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

Percentage Accurate: 85.3% → 99.5%

Time: 10.1s

Alternatives: 12

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+260}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - a}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+260)))
     (fma (/ y (- z a)) (- z t) x)
     (+ t_1 x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+260)) {
		tmp = fma((y / (z - a)), (z - t), x);
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+260))
		tmp = fma(Float64(y / Float64(z - a)), Float64(z - t), x);
	else
		tmp = Float64(t_1 + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+260]], $MachinePrecision]], N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision] + x), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -inf.0 or 4.9999999999999996e260 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 44.9%

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

      1. +-commutative 44.9%

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

      2. associate-*l/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 4.9999999999999996e260

   1. Initial program 99.1%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 5 \cdot 10^{+260}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - a}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a} + x\\ \end{array} \]

Alternative 2: 99.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+260}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+260)))
     (+ x (/ (- z t) (/ (- z a) y)))
     (+ t_1 x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+260)) {
		tmp = x + ((z - t) / ((z - a) / y));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+260)) {
		tmp = x + ((z - t) / ((z - a) / y));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (z - a)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+260):
		tmp = x + ((z - t) / ((z - a) / y))
	else:
		tmp = t_1 + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+260))
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(z - a) / y)));
	else
		tmp = Float64(t_1 + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (z - a);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+260)))
		tmp = x + ((z - t) / ((z - a) / y));
	else
		tmp = t_1 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+260]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -inf.0 or 4.9999999999999996e260 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 44.9%

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

      1. *-commutative 44.9%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 4.9999999999999996e260

   1. Initial program 99.1%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 5 \cdot 10^{+260}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a} + x\\ \end{array} \]

Alternative 3: 79.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{z - a}\\ t_2 := x + y \cdot \frac{z - t}{z}\\ t_3 := x + y \cdot \frac{t}{a}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+186}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-176}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+61}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y (- z a)))))
        (t_2 (+ x (* y (/ (- z t) z))))
        (t_3 (+ x (* y (/ t a)))))
   (if (<= z -1.5e+186)
     t_2
     (if (<= z -1.05e-20)
       t_1
       (if (<= z 2.75e-176)
         t_3
         (if (<= z 6.4e-61) t_1 (if (<= z 2.2e+61) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / (z - a)));
	double t_2 = x + (y * ((z - t) / z));
	double t_3 = x + (y * (t / a));
	double tmp;
	if (z <= -1.5e+186) {
		tmp = t_2;
	} else if (z <= -1.05e-20) {
		tmp = t_1;
	} else if (z <= 2.75e-176) {
		tmp = t_3;
	} else if (z <= 6.4e-61) {
		tmp = t_1;
	} else if (z <= 2.2e+61) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (z * (y / (z - a)))
    t_2 = x + (y * ((z - t) / z))
    t_3 = x + (y * (t / a))
    if (z <= (-1.5d+186)) then
        tmp = t_2
    else if (z <= (-1.05d-20)) then
        tmp = t_1
    else if (z <= 2.75d-176) then
        tmp = t_3
    else if (z <= 6.4d-61) then
        tmp = t_1
    else if (z <= 2.2d+61) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / (z - a)));
	double t_2 = x + (y * ((z - t) / z));
	double t_3 = x + (y * (t / a));
	double tmp;
	if (z <= -1.5e+186) {
		tmp = t_2;
	} else if (z <= -1.05e-20) {
		tmp = t_1;
	} else if (z <= 2.75e-176) {
		tmp = t_3;
	} else if (z <= 6.4e-61) {
		tmp = t_1;
	} else if (z <= 2.2e+61) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / (z - a)))
	t_2 = x + (y * ((z - t) / z))
	t_3 = x + (y * (t / a))
	tmp = 0
	if z <= -1.5e+186:
		tmp = t_2
	elif z <= -1.05e-20:
		tmp = t_1
	elif z <= 2.75e-176:
		tmp = t_3
	elif z <= 6.4e-61:
		tmp = t_1
	elif z <= 2.2e+61:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / Float64(z - a))))
	t_2 = Float64(x + Float64(y * Float64(Float64(z - t) / z)))
	t_3 = Float64(x + Float64(y * Float64(t / a)))
	tmp = 0.0
	if (z <= -1.5e+186)
		tmp = t_2;
	elseif (z <= -1.05e-20)
		tmp = t_1;
	elseif (z <= 2.75e-176)
		tmp = t_3;
	elseif (z <= 6.4e-61)
		tmp = t_1;
	elseif (z <= 2.2e+61)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / (z - a)));
	t_2 = x + (y * ((z - t) / z));
	t_3 = x + (y * (t / a));
	tmp = 0.0;
	if (z <= -1.5e+186)
		tmp = t_2;
	elseif (z <= -1.05e-20)
		tmp = t_1;
	elseif (z <= 2.75e-176)
		tmp = t_3;
	elseif (z <= 6.4e-61)
		tmp = t_1;
	elseif (z <= 2.2e+61)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e+186], t$95$2, If[LessEqual[z, -1.05e-20], t$95$1, If[LessEqual[z, 2.75e-176], t$95$3, If[LessEqual[z, 6.4e-61], t$95$1, If[LessEqual[z, 2.2e+61], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.49999999999999991e186 or 2.2e61 < z

   1. Initial program 71.9%

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

      1. *-commutative 71.9%

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

      2. associate-/l* 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in z around inf 82.6%

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

      1. associate-/r/ 91.1%

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

   6. Applied egg-rr 91.1%

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

   if -1.49999999999999991e186 < z < -1.0499999999999999e-20 or 2.75e-176 < z < 6.4000000000000003e-61

   1. Initial program 91.8%

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

   2. Taylor expanded in t around 0 79.9%

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

      1. +-commutative 79.9%

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

      2. associate-*l/ 86.8%

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

      3. *-commutative 86.8%

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

   4. Simplified 86.8%

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

   if -1.0499999999999999e-20 < z < 2.75e-176 or 6.4000000000000003e-61 < z < 2.2e61

   1. Initial program 95.5%

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

   2. Taylor expanded in z around 0 81.6%

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

      1. +-commutative 81.6%

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

      2. associate-/l* 85.9%

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

   4. Simplified 85.9%

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

      1. associate-/r/ 86.0%

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

   6. Applied egg-rr 86.0%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+186}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-20}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-176}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-61}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+61}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \]

Alternative 4: 79.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{z - a}\\ t_2 := x + y \cdot \frac{t}{a}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+185}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-176}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y (- z a))))) (t_2 (+ x (* y (/ t a)))))
   (if (<= z -2.2e+185)
     (+ x (/ y (/ z (- z t))))
     (if (<= z -1.9e-22)
       t_1
       (if (<= z 2.75e-176)
         t_2
         (if (<= z 8.6e-60)
           t_1
           (if (<= z 1.95e+61) t_2 (+ x (* y (/ (- z t) z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / (z - a)));
	double t_2 = x + (y * (t / a));
	double tmp;
	if (z <= -2.2e+185) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= -1.9e-22) {
		tmp = t_1;
	} else if (z <= 2.75e-176) {
		tmp = t_2;
	} else if (z <= 8.6e-60) {
		tmp = t_1;
	} else if (z <= 1.95e+61) {
		tmp = t_2;
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (y / (z - a)))
    t_2 = x + (y * (t / a))
    if (z <= (-2.2d+185)) then
        tmp = x + (y / (z / (z - t)))
    else if (z <= (-1.9d-22)) then
        tmp = t_1
    else if (z <= 2.75d-176) then
        tmp = t_2
    else if (z <= 8.6d-60) then
        tmp = t_1
    else if (z <= 1.95d+61) then
        tmp = t_2
    else
        tmp = x + (y * ((z - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / (z - a)));
	double t_2 = x + (y * (t / a));
	double tmp;
	if (z <= -2.2e+185) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= -1.9e-22) {
		tmp = t_1;
	} else if (z <= 2.75e-176) {
		tmp = t_2;
	} else if (z <= 8.6e-60) {
		tmp = t_1;
	} else if (z <= 1.95e+61) {
		tmp = t_2;
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / (z - a)))
	t_2 = x + (y * (t / a))
	tmp = 0
	if z <= -2.2e+185:
		tmp = x + (y / (z / (z - t)))
	elif z <= -1.9e-22:
		tmp = t_1
	elif z <= 2.75e-176:
		tmp = t_2
	elif z <= 8.6e-60:
		tmp = t_1
	elif z <= 1.95e+61:
		tmp = t_2
	else:
		tmp = x + (y * ((z - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / Float64(z - a))))
	t_2 = Float64(x + Float64(y * Float64(t / a)))
	tmp = 0.0
	if (z <= -2.2e+185)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (z <= -1.9e-22)
		tmp = t_1;
	elseif (z <= 2.75e-176)
		tmp = t_2;
	elseif (z <= 8.6e-60)
		tmp = t_1;
	elseif (z <= 1.95e+61)
		tmp = t_2;
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / (z - a)));
	t_2 = x + (y * (t / a));
	tmp = 0.0;
	if (z <= -2.2e+185)
		tmp = x + (y / (z / (z - t)));
	elseif (z <= -1.9e-22)
		tmp = t_1;
	elseif (z <= 2.75e-176)
		tmp = t_2;
	elseif (z <= 8.6e-60)
		tmp = t_1;
	elseif (z <= 1.95e+61)
		tmp = t_2;
	else
		tmp = x + (y * ((z - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+185], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.9e-22], t$95$1, If[LessEqual[z, 2.75e-176], t$95$2, If[LessEqual[z, 8.6e-60], t$95$1, If[LessEqual[z, 1.95e+61], t$95$2, N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.2000000000000001e185

   1. Initial program 63.6%

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

   2. Taylor expanded in a around 0 57.7%

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

      1. +-commutative 57.7%

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

      2. associate-/l* 91.2%

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

   4. Simplified 91.2%

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

   if -2.2000000000000001e185 < z < -1.90000000000000012e-22 or 2.75e-176 < z < 8.6000000000000001e-60

   1. Initial program 91.8%

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

   2. Taylor expanded in t around 0 79.9%

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

      1. +-commutative 79.9%

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

      2. associate-*l/ 86.8%

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

      3. *-commutative 86.8%

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

   4. Simplified 86.8%

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

   if -1.90000000000000012e-22 < z < 2.75e-176 or 8.6000000000000001e-60 < z < 1.94999999999999994e61

   1. Initial program 95.5%

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

   2. Taylor expanded in z around 0 81.6%

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

      1. +-commutative 81.6%

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

      2. associate-/l* 85.9%

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

   4. Simplified 85.9%

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

      1. associate-/r/ 86.0%

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

   6. Applied egg-rr 86.0%

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

   if 1.94999999999999994e61 < z

   1. Initial program 77.1%

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

      1. *-commutative 77.1%

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

      2. associate-/l* 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in z around inf 83.9%

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

      1. associate-/r/ 91.0%

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

   6. Applied egg-rr 91.0%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+185}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-22}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-176}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-60}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+61}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \]

Alternative 5: 58.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+66}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-242}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+114}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) (- t z))))
   (if (<= y -2.7e+134)
     t_1
     (if (<= y -7.2e+66)
       (+ y x)
       (if (<= y -5.4e+66)
         t_1
         (if (<= y -2.4e-242) x (if (<= y 1.15e+114) (+ y x) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * (t - z);
	double tmp;
	if (y <= -2.7e+134) {
		tmp = t_1;
	} else if (y <= -7.2e+66) {
		tmp = y + x;
	} else if (y <= -5.4e+66) {
		tmp = t_1;
	} else if (y <= -2.4e-242) {
		tmp = x;
	} else if (y <= 1.15e+114) {
		tmp = y + x;
	} 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 = (y / a) * (t - z)
    if (y <= (-2.7d+134)) then
        tmp = t_1
    else if (y <= (-7.2d+66)) then
        tmp = y + x
    else if (y <= (-5.4d+66)) then
        tmp = t_1
    else if (y <= (-2.4d-242)) then
        tmp = x
    else if (y <= 1.15d+114) then
        tmp = y + x
    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 = (y / a) * (t - z);
	double tmp;
	if (y <= -2.7e+134) {
		tmp = t_1;
	} else if (y <= -7.2e+66) {
		tmp = y + x;
	} else if (y <= -5.4e+66) {
		tmp = t_1;
	} else if (y <= -2.4e-242) {
		tmp = x;
	} else if (y <= 1.15e+114) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * (t - z)
	tmp = 0
	if y <= -2.7e+134:
		tmp = t_1
	elif y <= -7.2e+66:
		tmp = y + x
	elif y <= -5.4e+66:
		tmp = t_1
	elif y <= -2.4e-242:
		tmp = x
	elif y <= 1.15e+114:
		tmp = y + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * Float64(t - z))
	tmp = 0.0
	if (y <= -2.7e+134)
		tmp = t_1;
	elseif (y <= -7.2e+66)
		tmp = Float64(y + x);
	elseif (y <= -5.4e+66)
		tmp = t_1;
	elseif (y <= -2.4e-242)
		tmp = x;
	elseif (y <= 1.15e+114)
		tmp = Float64(y + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) * (t - z);
	tmp = 0.0;
	if (y <= -2.7e+134)
		tmp = t_1;
	elseif (y <= -7.2e+66)
		tmp = y + x;
	elseif (y <= -5.4e+66)
		tmp = t_1;
	elseif (y <= -2.4e-242)
		tmp = x;
	elseif (y <= 1.15e+114)
		tmp = y + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e+134], t$95$1, If[LessEqual[y, -7.2e+66], N[(y + x), $MachinePrecision], If[LessEqual[y, -5.4e+66], t$95$1, If[LessEqual[y, -2.4e-242], x, If[LessEqual[y, 1.15e+114], N[(y + x), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7e134 or -7.2e66 < y < -5.4e66 or 1.15e114 < y

   1. Initial program 68.1%

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

   2. Taylor expanded in a around inf 55.1%

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

      1. mul-1-neg 55.1%

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

      2. unsub-neg 55.1%

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

      3. associate-/l* 62.2%

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

   4. Simplified 62.2%

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

   5. Taylor expanded in x around 0 47.8%

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

      1. associate-*l/ 56.8%

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

      2. sub-neg 56.8%

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

      3. distribute-rgt-out 50.9%

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

      4. +-commutative 50.9%

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

      5. *-commutative 50.9%

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

      6. associate-*l/ 50.3%

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

      7. distribute-rgt-in 50.3%

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

      8. distribute-lft-neg-out 50.3%

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

      9. distribute-lft-neg-in 50.3%

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

      10. distribute-rgt-neg-in 50.3%

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

      11. metadata-eval 50.3%

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

      12. *-rgt-identity 50.3%

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

      13. *-commutative 50.3%

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

      14. mul-1-neg 50.3%

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

      15. sub-neg 50.3%

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

      16. associate-*l/ 50.9%

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

      17. *-commutative 50.9%

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

      18. distribute-lft-out-- 56.8%

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

   7. Simplified 56.8%

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

   if -2.7e134 < y < -7.2e66 or -2.4000000000000001e-242 < y < 1.15e114

   1. Initial program 91.7%

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

   2. Taylor expanded in z around inf 81.8%

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

      1. +-commutative 81.8%

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

   4. Simplified 81.8%

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

   if -5.4e66 < y < -2.4000000000000001e-242

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 75.3%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+134}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+66}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+66}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-242}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+114}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 6: 93.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+133}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+111}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a} + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7e+133)
   (+ x (/ y (/ z (- z t))))
   (if (<= z 5.8e+111)
     (+ (/ (* y (- z t)) (- z a)) x)
     (+ x (* y (/ (- z t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7e+133) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 5.8e+111) {
		tmp = ((y * (z - t)) / (z - a)) + x;
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7d+133)) then
        tmp = x + (y / (z / (z - t)))
    else if (z <= 5.8d+111) then
        tmp = ((y * (z - t)) / (z - a)) + x
    else
        tmp = x + (y * ((z - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7e+133) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 5.8e+111) {
		tmp = ((y * (z - t)) / (z - a)) + x;
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7e+133:
		tmp = x + (y / (z / (z - t)))
	elif z <= 5.8e+111:
		tmp = ((y * (z - t)) / (z - a)) + x
	else:
		tmp = x + (y * ((z - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7e+133)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (z <= 5.8e+111)
		tmp = Float64(Float64(Float64(y * Float64(z - t)) / Float64(z - a)) + x);
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7e+133)
		tmp = x + (y / (z / (z - t)));
	elseif (z <= 5.8e+111)
		tmp = ((y * (z - t)) / (z - a)) + x;
	else
		tmp = x + (y * ((z - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7e+133], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+111], N[(N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.9999999999999997e133

   1. Initial program 65.4%

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

   2. Taylor expanded in a around 0 60.4%

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

      1. +-commutative 60.4%

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

      2. associate-/l* 92.7%

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

   4. Simplified 92.7%

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

   if -6.9999999999999997e133 < z < 5.7999999999999999e111

   1. Initial program 94.6%

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

   if 5.7999999999999999e111 < z

   1. Initial program 73.5%

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

      1. *-commutative 73.5%

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

      2. associate-/l* 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in z around inf 86.6%

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

      1. associate-/r/ 95.5%

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

   6. Applied egg-rr 95.5%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+133}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+111}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a} + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \]

Alternative 7: 81.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-19} \lor \neg \left(z \leq 1.6 \cdot 10^{+63}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.3e-19) (not (<= z 1.6e+63)))
   (+ x (* y (/ (- z t) z)))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.3e-19) || !(z <= 1.6e+63)) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.3d-19)) .or. (.not. (z <= 1.6d+63))) then
        tmp = x + (y * ((z - t) / z))
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.3e-19) || !(z <= 1.6e+63)) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.3e-19) or not (z <= 1.6e+63):
		tmp = x + (y * ((z - t) / z))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.3e-19) || !(z <= 1.6e+63))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.3e-19) || ~((z <= 1.6e+63)))
		tmp = x + (y * ((z - t) / z));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.3e-19], N[Not[LessEqual[z, 1.6e+63]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2999999999999998e-19 or 1.60000000000000006e63 < z

   1. Initial program 76.3%

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

      1. *-commutative 76.3%

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

      2. associate-/l* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in z around inf 80.3%

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

      1. associate-/r/ 85.7%

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

   6. Applied egg-rr 85.7%

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

   if -2.2999999999999998e-19 < z < 1.60000000000000006e63

   1. Initial program 96.5%

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

   2. Taylor expanded in z around 0 79.8%

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

      1. +-commutative 79.8%

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

      2. associate-/l* 83.3%

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

   4. Simplified 83.3%

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

      1. associate-/r/ 83.3%

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

   6. Applied egg-rr 83.3%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-19} \lor \neg \left(z \leq 1.6 \cdot 10^{+63}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 8: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z - a}\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{-13} \lor \neg \left(t \leq 6.8 \cdot 10^{+62}\right):\\ \;\;\;\;x - t \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (- z a))))
   (if (or (<= t -8.2e-13) (not (<= t 6.8e+62)))
     (- x (* t t_1))
     (+ x (* z t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (z - a);
	double tmp;
	if ((t <= -8.2e-13) || !(t <= 6.8e+62)) {
		tmp = x - (t * t_1);
	} else {
		tmp = x + (z * 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 = y / (z - a)
    if ((t <= (-8.2d-13)) .or. (.not. (t <= 6.8d+62))) then
        tmp = x - (t * t_1)
    else
        tmp = x + (z * 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 = y / (z - a);
	double tmp;
	if ((t <= -8.2e-13) || !(t <= 6.8e+62)) {
		tmp = x - (t * t_1);
	} else {
		tmp = x + (z * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (z - a)
	tmp = 0
	if (t <= -8.2e-13) or not (t <= 6.8e+62):
		tmp = x - (t * t_1)
	else:
		tmp = x + (z * t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(z - a))
	tmp = 0.0
	if ((t <= -8.2e-13) || !(t <= 6.8e+62))
		tmp = Float64(x - Float64(t * t_1));
	else
		tmp = Float64(x + Float64(z * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (z - a);
	tmp = 0.0;
	if ((t <= -8.2e-13) || ~((t <= 6.8e+62)))
		tmp = x - (t * t_1);
	else
		tmp = x + (z * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -8.2e-13], N[Not[LessEqual[t, 6.8e+62]], $MachinePrecision]], N[(x - N[(t * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -8.2000000000000004e-13 or 6.80000000000000028e62 < t

   1. Initial program 91.0%

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

   2. Taylor expanded in t around inf 85.5%

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

      1. associate-*r/ 91.0%

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

      2. neg-mul-1 91.0%

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

      3. distribute-rgt-neg-in 91.0%

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

      4. distribute-neg-frac 91.0%

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

   4. Simplified 91.0%

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

   5. Taylor expanded in x around 0 85.5%

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

      1. mul-1-neg 85.5%

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

      2. associate-*r/ 91.0%

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

      3. sub-neg 91.0%

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

   7. Simplified 91.0%

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

   if -8.2000000000000004e-13 < t < 6.80000000000000028e62

   1. Initial program 83.2%

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

   2. Taylor expanded in t around 0 77.6%

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

      1. +-commutative 77.6%

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

      2. associate-*l/ 89.6%

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

      3. *-commutative 89.6%

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

   4. Simplified 89.6%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-13} \lor \neg \left(t \leq 6.8 \cdot 10^{+62}\right):\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \]

Alternative 9: 75.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+81} \lor \neg \left(z \leq 2.1 \cdot 10^{+61}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3e+81) (not (<= z 2.1e+61))) (+ y x) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3e+81) || !(z <= 2.1e+61)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * t) / 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 <= (-3d+81)) .or. (.not. (z <= 2.1d+61))) then
        tmp = y + x
    else
        tmp = x + ((y * t) / 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 <= -3e+81) || !(z <= 2.1e+61)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3e+81) or not (z <= 2.1e+61):
		tmp = y + x
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3e+81) || !(z <= 2.1e+61))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3e+81) || ~((z <= 2.1e+61)))
		tmp = y + x;
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3e+81], N[Not[LessEqual[z, 2.1e+61]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.99999999999999997e81 or 2.1000000000000001e61 < z

   1. Initial program 72.0%

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

   2. Taylor expanded in z around inf 81.2%

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

      1. +-commutative 81.2%

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

   4. Simplified 81.2%

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

   if -2.99999999999999997e81 < z < 2.1000000000000001e61

   1. Initial program 96.4%

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

   2. Taylor expanded in z around 0 78.1%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+81} \lor \neg \left(z \leq 2.1 \cdot 10^{+61}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 10: 76.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+81} \lor \neg \left(z \leq 1.3 \cdot 10^{+62}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.6e+81) (not (<= z 1.3e+62))) (+ y x) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.6e+81) || !(z <= 1.3e+62)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-7.6d+81)) .or. (.not. (z <= 1.3d+62))) then
        tmp = y + x
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.6e+81) || !(z <= 1.3e+62)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.6e+81) or not (z <= 1.3e+62):
		tmp = y + x
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.6e+81) || !(z <= 1.3e+62))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.6e+81) || ~((z <= 1.3e+62)))
		tmp = y + x;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.6e+81], N[Not[LessEqual[z, 1.3e+62]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.599999999999999e81 or 1.29999999999999992e62 < z

   1. Initial program 72.0%

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

   2. Taylor expanded in z around inf 81.2%

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

      1. +-commutative 81.2%

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

   4. Simplified 81.2%

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

   if -7.599999999999999e81 < z < 1.29999999999999992e62

   1. Initial program 96.4%

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

   2. Taylor expanded in z around 0 78.1%

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

      1. +-commutative 78.1%

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

      2. associate-/l* 80.8%

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

   4. Simplified 80.8%

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

      1. associate-/r/ 81.5%

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

   6. Applied egg-rr 81.5%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+81} \lor \neg \left(z \leq 1.3 \cdot 10^{+62}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 11: 63.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+152}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+135}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6e+152) x (if (<= a 3.7e+135) (+ y x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6e+152) {
		tmp = x;
	} else if (a <= 3.7e+135) {
		tmp = y + x;
	} 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 <= (-6d+152)) then
        tmp = x
    else if (a <= 3.7d+135) then
        tmp = y + x
    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 <= -6e+152) {
		tmp = x;
	} else if (a <= 3.7e+135) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6e+152:
		tmp = x
	elif a <= 3.7e+135:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6e+152)
		tmp = x;
	elseif (a <= 3.7e+135)
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6e+152)
		tmp = x;
	elseif (a <= 3.7e+135)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6e+152], x, If[LessEqual[a, 3.7e+135], N[(y + x), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -5.99999999999999981e152 or 3.69999999999999997e135 < a

   1. Initial program 87.9%

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

   2. Taylor expanded in x around inf 64.4%

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

   if -5.99999999999999981e152 < a < 3.69999999999999997e135

   1. Initial program 85.7%

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

   2. Taylor expanded in z around inf 69.1%

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

      1. +-commutative 69.1%

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

   4. Simplified 69.1%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+152}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+135}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 49.7% 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 86.4%

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

2. Taylor expanded in x around inf 53.5%

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

3. Final simplification 53.5%

   \[\leadsto x \]

Developer target: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023332 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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