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

Percentage Accurate: 86.1% → 99.7%

Time: 9.5s

Alternatives: 18

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: 86.1% 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: 99.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t}{a - z}, x\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+307}:\\ \;\;\;\;t\_1 + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (<= t_1 (- INFINITY))
     (fma (- y z) (/ t (- a z)) x)
     (if (<= t_1 1e+307) (+ t_1 x) (+ x (* t (/ (- y z) (- a z))))))))

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 = fma((y - z), (t / (a - z)), x);
	} else if (t_1 <= 1e+307) {
		tmp = t_1 + x;
	} else {
		tmp = x + (t * ((y - z) / (a - z)));
	}
	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 = fma(Float64(y - z), Float64(t / Float64(a - z)), x);
	elseif (t_1 <= 1e+307)
		tmp = Float64(t_1 + x);
	else
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	end
	return 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[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 1e+307], N[(t$95$1 + x), $MachinePrecision], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $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 42.3%

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

      1. +-commutative 42.3%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 9.99999999999999986e306

   1. Initial program 99.9%

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

   if 9.99999999999999986e306 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 37.4%

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

      1. +-commutative 37.4%

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

      2. *-commutative 37.4%

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

      3. associate-/l* 99.9%

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

   4. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t}{a - z}, x\right)\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq 10^{+307}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 10^{+307}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x\\ \end{array} \end{array} \]

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+307)))
     (+ x (* (- y z) (/ t (- a z))))
     (+ 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+307)) {
		tmp = x + ((y - z) * (t / (a - z)));
	} 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+307)) {
		tmp = x + ((y - z) * (t / (a - z)));
	} 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+307):
		tmp = x + ((y - z) * (t / (a - z)))
	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+307))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	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+307)))
		tmp = x + ((y - z) * (t / (a - z)));
	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+307]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $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 9.99999999999999986e306 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 40.0%

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

      1. associate-/l* 99.8%

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

      2. *-commutative 99.8%

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

   4. Applied egg-rr 99.8%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 9.99999999999999986e306

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -\infty \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \leq 10^{+307}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;t\_1 \leq 10^{+307}:\\ \;\;\;\;t\_1 + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (<= t_1 (- INFINITY))
     (+ x (* (- y z) (/ t (- a z))))
     (if (<= t_1 1e+307) (+ t_1 x) (+ x (* t (/ (- y z) (- a z))))))))

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) * (t / (a - z)));
	} else if (t_1 <= 1e+307) {
		tmp = t_1 + x;
	} else {
		tmp = x + (t * ((y - z) / (a - z)));
	}
	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) * (t / (a - z)));
	} else if (t_1 <= 1e+307) {
		tmp = t_1 + x;
	} else {
		tmp = x + (t * ((y - z) / (a - z)));
	}
	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) * (t / (a - z)))
	elif t_1 <= 1e+307:
		tmp = t_1 + x
	else:
		tmp = x + (t * ((y - z) / (a - z)))
	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(t / Float64(a - z))));
	elseif (t_1 <= 1e+307)
		tmp = Float64(t_1 + x);
	else
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	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) * (t / (a - z)));
	elseif (t_1 <= 1e+307)
		tmp = t_1 + x;
	else
		tmp = x + (t * ((y - z) / (a - z)));
	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[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+307], N[(t$95$1 + x), $MachinePrecision], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $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 42.3%

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

      1. associate-/l* 99.9%

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

      2. *-commutative 99.9%

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

   4. Applied egg-rr 99.9%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 9.99999999999999986e306

   1. Initial program 99.9%

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

   if 9.99999999999999986e306 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 37.4%

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

      1. +-commutative 37.4%

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

      2. *-commutative 37.4%

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

      3. associate-/l* 99.9%

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

   4. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -\infty:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq 10^{+307}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+168}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-19}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-68}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+120}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.6e+168)
   (+ t x)
   (if (<= z -5.2e-19)
     (- x (/ t (/ z y)))
     (if (<= z 4e-68)
       (+ x (* y (/ t a)))
       (if (<= z 4.5e+120) (- x (/ (* y t) z)) (+ t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.6e+168) {
		tmp = t + x;
	} else if (z <= -5.2e-19) {
		tmp = x - (t / (z / y));
	} else if (z <= 4e-68) {
		tmp = x + (y * (t / a));
	} else if (z <= 4.5e+120) {
		tmp = x - ((y * t) / z);
	} 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 (z <= (-3.6d+168)) then
        tmp = t + x
    else if (z <= (-5.2d-19)) then
        tmp = x - (t / (z / y))
    else if (z <= 4d-68) then
        tmp = x + (y * (t / a))
    else if (z <= 4.5d+120) then
        tmp = x - ((y * t) / z)
    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 (z <= -3.6e+168) {
		tmp = t + x;
	} else if (z <= -5.2e-19) {
		tmp = x - (t / (z / y));
	} else if (z <= 4e-68) {
		tmp = x + (y * (t / a));
	} else if (z <= 4.5e+120) {
		tmp = x - ((y * t) / z);
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.6e+168:
		tmp = t + x
	elif z <= -5.2e-19:
		tmp = x - (t / (z / y))
	elif z <= 4e-68:
		tmp = x + (y * (t / a))
	elif z <= 4.5e+120:
		tmp = x - ((y * t) / z)
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.6e+168)
		tmp = Float64(t + x);
	elseif (z <= -5.2e-19)
		tmp = Float64(x - Float64(t / Float64(z / y)));
	elseif (z <= 4e-68)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 4.5e+120)
		tmp = Float64(x - Float64(Float64(y * t) / z));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.6e+168)
		tmp = t + x;
	elseif (z <= -5.2e-19)
		tmp = x - (t / (z / y));
	elseif (z <= 4e-68)
		tmp = x + (y * (t / a));
	elseif (z <= 4.5e+120)
		tmp = x - ((y * t) / z);
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.6e+168], N[(t + x), $MachinePrecision], If[LessEqual[z, -5.2e-19], N[(x - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e-68], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+120], N[(x - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.5999999999999999e168 or 4.49999999999999977e120 < z

   1. Initial program 63.3%

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

   3. Taylor expanded in z around inf 84.6%

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

   if -3.5999999999999999e168 < z < -5.20000000000000026e-19

   1. Initial program 88.9%

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

      1. +-commutative 88.9%

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

      2. *-commutative 88.9%

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

      3. associate-/l* 97.7%

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

   4. Applied egg-rr 97.7%

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

   5. Taylor expanded in a around 0 75.7%

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

      1. mul-1-neg 75.7%

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

      2. unsub-neg 75.7%

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

      3. associate-/l* 81.5%

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

      4. div-sub 81.5%

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

      5. sub-neg 81.5%

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

      6. *-inverses 81.5%

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

      7. metadata-eval 81.5%

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

   7. Simplified 81.5%

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

   8. Taylor expanded in y around inf 75.4%

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

      1. clear-num 75.4%

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

      2. un-div-inv 77.0%

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

   10. Applied egg-rr 77.0%

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

   if -5.20000000000000026e-19 < z < 4.00000000000000027e-68

   1. Initial program 96.2%

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

   3. Taylor expanded in z around 0 73.9%

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

      1. *-commutative 73.9%

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

      2. associate-/l* 77.4%

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

   5. Applied egg-rr 77.4%

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

   if 4.00000000000000027e-68 < z < 4.49999999999999977e120

   1. Initial program 94.9%

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

      1. +-commutative 94.9%

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

      2. *-commutative 94.9%

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

      3. associate-/l* 97.4%

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

   4. Applied egg-rr 97.4%

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

   5. Taylor expanded in a around 0 84.8%

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

      1. mul-1-neg 84.8%

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

      2. unsub-neg 84.8%

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

      3. associate-/l* 79.9%

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

      4. div-sub 79.9%

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

      5. sub-neg 79.9%

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

      6. *-inverses 79.9%

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

      7. metadata-eval 79.9%

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

   7. Simplified 79.9%

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

   8. Taylor expanded in y around inf 71.7%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+168}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-19}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-68}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+120}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{t}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+171}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.75 \cdot 10^{-65}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+122}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ t (/ z y)))))
   (if (<= z -3.6e+171)
     (+ t x)
     (if (<= z -3.1e-20)
       t_1
       (if (<= z 3.75e-65)
         (+ x (* y (/ t a)))
         (if (<= z 2.7e+122) t_1 (+ t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t / (z / y));
	double tmp;
	if (z <= -3.6e+171) {
		tmp = t + x;
	} else if (z <= -3.1e-20) {
		tmp = t_1;
	} else if (z <= 3.75e-65) {
		tmp = x + (y * (t / a));
	} else if (z <= 2.7e+122) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x - (t / (z / y))
    if (z <= (-3.6d+171)) then
        tmp = t + x
    else if (z <= (-3.1d-20)) then
        tmp = t_1
    else if (z <= 3.75d-65) then
        tmp = x + (y * (t / a))
    else if (z <= 2.7d+122) then
        tmp = t_1
    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 t_1 = x - (t / (z / y));
	double tmp;
	if (z <= -3.6e+171) {
		tmp = t + x;
	} else if (z <= -3.1e-20) {
		tmp = t_1;
	} else if (z <= 3.75e-65) {
		tmp = x + (y * (t / a));
	} else if (z <= 2.7e+122) {
		tmp = t_1;
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t / (z / y))
	tmp = 0
	if z <= -3.6e+171:
		tmp = t + x
	elif z <= -3.1e-20:
		tmp = t_1
	elif z <= 3.75e-65:
		tmp = x + (y * (t / a))
	elif z <= 2.7e+122:
		tmp = t_1
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t / Float64(z / y)))
	tmp = 0.0
	if (z <= -3.6e+171)
		tmp = Float64(t + x);
	elseif (z <= -3.1e-20)
		tmp = t_1;
	elseif (z <= 3.75e-65)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 2.7e+122)
		tmp = t_1;
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (t / (z / y));
	tmp = 0.0;
	if (z <= -3.6e+171)
		tmp = t + x;
	elseif (z <= -3.1e-20)
		tmp = t_1;
	elseif (z <= 3.75e-65)
		tmp = x + (y * (t / a));
	elseif (z <= 2.7e+122)
		tmp = t_1;
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e+171], N[(t + x), $MachinePrecision], If[LessEqual[z, -3.1e-20], t$95$1, If[LessEqual[z, 3.75e-65], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e+122], t$95$1, N[(t + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.60000000000000018e171 or 2.6999999999999998e122 < z

   1. Initial program 63.3%

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

   3. Taylor expanded in z around inf 84.6%

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

   if -3.60000000000000018e171 < z < -3.1e-20 or 3.7500000000000001e-65 < z < 2.6999999999999998e122

   1. Initial program 91.7%

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

      1. +-commutative 91.7%

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

      2. *-commutative 91.7%

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

      3. associate-/l* 97.6%

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

   4. Applied egg-rr 97.6%

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

   5. Taylor expanded in a around 0 79.9%

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

      1. mul-1-neg 79.9%

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

      2. unsub-neg 79.9%

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

      3. associate-/l* 80.7%

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

      4. div-sub 80.7%

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

      5. sub-neg 80.7%

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

      6. *-inverses 80.7%

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

      7. metadata-eval 80.7%

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

   7. Simplified 80.7%

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

   8. Taylor expanded in y around inf 71.3%

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

      1. clear-num 71.3%

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

      2. un-div-inv 73.3%

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

   10. Applied egg-rr 73.3%

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

   if -3.1e-20 < z < 3.7500000000000001e-65

   1. Initial program 96.2%

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

   3. Taylor expanded in z around 0 73.9%

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

      1. *-commutative 73.9%

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

      2. associate-/l* 77.4%

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

   5. Applied egg-rr 77.4%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+171}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-20}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 3.75 \cdot 10^{-65}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+122}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -215:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+21}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+81}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+83}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -215.0)
   (+ t x)
   (if (<= z 2.5e+21)
     (+ x (* y (/ t a)))
     (if (<= z 2.75e+81)
       (* t (- 1.0 (/ y z)))
       (if (<= z 1.08e+83) (+ x (* t (/ y a))) (+ t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -215.0) {
		tmp = t + x;
	} else if (z <= 2.5e+21) {
		tmp = x + (y * (t / a));
	} else if (z <= 2.75e+81) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= 1.08e+83) {
		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 (z <= (-215.0d0)) then
        tmp = t + x
    else if (z <= 2.5d+21) then
        tmp = x + (y * (t / a))
    else if (z <= 2.75d+81) then
        tmp = t * (1.0d0 - (y / z))
    else if (z <= 1.08d+83) 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 (z <= -215.0) {
		tmp = t + x;
	} else if (z <= 2.5e+21) {
		tmp = x + (y * (t / a));
	} else if (z <= 2.75e+81) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= 1.08e+83) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -215.0:
		tmp = t + x
	elif z <= 2.5e+21:
		tmp = x + (y * (t / a))
	elif z <= 2.75e+81:
		tmp = t * (1.0 - (y / z))
	elif z <= 1.08e+83:
		tmp = x + (t * (y / a))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -215.0)
		tmp = Float64(t + x);
	elseif (z <= 2.5e+21)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 2.75e+81)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (z <= 1.08e+83)
		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 (z <= -215.0)
		tmp = t + x;
	elseif (z <= 2.5e+21)
		tmp = x + (y * (t / a));
	elseif (z <= 2.75e+81)
		tmp = t * (1.0 - (y / z));
	elseif (z <= 1.08e+83)
		tmp = x + (t * (y / a));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -215.0], N[(t + x), $MachinePrecision], If[LessEqual[z, 2.5e+21], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.75e+81], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.08e+83], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -215 or 1.08e83 < z

   1. Initial program 73.3%

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

   3. Taylor expanded in z around inf 76.1%

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

   if -215 < z < 2.5e21

   1. Initial program 96.9%

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

   3. Taylor expanded in z around 0 71.8%

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

      1. *-commutative 71.8%

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

      2. associate-/l* 74.7%

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

   5. Applied egg-rr 74.7%

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

   if 2.5e21 < z < 2.7500000000000002e81

   1. Initial program 92.4%

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

   3. Taylor expanded in t around inf 83.6%

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

   4. Taylor expanded in a around 0 76.2%

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

      1. mul-1-neg 76.2%

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

      2. unsub-neg 76.2%

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

   6. Simplified 76.2%

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

   if 2.7500000000000002e81 < z < 1.08e83

   1. Initial program 52.6%

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

   3. Taylor expanded in z around 0 52.6%

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

      1. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -215:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+21}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+81}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+83}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -120:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+81}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= z -120.0)
     (+ t x)
     (if (<= z 2.8e+21)
       t_1
       (if (<= z 2.1e+81)
         (* t (- 1.0 (/ y z)))
         (if (<= z 2.15e+82) t_1 (+ t 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 <= -120.0) {
		tmp = t + x;
	} else if (z <= 2.8e+21) {
		tmp = t_1;
	} else if (z <= 2.1e+81) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= 2.15e+82) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + (t * (y / a))
    if (z <= (-120.0d0)) then
        tmp = t + x
    else if (z <= 2.8d+21) then
        tmp = t_1
    else if (z <= 2.1d+81) then
        tmp = t * (1.0d0 - (y / z))
    else if (z <= 2.15d+82) then
        tmp = t_1
    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 t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -120.0) {
		tmp = t + x;
	} else if (z <= 2.8e+21) {
		tmp = t_1;
	} else if (z <= 2.1e+81) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= 2.15e+82) {
		tmp = t_1;
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if z <= -120.0:
		tmp = t + x
	elif z <= 2.8e+21:
		tmp = t_1
	elif z <= 2.1e+81:
		tmp = t * (1.0 - (y / z))
	elif z <= 2.15e+82:
		tmp = t_1
	else:
		tmp = t + 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 <= -120.0)
		tmp = Float64(t + x);
	elseif (z <= 2.8e+21)
		tmp = t_1;
	elseif (z <= 2.1e+81)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (z <= 2.15e+82)
		tmp = t_1;
	else
		tmp = Float64(t + 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 <= -120.0)
		tmp = t + x;
	elseif (z <= 2.8e+21)
		tmp = t_1;
	elseif (z <= 2.1e+81)
		tmp = t * (1.0 - (y / z));
	elseif (z <= 2.15e+82)
		tmp = t_1;
	else
		tmp = t + 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, -120.0], N[(t + x), $MachinePrecision], If[LessEqual[z, 2.8e+21], t$95$1, If[LessEqual[z, 2.1e+81], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e+82], t$95$1, N[(t + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -120 or 2.15000000000000007e82 < z

   1. Initial program 73.3%

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

   3. Taylor expanded in z around inf 76.1%

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

   if -120 < z < 2.8e21 or 2.0999999999999999e81 < z < 2.15000000000000007e82

   1. Initial program 96.1%

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

   3. Taylor expanded in z around 0 71.5%

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

      1. associate-/l* 71.3%

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

   5. Simplified 71.3%

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

   if 2.8e21 < z < 2.0999999999999999e81

   1. Initial program 92.4%

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

   3. Taylor expanded in t around inf 83.6%

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

   4. Taylor expanded in a around 0 76.2%

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

      1. mul-1-neg 76.2%

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

      2. unsub-neg 76.2%

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

   6. Simplified 76.2%

      \[\leadsto \color{blue}{t \cdot \left(1 - \frac{y}{z}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -120:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+21}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+81}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+82}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+20}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+230}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= y -3.2e+53)
     t_1
     (if (<= y 3.6e+20)
       (+ t x)
       (if (<= y 5.6e+65) t_1 (if (<= y 9.5e+230) (+ t x) (/ y (/ a t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (y <= -3.2e+53) {
		tmp = t_1;
	} else if (y <= 3.6e+20) {
		tmp = t + x;
	} else if (y <= 5.6e+65) {
		tmp = t_1;
	} else if (y <= 9.5e+230) {
		tmp = t + x;
	} else {
		tmp = y / (a / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (y <= (-3.2d+53)) then
        tmp = t_1
    else if (y <= 3.6d+20) then
        tmp = t + x
    else if (y <= 5.6d+65) then
        tmp = t_1
    else if (y <= 9.5d+230) then
        tmp = t + x
    else
        tmp = y / (a / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (y <= -3.2e+53) {
		tmp = t_1;
	} else if (y <= 3.6e+20) {
		tmp = t + x;
	} else if (y <= 5.6e+65) {
		tmp = t_1;
	} else if (y <= 9.5e+230) {
		tmp = t + x;
	} else {
		tmp = y / (a / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if y <= -3.2e+53:
		tmp = t_1
	elif y <= 3.6e+20:
		tmp = t + x
	elif y <= 5.6e+65:
		tmp = t_1
	elif y <= 9.5e+230:
		tmp = t + x
	else:
		tmp = y / (a / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (y <= -3.2e+53)
		tmp = t_1;
	elseif (y <= 3.6e+20)
		tmp = Float64(t + x);
	elseif (y <= 5.6e+65)
		tmp = t_1;
	elseif (y <= 9.5e+230)
		tmp = Float64(t + x);
	else
		tmp = Float64(y / Float64(a / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (y <= -3.2e+53)
		tmp = t_1;
	elseif (y <= 3.6e+20)
		tmp = t + x;
	elseif (y <= 5.6e+65)
		tmp = t_1;
	elseif (y <= 9.5e+230)
		tmp = t + x;
	else
		tmp = y / (a / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.2e+53], t$95$1, If[LessEqual[y, 3.6e+20], N[(t + x), $MachinePrecision], If[LessEqual[y, 5.6e+65], t$95$1, If[LessEqual[y, 9.5e+230], N[(t + x), $MachinePrecision], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.2e53 or 3.6e20 < y < 5.5999999999999998e65

   1. Initial program 81.5%

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

   3. Taylor expanded in t around inf 69.0%

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

   4. Taylor expanded in a around 0 60.2%

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

      1. mul-1-neg 60.2%

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

      2. unsub-neg 60.2%

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

   6. Simplified 60.2%

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

   if -3.2e53 < y < 3.6e20 or 5.5999999999999998e65 < y < 9.5000000000000002e230

   1. Initial program 87.6%

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

   3. Taylor expanded in z around inf 67.7%

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

   if 9.5000000000000002e230 < y

   1. Initial program 74.4%

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

   3. Taylor expanded in z around 0 51.7%

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

   4. Taylor expanded in y around inf 67.7%

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

   5. Taylor expanded in t around inf 54.5%

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

      1. clear-num 54.6%

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

      2. un-div-inv 54.6%

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

   7. Applied egg-rr 54.6%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+53}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+20}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+65}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+230}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+169}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -3.15 \cdot 10^{-26}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+25}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6e+169)
   (+ t x)
   (if (<= z -3.15e-26)
     (- x (* t (/ y z)))
     (if (<= z 1.45e+25) (+ x (* y (/ t a))) (+ t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6e+169) {
		tmp = t + x;
	} else if (z <= -3.15e-26) {
		tmp = x - (t * (y / z));
	} else if (z <= 1.45e+25) {
		tmp = x + (y * (t / 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 (z <= (-6d+169)) then
        tmp = t + x
    else if (z <= (-3.15d-26)) then
        tmp = x - (t * (y / z))
    else if (z <= 1.45d+25) then
        tmp = x + (y * (t / 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 (z <= -6e+169) {
		tmp = t + x;
	} else if (z <= -3.15e-26) {
		tmp = x - (t * (y / z));
	} else if (z <= 1.45e+25) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6e+169:
		tmp = t + x
	elif z <= -3.15e-26:
		tmp = x - (t * (y / z))
	elif z <= 1.45e+25:
		tmp = x + (y * (t / a))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6e+169)
		tmp = Float64(t + x);
	elseif (z <= -3.15e-26)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 1.45e+25)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6e+169)
		tmp = t + x;
	elseif (z <= -3.15e-26)
		tmp = x - (t * (y / z));
	elseif (z <= 1.45e+25)
		tmp = x + (y * (t / a));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6e+169], N[(t + x), $MachinePrecision], If[LessEqual[z, -3.15e-26], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+25], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.9999999999999999e169 or 1.44999999999999995e25 < z

   1. Initial program 69.7%

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

   3. Taylor expanded in z around inf 78.6%

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

   if -5.9999999999999999e169 < z < -3.15e-26

   1. Initial program 89.1%

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

      1. +-commutative 89.1%

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

      2. *-commutative 89.1%

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

      3. associate-/l* 97.7%

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

   4. Applied egg-rr 97.7%

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

   5. Taylor expanded in a around 0 74.6%

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

      1. mul-1-neg 74.6%

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

      2. unsub-neg 74.6%

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

      3. associate-/l* 80.3%

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

      4. div-sub 80.3%

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

      5. sub-neg 80.3%

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

      6. *-inverses 80.3%

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

      7. metadata-eval 80.3%

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

   7. Simplified 80.3%

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

   8. Taylor expanded in y around inf 75.4%

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

   if -3.15e-26 < z < 1.44999999999999995e25

   1. Initial program 96.0%

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

   3. Taylor expanded in z around 0 71.5%

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

      1. *-commutative 71.5%

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

      2. associate-/l* 74.4%

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

   5. Applied egg-rr 74.4%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+169}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -3.15 \cdot 10^{-26}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+25}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 87.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -54 \lor \neg \left(z \leq 2.8 \cdot 10^{+21}\right):\\ \;\;\;\;x + \left(t - t \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -54.0) (not (<= z 2.8e+21)))
   (+ x (- t (* t (/ y z))))
   (+ x (/ (* y t) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -54.0) || !(z <= 2.8e+21)) {
		tmp = x + (t - (t * (y / z)));
	} else {
		tmp = x + ((y * t) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-54.0d0)) .or. (.not. (z <= 2.8d+21))) then
        tmp = x + (t - (t * (y / z)))
    else
        tmp = x + ((y * t) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -54.0) || !(z <= 2.8e+21)) {
		tmp = x + (t - (t * (y / z)));
	} else {
		tmp = x + ((y * t) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -54.0) or not (z <= 2.8e+21):
		tmp = x + (t - (t * (y / z)))
	else:
		tmp = x + ((y * t) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -54.0) || !(z <= 2.8e+21))
		tmp = Float64(x + Float64(t - Float64(t * Float64(y / z))));
	else
		tmp = Float64(x + Float64(Float64(y * t) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -54.0) || ~((z <= 2.8e+21)))
		tmp = x + (t - (t * (y / z)));
	else
		tmp = x + ((y * t) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -54.0], N[Not[LessEqual[z, 2.8e+21]], $MachinePrecision]], N[(x + N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -54 or 2.8e21 < z

   1. Initial program 74.8%

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

      1. +-commutative 74.8%

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

      2. *-commutative 74.8%

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

      3. associate-/l* 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in t around 0 74.8%

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

      1. associate-*r/ 99.9%

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

      2. *-commutative 99.9%

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

      3. *-rgt-identity 99.9%

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

      4. associate-*r/ 99.8%

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

      5. associate-*r* 95.2%

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

      6. associate-*l/ 95.4%

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

      7. *-lft-identity 95.4%

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

   7. Simplified 95.4%

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

   8. Taylor expanded in a around 0 87.0%

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

      1. mul-1-neg 87.0%

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

      2. distribute-neg-frac2 87.0%

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

   10. Simplified 87.0%

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

   11. Taylor expanded in y around 0 81.0%

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

       1. mul-1-neg 81.0%

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

       2. associate-*r/ 90.8%

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

       3. unsub-neg 90.8%

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

   13. Simplified 90.8%

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

   if -54 < z < 2.8e21

   1. Initial program 96.9%

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

   3. Taylor expanded in y around inf 89.5%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -54 \lor \neg \left(z \leq 2.8 \cdot 10^{+21}\right):\\ \;\;\;\;x + \left(t - t \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 82.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+167} \lor \neg \left(z \leq 2.6 \cdot 10^{+121}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.8e+167) (not (<= z 2.6e+121)))
   (+ t x)
   (+ x (/ (* y t) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.8e+167) || !(z <= 2.6e+121)) {
		tmp = t + x;
	} else {
		tmp = x + ((y * t) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8.8d+167)) .or. (.not. (z <= 2.6d+121))) then
        tmp = t + x
    else
        tmp = x + ((y * t) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.8e+167) || !(z <= 2.6e+121)) {
		tmp = t + x;
	} else {
		tmp = x + ((y * t) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.8e+167) or not (z <= 2.6e+121):
		tmp = t + x
	else:
		tmp = x + ((y * t) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.8e+167) || !(z <= 2.6e+121))
		tmp = Float64(t + x);
	else
		tmp = Float64(x + Float64(Float64(y * t) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.8e+167) || ~((z <= 2.6e+121)))
		tmp = t + x;
	else
		tmp = x + ((y * t) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.8e+167], N[Not[LessEqual[z, 2.6e+121]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.80000000000000013e167 or 2.5999999999999999e121 < z

   1. Initial program 63.3%

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

   3. Taylor expanded in z around inf 84.6%

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

   if -8.80000000000000013e167 < z < 2.5999999999999999e121

   1. Initial program 94.2%

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

   3. Taylor expanded in y around inf 84.5%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+167} \lor \neg \left(z \leq 2.6 \cdot 10^{+121}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 87.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -145:\\ \;\;\;\;x + t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - t \cdot \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -145.0)
   (+ x (* t (/ (- z y) z)))
   (if (<= z 2.6e+21) (+ x (/ (* y t) (- a z))) (+ x (- t (* t (/ y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -145.0) {
		tmp = x + (t * ((z - y) / z));
	} else if (z <= 2.6e+21) {
		tmp = x + ((y * t) / (a - z));
	} else {
		tmp = x + (t - (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 (z <= (-145.0d0)) then
        tmp = x + (t * ((z - y) / z))
    else if (z <= 2.6d+21) then
        tmp = x + ((y * t) / (a - z))
    else
        tmp = x + (t - (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 (z <= -145.0) {
		tmp = x + (t * ((z - y) / z));
	} else if (z <= 2.6e+21) {
		tmp = x + ((y * t) / (a - z));
	} else {
		tmp = x + (t - (t * (y / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -145.0:
		tmp = x + (t * ((z - y) / z))
	elif z <= 2.6e+21:
		tmp = x + ((y * t) / (a - z))
	else:
		tmp = x + (t - (t * (y / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -145.0)
		tmp = Float64(x + Float64(t * Float64(Float64(z - y) / z)));
	elseif (z <= 2.6e+21)
		tmp = Float64(x + Float64(Float64(y * t) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(t - Float64(t * Float64(y / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -145.0)
		tmp = x + (t * ((z - y) / z));
	elseif (z <= 2.6e+21)
		tmp = x + ((y * t) / (a - z));
	else
		tmp = x + (t - (t * (y / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -145.0], N[(x + N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+21], N[(x + N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -145

   1. Initial program 76.9%

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

   3. Taylor expanded in a around 0 71.5%

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

      1. mul-1-neg 71.5%

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

      2. unsub-neg 71.5%

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

      3. associate-/l* 91.4%

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

   5. Simplified 91.4%

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

   if -145 < z < 2.6e21

   1. Initial program 96.9%

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

   3. Taylor expanded in y around inf 89.5%

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

   if 2.6e21 < z

   1. Initial program 72.0%

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

      1. +-commutative 72.0%

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

      2. *-commutative 72.0%

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

      3. associate-/l* 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in t around 0 72.0%

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

      1. associate-*r/ 99.9%

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

      2. *-commutative 99.9%

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

      3. *-rgt-identity 99.9%

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

      4. associate-*r/ 99.8%

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

      5. associate-*r* 94.9%

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

      6. associate-*l/ 95.0%

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

      7. *-lft-identity 95.0%

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

   7. Simplified 95.0%

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

   8. Taylor expanded in a around 0 86.7%

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

      1. mul-1-neg 86.7%

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

      2. distribute-neg-frac2 86.7%

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

   10. Simplified 86.7%

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

   11. Taylor expanded in y around 0 80.2%

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

       1. mul-1-neg 80.2%

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

       2. associate-*r/ 89.9%

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

       3. unsub-neg 89.9%

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

   13. Simplified 89.9%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -145:\\ \;\;\;\;x + t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - t \cdot \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+199}:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+231}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.7e+199)
   (* y (/ t (- z)))
   (if (<= y 8.8e+231) (+ t x) (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.7e+199) {
		tmp = y * (t / -z);
	} else if (y <= 8.8e+231) {
		tmp = t + x;
	} else {
		tmp = y / (a / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-4.7d+199)) then
        tmp = y * (t / -z)
    else if (y <= 8.8d+231) then
        tmp = t + x
    else
        tmp = y / (a / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.7e+199) {
		tmp = y * (t / -z);
	} else if (y <= 8.8e+231) {
		tmp = t + x;
	} else {
		tmp = y / (a / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4.7e+199:
		tmp = y * (t / -z)
	elif y <= 8.8e+231:
		tmp = t + x
	else:
		tmp = y / (a / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.7e+199)
		tmp = Float64(y * Float64(t / Float64(-z)));
	elseif (y <= 8.8e+231)
		tmp = Float64(t + x);
	else
		tmp = Float64(y / Float64(a / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -4.7e+199)
		tmp = y * (t / -z);
	elseif (y <= 8.8e+231)
		tmp = t + x;
	else
		tmp = y / (a / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.7e+199], N[(y * N[(t / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.8e+231], N[(t + x), $MachinePrecision], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.7000000000000001e199

   1. Initial program 82.7%

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

      1. +-commutative 82.7%

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

      2. *-commutative 82.7%

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

      3. associate-/l* 82.3%

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

   4. Applied egg-rr 82.3%

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

   5. Taylor expanded in a around 0 72.0%

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

      1. mul-1-neg 72.0%

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

      2. unsub-neg 72.0%

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

      3. associate-/l* 71.5%

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

      4. div-sub 71.5%

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

      5. sub-neg 71.5%

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

      6. *-inverses 71.5%

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

      7. metadata-eval 71.5%

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

   7. Simplified 71.5%

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

   8. Taylor expanded in y around inf 55.5%

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

   9. Taylor expanded in x around 0 53.2%

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

       1. mul-1-neg 53.2%

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

       2. associate-*r/ 42.9%

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

       3. *-commutative 42.9%

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

       4. associate-*l/ 53.2%

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

       5. associate-*r/ 50.0%

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

       6. distribute-rgt-neg-in 50.0%

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

       7. distribute-neg-frac2 50.0%

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

   11. Simplified 50.0%

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

   if -4.7000000000000001e199 < y < 8.79999999999999967e231

   1. Initial program 86.6%

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

   3. Taylor expanded in z around inf 63.4%

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

   if 8.79999999999999967e231 < y

   1. Initial program 74.4%

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

   3. Taylor expanded in z around 0 51.7%

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

   4. Taylor expanded in y around inf 67.7%

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

   5. Taylor expanded in t around inf 54.5%

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

      1. clear-num 54.6%

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

      2. un-div-inv 54.6%

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

   7. Applied egg-rr 54.6%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+199}:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+231}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 62.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -23 \lor \neg \left(z \leq 3.8 \cdot 10^{-73}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -23.0) (not (<= z 3.8e-73))) (+ t x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -23.0) || !(z <= 3.8e-73)) {
		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 <= (-23.0d0)) .or. (.not. (z <= 3.8d-73))) 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 <= -23.0) || !(z <= 3.8e-73)) {
		tmp = t + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -23.0) or not (z <= 3.8e-73):
		tmp = t + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -23.0) || !(z <= 3.8e-73))
		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 <= -23.0) || ~((z <= 3.8e-73)))
		tmp = t + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -23.0], N[Not[LessEqual[z, 3.8e-73]], $MachinePrecision]], N[(t + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -23 or 3.8000000000000003e-73 < z

   1. Initial program 77.6%

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

   3. Taylor expanded in z around inf 69.7%

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

   if -23 < z < 3.8000000000000003e-73

   1. Initial program 96.3%

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

   3. Taylor expanded in x around inf 48.0%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -23 \lor \neg \left(z \leq 3.8 \cdot 10^{-73}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 95.7% accurate, 1.0× speedup

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 85.1%

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

   1. associate-/l* 96.0%

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

   2. *-commutative 96.0%

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

4. Applied egg-rr 96.0%

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

5. Final simplification 96.0%

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

Alternative 16: 60.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.6 \cdot 10^{+229}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 4.6e+229) (+ t x) (/ y (/ a t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 4.6e+229) {
		tmp = t + x;
	} else {
		tmp = y / (a / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= 4.6d+229) then
        tmp = t + x
    else
        tmp = y / (a / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 4.6e+229) {
		tmp = t + x;
	} else {
		tmp = y / (a / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 4.6e+229:
		tmp = t + x
	else:
		tmp = y / (a / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 4.6e+229)
		tmp = Float64(t + x);
	else
		tmp = Float64(y / Float64(a / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 4.6e+229)
		tmp = t + x;
	else
		tmp = y / (a / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 4.6e+229], N[(t + x), $MachinePrecision], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.5999999999999999e229

   1. Initial program 86.2%

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

   3. Taylor expanded in z around inf 59.6%

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

   if 4.5999999999999999e229 < y

   1. Initial program 74.4%

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

   3. Taylor expanded in z around 0 51.7%

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

   4. Taylor expanded in y around inf 67.7%

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

   5. Taylor expanded in t around inf 54.5%

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

      1. clear-num 54.6%

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

      2. un-div-inv 54.6%

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

   7. Applied egg-rr 54.6%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.6 \cdot 10^{+229}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 60.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.3 \cdot 10^{+232}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 3.3e+232) (+ t x) (* y (/ t a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 3.3e+232) {
		tmp = t + x;
	} else {
		tmp = 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 (y <= 3.3d+232) then
        tmp = t + x
    else
        tmp = 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 (y <= 3.3e+232) {
		tmp = t + x;
	} else {
		tmp = y * (t / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 3.3e+232:
		tmp = t + x
	else:
		tmp = y * (t / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 3.3e+232)
		tmp = Float64(t + x);
	else
		tmp = Float64(y * Float64(t / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 3.3e+232)
		tmp = t + x;
	else
		tmp = y * (t / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 3.3e+232], N[(t + x), $MachinePrecision], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.3e232

   1. Initial program 86.2%

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

   3. Taylor expanded in z around inf 59.6%

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

   if 3.3e232 < y

   1. Initial program 74.4%

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

   3. Taylor expanded in z around 0 51.7%

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

   4. Taylor expanded in y around inf 67.7%

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

   5. Taylor expanded in t around inf 54.5%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.3 \cdot 10^{+232}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 50.1% 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 85.1%

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

3. Taylor expanded in x around inf 47.9%

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

Developer target: 99.2% 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 2024096 
(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))))