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

Percentage Accurate: 85.5% → 99.4%

Time: 10.3s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x - \frac{y - z}{\frac{z - a}{t}}\\ \mathbf{elif}\;t\_1 \leq 10^{+261}:\\ \;\;\;\;t\_1 + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z - a} \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (<= t_1 (- INFINITY))
     (- x (/ (- y z) (/ (- z a) t)))
     (if (<= t_1 1e+261) (+ t_1 x) (+ x (* (/ t (- z a)) (- z y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x - ((y - z) / ((z - a) / t));
	} else if (t_1 <= 1e+261) {
		tmp = t_1 + x;
	} else {
		tmp = x + ((t / (z - a)) * (z - y));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x - ((y - z) / ((z - a) / t));
	} else if (t_1 <= 1e+261) {
		tmp = t_1 + x;
	} else {
		tmp = x + ((t / (z - a)) * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - z) * t) / (a - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x - ((y - z) / ((z - a) / t))
	elif t_1 <= 1e+261:
		tmp = t_1 + x
	else:
		tmp = x + ((t / (z - a)) * (z - y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x - Float64(Float64(y - z) / Float64(Float64(z - a) / t)));
	elseif (t_1 <= 1e+261)
		tmp = Float64(t_1 + x);
	else
		tmp = Float64(x + Float64(Float64(t / Float64(z - a)) * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x - ((y - z) / ((z - a) / t));
	elseif (t_1 <= 1e+261)
		tmp = t_1 + x;
	else
		tmp = x + ((t / (z - a)) * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+261], N[(t$95$1 + x), $MachinePrecision], N[(x + N[(N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 30.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 9.9999999999999993e260

   1. Initial program 99.4%

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

   if 9.9999999999999993e260 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 34.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -\infty:\\ \;\;\;\;x - \frac{y - z}{\frac{z - a}{t}}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq 10^{+261}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z - a} \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 10^{+261}\right):\\ \;\;\;\;x + \frac{t}{z - a} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+261)))
     (+ x (* (/ t (- z a)) (- z y)))
     (+ t_1 x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+261)) {
		tmp = x + ((t / (z - a)) * (z - 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) / (a - z);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+261)) {
		tmp = x + ((t / (z - a)) * (z - y));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - z) * t) / (a - z)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+261):
		tmp = x + ((t / (z - a)) * (z - y))
	else:
		tmp = t_1 + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+261))
		tmp = Float64(x + Float64(Float64(t / Float64(z - a)) * Float64(z - 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) / (a - z);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+261)))
		tmp = x + ((t / (z - a)) * (z - y));
	else
		tmp = t_1 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+261]], $MachinePrecision]], N[(x + N[(N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0 or 9.9999999999999993e260 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 32.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 9.9999999999999993e260

   1. Initial program 99.4%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -\infty \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \leq 10^{+261}\right):\\ \;\;\;\;x + \frac{t}{z - a} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{-129}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;a \leq 18:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.45e-22)
   (+ x (/ t (/ a y)))
   (if (<= a 1.18e-129)
     (+ t x)
     (if (<= a 3.1e-52)
       (* t (/ (- z y) (- z a)))
       (if (<= a 18.0) (+ t x) (+ x (* y (/ t a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.45e-22) {
		tmp = x + (t / (a / y));
	} else if (a <= 1.18e-129) {
		tmp = t + x;
	} else if (a <= 3.1e-52) {
		tmp = t * ((z - y) / (z - a));
	} else if (a <= 18.0) {
		tmp = t + 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 (a <= (-1.45d-22)) then
        tmp = x + (t / (a / y))
    else if (a <= 1.18d-129) then
        tmp = t + x
    else if (a <= 3.1d-52) then
        tmp = t * ((z - y) / (z - a))
    else if (a <= 18.0d0) then
        tmp = t + 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 (a <= -1.45e-22) {
		tmp = x + (t / (a / y));
	} else if (a <= 1.18e-129) {
		tmp = t + x;
	} else if (a <= 3.1e-52) {
		tmp = t * ((z - y) / (z - a));
	} else if (a <= 18.0) {
		tmp = t + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.45e-22:
		tmp = x + (t / (a / y))
	elif a <= 1.18e-129:
		tmp = t + x
	elif a <= 3.1e-52:
		tmp = t * ((z - y) / (z - a))
	elif a <= 18.0:
		tmp = t + x
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.45e-22)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (a <= 1.18e-129)
		tmp = Float64(t + x);
	elseif (a <= 3.1e-52)
		tmp = Float64(t * Float64(Float64(z - y) / Float64(z - a)));
	elseif (a <= 18.0)
		tmp = Float64(t + 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 (a <= -1.45e-22)
		tmp = x + (t / (a / y));
	elseif (a <= 1.18e-129)
		tmp = t + x;
	elseif (a <= 3.1e-52)
		tmp = t * ((z - y) / (z - a));
	elseif (a <= 18.0)
		tmp = t + x;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.45e-22], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.18e-129], N[(t + x), $MachinePrecision], If[LessEqual[a, 3.1e-52], N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 18.0], N[(t + x), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.4500000000000001e-22

   1. Initial program 91.8%

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

      1. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in z around 0 82.3%

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

      1. +-commutative 82.3%

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

      2. associate-/l* 84.1%

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

   7. Simplified 84.1%

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

      1. clear-num 84.1%

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

      2. un-div-inv 84.2%

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

   9. Applied egg-rr 84.2%

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

   if -1.4500000000000001e-22 < a < 1.1800000000000001e-129 or 3.0999999999999999e-52 < a < 18

   1. Initial program 82.6%

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

      1. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in z around inf 83.1%

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

   if 1.1800000000000001e-129 < a < 3.0999999999999999e-52

   1. Initial program 99.7%

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

      1. associate-/l* 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in x around inf 87.2%

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

      1. associate-/l* 87.3%

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

      2. *-commutative 87.3%

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

   7. Simplified 87.3%

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

   8. Taylor expanded in x around 0 72.9%

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

      1. associate-/l* 72.9%

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

   10. Simplified 72.9%

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

   if 18 < a

   1. Initial program 85.5%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in z around 0 80.7%

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

      1. +-commutative 80.7%

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

      2. associate-/l* 85.1%

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

   7. Simplified 85.1%

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

      1. clear-num 85.1%

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

      2. un-div-inv 85.1%

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

   9. Applied egg-rr 85.1%

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

       1. associate-/r/ 85.2%

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

   11. Simplified 85.2%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{-129}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;a \leq 18:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-139} \lor \neg \left(x \leq 8.5 \cdot 10^{-143}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.25e-139) (not (<= x 8.5e-143)))
   (+ x (* t (/ y (- a z))))
   (* t (/ (- z y) (- z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.25e-139) || !(x <= 8.5e-143)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = t * ((z - y) / (z - a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-1.25d-139)) .or. (.not. (x <= 8.5d-143))) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = t * ((z - y) / (z - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.25e-139) || !(x <= 8.5e-143)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = t * ((z - y) / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.25e-139) or not (x <= 8.5e-143):
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = t * ((z - y) / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.25e-139) || !(x <= 8.5e-143))
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(t * Float64(Float64(z - y) / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.25e-139) || ~((x <= 8.5e-143)))
		tmp = x + (t * (y / (a - z)));
	else
		tmp = t * ((z - y) / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.25e-139], N[Not[LessEqual[x, 8.5e-143]], $MachinePrecision]], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.25000000000000008e-139 or 8.50000000000000072e-143 < x

   1. Initial program 88.4%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in y around inf 89.6%

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

      1. associate-/l* 92.8%

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

   7. Simplified 92.8%

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

   if -1.25000000000000008e-139 < x < 8.50000000000000072e-143

   1. Initial program 82.2%

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

      1. associate-/l* 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in x around inf 67.6%

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

      1. associate-/l* 64.6%

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

      2. *-commutative 64.6%

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

   7. Simplified 64.6%

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

   8. Taylor expanded in x around 0 67.9%

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

      1. associate-/l* 84.0%

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

   10. Simplified 84.0%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-139} \lor \neg \left(x \leq 8.5 \cdot 10^{-143}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-140}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{-141}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{z - a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -7.2e-140)
   (+ x (* t (/ y (- a z))))
   (if (<= x 1.16e-141) (* t (/ (- z y) (- z a))) (- x (/ y (/ (- z a) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -7.2e-140) {
		tmp = x + (t * (y / (a - z)));
	} else if (x <= 1.16e-141) {
		tmp = t * ((z - y) / (z - a));
	} else {
		tmp = x - (y / ((z - a) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-7.2d-140)) then
        tmp = x + (t * (y / (a - z)))
    else if (x <= 1.16d-141) then
        tmp = t * ((z - y) / (z - a))
    else
        tmp = x - (y / ((z - a) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -7.2e-140) {
		tmp = x + (t * (y / (a - z)));
	} else if (x <= 1.16e-141) {
		tmp = t * ((z - y) / (z - a));
	} else {
		tmp = x - (y / ((z - a) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -7.2e-140:
		tmp = x + (t * (y / (a - z)))
	elif x <= 1.16e-141:
		tmp = t * ((z - y) / (z - a))
	else:
		tmp = x - (y / ((z - a) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -7.2e-140)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	elseif (x <= 1.16e-141)
		tmp = Float64(t * Float64(Float64(z - y) / Float64(z - a)));
	else
		tmp = Float64(x - Float64(y / Float64(Float64(z - a) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -7.2e-140)
		tmp = x + (t * (y / (a - z)));
	elseif (x <= 1.16e-141)
		tmp = t * ((z - y) / (z - a));
	else
		tmp = x - (y / ((z - a) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -7.2e-140], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.16e-141], N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.2000000000000001e-140

   1. Initial program 90.9%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in y around inf 91.3%

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

      1. associate-/l* 94.3%

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

   7. Simplified 94.3%

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

   if -7.2000000000000001e-140 < x < 1.15999999999999996e-141

   1. Initial program 82.2%

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

      1. associate-/l* 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in x around inf 67.6%

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

      1. associate-/l* 64.6%

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

      2. *-commutative 64.6%

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

   7. Simplified 64.6%

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

   8. Taylor expanded in x around 0 67.9%

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

      1. associate-/l* 84.0%

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

   10. Simplified 84.0%

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

   if 1.15999999999999996e-141 < x

   1. Initial program 85.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 87.6%

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

      1. div-inv 87.6%

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

      2. *-commutative 87.6%

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

      3. associate-*l* 92.0%

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

      4. div-inv 92.0%

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

      5. clear-num 92.0%

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

      6. div-inv 92.1%

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

      7. add-cube-cbrt 91.9%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{\frac{a - z}{t}} \]

      8. *-un-lft-identity 91.9%

         \[\leadsto x + \frac{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}{\color{blue}{1 \cdot \frac{a - z}{t}}} \]

      9. times-frac 91.9%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{a - z}{t}}} \]

      10. pow2 91.9%

          \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{y}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{a - z}{t}} \]

   7. Applied egg-rr 91.9%

      \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{a - z}{t}}} \]
   8. Step-by-step derivation

      1. times-frac 91.9%

         \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2} \cdot \sqrt[3]{y}}{1 \cdot \frac{a - z}{t}}} \]

      2. unpow2 91.9%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)} \cdot \sqrt[3]{y}}{1 \cdot \frac{a - z}{t}} \]

      3. rem-3cbrt-lft 92.1%

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

      4. *-lft-identity 92.1%

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

   9. Simplified 92.1%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-140}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{-141}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{z - a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+62}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+51}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{z - a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1e+62)
   (+ x (* t (/ y (- a z))))
   (if (<= y 7.2e+51) (+ x (* t (/ z (- z a)))) (- x (/ y (/ (- z a) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1e+62) {
		tmp = x + (t * (y / (a - z)));
	} else if (y <= 7.2e+51) {
		tmp = x + (t * (z / (z - a)));
	} else {
		tmp = x - (y / ((z - a) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1d+62)) then
        tmp = x + (t * (y / (a - z)))
    else if (y <= 7.2d+51) then
        tmp = x + (t * (z / (z - a)))
    else
        tmp = x - (y / ((z - a) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1e+62) {
		tmp = x + (t * (y / (a - z)));
	} else if (y <= 7.2e+51) {
		tmp = x + (t * (z / (z - a)));
	} else {
		tmp = x - (y / ((z - a) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1e+62:
		tmp = x + (t * (y / (a - z)))
	elif y <= 7.2e+51:
		tmp = x + (t * (z / (z - a)))
	else:
		tmp = x - (y / ((z - a) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1e+62)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	elseif (y <= 7.2e+51)
		tmp = Float64(x + Float64(t * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x - Float64(y / Float64(Float64(z - a) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1e+62)
		tmp = x + (t * (y / (a - z)));
	elseif (y <= 7.2e+51)
		tmp = x + (t * (z / (z - a)));
	else
		tmp = x - (y / ((z - a) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1e+62], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e+51], N[(x + N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.00000000000000004e62

   1. Initial program 90.2%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in y around inf 88.5%

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

      1. associate-/l* 95.6%

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

   7. Simplified 95.6%

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

   if -1.00000000000000004e62 < y < 7.20000000000000022e51

   1. Initial program 85.4%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

      1. clear-num 93.8%

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

      2. un-div-inv 94.9%

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

   6. Applied egg-rr 94.9%

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

   7. Taylor expanded in y around 0 77.1%

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

      1. mul-1-neg 77.1%

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

      2. *-commutative 77.1%

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

      3. associate-*r/ 87.2%

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

      4. unsub-neg 87.2%

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

      5. associate-*r/ 77.1%

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

      6. *-commutative 77.1%

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

      7. associate-/l* 90.3%

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

   9. Simplified 90.3%

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

   if 7.20000000000000022e51 < y

   1. Initial program 87.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 87.8%

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

      1. div-inv 87.7%

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

      2. *-commutative 87.7%

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

      3. associate-*l* 97.3%

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

      4. div-inv 97.3%

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

      5. clear-num 97.5%

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

      6. div-inv 97.5%

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

      7. add-cube-cbrt 96.9%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{\frac{a - z}{t}} \]

      8. *-un-lft-identity 96.9%

         \[\leadsto x + \frac{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}{\color{blue}{1 \cdot \frac{a - z}{t}}} \]

      9. times-frac 96.9%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{a - z}{t}}} \]

      10. pow2 96.9%

          \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{y}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{a - z}{t}} \]

   7. Applied egg-rr 96.9%

      \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{a - z}{t}}} \]
   8. Step-by-step derivation

      1. times-frac 96.9%

         \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2} \cdot \sqrt[3]{y}}{1 \cdot \frac{a - z}{t}}} \]

      2. unpow2 96.9%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)} \cdot \sqrt[3]{y}}{1 \cdot \frac{a - z}{t}} \]

      3. rem-3cbrt-lft 97.5%

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

      4. *-lft-identity 97.5%

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

   9. Simplified 97.5%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+62}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+51}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{z - a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+26} \lor \neg \left(z \leq 3.7 \cdot 10^{+28}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.9e+26) (not (<= z 3.7e+28))) (+ t x) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.9e+26) || !(z <= 3.7e+28)) {
		tmp = t + 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 <= (-2.9d+26)) .or. (.not. (z <= 3.7d+28))) then
        tmp = t + 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 <= -2.9e+26) || !(z <= 3.7e+28)) {
		tmp = t + x;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.9e+26) or not (z <= 3.7e+28):
		tmp = t + x
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.9e+26) || !(z <= 3.7e+28))
		tmp = Float64(t + 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 <= -2.9e+26) || ~((z <= 3.7e+28)))
		tmp = t + x;
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.9e+26], N[Not[LessEqual[z, 3.7e+28]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9e26 or 3.6999999999999999e28 < z

   1. Initial program 73.4%

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

      1. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in z around inf 78.8%

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

   if -2.9e26 < z < 3.6999999999999999e28

   1. Initial program 99.1%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in z around 0 83.8%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+26} \lor \neg \left(z \leq 3.7 \cdot 10^{+28}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{-23} \lor \neg \left(a \leq 7.4 \cdot 10^{-129}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -9e-23) (not (<= a 7.4e-129))) (+ x (* t (/ y a))) (+ t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -9e-23) || !(a <= 7.4e-129)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t + 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 <= (-9d-23)) .or. (.not. (a <= 7.4d-129))) then
        tmp = x + (t * (y / a))
    else
        tmp = t + 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 <= -9e-23) || !(a <= 7.4e-129)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -9e-23) or not (a <= 7.4e-129):
		tmp = x + (t * (y / a))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -9e-23) || !(a <= 7.4e-129))
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -9e-23) || ~((a <= 7.4e-129)))
		tmp = x + (t * (y / a));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -9e-23], N[Not[LessEqual[a, 7.4e-129]], $MachinePrecision]], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.9999999999999995e-23 or 7.4000000000000005e-129 < a

   1. Initial program 89.4%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in z around 0 78.4%

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

      1. +-commutative 78.4%

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

      2. associate-/l* 81.0%

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

   7. Simplified 81.0%

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

   if -8.9999999999999995e-23 < a < 7.4000000000000005e-129

   1. Initial program 82.4%

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

      1. associate-/l* 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in z around inf 81.9%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{-23} \lor \neg \left(a \leq 7.4 \cdot 10^{-129}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-23}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-129}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e-23)
   (+ x (/ t (/ a y)))
   (if (<= a 1.02e-129) (+ t x) (+ x (* t (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e-23) {
		tmp = x + (t / (a / y));
	} else if (a <= 1.02e-129) {
		tmp = t + 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 (a <= (-9.5d-23)) then
        tmp = x + (t / (a / y))
    else if (a <= 1.02d-129) then
        tmp = t + 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 (a <= -9.5e-23) {
		tmp = x + (t / (a / y));
	} else if (a <= 1.02e-129) {
		tmp = t + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.5e-23:
		tmp = x + (t / (a / y))
	elif a <= 1.02e-129:
		tmp = t + x
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e-23)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (a <= 1.02e-129)
		tmp = Float64(t + 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 (a <= -9.5e-23)
		tmp = x + (t / (a / y));
	elseif (a <= 1.02e-129)
		tmp = t + x;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e-23], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.02e-129], N[(t + x), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.50000000000000058e-23

   1. Initial program 91.8%

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

      1. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in z around 0 82.3%

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

      1. +-commutative 82.3%

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

      2. associate-/l* 84.1%

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

   7. Simplified 84.1%

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

      1. clear-num 84.1%

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

      2. un-div-inv 84.2%

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

   9. Applied egg-rr 84.2%

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

   if -9.50000000000000058e-23 < a < 1.02e-129

   1. Initial program 82.4%

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

      1. associate-/l* 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in z around inf 81.9%

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

   if 1.02e-129 < a

   1. Initial program 87.5%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in z around 0 75.5%

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

      1. +-commutative 75.5%

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

      2. associate-/l* 78.6%

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

   7. Simplified 78.6%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-23}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-129}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+91} \lor \neg \left(z \leq 6.2 \cdot 10^{+27}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.5e+91) (not (<= z 6.2e+27))) (+ t x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.5e+91) || !(z <= 6.2e+27)) {
		tmp = t + 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 <= (-4.5d+91)) .or. (.not. (z <= 6.2d+27))) then
        tmp = t + 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 <= -4.5e+91) || !(z <= 6.2e+27)) {
		tmp = t + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.5e+91) or not (z <= 6.2e+27):
		tmp = t + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.5e+91) || !(z <= 6.2e+27))
		tmp = Float64(t + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.5e+91) || ~((z <= 6.2e+27)))
		tmp = t + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.5e+91], N[Not[LessEqual[z, 6.2e+27]], $MachinePrecision]], N[(t + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.5e91 or 6.19999999999999992e27 < z

   1. Initial program 70.5%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in z around inf 83.6%

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

   if -4.5e91 < z < 6.19999999999999992e27

   1. Initial program 97.4%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in x around inf 60.6%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+91} \lor \neg \left(z \leq 6.2 \cdot 10^{+27}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-148}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.1e-139) x (if (<= x 1.35e-148) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.1e-139) {
		tmp = x;
	} else if (x <= 1.35e-148) {
		tmp = t;
	} 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 <= (-1.1d-139)) then
        tmp = x
    else if (x <= 1.35d-148) then
        tmp = t
    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 <= -1.1e-139) {
		tmp = x;
	} else if (x <= 1.35e-148) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.1e-139:
		tmp = x
	elif x <= 1.35e-148:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.1e-139)
		tmp = x;
	elseif (x <= 1.35e-148)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.1e-139)
		tmp = x;
	elseif (x <= 1.35e-148)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.1e-139], x, If[LessEqual[x, 1.35e-148], t, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.10000000000000005e-139 or 1.34999999999999994e-148 < x

   1. Initial program 88.4%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in x around inf 73.9%

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

   if -1.10000000000000005e-139 < x < 1.34999999999999994e-148

   1. Initial program 82.2%

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

      1. associate-/l* 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in x around inf 67.6%

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

      1. associate-/l* 64.6%

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

      2. *-commutative 64.6%

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

   7. Simplified 64.6%

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

   8. Taylor expanded in x around 0 67.9%

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

      1. associate-/l* 84.0%

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

   10. Simplified 84.0%

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

   11. Taylor expanded in z around inf 36.8%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-148}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.9%

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

   1. associate-/l* 94.7%

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

3. Simplified 94.7%

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

5. Final simplification 94.7%

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

Alternative 13: 18.4% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.9%

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

   1. associate-/l* 94.7%

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

3. Simplified 94.7%

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

5. Taylor expanded in x around inf 81.6%

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

   1. associate-/l* 88.9%

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

   2. *-commutative 88.9%

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

7. Simplified 88.9%

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

8. Taylor expanded in x around 0 34.6%

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

   1. associate-/l* 42.4%

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

10. Simplified 42.4%

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

11. Taylor expanded in z around inf 15.5%

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

12. Final simplification 15.5%

    \[\leadsto t \]
13. Add Preprocessing

Developer target: 99.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{a - z} \cdot t\\ \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y z) (- a z)) t))))
   (if (< t -1.0682974490174067e-39)
     t_1
     (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - z) / (a - z)) * t)
    if (t < (-1.0682974490174067d-39)) then
        tmp = t_1
    else if (t < 3.9110949887586375d-141) then
        tmp = x + (((y - z) * t) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) / (a - z)) * t)
	tmp = 0
	if t < -1.0682974490174067e-39:
		tmp = t_1
	elif t < 3.9110949887586375e-141:
		tmp = x + (((y - z) * t) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * t))
	tmp = 0.0
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) / (a - z)) * t);
	tmp = 0.0;
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = x + (((y - z) * t) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.0682974490174067e-39], t$95$1, If[Less[t, 3.9110949887586375e-141], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024055 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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