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

Percentage Accurate: 85.8% → 99.6%

Time: 9.2s

Alternatives: 15

Speedup: 0.3×

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: 85.8% 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: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+294}\right):\\ \;\;\;\;x + \frac{1}{\frac{\frac{z - a}{y}}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

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+294)))
     (+ x (/ 1.0 (/ (/ (- z a) y) (- z t))))
     (+ x t_1))))

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+294)) {
		tmp = x + (1.0 / (((z - a) / y) / (z - t)));
	} 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 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+294)) {
		tmp = x + (1.0 / (((z - a) / y) / (z - t)));
	} else {
		tmp = x + t_1;
	}
	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+294):
		tmp = x + (1.0 / (((z - a) / y) / (z - t)))
	else:
		tmp = x + t_1
	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+294))
		tmp = Float64(x + Float64(1.0 / Float64(Float64(Float64(z - a) / y) / Float64(z - t))));
	else
		tmp = Float64(x + t_1);
	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+294)))
		tmp = x + (1.0 / (((z - a) / y) / (z - t)));
	else
		tmp = x + t_1;
	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+294]], $MachinePrecision]], N[(x + N[(1.0 / N[(N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $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 z a)) < -inf.0 or 4.9999999999999999e294 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 41.3%

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

      1. clear-num 41.3%

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

      2. inv-pow 41.3%

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

   4. Applied egg-rr 41.3%

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

      1. unpow-1 41.3%

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

      2. associate-/r* 99.7%

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

   6. Simplified 99.7%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 4.9999999999999999e294

   1. Initial program 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 5 \cdot 10^{+294}\right):\\ \;\;\;\;x + \frac{1}{\frac{\frac{z - a}{y}}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.2% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.2%

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

   1. +-commutative 85.2%

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

   2. associate-/l* 98.1%

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

   3. fma-define 98.1%

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

3. Simplified 98.1%

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

Alternative 3: 96.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+294}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{\frac{z - a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (<= t_1 (- INFINITY))
     (* (- z t) (/ y (- z a)))
     (if (<= t_1 5e+294) (+ x t_1) (/ (- z t) (/ (- z a) y))))))

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)) {
		tmp = (z - t) * (y / (z - a));
	} else if (t_1 <= 5e+294) {
		tmp = x + t_1;
	} else {
		tmp = (z - t) / ((z - a) / y);
	}
	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) {
		tmp = (z - t) * (y / (z - a));
	} else if (t_1 <= 5e+294) {
		tmp = x + t_1;
	} else {
		tmp = (z - t) / ((z - a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (z - a)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (z - t) * (y / (z - a))
	elif t_1 <= 5e+294:
		tmp = x + t_1
	else:
		tmp = (z - t) / ((z - a) / y)
	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))
		tmp = Float64(Float64(z - t) * Float64(y / Float64(z - a)));
	elseif (t_1 <= 5e+294)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(Float64(z - t) / Float64(Float64(z - a) / y));
	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)
		tmp = (z - t) * (y / (z - a));
	elseif (t_1 <= 5e+294)
		tmp = x + t_1;
	else
		tmp = (z - t) / ((z - a) / y);
	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[LessEqual[t$95$1, (-Infinity)], N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+294], N[(x + t$95$1), $MachinePrecision], N[(N[(z - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 42.4%

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

   3. Taylor expanded in x around 0 42.4%

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

      1. associate-*l/ 89.5%

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

   5. Simplified 89.5%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 4.9999999999999999e294

   1. Initial program 99.9%

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

   if 4.9999999999999999e294 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 39.8%

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

   3. Taylor expanded in x around 0 39.8%

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

      1. associate-*l/ 96.3%

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

   5. Simplified 96.3%

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

      1. clear-num 96.1%

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

      2. associate-*l/ 96.4%

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

      3. *-un-lft-identity 96.4%

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

   7. Applied egg-rr 96.4%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq 5 \cdot 10^{+294}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{\frac{z - a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(1 - \frac{t}{z}\right)\\ t_2 := x + y \cdot \frac{t - z}{a}\\ \mathbf{if}\;a \leq -1.26 \cdot 10^{-25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (- 1.0 (/ t z))))) (t_2 (+ x (* y (/ (- t z) a)))))
   (if (<= a -1.26e-25)
     t_2
     (if (<= a 2.9e-109)
       t_1
       (if (<= a 3.2e-49) (+ x (/ (* y t) a)) (if (<= a 7.5e-11) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double t_2 = x + (y * ((t - z) / a));
	double tmp;
	if (a <= -1.26e-25) {
		tmp = t_2;
	} else if (a <= 2.9e-109) {
		tmp = t_1;
	} else if (a <= 3.2e-49) {
		tmp = x + ((y * t) / a);
	} else if (a <= 7.5e-11) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * (1.0d0 - (t / z)))
    t_2 = x + (y * ((t - z) / a))
    if (a <= (-1.26d-25)) then
        tmp = t_2
    else if (a <= 2.9d-109) then
        tmp = t_1
    else if (a <= 3.2d-49) then
        tmp = x + ((y * t) / a)
    else if (a <= 7.5d-11) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double t_2 = x + (y * ((t - z) / a));
	double tmp;
	if (a <= -1.26e-25) {
		tmp = t_2;
	} else if (a <= 2.9e-109) {
		tmp = t_1;
	} else if (a <= 3.2e-49) {
		tmp = x + ((y * t) / a);
	} else if (a <= 7.5e-11) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (1.0 - (t / z)))
	t_2 = x + (y * ((t - z) / a))
	tmp = 0
	if a <= -1.26e-25:
		tmp = t_2
	elif a <= 2.9e-109:
		tmp = t_1
	elif a <= 3.2e-49:
		tmp = x + ((y * t) / a)
	elif a <= 7.5e-11:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))))
	t_2 = Float64(x + Float64(y * Float64(Float64(t - z) / a)))
	tmp = 0.0
	if (a <= -1.26e-25)
		tmp = t_2;
	elseif (a <= 2.9e-109)
		tmp = t_1;
	elseif (a <= 3.2e-49)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= 7.5e-11)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (1.0 - (t / z)));
	t_2 = x + (y * ((t - z) / a));
	tmp = 0.0;
	if (a <= -1.26e-25)
		tmp = t_2;
	elseif (a <= 2.9e-109)
		tmp = t_1;
	elseif (a <= 3.2e-49)
		tmp = x + ((y * t) / a);
	elseif (a <= 7.5e-11)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.26e-25], t$95$2, If[LessEqual[a, 2.9e-109], t$95$1, If[LessEqual[a, 3.2e-49], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e-11], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.26e-25 or 7.5e-11 < a

   1. Initial program 82.8%

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

   3. Taylor expanded in a around inf 77.7%

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

      1. mul-1-neg 77.7%

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

      2. unsub-neg 77.7%

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

      3. associate-/l* 89.3%

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

   5. Simplified 89.3%

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

   if -1.26e-25 < a < 2.9e-109 or 3.20000000000000002e-49 < a < 7.5e-11

   1. Initial program 88.3%

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

   3. Taylor expanded in a around 0 78.2%

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

      1. associate-/l* 89.6%

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

      2. div-sub 89.6%

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

      3. *-inverses 89.6%

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

   5. Simplified 89.6%

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

   if 2.9e-109 < a < 3.20000000000000002e-49

   1. Initial program 79.7%

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

   3. Taylor expanded in z around 0 80.4%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.26 \cdot 10^{-25}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-109}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-11}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(1 - \frac{t}{z}\right)\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{-39}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-47}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (- 1.0 (/ t z))))) (t_2 (+ x (* t (/ y a)))))
   (if (<= a -2.8e-39)
     t_2
     (if (<= a 3.2e-112)
       t_1
       (if (<= a 5e-47) (+ x (/ (* y t) a)) (if (<= a 1.5e-9) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double t_2 = x + (t * (y / a));
	double tmp;
	if (a <= -2.8e-39) {
		tmp = t_2;
	} else if (a <= 3.2e-112) {
		tmp = t_1;
	} else if (a <= 5e-47) {
		tmp = x + ((y * t) / a);
	} else if (a <= 1.5e-9) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * (1.0d0 - (t / z)))
    t_2 = x + (t * (y / a))
    if (a <= (-2.8d-39)) then
        tmp = t_2
    else if (a <= 3.2d-112) then
        tmp = t_1
    else if (a <= 5d-47) then
        tmp = x + ((y * t) / a)
    else if (a <= 1.5d-9) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double t_2 = x + (t * (y / a));
	double tmp;
	if (a <= -2.8e-39) {
		tmp = t_2;
	} else if (a <= 3.2e-112) {
		tmp = t_1;
	} else if (a <= 5e-47) {
		tmp = x + ((y * t) / a);
	} else if (a <= 1.5e-9) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (1.0 - (t / z)))
	t_2 = x + (t * (y / a))
	tmp = 0
	if a <= -2.8e-39:
		tmp = t_2
	elif a <= 3.2e-112:
		tmp = t_1
	elif a <= 5e-47:
		tmp = x + ((y * t) / a)
	elif a <= 1.5e-9:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))))
	t_2 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (a <= -2.8e-39)
		tmp = t_2;
	elseif (a <= 3.2e-112)
		tmp = t_1;
	elseif (a <= 5e-47)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= 1.5e-9)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (1.0 - (t / z)));
	t_2 = x + (t * (y / a));
	tmp = 0.0;
	if (a <= -2.8e-39)
		tmp = t_2;
	elseif (a <= 3.2e-112)
		tmp = t_1;
	elseif (a <= 5e-47)
		tmp = x + ((y * t) / a);
	elseif (a <= 1.5e-9)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.8e-39], t$95$2, If[LessEqual[a, 3.2e-112], t$95$1, If[LessEqual[a, 5e-47], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e-9], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.8000000000000001e-39 or 1.49999999999999999e-9 < a

   1. Initial program 83.2%

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

   3. Taylor expanded in z around 0 69.1%

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

      1. +-commutative 69.1%

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

      2. associate-/l* 78.9%

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

   5. Simplified 78.9%

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

   if -2.8000000000000001e-39 < a < 3.19999999999999993e-112 or 5.00000000000000011e-47 < a < 1.49999999999999999e-9

   1. Initial program 88.0%

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

   3. Taylor expanded in a around 0 78.5%

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

      1. associate-/l* 90.2%

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

      2. div-sub 90.2%

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

      3. *-inverses 90.2%

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

   5. Simplified 90.2%

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

   if 3.19999999999999993e-112 < a < 5.00000000000000011e-47

   1. Initial program 79.7%

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

   3. Taylor expanded in z around 0 80.4%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-39}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-112}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-47}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-9}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.22 \cdot 10^{+61}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+64}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= z -1.22e+61)
     (+ y x)
     (if (<= z 1000.0)
       t_1
       (if (<= z 1.25e+64)
         (- x (* y (/ t z)))
         (if (<= z 8.8e+76) t_1 (+ y x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -1.22e+61) {
		tmp = y + x;
	} else if (z <= 1000.0) {
		tmp = t_1;
	} else if (z <= 1.25e+64) {
		tmp = x - (y * (t / z));
	} else if (z <= 8.8e+76) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + (t * (y / a))
    if (z <= (-1.22d+61)) then
        tmp = y + x
    else if (z <= 1000.0d0) then
        tmp = t_1
    else if (z <= 1.25d+64) then
        tmp = x - (y * (t / z))
    else if (z <= 8.8d+76) then
        tmp = t_1
    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 t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -1.22e+61) {
		tmp = y + x;
	} else if (z <= 1000.0) {
		tmp = t_1;
	} else if (z <= 1.25e+64) {
		tmp = x - (y * (t / z));
	} else if (z <= 8.8e+76) {
		tmp = t_1;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if z <= -1.22e+61:
		tmp = y + x
	elif z <= 1000.0:
		tmp = t_1
	elif z <= 1.25e+64:
		tmp = x - (y * (t / z))
	elif z <= 8.8e+76:
		tmp = t_1
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (z <= -1.22e+61)
		tmp = Float64(y + x);
	elseif (z <= 1000.0)
		tmp = t_1;
	elseif (z <= 1.25e+64)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	elseif (z <= 8.8e+76)
		tmp = t_1;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (z <= -1.22e+61)
		tmp = y + x;
	elseif (z <= 1000.0)
		tmp = t_1;
	elseif (z <= 1.25e+64)
		tmp = x - (y * (t / z));
	elseif (z <= 8.8e+76)
		tmp = t_1;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.22e+61], N[(y + x), $MachinePrecision], If[LessEqual[z, 1000.0], t$95$1, If[LessEqual[z, 1.25e+64], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e+76], t$95$1, N[(y + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.22e61 or 8.8000000000000002e76 < z

   1. Initial program 73.8%

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

   3. Taylor expanded in z around inf 78.7%

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

      1. +-commutative 78.7%

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

   5. Simplified 78.7%

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

   if -1.22e61 < z < 1e3 or 1.25e64 < z < 8.8000000000000002e76

   1. Initial program 92.6%

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

   3. Taylor expanded in z around 0 70.9%

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

      1. +-commutative 70.9%

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

      2. associate-/l* 76.4%

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

   5. Simplified 76.4%

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

   if 1e3 < z < 1.25e64

   1. Initial program 93.7%

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

   3. Taylor expanded in a around 0 68.0%

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

      1. associate-/l* 74.0%

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

      2. div-sub 73.9%

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

      3. *-inverses 73.9%

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

   5. Simplified 73.9%

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

   6. Taylor expanded in t around inf 61.9%

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

      1. mul-1-neg 61.9%

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

      2. distribute-frac-neg2 61.9%

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

      3. associate-*l/ 62.9%

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

      4. *-commutative 62.9%

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

   8. Simplified 62.9%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+61}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1000:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+64}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+76}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-53}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+140}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z t) (/ y (- z a)))))
   (if (<= y -2.6e+17)
     t_1
     (if (<= y 4e-53) (+ y x) (if (<= y 1.35e+140) (+ x (/ (* y t) a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * (y / (z - a));
	double tmp;
	if (y <= -2.6e+17) {
		tmp = t_1;
	} else if (y <= 4e-53) {
		tmp = y + x;
	} else if (y <= 1.35e+140) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) * (y / (z - a))
    if (y <= (-2.6d+17)) then
        tmp = t_1
    else if (y <= 4d-53) then
        tmp = y + x
    else if (y <= 1.35d+140) then
        tmp = x + ((y * t) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * (y / (z - a));
	double tmp;
	if (y <= -2.6e+17) {
		tmp = t_1;
	} else if (y <= 4e-53) {
		tmp = y + x;
	} else if (y <= 1.35e+140) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) * (y / (z - a))
	tmp = 0
	if y <= -2.6e+17:
		tmp = t_1
	elif y <= 4e-53:
		tmp = y + x
	elif y <= 1.35e+140:
		tmp = x + ((y * t) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) * Float64(y / Float64(z - a)))
	tmp = 0.0
	if (y <= -2.6e+17)
		tmp = t_1;
	elseif (y <= 4e-53)
		tmp = Float64(y + x);
	elseif (y <= 1.35e+140)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) * (y / (z - a));
	tmp = 0.0;
	if (y <= -2.6e+17)
		tmp = t_1;
	elseif (y <= 4e-53)
		tmp = y + x;
	elseif (y <= 1.35e+140)
		tmp = x + ((y * t) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+17], t$95$1, If[LessEqual[y, 4e-53], N[(y + x), $MachinePrecision], If[LessEqual[y, 1.35e+140], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6e17 or 1.35000000000000009e140 < y

   1. Initial program 62.4%

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

   3. Taylor expanded in x around 0 45.1%

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

      1. associate-*l/ 74.8%

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

   5. Simplified 74.8%

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

   if -2.6e17 < y < 4.00000000000000012e-53

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 82.1%

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

      1. +-commutative 82.1%

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

   5. Simplified 82.1%

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

   if 4.00000000000000012e-53 < y < 1.35000000000000009e140

   1. Initial program 95.5%

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

   3. Taylor expanded in z around 0 74.1%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+17}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-53}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+140}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-246}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-232}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.8e-246)
   (+ y x)
   (if (<= z 3.5e-232) (* t (/ y a)) (if (<= z 3.4e-9) x (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.8e-246) {
		tmp = y + x;
	} else if (z <= 3.5e-232) {
		tmp = t * (y / a);
	} else if (z <= 3.4e-9) {
		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 (z <= (-3.8d-246)) then
        tmp = y + x
    else if (z <= 3.5d-232) then
        tmp = t * (y / a)
    else if (z <= 3.4d-9) 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 (z <= -3.8e-246) {
		tmp = y + x;
	} else if (z <= 3.5e-232) {
		tmp = t * (y / a);
	} else if (z <= 3.4e-9) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.8e-246:
		tmp = y + x
	elif z <= 3.5e-232:
		tmp = t * (y / a)
	elif z <= 3.4e-9:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.8e-246)
		tmp = Float64(y + x);
	elseif (z <= 3.5e-232)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 3.4e-9)
		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 (z <= -3.8e-246)
		tmp = y + x;
	elseif (z <= 3.5e-232)
		tmp = t * (y / a);
	elseif (z <= 3.4e-9)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.8e-246], N[(y + x), $MachinePrecision], If[LessEqual[z, 3.5e-232], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e-9], x, N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.79999999999999976e-246 or 3.3999999999999998e-9 < z

   1. Initial program 82.3%

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

   3. Taylor expanded in z around inf 65.0%

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

      1. +-commutative 65.0%

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

   5. Simplified 65.0%

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

   if -3.79999999999999976e-246 < z < 3.4999999999999998e-232

   1. Initial program 86.6%

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

   3. Taylor expanded in x around 0 58.9%

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

      1. associate-*l/ 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in z around 0 54.7%

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

      1. associate-*r/ 64.8%

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

   8. Simplified 64.8%

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

   if 3.4999999999999998e-232 < z < 3.3999999999999998e-9

   1. Initial program 95.8%

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

   3. Taylor expanded in x around inf 59.7%

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

Alternative 9: 76.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+59} \lor \neg \left(z \leq 3.7 \cdot 10^{+78}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.3e+59) (not (<= z 3.7e+78))) (+ y x) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.3e+59) || !(z <= 3.7e+78)) {
		tmp = y + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.3d+59)) .or. (.not. (z <= 3.7d+78))) then
        tmp = y + x
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.3e+59) || !(z <= 3.7e+78)) {
		tmp = y + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.3e+59) or not (z <= 3.7e+78):
		tmp = y + x
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.3e+59) || !(z <= 3.7e+78))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.3e+59) || ~((z <= 3.7e+78)))
		tmp = y + x;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.3e+59], N[Not[LessEqual[z, 3.7e+78]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2999999999999999e59 or 3.69999999999999985e78 < z

   1. Initial program 73.8%

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

   3. Taylor expanded in z around inf 78.7%

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

      1. +-commutative 78.7%

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

   5. Simplified 78.7%

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

   if -3.2999999999999999e59 < z < 3.69999999999999985e78

   1. Initial program 92.7%

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

   3. Taylor expanded in z around 0 67.5%

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

      1. +-commutative 67.5%

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

      2. associate-/l* 72.5%

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

   5. Simplified 72.5%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+59} \lor \neg \left(z \leq 3.7 \cdot 10^{+78}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+40} \lor \neg \left(z \leq 5.9 \cdot 10^{+26}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.2e+40) (not (<= z 5.9e+26))) (+ y x) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.2e+40) || !(z <= 5.9e+26)) {
		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 <= (-3.2d+40)) .or. (.not. (z <= 5.9d+26))) 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 <= -3.2e+40) || !(z <= 5.9e+26)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.2e+40) or not (z <= 5.9e+26):
		tmp = y + x
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.2e+40) || !(z <= 5.9e+26))
		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 <= -3.2e+40) || ~((z <= 5.9e+26)))
		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, -3.2e+40], N[Not[LessEqual[z, 5.9e+26]], $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 < -3.19999999999999981e40 or 5.9000000000000003e26 < z

   1. Initial program 74.2%

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

   3. Taylor expanded in z around inf 72.6%

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

      1. +-commutative 72.6%

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

   5. Simplified 72.6%

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

   if -3.19999999999999981e40 < z < 5.9000000000000003e26

   1. Initial program 94.5%

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

   3. Taylor expanded in z around 0 72.6%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+40} \lor \neg \left(z \leq 5.9 \cdot 10^{+26}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+148}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+118}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.06e+148)
   (* t (/ y a))
   (if (<= t 1.9e+118) (+ y x) (* y (/ (- z t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.06e+148) {
		tmp = t * (y / a);
	} else if (t <= 1.9e+118) {
		tmp = y + x;
	} else {
		tmp = 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 (t <= (-1.06d+148)) then
        tmp = t * (y / a)
    else if (t <= 1.9d+118) then
        tmp = y + x
    else
        tmp = 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 (t <= -1.06e+148) {
		tmp = t * (y / a);
	} else if (t <= 1.9e+118) {
		tmp = y + x;
	} else {
		tmp = y * ((z - t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.06e+148:
		tmp = t * (y / a)
	elif t <= 1.9e+118:
		tmp = y + x
	else:
		tmp = y * ((z - t) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.06e+148)
		tmp = Float64(t * Float64(y / a));
	elseif (t <= 1.9e+118)
		tmp = Float64(y + x);
	else
		tmp = 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 (t <= -1.06e+148)
		tmp = t * (y / a);
	elseif (t <= 1.9e+118)
		tmp = y + x;
	else
		tmp = y * ((z - t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.06e+148], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e+118], N[(y + x), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.06e148

   1. Initial program 69.9%

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

   3. Taylor expanded in x around 0 47.2%

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

      1. associate-*l/ 74.4%

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

   5. Simplified 74.4%

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

   6. Taylor expanded in z around 0 32.6%

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

      1. associate-*r/ 51.7%

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

   8. Simplified 51.7%

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

   if -1.06e148 < t < 1.90000000000000008e118

   1. Initial program 89.4%

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

   3. Taylor expanded in z around inf 69.2%

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

      1. +-commutative 69.2%

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

   5. Simplified 69.2%

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

   if 1.90000000000000008e118 < t

   1. Initial program 79.5%

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

   3. Taylor expanded in x around 0 58.1%

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

      1. associate-*l/ 69.5%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in a around 0 40.8%

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

      1. associate-/l* 51.9%

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

   8. Simplified 51.9%

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

Alternative 12: 59.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+147}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+270}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8.2e+147)
   (* t (/ y a))
   (if (<= t 8.6e+270) (+ y x) (* t (/ y (- z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8.2e+147) {
		tmp = t * (y / a);
	} else if (t <= 8.6e+270) {
		tmp = y + x;
	} else {
		tmp = t * (y / -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 <= (-8.2d+147)) then
        tmp = t * (y / a)
    else if (t <= 8.6d+270) then
        tmp = y + x
    else
        tmp = t * (y / -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 <= -8.2e+147) {
		tmp = t * (y / a);
	} else if (t <= 8.6e+270) {
		tmp = y + x;
	} else {
		tmp = t * (y / -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8.2e+147:
		tmp = t * (y / a)
	elif t <= 8.6e+270:
		tmp = y + x
	else:
		tmp = t * (y / -z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8.2e+147)
		tmp = Float64(t * Float64(y / a));
	elseif (t <= 8.6e+270)
		tmp = Float64(y + x);
	else
		tmp = Float64(t * Float64(y / Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -8.2e+147)
		tmp = t * (y / a);
	elseif (t <= 8.6e+270)
		tmp = y + x;
	else
		tmp = t * (y / -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8.2e+147], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.6e+270], N[(y + x), $MachinePrecision], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.19999999999999932e147

   1. Initial program 69.9%

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

   3. Taylor expanded in x around 0 47.2%

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

      1. associate-*l/ 74.4%

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

   5. Simplified 74.4%

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

   6. Taylor expanded in z around 0 32.6%

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

      1. associate-*r/ 51.7%

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

   8. Simplified 51.7%

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

   if -8.19999999999999932e147 < t < 8.5999999999999999e270

   1. Initial program 88.5%

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

   3. Taylor expanded in z around inf 65.2%

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

      1. +-commutative 65.2%

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

   5. Simplified 65.2%

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

   if 8.5999999999999999e270 < t

   1. Initial program 73.7%

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

      1. +-commutative 73.7%

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

      2. *-commutative 73.7%

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

      3. associate-/l* 99.9%

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

      4. fma-define 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around inf 59.5%

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

      1. associate-/l* 85.8%

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

      2. associate-*r* 85.8%

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

      3. neg-mul-1 85.8%

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

      4. *-commutative 85.8%

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

   9. Simplified 85.8%

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

   10. Taylor expanded in z around inf 64.3%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+147}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+270}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-36} \lor \neg \left(z \leq 1.6 \cdot 10^{-8}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.6e-36) (not (<= z 1.6e-8))) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.6e-36) || !(z <= 1.6e-8)) {
		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 ((z <= (-7.6d-36)) .or. (.not. (z <= 1.6d-8))) 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 ((z <= -7.6e-36) || !(z <= 1.6e-8)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.6e-36) or not (z <= 1.6e-8):
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.6e-36) || !(z <= 1.6e-8))
		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 ((z <= -7.6e-36) || ~((z <= 1.6e-8)))
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.6e-36], N[Not[LessEqual[z, 1.6e-8]], $MachinePrecision]], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -7.59999999999999942e-36 or 1.6000000000000001e-8 < z

   1. Initial program 79.0%

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

   3. Taylor expanded in z around inf 69.0%

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

      1. +-commutative 69.0%

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

   5. Simplified 69.0%

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

   if -7.59999999999999942e-36 < z < 1.6000000000000001e-8

   1. Initial program 93.2%

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

   3. Taylor expanded in x around inf 52.7%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-36} \lor \neg \left(z \leq 1.6 \cdot 10^{-8}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-148}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-288}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -5.6e-148) x (if (<= x 6e-288) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5.6e-148) {
		tmp = x;
	} else if (x <= 6e-288) {
		tmp = y;
	} 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 (x <= (-5.6d-148)) then
        tmp = x
    else if (x <= 6d-288) then
        tmp = y
    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 (x <= -5.6e-148) {
		tmp = x;
	} else if (x <= 6e-288) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -5.6e-148:
		tmp = x
	elif x <= 6e-288:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -5.6e-148)
		tmp = x;
	elseif (x <= 6e-288)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -5.6e-148)
		tmp = x;
	elseif (x <= 6e-288)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -5.6e-148], x, If[LessEqual[x, 6e-288], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.6e-148 or 5.99999999999999998e-288 < x

   1. Initial program 85.1%

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

   3. Taylor expanded in x around inf 58.4%

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

   if -5.6e-148 < x < 5.99999999999999998e-288

   1. Initial program 85.7%

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

   3. Taylor expanded in x around 0 79.8%

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

      1. associate-*l/ 75.8%

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

   5. Simplified 75.8%

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

   6. Taylor expanded in z around inf 46.5%

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

Alternative 15: 51.1% 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 85.2%

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

3. Taylor expanded in x around inf 49.4%

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

Developer target: 98.3% 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 2024085 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (+ x (/ y (/ (- z a) (- z t))))

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