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

Percentage Accurate: 86.1% → 99.3%

Time: 13.8s

Alternatives: 17

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: 99.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - z}{a - z}\\ t_2 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+214}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, t, x\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+307}:\\ \;\;\;\;t\_2 + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y z) (- a z))) (t_2 (/ (* (- y z) t) (- a z))))
   (if (<= t_2 -5e+214)
     (fma t_1 t x)
     (if (<= t_2 1e+307) (+ t_2 x) (+ x (* t t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) / (a - z);
	double t_2 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_2 <= -5e+214) {
		tmp = fma(t_1, t, x);
	} else if (t_2 <= 1e+307) {
		tmp = t_2 + x;
	} else {
		tmp = x + (t * t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) / Float64(a - z))
	t_2 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_2 <= -5e+214)
		tmp = fma(t_1, t, x);
	elseif (t_2 <= 1e+307)
		tmp = Float64(t_2 + x);
	else
		tmp = Float64(x + Float64(t * t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+214], N[(t$95$1 * t + x), $MachinePrecision], If[LessEqual[t$95$2, 1e+307], N[(t$95$2 + x), $MachinePrecision], N[(x + N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -4.99999999999999953e214

   1. Initial program 47.0%

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

      1. +-commutative 47.0%

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

      2. associate-*l/ 99.8%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

   if -4.99999999999999953e214 < (/.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. Step-by-step derivation

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -5 \cdot 10^{+214}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t, x\right)\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq 10^{+307}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+214} \lor \neg \left(t\_1 \leq 10^{+307}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (or (<= t_1 -5e+214) (not (<= t_1 1e+307)))
     (+ x (* t (/ (- y z) (- 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 <= -5e+214) || !(t_1 <= 1e+307)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = t_1 + 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 = ((y - z) * t) / (a - z)
    if ((t_1 <= (-5d+214)) .or. (.not. (t_1 <= 1d+307))) then
        tmp = x + (t * ((y - z) / (a - z)))
    else
        tmp = t_1 + 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 = ((y - z) * t) / (a - z);
	double tmp;
	if ((t_1 <= -5e+214) || !(t_1 <= 1e+307)) {
		tmp = x + (t * ((y - z) / (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 <= -5e+214) or not (t_1 <= 1e+307):
		tmp = x + (t * ((y - z) / (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 <= -5e+214) || !(t_1 <= 1e+307))
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / 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 <= -5e+214) || ~((t_1 <= 1e+307)))
		tmp = x + (t * ((y - z) / (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, -5e+214], N[Not[LessEqual[t$95$1, 1e+307]], $MachinePrecision]], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / 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)) < -4.99999999999999953e214 or 9.99999999999999986e306 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 42.7%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   if -4.99999999999999953e214 < (/.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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -5 \cdot 10^{+214} \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \leq 10^{+307}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.7% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (<= t_1 (- INFINITY))
     (+ x (/ (- y z) (/ (- a z) t)))
     (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) / ((a - z) / t));
	} 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) / ((a - z) / t));
	} 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) / ((a - z) / t))
	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(Float64(a - z) / t)));
	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) / ((a - z) / t));
	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[(N[(a - z), $MachinePrecision] / t), $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. Step-by-step derivation

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 4: 76.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{t}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -9.6 \cdot 10^{+171}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-64}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ t (/ z y)))))
   (if (<= z -9.6e+171)
     (+ t x)
     (if (<= z -5e-21)
       t_1
       (if (<= z 2.4e-64)
         (+ x (* y (/ t a)))
         (if (<= z 3.3e+121) 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 <= -9.6e+171) {
		tmp = t + x;
	} else if (z <= -5e-21) {
		tmp = t_1;
	} else if (z <= 2.4e-64) {
		tmp = x + (y * (t / a));
	} else if (z <= 3.3e+121) {
		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 <= (-9.6d+171)) then
        tmp = t + x
    else if (z <= (-5d-21)) then
        tmp = t_1
    else if (z <= 2.4d-64) then
        tmp = x + (y * (t / a))
    else if (z <= 3.3d+121) 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 <= -9.6e+171) {
		tmp = t + x;
	} else if (z <= -5e-21) {
		tmp = t_1;
	} else if (z <= 2.4e-64) {
		tmp = x + (y * (t / a));
	} else if (z <= 3.3e+121) {
		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 <= -9.6e+171:
		tmp = t + x
	elif z <= -5e-21:
		tmp = t_1
	elif z <= 2.4e-64:
		tmp = x + (y * (t / a))
	elif z <= 3.3e+121:
		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 <= -9.6e+171)
		tmp = Float64(t + x);
	elseif (z <= -5e-21)
		tmp = t_1;
	elseif (z <= 2.4e-64)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 3.3e+121)
		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 <= -9.6e+171)
		tmp = t + x;
	elseif (z <= -5e-21)
		tmp = t_1;
	elseif (z <= 2.4e-64)
		tmp = x + (y * (t / a));
	elseif (z <= 3.3e+121)
		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, -9.6e+171], N[(t + x), $MachinePrecision], If[LessEqual[z, -5e-21], t$95$1, If[LessEqual[z, 2.4e-64], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+121], t$95$1, N[(t + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5999999999999999e171 or 3.29999999999999979e121 < z

   1. Initial program 63.3%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 84.6%

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

   if -9.5999999999999999e171 < z < -4.99999999999999973e-21 or 2.39999999999999998e-64 < z < 3.29999999999999979e121

   1. Initial program 91.7%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   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* 82.7%

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

   7. Simplified 82.7%

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

   8. Taylor expanded in z around 0 73.3%

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

   if -4.99999999999999973e-21 < z < 2.39999999999999998e-64

   1. Initial program 96.2%

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

      1. associate-*l/ 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in y around inf 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-*r/ 92.1%

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

   7. Simplified 92.1%

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

   8. Taylor expanded in a around inf 73.9%

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

      1. +-commutative 73.9%

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

      2. associate-/l* 72.9%

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

      3. associate-/r/ 77.4%

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

   10. Simplified 77.4%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+171}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-21}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-64}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+121}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+172}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-18}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-68}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+120}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.7e+172)
   (+ t x)
   (if (<= z -3.2e-18)
     (- x (/ t (/ z y)))
     (if (<= z 1.05e-68)
       (+ x (* y (/ t a)))
       (if (<= z 1.25e+120) (- x (/ (* y t) z)) (+ t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.7e+172) {
		tmp = t + x;
	} else if (z <= -3.2e-18) {
		tmp = x - (t / (z / y));
	} else if (z <= 1.05e-68) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.25e+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 <= (-2.7d+172)) then
        tmp = t + x
    else if (z <= (-3.2d-18)) then
        tmp = x - (t / (z / y))
    else if (z <= 1.05d-68) then
        tmp = x + (y * (t / a))
    else if (z <= 1.25d+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 <= -2.7e+172) {
		tmp = t + x;
	} else if (z <= -3.2e-18) {
		tmp = x - (t / (z / y));
	} else if (z <= 1.05e-68) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.25e+120) {
		tmp = x - ((y * t) / z);
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.7e+172:
		tmp = t + x
	elif z <= -3.2e-18:
		tmp = x - (t / (z / y))
	elif z <= 1.05e-68:
		tmp = x + (y * (t / a))
	elif z <= 1.25e+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 <= -2.7e+172)
		tmp = Float64(t + x);
	elseif (z <= -3.2e-18)
		tmp = Float64(x - Float64(t / Float64(z / y)));
	elseif (z <= 1.05e-68)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 1.25e+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 <= -2.7e+172)
		tmp = t + x;
	elseif (z <= -3.2e-18)
		tmp = x - (t / (z / y));
	elseif (z <= 1.05e-68)
		tmp = x + (y * (t / a));
	elseif (z <= 1.25e+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, -2.7e+172], N[(t + x), $MachinePrecision], If[LessEqual[z, -3.2e-18], N[(x - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-68], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+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 < -2.7e172 or 1.25000000000000005e120 < z

   1. Initial program 63.3%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 84.6%

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

   if -2.7e172 < z < -3.1999999999999999e-18

   1. Initial program 88.9%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   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* 83.1%

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

   7. Simplified 83.1%

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

   8. Taylor expanded in z around 0 77.0%

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

   if -3.1999999999999999e-18 < z < 1.05000000000000004e-68

   1. Initial program 96.2%

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

      1. associate-*l/ 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in y around inf 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-*r/ 92.1%

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

   7. Simplified 92.1%

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

   8. Taylor expanded in a around inf 73.9%

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

      1. +-commutative 73.9%

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

      2. associate-/l* 72.9%

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

      3. associate-/r/ 77.4%

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

   10. Simplified 77.4%

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

   if 1.05000000000000004e-68 < z < 1.25000000000000005e120

   1. Initial program 94.9%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   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* 82.2%

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

   7. Simplified 82.2%

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

   8. Taylor expanded in z around 0 71.7%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+172}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-18}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-68}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+120}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+168}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-19}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-65}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+120}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.22e+168)
   (+ t x)
   (if (<= z -6.5e-19)
     (- x (* y (/ t z)))
     (if (<= z 3.7e-65)
       (+ x (* y (/ t a)))
       (if (<= z 1.45e+120) (- x (/ (* y t) z)) (+ t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.22e+168) {
		tmp = t + x;
	} else if (z <= -6.5e-19) {
		tmp = x - (y * (t / z));
	} else if (z <= 3.7e-65) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.45e+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 <= (-1.22d+168)) then
        tmp = t + x
    else if (z <= (-6.5d-19)) then
        tmp = x - (y * (t / z))
    else if (z <= 3.7d-65) then
        tmp = x + (y * (t / a))
    else if (z <= 1.45d+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 <= -1.22e+168) {
		tmp = t + x;
	} else if (z <= -6.5e-19) {
		tmp = x - (y * (t / z));
	} else if (z <= 3.7e-65) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.45e+120) {
		tmp = x - ((y * t) / z);
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.22e+168:
		tmp = t + x
	elif z <= -6.5e-19:
		tmp = x - (y * (t / z))
	elif z <= 3.7e-65:
		tmp = x + (y * (t / a))
	elif z <= 1.45e+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 <= -1.22e+168)
		tmp = Float64(t + x);
	elseif (z <= -6.5e-19)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	elseif (z <= 3.7e-65)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 1.45e+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 <= -1.22e+168)
		tmp = t + x;
	elseif (z <= -6.5e-19)
		tmp = x - (y * (t / z));
	elseif (z <= 3.7e-65)
		tmp = x + (y * (t / a));
	elseif (z <= 1.45e+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, -1.22e+168], N[(t + x), $MachinePrecision], If[LessEqual[z, -6.5e-19], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e-65], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+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 < -1.21999999999999991e168 or 1.4500000000000001e120 < z

   1. Initial program 63.3%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 84.6%

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

   if -1.21999999999999991e168 < z < -6.5000000000000001e-19

   1. Initial program 88.9%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in y around inf 77.7%

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

      1. *-commutative 77.7%

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

      2. associate-*r/ 81.9%

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

   7. Simplified 81.9%

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

   8. Taylor expanded in a around 0 77.5%

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

      1. associate-*r/ 77.5%

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

      2. neg-mul-1 77.5%

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

   10. Simplified 77.5%

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

   if -6.5000000000000001e-19 < z < 3.7e-65

   1. Initial program 96.2%

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

      1. associate-*l/ 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in y around inf 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-*r/ 92.1%

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

   7. Simplified 92.1%

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

   8. Taylor expanded in a around inf 73.9%

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

      1. +-commutative 73.9%

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

      2. associate-/l* 72.9%

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

      3. associate-/r/ 77.4%

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

   10. Simplified 77.4%

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

   if 3.7e-65 < z < 1.4500000000000001e120

   1. Initial program 94.9%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   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* 82.2%

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

   7. Simplified 82.2%

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

   8. Taylor expanded in z around 0 71.7%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+168}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-19}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-65}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+120}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+170}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-19}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+25}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.1e+170)
   (+ t x)
   (if (<= z -4.3e-19)
     (- x (* t (/ y z)))
     (if (<= z 3.1e+25) (+ x (* y (/ t a))) (+ t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.1e+170) {
		tmp = t + x;
	} else if (z <= -4.3e-19) {
		tmp = x - (t * (y / z));
	} else if (z <= 3.1e+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 <= (-2.1d+170)) then
        tmp = t + x
    else if (z <= (-4.3d-19)) then
        tmp = x - (t * (y / z))
    else if (z <= 3.1d+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 <= -2.1e+170) {
		tmp = t + x;
	} else if (z <= -4.3e-19) {
		tmp = x - (t * (y / z));
	} else if (z <= 3.1e+25) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.1e+170:
		tmp = t + x
	elif z <= -4.3e-19:
		tmp = x - (t * (y / z))
	elif z <= 3.1e+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 <= -2.1e+170)
		tmp = Float64(t + x);
	elseif (z <= -4.3e-19)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 3.1e+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 <= -2.1e+170)
		tmp = t + x;
	elseif (z <= -4.3e-19)
		tmp = x - (t * (y / z));
	elseif (z <= 3.1e+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, -2.1e+170], N[(t + x), $MachinePrecision], If[LessEqual[z, -4.3e-19], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e+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 < -2.09999999999999998e170 or 3.0999999999999998e25 < z

   1. Initial program 69.7%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 78.6%

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

   if -2.09999999999999998e170 < z < -4.3e-19

   1. Initial program 88.9%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in y around inf 77.7%

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

      1. *-commutative 77.7%

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

      2. associate-*r/ 81.9%

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

   7. Simplified 81.9%

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

   8. Taylor expanded in a around 0 73.3%

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

      1. mul-1-neg 73.3%

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

      2. unsub-neg 73.3%

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

      3. associate-*r/ 75.4%

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

   10. Simplified 75.4%

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

   if -4.3e-19 < z < 3.0999999999999998e25

   1. Initial program 96.0%

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

      1. associate-*l/ 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in y around inf 89.4%

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

      1. *-commutative 89.4%

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

      2. associate-*r/ 90.9%

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

   7. Simplified 90.9%

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

   8. Taylor expanded in a around inf 71.5%

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

      1. +-commutative 71.5%

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

      2. associate-/l* 70.6%

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

      3. associate-/r/ 74.5%

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

   10. Simplified 74.5%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+170}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-19}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+25}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -54 \lor \neg \left(z \leq 2.9 \cdot 10^{+21}\right):\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -54.0) (not (<= z 2.9e+21)))
   (+ x (* t (- 1.0 (/ 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 <= 2.9e+21)) {
		tmp = x + (t * (1.0 - (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 <= 2.9d+21))) then
        tmp = x + (t * (1.0d0 - (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 <= 2.9e+21)) {
		tmp = x + (t * (1.0 - (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 <= 2.9e+21):
		tmp = x + (t * (1.0 - (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 <= 2.9e+21))
		tmp = Float64(x + Float64(t * Float64(1.0 - Float64(y / z))));
	else
		tmp = Float64(x + Float64(y * Float64(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 <= 2.9e+21)))
		tmp = x + (t * (1.0 - (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, 2.9e+21]], $MachinePrecision]], N[(x + N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -54 or 2.9e21 < z

   1. Initial program 74.8%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 90.8%

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

      1. mul-1-neg 90.8%

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

      2. div-sub 90.8%

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

      3. sub-neg 90.8%

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

      4. *-inverses 90.8%

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

      5. metadata-eval 90.8%

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

   7. Simplified 90.8%

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

   8. Taylor expanded in y around 0 81.0%

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

      1. mul-1-neg 81.0%

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

      2. *-commutative 81.0%

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

      3. associate-*l/ 90.8%

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

      4. distribute-lft-neg-out 90.8%

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

      5. distribute-frac-neg 90.8%

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

      6. *-lft-identity 90.8%

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

      7. distribute-rgt-in 90.8%

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

      8. distribute-frac-neg 90.8%

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

      9. sub-neg 90.8%

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

   10. Simplified 90.8%

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

   if -54 < z < 2.9e21

   1. Initial program 96.9%

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

      1. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in y around inf 89.5%

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

      1. *-commutative 89.5%

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

      2. associate-*r/ 91.0%

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

   7. Simplified 91.0%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -54 \lor \neg \left(z \leq 2.9 \cdot 10^{+21}\right):\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.8 \cdot 10^{+58}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 1.36 \cdot 10^{-28}:\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.8e+58)
   (+ x (* y (/ t a)))
   (if (<= a 1.36e-28) (+ x (* t (- 1.0 (/ y z)))) (+ x (* t (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.8e+58) {
		tmp = x + (y * (t / a));
	} else if (a <= 1.36e-28) {
		tmp = x + (t * (1.0 - (y / z)));
	} 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 <= (-9.8d+58)) then
        tmp = x + (y * (t / a))
    else if (a <= 1.36d-28) then
        tmp = x + (t * (1.0d0 - (y / z)))
    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 <= -9.8e+58) {
		tmp = x + (y * (t / a));
	} else if (a <= 1.36e-28) {
		tmp = x + (t * (1.0 - (y / z)));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.8e+58:
		tmp = x + (y * (t / a))
	elif a <= 1.36e-28:
		tmp = x + (t * (1.0 - (y / z)))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.8e+58)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (a <= 1.36e-28)
		tmp = Float64(x + Float64(t * Float64(1.0 - Float64(y / z))));
	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 <= -9.8e+58)
		tmp = x + (y * (t / a));
	elseif (a <= 1.36e-28)
		tmp = x + (t * (1.0 - (y / z)));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.8e+58], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.36e-28], N[(x + N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.80000000000000037e58

   1. Initial program 81.6%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 77.6%

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

      1. *-commutative 77.6%

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

      2. associate-*r/ 81.2%

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

   7. Simplified 81.2%

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

   8. Taylor expanded in a around inf 74.3%

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

      1. +-commutative 74.3%

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

      2. associate-/l* 78.2%

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

      3. associate-/r/ 78.9%

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

   10. Simplified 78.9%

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

   if -9.80000000000000037e58 < a < 1.35999999999999989e-28

   1. Initial program 89.3%

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

      1. associate-*l/ 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in a around 0 85.2%

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

      1. mul-1-neg 85.2%

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

      2. div-sub 85.2%

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

      3. sub-neg 85.2%

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

      4. *-inverses 85.2%

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

      5. metadata-eval 85.2%

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

   7. Simplified 85.2%

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

   8. Taylor expanded in y around 0 84.4%

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

      1. mul-1-neg 84.4%

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

      2. *-commutative 84.4%

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

      3. associate-*l/ 85.2%

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

      4. distribute-lft-neg-out 85.2%

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

      5. distribute-frac-neg 85.2%

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

      6. *-lft-identity 85.2%

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

      7. distribute-rgt-in 85.2%

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

      8. distribute-frac-neg 85.2%

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

      9. sub-neg 85.2%

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

   10. Simplified 85.2%

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

   if 1.35999999999999989e-28 < a

   1. Initial program 78.6%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 82.2%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.8 \cdot 10^{+58}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 1.36 \cdot 10^{-28}:\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 87.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -205:\\ \;\;\;\;x - t \cdot \frac{y - z}{z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+21}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -205.0)
   (- x (* t (/ (- y z) z)))
   (if (<= z 2.6e+21) (+ x (* y (/ t (- a z)))) (+ x (* t (- 1.0 (/ y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -205.0) {
		tmp = x - (t * ((y - z) / z));
	} else if (z <= 2.6e+21) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (t * (1.0 - (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 <= (-205.0d0)) then
        tmp = x - (t * ((y - z) / z))
    else if (z <= 2.6d+21) then
        tmp = x + (y * (t / (a - z)))
    else
        tmp = x + (t * (1.0d0 - (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 <= -205.0) {
		tmp = x - (t * ((y - z) / z));
	} else if (z <= 2.6e+21) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (t * (1.0 - (y / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -205.0:
		tmp = x - (t * ((y - z) / z))
	elif z <= 2.6e+21:
		tmp = x + (y * (t / (a - z)))
	else:
		tmp = x + (t * (1.0 - (y / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -205.0)
		tmp = Float64(x - Float64(t * Float64(Float64(y - z) / z)));
	elseif (z <= 2.6e+21)
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	else
		tmp = Float64(x + Float64(t * Float64(1.0 - Float64(y / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -205.0)
		tmp = x - (t * ((y - z) / z));
	elseif (z <= 2.6e+21)
		tmp = x + (y * (t / (a - z)));
	else
		tmp = x + (t * (1.0 - (y / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -205.0], N[(x - N[(t * N[(N[(y - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+21], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -205

   1. Initial program 76.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 71.5%

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

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

   7. Simplified 91.4%

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

      1. clear-num 91.4%

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

      2. associate-/r/ 91.4%

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

      3. clear-num 91.4%

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

   9. Applied egg-rr 91.4%

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

   if -205 < z < 2.6e21

   1. Initial program 96.9%

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

      1. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in y around inf 89.5%

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

      1. *-commutative 89.5%

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

      2. associate-*r/ 91.0%

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

   7. Simplified 91.0%

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

   if 2.6e21 < z

   1. Initial program 72.0%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 89.9%

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

      1. mul-1-neg 89.9%

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

      2. div-sub 89.9%

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

      3. sub-neg 89.9%

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

      4. *-inverses 89.9%

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

      5. metadata-eval 89.9%

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

   7. Simplified 89.9%

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

   8. Taylor expanded in y around 0 80.2%

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

      1. mul-1-neg 80.2%

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

      2. *-commutative 80.2%

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

      3. associate-*l/ 89.9%

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

      4. distribute-lft-neg-out 89.9%

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

      5. distribute-frac-neg 89.9%

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

      6. *-lft-identity 89.9%

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

      7. distribute-rgt-in 89.9%

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

      8. distribute-frac-neg 89.9%

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

      9. sub-neg 89.9%

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

   10. Simplified 89.9%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -205:\\ \;\;\;\;x - t \cdot \frac{y - z}{z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+21}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -40 \lor \neg \left(z \leq 1.7 \cdot 10^{+25}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -40.0) (not (<= z 1.7e+25))) (+ t x) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -40.0) || !(z <= 1.7e+25)) {
		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 ((z <= (-40.0d0)) .or. (.not. (z <= 1.7d+25))) 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 ((z <= -40.0) || !(z <= 1.7e+25)) {
		tmp = t + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -40.0) or not (z <= 1.7e+25):
		tmp = t + x
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -40.0) || !(z <= 1.7e+25))
		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 ((z <= -40.0) || ~((z <= 1.7e+25)))
		tmp = t + x;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -40.0], N[Not[LessEqual[z, 1.7e+25]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -40 or 1.69999999999999992e25 < z

   1. Initial program 75.0%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 73.9%

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

   if -40 < z < 1.69999999999999992e25

   1. Initial program 96.1%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in z around 0 70.0%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -40 \lor \neg \left(z \leq 1.7 \cdot 10^{+25}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 75.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -75 \lor \neg \left(z \leq 2.5 \cdot 10^{+25}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -75.0) (not (<= z 2.5e+25))) (+ t x) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -75.0) || !(z <= 2.5e+25)) {
		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 <= (-75.0d0)) .or. (.not. (z <= 2.5d+25))) 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 <= -75.0) || !(z <= 2.5e+25)) {
		tmp = t + x;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -75.0) or not (z <= 2.5e+25):
		tmp = t + x
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -75.0) || !(z <= 2.5e+25))
		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 <= -75.0) || ~((z <= 2.5e+25)))
		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, -75.0], N[Not[LessEqual[z, 2.5e+25]], $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 < -75 or 2.50000000000000012e25 < z

   1. Initial program 75.0%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 73.9%

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

   if -75 < z < 2.50000000000000012e25

   1. Initial program 96.1%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in z around 0 70.9%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -75 \lor \neg \left(z \leq 2.5 \cdot 10^{+25}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 76.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -40 \lor \neg \left(z \leq 1.36 \cdot 10^{+25}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -40.0) (not (<= z 1.36e+25))) (+ t x) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -40.0) || !(z <= 1.36e+25)) {
		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 <= (-40.0d0)) .or. (.not. (z <= 1.36d+25))) 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 <= -40.0) || !(z <= 1.36e+25)) {
		tmp = t + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -40.0) or not (z <= 1.36e+25):
		tmp = t + x
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -40.0) || !(z <= 1.36e+25))
		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 ((z <= -40.0) || ~((z <= 1.36e+25)))
		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, -40.0], N[Not[LessEqual[z, 1.36e+25]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -40 or 1.36e25 < z

   1. Initial program 75.0%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 73.9%

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

   if -40 < z < 1.36e25

   1. Initial program 96.1%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in y around inf 89.0%

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

      1. *-commutative 89.0%

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

      2. associate-*r/ 90.4%

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

   7. Simplified 90.4%

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

   8. Taylor expanded in a around inf 70.9%

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

      1. +-commutative 70.9%

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

      2. associate-/l* 70.0%

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

      3. associate-/r/ 73.7%

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

   10. Simplified 73.7%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -40 \lor \neg \left(z \leq 1.36 \cdot 10^{+25}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 62.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -70 \lor \neg \left(z \leq 3.4 \cdot 10^{-71}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -70.0) (not (<= z 3.4e-71))) (+ t x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -70.0) || !(z <= 3.4e-71)) {
		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 <= (-70.0d0)) .or. (.not. (z <= 3.4d-71))) 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 <= -70.0) || !(z <= 3.4e-71)) {
		tmp = t + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -70.0) or not (z <= 3.4e-71):
		tmp = t + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -70.0) || !(z <= 3.4e-71))
		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 <= -70.0) || ~((z <= 3.4e-71)))
		tmp = t + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -70.0], N[Not[LessEqual[z, 3.4e-71]], $MachinePrecision]], N[(t + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -70 or 3.40000000000000003e-71 < z

   1. Initial program 77.6%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in z around inf 69.7%

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

   if -70 < z < 3.40000000000000003e-71

   1. Initial program 96.3%

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

      1. associate-*l/ 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in x around inf 48.0%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -70 \lor \neg \left(z \leq 3.4 \cdot 10^{-71}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+199}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+169}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.45e+199) t (if (<= t 3.1e+169) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.45e+199) {
		tmp = t;
	} else if (t <= 3.1e+169) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.45d+199)) then
        tmp = t
    else if (t <= 3.1d+169) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.45e+199) {
		tmp = t;
	} else if (t <= 3.1e+169) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.45e+199:
		tmp = t
	elif t <= 3.1e+169:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.45e+199)
		tmp = t;
	elseif (t <= 3.1e+169)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.45e+199)
		tmp = t;
	elseif (t <= 3.1e+169)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.45e+199], t, If[LessEqual[t, 3.1e+169], x, t]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4499999999999999e199 or 3.1e169 < t

   1. Initial program 60.1%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 40.1%

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

   6. Taylor expanded in x around 0 34.9%

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

   if -1.4499999999999999e199 < t < 3.1e169

   1. Initial program 91.5%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in x around inf 58.2%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+199}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+169}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.1%

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

   1. associate-*l/ 96.5%

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

3. Simplified 96.5%

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

5. Final simplification 96.5%

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

Alternative 17: 18.6% 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 85.1%

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

   1. associate-*l/ 96.5%

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

3. Simplified 96.5%

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

5. Taylor expanded in z around inf 56.2%

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

6. Taylor expanded in x around 0 16.7%

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

7. Final simplification 16.7%

   \[\leadsto t \]
8. 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

  :herbie-target
  (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))))