t < 3.24999999999999984e-49

   1. Initial program 94.3%

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

   2. Taylor expanded in t around 0 80.1%

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

      1. +-commutative 80.1%

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

      2. associate-/l* 83.7%

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

   4. Simplified 83.7%

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

      1. associate-/r/ 83.0%

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

   6. Applied egg-rr 83.0%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{-104} \lor \neg \left(t \leq 3.25 \cdot 10^{-49}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 13: 75.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{-103}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-52}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.05e-103)
   (+ y x)
   (if (<= t 2.75e-52) (+ x (/ y (/ a z))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.05e-103) {
		tmp = y + x;
	} else if (t <= 2.75e-52) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y + 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 (t <= (-2.05d-103)) then
        tmp = y + x
    else if (t <= 2.75d-52) then
        tmp = x + (y / (a / z))
    else
        tmp = y + 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 (t <= -2.05e-103) {
		tmp = y + x;
	} else if (t <= 2.75e-52) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.05e-103:
		tmp = y + x
	elif t <= 2.75e-52:
		tmp = x + (y / (a / z))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.05e-103)
		tmp = Float64(y + x);
	elseif (t <= 2.75e-52)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.05e-103)
		tmp = y + x;
	elseif (t <= 2.75e-52)
		tmp = x + (y / (a / z));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.05e-103], N[(y + x), $MachinePrecision], If[LessEqual[t, 2.75e-52], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.04999999999999998e-103 or 2.75e-52 < t

   1. Initial program 83.7%

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

   2. Taylor expanded in t around inf 73.8%

      \[\leadsto \color{blue}{x + y} \]
   3. Step-by-step derivation

      1. +-commutative 73.8%

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

   4. Simplified 73.8%

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

   if -2.04999999999999998e-103 < t < 2.75e-52

   1. Initial program 94.3%

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

   2. Taylor expanded in t around 0 80.1%

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

      1. +-commutative 80.1%

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

      2. associate-/l* 83.7%

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

   4. Simplified 83.7%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{-103}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-52}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 14: 64.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-125}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-50}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.7e-125) (+ y x) (if (<= t 4.4e-50) x (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.7e-125) {
		tmp = y + x;
	} else if (t <= 4.4e-50) {
		tmp = x;
	} else {
		tmp = y + 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 (t <= (-3.7d-125)) then
        tmp = y + x
    else if (t <= 4.4d-50) then
        tmp = x
    else
        tmp = y + 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 (t <= -3.7e-125) {
		tmp = y + x;
	} else if (t <= 4.4e-50) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.7e-125:
		tmp = y + x
	elif t <= 4.4e-50:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.7e-125)
		tmp = Float64(y + x);
	elseif (t <= 4.4e-50)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.7e-125)
		tmp = y + x;
	elseif (t <= 4.4e-50)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.7e-125], N[(y + x), $MachinePrecision], If[LessEqual[t, 4.4e-50], x, N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.6999999999999999e-125 or 4.3999999999999998e-50 < t

   1. Initial program 83.6%

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

   2. Taylor expanded in t around inf 72.8%

      \[\leadsto \color{blue}{x + y} \]
   3. Step-by-step derivation

      1. +-commutative 72.8%

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

   4. Simplified 72.8%

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

   if -3.6999999999999999e-125 < t < 4.3999999999999998e-50

   1. Initial program 95.1%

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

   2. Taylor expanded in x around inf 51.8%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-125}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-50}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 15: 51.7% accurate, 11.0× 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 87.3%

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

2. Taylor expanded in x around inf 54.0%

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

3. Final simplification 54.0%

   \[\leadsto x \]

Developer target: 98.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{\frac{a - t}{z - t}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023293 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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