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

Percentage Accurate: 86.1% → 99.7%

Time: 9.4s

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: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / 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, (-Infinity)], N[(N[(y - z), $MachinePrecision] * t$95$1 + x), $MachinePrecision], If[LessEqual[t$95$2, 1e+307], N[(t$95$2 + x), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $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. Step-by-step derivation

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   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: 61.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+89} \lor \neg \left(y \leq 2 \cdot 10^{-6}\right) \land \left(y \leq 1.12 \cdot 10^{+66} \lor \neg \left(y \leq 1.58 \cdot 10^{+130}\right)\right):\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -4.5e+89)
         (and (not (<= y 2e-6)) (or (<= y 1.12e+66) (not (<= y 1.58e+130)))))
   (* t (/ y (- a z)))
   (+ t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.5e+89) || (!(y <= 2e-6) && ((y <= 1.12e+66) || !(y <= 1.58e+130)))) {
		tmp = t * (y / (a - 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 ((y <= (-4.5d+89)) .or. (.not. (y <= 2d-6)) .and. (y <= 1.12d+66) .or. (.not. (y <= 1.58d+130))) then
        tmp = t * (y / (a - 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 ((y <= -4.5e+89) || (!(y <= 2e-6) && ((y <= 1.12e+66) || !(y <= 1.58e+130)))) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -4.5e+89) or (not (y <= 2e-6) and ((y <= 1.12e+66) or not (y <= 1.58e+130))):
		tmp = t * (y / (a - z))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -4.5e+89) || (!(y <= 2e-6) && ((y <= 1.12e+66) || !(y <= 1.58e+130))))
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -4.5e+89) || (~((y <= 2e-6)) && ((y <= 1.12e+66) || ~((y <= 1.58e+130)))))
		tmp = t * (y / (a - z));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -4.5e+89], And[N[Not[LessEqual[y, 2e-6]], $MachinePrecision], Or[LessEqual[y, 1.12e+66], N[Not[LessEqual[y, 1.58e+130]], $MachinePrecision]]]], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5e89 or 1.99999999999999991e-6 < y < 1.12e66 or 1.57999999999999994e130 < y

   1. Initial program 80.3%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in x around inf 70.6%

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

      1. +-commutative 70.6%

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

      2. associate-/l* 70.7%

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

      3. fma-define 70.7%

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

      4. *-commutative 70.7%

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

      5. associate-/r* 73.7%

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

   7. Simplified 73.7%

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

   8. Taylor expanded in y around inf 57.9%

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

      1. associate-/l* 58.9%

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

   10. Simplified 58.9%

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

   if -4.5e89 < y < 1.99999999999999991e-6 or 1.12e66 < y < 1.57999999999999994e130

   1. Initial program 88.5%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in z around inf 73.9%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+89} \lor \neg \left(y \leq 2 \cdot 10^{-6}\right) \land \left(y \leq 1.12 \cdot 10^{+66} \lor \neg \left(y \leq 1.58 \cdot 10^{+130}\right)\right):\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+168}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-25}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-66}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+120}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.9e+168)
   (+ t x)
   (if (<= z -2.8e-25)
     (- x (* y (/ t z)))
     (if (<= z 1.95e-66)
       (+ x (* y (/ t a)))
       (if (<= z 1.4e+120) (- x (/ (* y t) z)) (+ t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.9e+168) {
		tmp = t + x;
	} else if (z <= -2.8e-25) {
		tmp = x - (y * (t / z));
	} else if (z <= 1.95e-66) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.4e+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 <= (-2.9d+168)) then
        tmp = t + x
    else if (z <= (-2.8d-25)) then
        tmp = x - (y * (t / z))
    else if (z <= 1.95d-66) then
        tmp = x + (y * (t / a))
    else if (z <= 1.4d+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 <= -2.9e+168) {
		tmp = t + x;
	} else if (z <= -2.8e-25) {
		tmp = x - (y * (t / z));
	} else if (z <= 1.95e-66) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.4e+120) {
		tmp = x - ((y * t) / z);
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.9e+168:
		tmp = t + x
	elif z <= -2.8e-25:
		tmp = x - (y * (t / z))
	elif z <= 1.95e-66:
		tmp = x + (y * (t / a))
	elif z <= 1.4e+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 <= -2.9e+168)
		tmp = Float64(t + x);
	elseif (z <= -2.8e-25)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	elseif (z <= 1.95e-66)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 1.4e+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 <= -2.9e+168)
		tmp = t + x;
	elseif (z <= -2.8e-25)
		tmp = x - (y * (t / z));
	elseif (z <= 1.95e-66)
		tmp = x + (y * (t / a));
	elseif (z <= 1.4e+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, -2.9e+168], N[(t + x), $MachinePrecision], If[LessEqual[z, -2.8e-25], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e-66], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+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 < -2.9e168 or 1.4e120 < z

   1. Initial program 63.3%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in z around inf 84.6%

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

   if -2.9e168 < z < -2.79999999999999988e-25

   1. Initial program 89.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 77.7%

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

      1. associate-*l/ 81.8%

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

      2. *-commutative 81.8%

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

   7. Simplified 81.8%

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

   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/ 82.3%

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

      2. neg-mul-1 82.3%

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

   10. Simplified 77.5%

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

   if -2.79999999999999988e-25 < z < 1.94999999999999991e-66

   1. Initial program 96.2%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in y around inf 90.4%

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

      1. associate-*l/ 92.3%

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

      2. *-commutative 92.3%

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

   7. Simplified 92.3%

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

   8. Taylor expanded in a around inf 77.5%

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

   if 1.94999999999999991e-66 < z < 1.4e120

   1. Initial program 94.9%

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

      1. associate-/l* 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in y around inf 76.8%

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

      1. associate-*l/ 79.3%

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

      2. *-commutative 79.3%

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

   7. Simplified 79.3%

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

   8. Taylor expanded in a around 0 71.7%

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

      1. mul-1-neg 71.7%

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

      2. unsub-neg 71.7%

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

      3. associate-/l* 66.7%

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

   10. Simplified 66.7%

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

   11. Taylor expanded in t 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+168}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-25}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-66}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+120}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+168}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-28}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-70}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.48 \cdot 10^{+122}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.22e+168)
   (+ t x)
   (if (<= z -2.65e-28)
     (- x (* t (/ y z)))
     (if (<= z 9.5e-70)
       (+ x (* y (/ t a)))
       (if (<= z 1.48e+122) (- 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 <= -2.65e-28) {
		tmp = x - (t * (y / z));
	} else if (z <= 9.5e-70) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.48e+122) {
		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 <= (-2.65d-28)) then
        tmp = x - (t * (y / z))
    else if (z <= 9.5d-70) then
        tmp = x + (y * (t / a))
    else if (z <= 1.48d+122) 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 <= -2.65e-28) {
		tmp = x - (t * (y / z));
	} else if (z <= 9.5e-70) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.48e+122) {
		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 <= -2.65e-28:
		tmp = x - (t * (y / z))
	elif z <= 9.5e-70:
		tmp = x + (y * (t / a))
	elif z <= 1.48e+122:
		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 <= -2.65e-28)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 9.5e-70)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 1.48e+122)
		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 <= -2.65e-28)
		tmp = x - (t * (y / z));
	elseif (z <= 9.5e-70)
		tmp = x + (y * (t / a));
	elseif (z <= 1.48e+122)
		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, -2.65e-28], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-70], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.48e+122], 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 1.48000000000000005e122 < z

   1. Initial program 63.3%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in z around inf 84.6%

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

   if -1.21999999999999991e168 < z < -2.64999999999999994e-28

   1. Initial program 89.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 77.7%

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

      1. associate-*l/ 81.8%

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

      2. *-commutative 81.8%

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

   7. Simplified 81.8%

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

   8. Taylor expanded in a around 0 73.4%

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

      1. mul-1-neg 73.4%

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

      2. unsub-neg 73.4%

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

      3. associate-/l* 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 -2.64999999999999994e-28 < z < 9.4999999999999994e-70

   1. Initial program 96.2%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in y around inf 90.4%

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

      1. associate-*l/ 92.3%

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

      2. *-commutative 92.3%

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

   7. Simplified 92.3%

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

   8. Taylor expanded in a around inf 77.5%

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

   if 9.4999999999999994e-70 < z < 1.48000000000000005e122

   1. Initial program 94.9%

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

      1. associate-/l* 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in y around inf 76.8%

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

      1. associate-*l/ 79.3%

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

      2. *-commutative 79.3%

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

   7. Simplified 79.3%

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

   8. Taylor expanded in a around 0 71.7%

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

      1. mul-1-neg 71.7%

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

      2. unsub-neg 71.7%

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

      3. associate-/l* 66.7%

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

   10. Simplified 66.7%

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

   11. Taylor expanded in t around 0 71.7%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+168}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-28}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-70}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.48 \cdot 10^{+122}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -165:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= z -165.0)
     (+ t x)
     (if (<= z 1.16e-110)
       t_1
       (if (<= z 6.2e-37)
         (* y (/ t (- a z)))
         (if (<= z 2.9e+25) 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 <= -165.0) {
		tmp = t + x;
	} else if (z <= 1.16e-110) {
		tmp = t_1;
	} else if (z <= 6.2e-37) {
		tmp = y * (t / (a - z));
	} else if (z <= 2.9e+25) {
		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 <= (-165.0d0)) then
        tmp = t + x
    else if (z <= 1.16d-110) then
        tmp = t_1
    else if (z <= 6.2d-37) then
        tmp = y * (t / (a - z))
    else if (z <= 2.9d+25) 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 <= -165.0) {
		tmp = t + x;
	} else if (z <= 1.16e-110) {
		tmp = t_1;
	} else if (z <= 6.2e-37) {
		tmp = y * (t / (a - z));
	} else if (z <= 2.9e+25) {
		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 <= -165.0:
		tmp = t + x
	elif z <= 1.16e-110:
		tmp = t_1
	elif z <= 6.2e-37:
		tmp = y * (t / (a - z))
	elif z <= 2.9e+25:
		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 <= -165.0)
		tmp = Float64(t + x);
	elseif (z <= 1.16e-110)
		tmp = t_1;
	elseif (z <= 6.2e-37)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (z <= 2.9e+25)
		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 <= -165.0)
		tmp = t + x;
	elseif (z <= 1.16e-110)
		tmp = t_1;
	elseif (z <= 6.2e-37)
		tmp = y * (t / (a - z));
	elseif (z <= 2.9e+25)
		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, -165.0], N[(t + x), $MachinePrecision], If[LessEqual[z, 1.16e-110], t$95$1, If[LessEqual[z, 6.2e-37], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+25], t$95$1, N[(t + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -165 or 2.8999999999999999e25 < z

   1. Initial program 75.0%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in z around inf 73.9%

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

   if -165 < z < 1.16000000000000001e-110 or 6.19999999999999987e-37 < z < 2.8999999999999999e25

   1. Initial program 96.4%

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

      1. associate-/l* 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in y around inf 90.7%

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

      1. associate-*l/ 91.5%

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

      2. *-commutative 91.5%

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

   7. Simplified 91.5%

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

   8. Taylor expanded in y around inf 86.0%

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

   9. Taylor expanded in a around inf 75.1%

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

       1. associate-/l* 74.3%

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

   11. Simplified 74.3%

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

   if 1.16000000000000001e-110 < z < 6.19999999999999987e-37

   1. Initial program 94.6%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in y around inf 77.8%

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

      1. associate-*l/ 83.7%

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

      2. *-commutative 83.7%

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

   7. Simplified 83.7%

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

   8. Taylor expanded in y around inf 83.7%

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

   9. Taylor expanded in y around inf 60.9%

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

       1. associate-*l/ 66.8%

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

       2. *-commutative 66.8%

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

   11. Simplified 66.8%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -165:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-110}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+25}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{a - z}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-6}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+130}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ t (- a z)))))
   (if (<= y -2.7e+93)
     t_1
     (if (<= y 2e-6)
       (+ t x)
       (if (<= y 1.15e+66)
         (* t (/ y (- a z)))
         (if (<= y 1.6e+130) (+ t x) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / (a - z));
	double tmp;
	if (y <= -2.7e+93) {
		tmp = t_1;
	} else if (y <= 2e-6) {
		tmp = t + x;
	} else if (y <= 1.15e+66) {
		tmp = t * (y / (a - z));
	} else if (y <= 1.6e+130) {
		tmp = t + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t / (a - z))
    if (y <= (-2.7d+93)) then
        tmp = t_1
    else if (y <= 2d-6) then
        tmp = t + x
    else if (y <= 1.15d+66) then
        tmp = t * (y / (a - z))
    else if (y <= 1.6d+130) then
        tmp = t + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / (a - z));
	double tmp;
	if (y <= -2.7e+93) {
		tmp = t_1;
	} else if (y <= 2e-6) {
		tmp = t + x;
	} else if (y <= 1.15e+66) {
		tmp = t * (y / (a - z));
	} else if (y <= 1.6e+130) {
		tmp = t + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (t / (a - z))
	tmp = 0
	if y <= -2.7e+93:
		tmp = t_1
	elif y <= 2e-6:
		tmp = t + x
	elif y <= 1.15e+66:
		tmp = t * (y / (a - z))
	elif y <= 1.6e+130:
		tmp = t + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / Float64(a - z)))
	tmp = 0.0
	if (y <= -2.7e+93)
		tmp = t_1;
	elseif (y <= 2e-6)
		tmp = Float64(t + x);
	elseif (y <= 1.15e+66)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (y <= 1.6e+130)
		tmp = Float64(t + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (t / (a - z));
	tmp = 0.0;
	if (y <= -2.7e+93)
		tmp = t_1;
	elseif (y <= 2e-6)
		tmp = t + x;
	elseif (y <= 1.15e+66)
		tmp = t * (y / (a - z));
	elseif (y <= 1.6e+130)
		tmp = t + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e+93], t$95$1, If[LessEqual[y, 2e-6], N[(t + x), $MachinePrecision], If[LessEqual[y, 1.15e+66], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e+130], N[(t + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6999999999999999e93 or 1.6e130 < y

   1. Initial program 78.9%

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

      1. associate-/l* 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in y around inf 75.6%

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

      1. associate-*l/ 87.2%

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

      2. *-commutative 87.2%

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

   7. Simplified 87.2%

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

   8. Taylor expanded in y around inf 86.6%

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

   9. Taylor expanded in y around inf 57.9%

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

       1. associate-*l/ 64.0%

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

       2. *-commutative 64.0%

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

   11. Simplified 64.0%

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

   if -2.6999999999999999e93 < y < 1.99999999999999991e-6 or 1.15e66 < y < 1.6e130

   1. Initial program 88.5%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in z around inf 73.9%

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

   if 1.99999999999999991e-6 < y < 1.15e66

   1. Initial program 88.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 81.9%

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

      1. +-commutative 81.9%

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

      2. associate-/l* 76.2%

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

      3. fma-define 76.2%

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

      4. *-commutative 76.2%

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

      5. associate-/r* 76.2%

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

   7. Simplified 76.2%

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

   8. Taylor expanded in y around inf 58.3%

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

      1. associate-/l* 58.4%

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

   10. Simplified 58.4%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-6}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+130}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+168}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-25}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 10^{+26}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e+168)
   (+ t x)
   (if (<= z -2.8e-25)
     (- x (* t (/ y z)))
     (if (<= z 1e+26) (+ x (* y (/ t a))) (+ t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+168) {
		tmp = t + x;
	} else if (z <= -2.8e-25) {
		tmp = x - (t * (y / z));
	} else if (z <= 1e+26) {
		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 <= (-5.5d+168)) then
        tmp = t + x
    else if (z <= (-2.8d-25)) then
        tmp = x - (t * (y / z))
    else if (z <= 1d+26) 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 <= -5.5e+168) {
		tmp = t + x;
	} else if (z <= -2.8e-25) {
		tmp = x - (t * (y / z));
	} else if (z <= 1e+26) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e+168:
		tmp = t + x
	elif z <= -2.8e-25:
		tmp = x - (t * (y / z))
	elif z <= 1e+26:
		tmp = x + (y * (t / a))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e+168)
		tmp = Float64(t + x);
	elseif (z <= -2.8e-25)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 1e+26)
		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 <= -5.5e+168)
		tmp = t + x;
	elseif (z <= -2.8e-25)
		tmp = x - (t * (y / z));
	elseif (z <= 1e+26)
		tmp = x + (y * (t / a));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e+168], N[(t + x), $MachinePrecision], If[LessEqual[z, -2.8e-25], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+26], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.5000000000000001e168 or 1.00000000000000005e26 < z

   1. Initial program 69.7%

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

      1. associate-/l* 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in z around inf 78.6%

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

   if -5.5000000000000001e168 < z < -2.79999999999999988e-25

   1. Initial program 89.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 77.7%

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

      1. associate-*l/ 81.8%

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

      2. *-commutative 81.8%

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

   7. Simplified 81.8%

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

   8. Taylor expanded in a around 0 73.4%

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

      1. mul-1-neg 73.4%

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

      2. unsub-neg 73.4%

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

      3. associate-/l* 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 -2.79999999999999988e-25 < z < 1.00000000000000005e26

   1. Initial program 96.0%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t}{a - z}} \]
   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. associate-*l/ 91.0%

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

      2. *-commutative 91.0%

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

   7. Simplified 91.0%

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

   8. Taylor expanded in a around inf 74.4%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+168}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-25}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 10^{+26}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.8% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -54.0) (not (<= z 2.9e+21)))
   (+ x (- t (* 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 <= 2.9e+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 <= 2.9d+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 <= 2.9e+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 <= 2.9e+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 <= 2.9e+21))
		tmp = Float64(x + Float64(t - Float64(t * 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 - (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, 2.9e+21]], $MachinePrecision]], N[(x + N[(t - N[(t * 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* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in a around 0 87.0%

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

      1. associate-*r/ 87.0%

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

      2. neg-mul-1 87.0%

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

   7. Simplified 87.0%

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

   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. associate-*l/ 90.0%

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

      2. associate-/r/ 90.8%

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

      3. neg-mul-1 90.8%

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

      4. unsub-neg 90.8%

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

      5. associate-/r/ 90.0%

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

      6. associate-*l/ 81.0%

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

      7. associate-*r/ 90.8%

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

   10. Simplified 90.8%

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

   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* 96.8%

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

   3. Simplified 96.8%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t}{a - z}} \]
   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. associate-*l/ 91.0%

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

      2. *-commutative 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%

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

Alternative 10: 84.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+168} \lor \neg \left(z \leq 5.4 \cdot 10^{+121}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.55e+168) (not (<= z 5.4e+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 <= -1.55e+168) || !(z <= 5.4e+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 <= (-1.55d+168)) .or. (.not. (z <= 5.4d+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 <= -1.55e+168) || !(z <= 5.4e+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 <= -1.55e+168) or not (z <= 5.4e+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 <= -1.55e+168) || !(z <= 5.4e+121))
		tmp = Float64(t + x);
	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 <= -1.55e+168) || ~((z <= 5.4e+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, -1.55e+168], N[Not[LessEqual[z, 5.4e+121]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.54999999999999998e168 or 5.4000000000000004e121 < z

   1. Initial program 63.3%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in z around inf 84.6%

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

   if -1.54999999999999998e168 < z < 5.4000000000000004e121

   1. Initial program 94.2%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in y around inf 84.5%

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

      1. associate-*l/ 87.0%

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

      2. *-commutative 87.0%

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

   7. Simplified 87.0%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+168} \lor \neg \left(z \leq 5.4 \cdot 10^{+121}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 87.8% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -205.0)
   (+ 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 <= -205.0) {
		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 <= (-205.0d0)) 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 <= -205.0) {
		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 <= -205.0:
		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 <= -205.0)
		tmp = Float64(x + Float64(t * Float64(Float64(z - y) / z)));
	elseif (z <= 2.6e+21)
		tmp = Float64(x + Float64(y * Float64(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 <= -205.0)
		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, -205.0], N[(x + N[(t * N[(N[(z - y), $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[(t * 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* 95.6%

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

   3. Simplified 95.6%

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

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

   7. Simplified 91.4%

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

   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* 96.8%

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

   3. Simplified 96.8%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t}{a - z}} \]
   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. associate-*l/ 91.0%

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

      2. *-commutative 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* 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in a around 0 86.7%

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

      1. associate-*r/ 86.7%

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

      2. neg-mul-1 86.7%

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

   7. Simplified 86.7%

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

   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. associate-*l/ 88.3%

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

      2. associate-/r/ 89.9%

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

      3. neg-mul-1 89.9%

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

      4. unsub-neg 89.9%

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

      5. associate-/r/ 88.3%

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

      6. associate-*l/ 80.2%

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

      7. associate-*r/ 89.9%

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

   10. Simplified 89.9%

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

4. Final simplification 90.9%

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

Alternative 12: 76.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -205 \lor \neg \left(z \leq 1.5 \cdot 10^{+25}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -205.0) (not (<= z 1.5e+25))) (+ t x) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -205.0) || !(z <= 1.5e+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 <= (-205.0d0)) .or. (.not. (z <= 1.5d+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 <= -205.0) || !(z <= 1.5e+25)) {
		tmp = t + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -205.0) or not (z <= 1.5e+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 <= -205.0) || !(z <= 1.5e+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 <= -205.0) || ~((z <= 1.5e+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, -205.0], N[Not[LessEqual[z, 1.5e+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 < -205 or 1.50000000000000003e25 < z

   1. Initial program 75.0%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in z around inf 73.9%

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

   if -205 < z < 1.50000000000000003e25

   1. Initial program 96.1%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t}{a - z}} \]
   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. associate-*l/ 90.4%

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

      2. *-commutative 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 73.7%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -205 \lor \neg \left(z \leq 1.5 \cdot 10^{+25}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+200}:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+227}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -9e+200)
   (* y (/ t (- z)))
   (if (<= y 9.2e+227) (+ t x) (* (/ y z) (- t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -9e+200) {
		tmp = y * (t / -z);
	} else if (y <= 9.2e+227) {
		tmp = t + x;
	} else {
		tmp = (y / z) * -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 <= (-9d+200)) then
        tmp = y * (t / -z)
    else if (y <= 9.2d+227) then
        tmp = t + x
    else
        tmp = (y / z) * -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 <= -9e+200) {
		tmp = y * (t / -z);
	} else if (y <= 9.2e+227) {
		tmp = t + x;
	} else {
		tmp = (y / z) * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -9e+200:
		tmp = y * (t / -z)
	elif y <= 9.2e+227:
		tmp = t + x
	else:
		tmp = (y / z) * -t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -9e+200)
		tmp = Float64(y * Float64(t / Float64(-z)));
	elseif (y <= 9.2e+227)
		tmp = Float64(t + x);
	else
		tmp = Float64(Float64(y / z) * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -9e+200)
		tmp = y * (t / -z);
	elseif (y <= 9.2e+227)
		tmp = t + x;
	else
		tmp = (y / z) * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -9e+200], N[(y * N[(t / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e+227], N[(t + x), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * (-t)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.99999999999999939e200

   1. Initial program 82.7%

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

      1. associate-/l* 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in y around inf 76.1%

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

      1. associate-*l/ 80.3%

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

      2. *-commutative 80.3%

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

   7. Simplified 80.3%

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

   8. Taylor expanded in a around 0 65.5%

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

      1. mul-1-neg 65.5%

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

      2. unsub-neg 65.5%

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

      3. associate-/l* 55.5%

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

   10. Simplified 55.5%

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

   11. Taylor expanded in x around 0 53.2%

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

       1. associate-*l/ 50.0%

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

       2. associate-/r/ 45.5%

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

       3. associate-*r/ 45.5%

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

       4. neg-mul-1 45.5%

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

   13. Simplified 45.5%

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

       1. distribute-frac-neg 45.5%

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

       2. associate-/r/ 50.0%

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

       3. distribute-rgt-neg-in 50.0%

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

   15. Applied egg-rr 50.0%

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

   if -8.99999999999999939e200 < y < 9.1999999999999992e227

   1. Initial program 86.6%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in z around inf 63.4%

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

   if 9.1999999999999992e227 < y

   1. Initial program 74.4%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 74.4%

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

      1. associate-*l/ 99.6%

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

      2. *-commutative 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in a around 0 51.0%

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

      1. mul-1-neg 51.0%

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

      2. unsub-neg 51.0%

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

      3. associate-/l* 60.1%

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

   10. Simplified 60.1%

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

   11. Taylor expanded in x around 0 42.4%

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

       1. associate-*l/ 46.8%

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

       2. associate-/r/ 46.8%

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

       3. associate-*r/ 46.8%

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

       4. neg-mul-1 46.8%

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

   13. Simplified 46.8%

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

   14. Taylor expanded in t around 0 42.4%

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

       1. associate-*r/ 47.0%

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

       2. neg-mul-1 47.0%

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

       3. distribute-rgt-neg-in 47.0%

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

       4. distribute-neg-frac 47.0%

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

   16. Simplified 47.0%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+200}:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+227}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 62.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -27 \lor \neg \left(z \leq 6.8 \cdot 10^{-74}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -27.0) (not (<= z 6.8e-74))) (+ t x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -27.0) || !(z <= 6.8e-74)) {
		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 <= (-27.0d0)) .or. (.not. (z <= 6.8d-74))) 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 <= -27.0) || !(z <= 6.8e-74)) {
		tmp = t + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -27.0) or not (z <= 6.8e-74):
		tmp = t + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -27.0) || !(z <= 6.8e-74))
		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 <= -27.0) || ~((z <= 6.8e-74)))
		tmp = t + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -27.0], N[Not[LessEqual[z, 6.8e-74]], $MachinePrecision]], N[(t + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -27 or 6.8000000000000001e-74 < z

   1. Initial program 77.6%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in z around inf 69.7%

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

   if -27 < z < 6.8000000000000001e-74

   1. Initial program 96.3%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in x around inf 48.0%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -27 \lor \neg \left(z \leq 6.8 \cdot 10^{-74}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 60.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.52 \cdot 10^{+229}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 1.52e+229) (+ t x) (* (/ y z) (- t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.52e+229) {
		tmp = t + x;
	} else {
		tmp = (y / z) * -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 <= 1.52d+229) then
        tmp = t + x
    else
        tmp = (y / z) * -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 <= 1.52e+229) {
		tmp = t + x;
	} else {
		tmp = (y / z) * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 1.52e+229:
		tmp = t + x
	else:
		tmp = (y / z) * -t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 1.52e+229)
		tmp = Float64(t + x);
	else
		tmp = Float64(Float64(y / z) * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 1.52e+229)
		tmp = t + x;
	else
		tmp = (y / z) * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 1.52e+229], N[(t + x), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.5200000000000001e229

   1. Initial program 86.2%

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

      1. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in z around inf 59.6%

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

   if 1.5200000000000001e229 < y

   1. Initial program 74.4%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 74.4%

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

      1. associate-*l/ 99.6%

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

      2. *-commutative 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in a around 0 51.0%

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

      1. mul-1-neg 51.0%

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

      2. unsub-neg 51.0%

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

      3. associate-/l* 60.1%

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

   10. Simplified 60.1%

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

   11. Taylor expanded in x around 0 42.4%

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

       1. associate-*l/ 46.8%

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

       2. associate-/r/ 46.8%

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

       3. associate-*r/ 46.8%

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

       4. neg-mul-1 46.8%

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

   13. Simplified 46.8%

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

   14. Taylor expanded in t around 0 42.4%

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

       1. associate-*r/ 47.0%

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

       2. neg-mul-1 47.0%

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

       3. distribute-rgt-neg-in 47.0%

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

       4. distribute-neg-frac 47.0%

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

   16. Simplified 47.0%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.52 \cdot 10^{+229}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 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. Step-by-step derivation

   1. associate-/l* 96.0%

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

3. Simplified 96.0%

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

Alternative 17: 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. Step-by-step derivation

   1. associate-/l* 96.0%

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

3. Simplified 96.0%

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

5. Taylor expanded in x around inf 47.9%

   \[\leadsto \color{blue}{x} \]
6. 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))))