Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3

Percentage Accurate: 67.1% → 88.2%

Time: 16.9s

Alternatives: 23

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{y - x}\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+91}:\\ \;\;\;\;y + \frac{a - z}{t_1}\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+164}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - \frac{z}{t_1}\right) + \frac{a}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (- y x))))
   (if (<= t -5.5e+91)
     (+ y (/ (- a z) t_1))
     (if (<= t 4.7e+164)
       (- x (/ (- x y) (/ (- a t) (- z t))))
       (+ (- y (/ z t_1)) (/ a t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (y - x);
	double tmp;
	if (t <= -5.5e+91) {
		tmp = y + ((a - z) / t_1);
	} else if (t <= 4.7e+164) {
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	} else {
		tmp = (y - (z / t_1)) + (a / 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 = t / (y - x)
    if (t <= (-5.5d+91)) then
        tmp = y + ((a - z) / t_1)
    else if (t <= 4.7d+164) then
        tmp = x - ((x - y) / ((a - t) / (z - t)))
    else
        tmp = (y - (z / t_1)) + (a / 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 = t / (y - x);
	double tmp;
	if (t <= -5.5e+91) {
		tmp = y + ((a - z) / t_1);
	} else if (t <= 4.7e+164) {
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	} else {
		tmp = (y - (z / t_1)) + (a / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (y - x)
	tmp = 0
	if t <= -5.5e+91:
		tmp = y + ((a - z) / t_1)
	elif t <= 4.7e+164:
		tmp = x - ((x - y) / ((a - t) / (z - t)))
	else:
		tmp = (y - (z / t_1)) + (a / t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(y - x))
	tmp = 0.0
	if (t <= -5.5e+91)
		tmp = Float64(y + Float64(Float64(a - z) / t_1));
	elseif (t <= 4.7e+164)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(Float64(y - Float64(z / t_1)) + Float64(a / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (y - x);
	tmp = 0.0;
	if (t <= -5.5e+91)
		tmp = y + ((a - z) / t_1);
	elseif (t <= 4.7e+164)
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	else
		tmp = (y - (z / t_1)) + (a / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.5e+91], N[(y + N[(N[(a - z), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.7e+164], N[(x - N[(N[(x - y), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - N[(z / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(a / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.4999999999999998e91

   1. Initial program 34.4%

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

      1. associate-/l* 57.1%

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

   3. Simplified 57.1%

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

   4. Taylor expanded in t around inf 60.2%

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

      1. sub-neg 60.2%

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

      2. +-commutative 60.2%

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

      3. mul-1-neg 60.2%

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

      4. unsub-neg 60.2%

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

      5. associate-/l* 69.6%

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

      6. mul-1-neg 69.6%

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

      7. remove-double-neg 69.6%

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

      8. associate-/l* 88.5%

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

   6. Simplified 88.5%

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

      1. associate-+l- 88.5%

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

      2. sub-div 88.5%

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

   8. Applied egg-rr 88.5%

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

   if -5.4999999999999998e91 < t < 4.69999999999999955e164

   1. Initial program 84.4%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   if 4.69999999999999955e164 < t

   1. Initial program 27.1%

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

      1. associate-/l* 62.4%

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

   3. Simplified 62.4%

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

   4. Taylor expanded in t around inf 74.4%

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

      1. sub-neg 74.4%

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

      2. +-commutative 74.4%

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

      3. mul-1-neg 74.4%

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

      4. unsub-neg 74.4%

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

      5. associate-/l* 79.1%

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

      6. mul-1-neg 79.1%

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

      7. remove-double-neg 79.1%

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

      8. associate-/l* 89.6%

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

   6. Simplified 89.6%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+91}:\\ \;\;\;\;y + \frac{a - z}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+164}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - \frac{z}{\frac{t}{y - x}}\right) + \frac{a}{\frac{t}{y - x}}\\ \end{array} \]

Alternative 2: 54.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -9 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-53}:\\ \;\;\;\;y - \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-190}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))))
   (if (<= a -9e-13)
     t_1
     (if (<= a -1.8e-53)
       (- y (/ (* y z) t))
       (if (<= a -5.5e-73)
         t_1
         (if (<= a -3e-190)
           (* (/ z t) (- x y))
           (if (<= a 1.25e-37) (* y (- 1.0 (/ z t))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (a <= -9e-13) {
		tmp = t_1;
	} else if (a <= -1.8e-53) {
		tmp = y - ((y * z) / t);
	} else if (a <= -5.5e-73) {
		tmp = t_1;
	} else if (a <= -3e-190) {
		tmp = (z / t) * (x - y);
	} else if (a <= 1.25e-37) {
		tmp = y * (1.0 - (z / t));
	} 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 + (z * (y / a))
    if (a <= (-9d-13)) then
        tmp = t_1
    else if (a <= (-1.8d-53)) then
        tmp = y - ((y * z) / t)
    else if (a <= (-5.5d-73)) then
        tmp = t_1
    else if (a <= (-3d-190)) then
        tmp = (z / t) * (x - y)
    else if (a <= 1.25d-37) then
        tmp = y * (1.0d0 - (z / t))
    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 + (z * (y / a));
	double tmp;
	if (a <= -9e-13) {
		tmp = t_1;
	} else if (a <= -1.8e-53) {
		tmp = y - ((y * z) / t);
	} else if (a <= -5.5e-73) {
		tmp = t_1;
	} else if (a <= -3e-190) {
		tmp = (z / t) * (x - y);
	} else if (a <= 1.25e-37) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	tmp = 0
	if a <= -9e-13:
		tmp = t_1
	elif a <= -1.8e-53:
		tmp = y - ((y * z) / t)
	elif a <= -5.5e-73:
		tmp = t_1
	elif a <= -3e-190:
		tmp = (z / t) * (x - y)
	elif a <= 1.25e-37:
		tmp = y * (1.0 - (z / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	tmp = 0.0
	if (a <= -9e-13)
		tmp = t_1;
	elseif (a <= -1.8e-53)
		tmp = Float64(y - Float64(Float64(y * z) / t));
	elseif (a <= -5.5e-73)
		tmp = t_1;
	elseif (a <= -3e-190)
		tmp = Float64(Float64(z / t) * Float64(x - y));
	elseif (a <= 1.25e-37)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	tmp = 0.0;
	if (a <= -9e-13)
		tmp = t_1;
	elseif (a <= -1.8e-53)
		tmp = y - ((y * z) / t);
	elseif (a <= -5.5e-73)
		tmp = t_1;
	elseif (a <= -3e-190)
		tmp = (z / t) * (x - y);
	elseif (a <= 1.25e-37)
		tmp = y * (1.0 - (z / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9e-13], t$95$1, If[LessEqual[a, -1.8e-53], N[(y - N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.5e-73], t$95$1, If[LessEqual[a, -3e-190], N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e-37], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9e-13 or -1.7999999999999999e-53 < a < -5.50000000000000006e-73 or 1.2499999999999999e-37 < a

   1. Initial program 68.2%

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

      1. associate-/l* 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in t around 0 69.6%

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

   5. Taylor expanded in y around inf 54.5%

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

      1. associate-/l* 59.8%

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

      2. associate-/r/ 59.0%

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

   7. Simplified 59.0%

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

   if -9e-13 < a < -1.7999999999999999e-53

   1. Initial program 74.3%

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

      1. associate-/l* 79.8%

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

   3. Simplified 79.8%

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

   4. Taylor expanded in t around inf 74.5%

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

      1. sub-neg 74.5%

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

      2. +-commutative 74.5%

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

      3. mul-1-neg 74.5%

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

      4. unsub-neg 74.5%

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

      5. associate-/l* 74.5%

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

      6. mul-1-neg 74.5%

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

      7. remove-double-neg 74.5%

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

      8. associate-/l* 74.5%

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

   6. Simplified 74.5%

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

   7. Taylor expanded in a around 0 74.5%

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

   8. Taylor expanded in y around inf 63.7%

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

   if -5.50000000000000006e-73 < a < -2.9999999999999998e-190

   1. Initial program 69.8%

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

      1. associate-/l* 72.1%

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

   3. Simplified 72.1%

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

   4. Taylor expanded in t around inf 78.5%

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

      1. sub-neg 78.5%

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

      2. +-commutative 78.5%

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

      3. mul-1-neg 78.5%

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

      4. unsub-neg 78.5%

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

      5. associate-/l* 81.7%

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

      6. mul-1-neg 81.7%

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

      7. remove-double-neg 81.7%

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

      8. associate-/l* 81.6%

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

   6. Simplified 81.6%

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

   7. Taylor expanded in z around -inf 61.6%

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

      1. mul-1-neg 61.6%

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

      2. associate-*r/ 64.8%

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

      3. *-commutative 64.8%

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

      4. distribute-rgt-neg-in 64.8%

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

   9. Simplified 64.8%

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

   if -2.9999999999999998e-190 < a < 1.2499999999999999e-37

   1. Initial program 73.6%

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

      1. associate-/l* 81.5%

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

   3. Simplified 81.5%

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

   4. Taylor expanded in t around inf 73.9%

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

      1. sub-neg 73.9%

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

      2. +-commutative 73.9%

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

      3. mul-1-neg 73.9%

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

      4. unsub-neg 73.9%

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

      5. associate-/l* 75.4%

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

      6. mul-1-neg 75.4%

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

      7. remove-double-neg 75.4%

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

      8. associate-/l* 68.4%

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

   6. Simplified 68.4%

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

   7. Taylor expanded in a around 0 73.7%

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

   8. Taylor expanded in y around inf 61.3%

      \[\leadsto \color{blue}{\left(1 - \frac{z}{t}\right) \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{-13}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-53}:\\ \;\;\;\;y - \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-73}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-190}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 3: 67.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -14.5:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.36 \cdot 10^{-42}:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+167}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+285}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -14.5)
   (+ x (/ (- y x) (/ a z)))
   (if (<= a 1.36e-42)
     (+ y (/ (* z (- x y)) t))
     (if (<= a 2.2e+167)
       (+ x (/ z (/ a (- y x))))
       (if (<= a 8.5e+285) (+ x (* (- z t) (/ y a))) (* x (- 1.0 (/ z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -14.5) {
		tmp = x + ((y - x) / (a / z));
	} else if (a <= 1.36e-42) {
		tmp = y + ((z * (x - y)) / t);
	} else if (a <= 2.2e+167) {
		tmp = x + (z / (a / (y - x)));
	} else if (a <= 8.5e+285) {
		tmp = x + ((z - t) * (y / a));
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-14.5d0)) then
        tmp = x + ((y - x) / (a / z))
    else if (a <= 1.36d-42) then
        tmp = y + ((z * (x - y)) / t)
    else if (a <= 2.2d+167) then
        tmp = x + (z / (a / (y - x)))
    else if (a <= 8.5d+285) then
        tmp = x + ((z - t) * (y / a))
    else
        tmp = x * (1.0d0 - (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -14.5) {
		tmp = x + ((y - x) / (a / z));
	} else if (a <= 1.36e-42) {
		tmp = y + ((z * (x - y)) / t);
	} else if (a <= 2.2e+167) {
		tmp = x + (z / (a / (y - x)));
	} else if (a <= 8.5e+285) {
		tmp = x + ((z - t) * (y / a));
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -14.5:
		tmp = x + ((y - x) / (a / z))
	elif a <= 1.36e-42:
		tmp = y + ((z * (x - y)) / t)
	elif a <= 2.2e+167:
		tmp = x + (z / (a / (y - x)))
	elif a <= 8.5e+285:
		tmp = x + ((z - t) * (y / a))
	else:
		tmp = x * (1.0 - (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -14.5)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (a <= 1.36e-42)
		tmp = Float64(y + Float64(Float64(z * Float64(x - y)) / t));
	elseif (a <= 2.2e+167)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (a <= 8.5e+285)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / a)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -14.5)
		tmp = x + ((y - x) / (a / z));
	elseif (a <= 1.36e-42)
		tmp = y + ((z * (x - y)) / t);
	elseif (a <= 2.2e+167)
		tmp = x + (z / (a / (y - x)));
	elseif (a <= 8.5e+285)
		tmp = x + ((z - t) * (y / a));
	else
		tmp = x * (1.0 - (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -14.5], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.36e-42], N[(y + N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e+167], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e+285], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -14.5

   1. Initial program 68.6%

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

      1. associate-/l* 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in t around 0 68.3%

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

   if -14.5 < a < 1.36e-42

   1. Initial program 73.8%

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

      1. associate-/l* 80.4%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in t around inf 73.5%

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

      1. sub-neg 73.5%

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

      2. +-commutative 73.5%

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

      3. mul-1-neg 73.5%

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

      4. unsub-neg 73.5%

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

      5. associate-/l* 75.1%

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

      6. mul-1-neg 75.1%

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

      7. remove-double-neg 75.1%

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

      8. associate-/l* 70.8%

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

   6. Simplified 70.8%

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

   7. Taylor expanded in a around 0 73.2%

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

   if 1.36e-42 < a < 2.20000000000000003e167

   1. Initial program 71.5%

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

      1. associate-/l* 82.2%

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

   3. Simplified 82.2%

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

   4. Taylor expanded in t around 0 64.0%

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

      1. +-commutative 64.0%

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

      2. *-commutative 64.0%

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

      3. associate-/l* 70.1%

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

   6. Simplified 70.1%

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

   if 2.20000000000000003e167 < a < 8.5e285

   1. Initial program 58.9%

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

      1. associate-/l* 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in a around inf 82.5%

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

   5. Taylor expanded in y around inf 59.0%

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

      1. associate-/l* 79.9%

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

      2. associate-/r/ 79.7%

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

   7. Simplified 79.7%

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

   if 8.5e285 < a

   1. Initial program 57.9%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 86.4%

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

      1. mul-1-neg 86.4%

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

      2. unsub-neg 86.4%

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

   6. Simplified 86.4%

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

   7. Taylor expanded in t around 0 86.4%

      \[\leadsto \color{blue}{\left(1 - \frac{z}{a}\right)} \cdot x \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -14.5:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.36 \cdot 10^{-42}:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+167}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+285}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]

Alternative 4: 81.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.4 \cdot 10^{+86} \lor \neg \left(t \leq 1.05 \cdot 10^{+156}\right):\\ \;\;\;\;y + \frac{a - z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\left(z - t\right) \cdot \left(x - y\right)}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -9.4e+86) (not (<= t 1.05e+156)))
   (+ y (/ (- a z) (/ t (- y x))))
   (- x (/ (* (- z t) (- x y)) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.4e+86) || !(t <= 1.05e+156)) {
		tmp = y + ((a - z) / (t / (y - x)));
	} else {
		tmp = x - (((z - t) * (x - y)) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-9.4d+86)) .or. (.not. (t <= 1.05d+156))) then
        tmp = y + ((a - z) / (t / (y - x)))
    else
        tmp = x - (((z - t) * (x - y)) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.4e+86) || !(t <= 1.05e+156)) {
		tmp = y + ((a - z) / (t / (y - x)));
	} else {
		tmp = x - (((z - t) * (x - y)) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -9.4e+86) or not (t <= 1.05e+156):
		tmp = y + ((a - z) / (t / (y - x)))
	else:
		tmp = x - (((z - t) * (x - y)) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -9.4e+86) || !(t <= 1.05e+156))
		tmp = Float64(y + Float64(Float64(a - z) / Float64(t / Float64(y - x))));
	else
		tmp = Float64(x - Float64(Float64(Float64(z - t) * Float64(x - y)) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -9.4e+86) || ~((t <= 1.05e+156)))
		tmp = y + ((a - z) / (t / (y - x)));
	else
		tmp = x - (((z - t) * (x - y)) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -9.4e+86], N[Not[LessEqual[t, 1.05e+156]], $MachinePrecision]], N[(y + N[(N[(a - z), $MachinePrecision] / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(z - t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.4000000000000004e86 or 1.04999999999999991e156 < t

   1. Initial program 32.9%

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

      1. associate-/l* 59.7%

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

   3. Simplified 59.7%

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

   4. Taylor expanded in t around inf 63.7%

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

      1. sub-neg 63.7%

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

      2. +-commutative 63.7%

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

      3. mul-1-neg 63.7%

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

      4. unsub-neg 63.7%

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

      5. associate-/l* 71.6%

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

      6. mul-1-neg 71.6%

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

      7. remove-double-neg 71.6%

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

      8. associate-/l* 87.8%

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

   6. Simplified 87.8%

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

      1. associate-+l- 87.8%

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

      2. sub-div 87.8%

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

   8. Applied egg-rr 87.8%

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

   if -9.4000000000000004e86 < t < 1.04999999999999991e156

   1. Initial program 84.8%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.4 \cdot 10^{+86} \lor \neg \left(t \leq 1.05 \cdot 10^{+156}\right):\\ \;\;\;\;y + \frac{a - z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\left(z - t\right) \cdot \left(x - y\right)}{a - t}\\ \end{array} \]

Alternative 5: 88.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+93} \lor \neg \left(t \leq 8 \cdot 10^{+158}\right):\\ \;\;\;\;y + \frac{a - z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.6e+93) (not (<= t 8e+158)))
   (+ y (/ (- a z) (/ t (- y x))))
   (- x (/ (- x y) (/ (- a t) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.6e+93) || !(t <= 8e+158)) {
		tmp = y + ((a - z) / (t / (y - x)));
	} else {
		tmp = x - ((x - y) / ((a - t) / (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 ((t <= (-4.6d+93)) .or. (.not. (t <= 8d+158))) then
        tmp = y + ((a - z) / (t / (y - x)))
    else
        tmp = x - ((x - y) / ((a - t) / (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 ((t <= -4.6e+93) || !(t <= 8e+158)) {
		tmp = y + ((a - z) / (t / (y - x)));
	} else {
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.6e+93) or not (t <= 8e+158):
		tmp = y + ((a - z) / (t / (y - x)))
	else:
		tmp = x - ((x - y) / ((a - t) / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.6e+93) || !(t <= 8e+158))
		tmp = Float64(y + Float64(Float64(a - z) / Float64(t / Float64(y - x))));
	else
		tmp = Float64(x - Float64(Float64(x - y) / Float64(Float64(a - t) / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.6e+93) || ~((t <= 8e+158)))
		tmp = y + ((a - z) / (t / (y - x)));
	else
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.6e+93], N[Not[LessEqual[t, 8e+158]], $MachinePrecision]], N[(y + N[(N[(a - z), $MachinePrecision] / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x - y), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.6000000000000003e93 or 7.99999999999999962e158 < t

   1. Initial program 32.4%

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

      1. associate-/l* 58.5%

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

   3. Simplified 58.5%

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

   4. Taylor expanded in t around inf 64.1%

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

      1. sub-neg 64.1%

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

      2. +-commutative 64.1%

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

      3. mul-1-neg 64.1%

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

      4. unsub-neg 64.1%

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

      5. associate-/l* 72.2%

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

      6. mul-1-neg 72.2%

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

      7. remove-double-neg 72.2%

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

      8. associate-/l* 88.8%

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

   6. Simplified 88.8%

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

      1. associate-+l- 88.8%

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

      2. sub-div 88.8%

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

   8. Applied egg-rr 88.8%

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

   if -4.6000000000000003e93 < t < 7.99999999999999962e158

   1. Initial program 84.4%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+93} \lor \neg \left(t \leq 8 \cdot 10^{+158}\right):\\ \;\;\;\;y + \frac{a - z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \end{array} \]

Alternative 6: 59.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+280}:\\ \;\;\;\;\frac{-x}{\frac{t}{a - z}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= x -7.5e+44)
     t_1
     (if (<= x 1.4e-22)
       (* y (/ (- z t) (- a t)))
       (if (<= x 1.9e+261)
         t_1
         (if (<= x 4.1e+280) (/ (- x) (/ t (- a z))) (+ x (* z (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (x <= -7.5e+44) {
		tmp = t_1;
	} else if (x <= 1.4e-22) {
		tmp = y * ((z - t) / (a - t));
	} else if (x <= 1.9e+261) {
		tmp = t_1;
	} else if (x <= 4.1e+280) {
		tmp = -x / (t / (a - z));
	} else {
		tmp = x + (z * (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) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (x <= (-7.5d+44)) then
        tmp = t_1
    else if (x <= 1.4d-22) then
        tmp = y * ((z - t) / (a - t))
    else if (x <= 1.9d+261) then
        tmp = t_1
    else if (x <= 4.1d+280) then
        tmp = -x / (t / (a - z))
    else
        tmp = x + (z * (y / a))
    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 * (1.0 - (z / a));
	double tmp;
	if (x <= -7.5e+44) {
		tmp = t_1;
	} else if (x <= 1.4e-22) {
		tmp = y * ((z - t) / (a - t));
	} else if (x <= 1.9e+261) {
		tmp = t_1;
	} else if (x <= 4.1e+280) {
		tmp = -x / (t / (a - z));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if x <= -7.5e+44:
		tmp = t_1
	elif x <= 1.4e-22:
		tmp = y * ((z - t) / (a - t))
	elif x <= 1.9e+261:
		tmp = t_1
	elif x <= 4.1e+280:
		tmp = -x / (t / (a - z))
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (x <= -7.5e+44)
		tmp = t_1;
	elseif (x <= 1.4e-22)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (x <= 1.9e+261)
		tmp = t_1;
	elseif (x <= 4.1e+280)
		tmp = Float64(Float64(-x) / Float64(t / Float64(a - z)));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (x <= -7.5e+44)
		tmp = t_1;
	elseif (x <= 1.4e-22)
		tmp = y * ((z - t) / (a - t));
	elseif (x <= 1.9e+261)
		tmp = t_1;
	elseif (x <= 4.1e+280)
		tmp = -x / (t / (a - z));
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.5e+44], t$95$1, If[LessEqual[x, 1.4e-22], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e+261], t$95$1, If[LessEqual[x, 4.1e+280], N[((-x) / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.50000000000000027e44 or 1.39999999999999997e-22 < x < 1.9000000000000001e261

   1. Initial program 65.6%

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

      1. associate-/l* 80.2%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in x around inf 67.1%

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

      1. mul-1-neg 67.1%

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

      2. unsub-neg 67.1%

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

   6. Simplified 67.1%

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

   7. Taylor expanded in t around 0 55.0%

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

   if -7.50000000000000027e44 < x < 1.39999999999999997e-22

   1. Initial program 77.8%

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

      1. associate-/l* 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in x around 0 62.7%

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

      1. associate-*r/ 76.3%

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

   6. Simplified 76.3%

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

   if 1.9000000000000001e261 < x < 4.09999999999999997e280

   1. Initial program 40.1%

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

      1. associate-/l* 59.6%

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

   3. Simplified 59.6%

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

   4. Taylor expanded in x around inf 59.2%

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

      1. mul-1-neg 59.2%

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

      2. unsub-neg 59.2%

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

   6. Simplified 59.2%

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

   7. Taylor expanded in t around inf 62.6%

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

      1. mul-1-neg 62.6%

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

      2. *-commutative 62.6%

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

      3. mul-1-neg 62.6%

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

      4. +-commutative 62.6%

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

      5. sub-neg 62.6%

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

      6. associate-/l* 99.7%

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

      7. distribute-neg-frac 99.7%

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

   9. Simplified 99.7%

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

   if 4.09999999999999997e280 < x

   1. Initial program 46.1%

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

      1. associate-/l* 67.4%

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

   3. Simplified 67.4%

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

   4. Taylor expanded in t around 0 56.3%

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

   5. Taylor expanded in y around inf 67.9%

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

      1. associate-/l* 67.9%

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

      2. associate-/r/ 67.9%

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

   7. Simplified 67.9%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+261}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+280}:\\ \;\;\;\;\frac{-x}{\frac{t}{a - z}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 7: 38.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -1.08 \cdot 10^{+89}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-274}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-228}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-176}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 10^{+96}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z a))))
   (if (<= t -1.08e+89)
     y
     (if (<= t -1.12e-274)
       x
       (if (<= t 1.7e-228)
         t_1
         (if (<= t 2.7e-176)
           x
           (if (<= t 3.3e-37) t_1 (if (<= t 1e+96) x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double tmp;
	if (t <= -1.08e+89) {
		tmp = y;
	} else if (t <= -1.12e-274) {
		tmp = x;
	} else if (t <= 1.7e-228) {
		tmp = t_1;
	} else if (t <= 2.7e-176) {
		tmp = x;
	} else if (t <= 3.3e-37) {
		tmp = t_1;
	} else if (t <= 1e+96) {
		tmp = x;
	} else {
		tmp = y;
	}
	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 / a)
    if (t <= (-1.08d+89)) then
        tmp = y
    else if (t <= (-1.12d-274)) then
        tmp = x
    else if (t <= 1.7d-228) then
        tmp = t_1
    else if (t <= 2.7d-176) then
        tmp = x
    else if (t <= 3.3d-37) then
        tmp = t_1
    else if (t <= 1d+96) then
        tmp = x
    else
        tmp = y
    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 / a);
	double tmp;
	if (t <= -1.08e+89) {
		tmp = y;
	} else if (t <= -1.12e-274) {
		tmp = x;
	} else if (t <= 1.7e-228) {
		tmp = t_1;
	} else if (t <= 2.7e-176) {
		tmp = x;
	} else if (t <= 3.3e-37) {
		tmp = t_1;
	} else if (t <= 1e+96) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / a)
	tmp = 0
	if t <= -1.08e+89:
		tmp = y
	elif t <= -1.12e-274:
		tmp = x
	elif t <= 1.7e-228:
		tmp = t_1
	elif t <= 2.7e-176:
		tmp = x
	elif t <= 3.3e-37:
		tmp = t_1
	elif t <= 1e+96:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / a))
	tmp = 0.0
	if (t <= -1.08e+89)
		tmp = y;
	elseif (t <= -1.12e-274)
		tmp = x;
	elseif (t <= 1.7e-228)
		tmp = t_1;
	elseif (t <= 2.7e-176)
		tmp = x;
	elseif (t <= 3.3e-37)
		tmp = t_1;
	elseif (t <= 1e+96)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / a);
	tmp = 0.0;
	if (t <= -1.08e+89)
		tmp = y;
	elseif (t <= -1.12e-274)
		tmp = x;
	elseif (t <= 1.7e-228)
		tmp = t_1;
	elseif (t <= 2.7e-176)
		tmp = x;
	elseif (t <= 3.3e-37)
		tmp = t_1;
	elseif (t <= 1e+96)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.08e+89], y, If[LessEqual[t, -1.12e-274], x, If[LessEqual[t, 1.7e-228], t$95$1, If[LessEqual[t, 2.7e-176], x, If[LessEqual[t, 3.3e-37], t$95$1, If[LessEqual[t, 1e+96], x, y]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.08000000000000006e89 or 1.00000000000000005e96 < t

   1. Initial program 36.9%

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

      1. associate-/l* 61.5%

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

   3. Simplified 61.5%

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

   4. Taylor expanded in t around inf 46.8%

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

   if -1.08000000000000006e89 < t < -1.11999999999999998e-274 or 1.69999999999999995e-228 < t < 2.6999999999999998e-176 or 3.29999999999999982e-37 < t < 1.00000000000000005e96

   1. Initial program 82.9%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in a around inf 36.5%

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

   if -1.11999999999999998e-274 < t < 1.69999999999999995e-228 or 2.6999999999999998e-176 < t < 3.29999999999999982e-37

   1. Initial program 89.1%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in x around 0 48.3%

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

      1. associate-*r/ 53.7%

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

   6. Simplified 53.7%

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

   7. Taylor expanded in t around 0 50.1%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.08 \cdot 10^{+89}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-274}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-228}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-176}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 10^{+96}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8: 54.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.85:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-76}:\\ \;\;\;\;y + \frac{z \cdot x}{t}\\ \mathbf{elif}\;a \leq -5.55 \cdot 10^{-191}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))))
   (if (<= a -1.85)
     t_1
     (if (<= a -4.4e-76)
       (+ y (/ (* z x) t))
       (if (<= a -5.55e-191)
         (* (/ z t) (- x y))
         (if (<= a 6.5e-39) (* y (- 1.0 (/ z t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (a <= -1.85) {
		tmp = t_1;
	} else if (a <= -4.4e-76) {
		tmp = y + ((z * x) / t);
	} else if (a <= -5.55e-191) {
		tmp = (z / t) * (x - y);
	} else if (a <= 6.5e-39) {
		tmp = y * (1.0 - (z / t));
	} 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 + (z * (y / a))
    if (a <= (-1.85d0)) then
        tmp = t_1
    else if (a <= (-4.4d-76)) then
        tmp = y + ((z * x) / t)
    else if (a <= (-5.55d-191)) then
        tmp = (z / t) * (x - y)
    else if (a <= 6.5d-39) then
        tmp = y * (1.0d0 - (z / t))
    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 + (z * (y / a));
	double tmp;
	if (a <= -1.85) {
		tmp = t_1;
	} else if (a <= -4.4e-76) {
		tmp = y + ((z * x) / t);
	} else if (a <= -5.55e-191) {
		tmp = (z / t) * (x - y);
	} else if (a <= 6.5e-39) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	tmp = 0
	if a <= -1.85:
		tmp = t_1
	elif a <= -4.4e-76:
		tmp = y + ((z * x) / t)
	elif a <= -5.55e-191:
		tmp = (z / t) * (x - y)
	elif a <= 6.5e-39:
		tmp = y * (1.0 - (z / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	tmp = 0.0
	if (a <= -1.85)
		tmp = t_1;
	elseif (a <= -4.4e-76)
		tmp = Float64(y + Float64(Float64(z * x) / t));
	elseif (a <= -5.55e-191)
		tmp = Float64(Float64(z / t) * Float64(x - y));
	elseif (a <= 6.5e-39)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	tmp = 0.0;
	if (a <= -1.85)
		tmp = t_1;
	elseif (a <= -4.4e-76)
		tmp = y + ((z * x) / t);
	elseif (a <= -5.55e-191)
		tmp = (z / t) * (x - y);
	elseif (a <= 6.5e-39)
		tmp = y * (1.0 - (z / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.85], t$95$1, If[LessEqual[a, -4.4e-76], N[(y + N[(N[(z * x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.55e-191], N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-39], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.8500000000000001 or 6.50000000000000027e-39 < a

   1. Initial program 67.3%

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

      1. associate-/l* 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in t around 0 69.4%

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

   5. Taylor expanded in y around inf 53.6%

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

      1. associate-/l* 59.1%

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

      2. associate-/r/ 58.3%

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

   7. Simplified 58.3%

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

   if -1.8500000000000001 < a < -4.39999999999999999e-76

   1. Initial program 75.3%

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

      1. associate-/l* 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in t around inf 64.5%

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

      1. sub-neg 64.5%

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

      2. +-commutative 64.5%

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

      3. mul-1-neg 64.5%

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

      4. unsub-neg 64.5%

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

      5. associate-/l* 64.4%

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

      6. mul-1-neg 64.4%

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

      7. remove-double-neg 64.4%

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

      8. associate-/l* 64.4%

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

   6. Simplified 64.4%

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

   7. Taylor expanded in a around 0 64.4%

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

   8. Taylor expanded in y around 0 59.8%

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

      1. associate-*r/ 59.8%

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

      2. associate-*r* 59.8%

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

      3. mul-1-neg 59.8%

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

   10. Simplified 59.8%

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

   if -4.39999999999999999e-76 < a < -5.55000000000000017e-191

   1. Initial program 72.1%

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

      1. associate-/l* 74.5%

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

   3. Simplified 74.5%

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

   4. Taylor expanded in t around inf 77.7%

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

      1. sub-neg 77.7%

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

      2. +-commutative 77.7%

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

      3. mul-1-neg 77.7%

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

      4. unsub-neg 77.7%

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

      5. associate-/l* 81.0%

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

      6. mul-1-neg 81.0%

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

      7. remove-double-neg 81.0%

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

      8. associate-/l* 80.9%

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

   6. Simplified 80.9%

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

   7. Taylor expanded in z around -inf 63.6%

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

      1. mul-1-neg 63.6%

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

      2. associate-*r/ 66.9%

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

      3. *-commutative 66.9%

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

      4. distribute-rgt-neg-in 66.9%

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

   9. Simplified 66.9%

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

   if -5.55000000000000017e-191 < a < 6.50000000000000027e-39

   1. Initial program 73.6%

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

      1. associate-/l* 81.5%

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

   3. Simplified 81.5%

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

   4. Taylor expanded in t around inf 73.9%

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

      1. sub-neg 73.9%

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

      2. +-commutative 73.9%

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

      3. mul-1-neg 73.9%

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

      4. unsub-neg 73.9%

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

      5. associate-/l* 75.4%

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

      6. mul-1-neg 75.4%

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

      7. remove-double-neg 75.4%

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

      8. associate-/l* 68.4%

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

   6. Simplified 68.4%

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

   7. Taylor expanded in a around 0 73.7%

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

   8. Taylor expanded in y around inf 61.3%

      \[\leadsto \color{blue}{\left(1 - \frac{z}{t}\right) \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.85:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-76}:\\ \;\;\;\;y + \frac{z \cdot x}{t}\\ \mathbf{elif}\;a \leq -5.55 \cdot 10^{-191}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 9: 54.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -3.1:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-76}:\\ \;\;\;\;y + \frac{z \cdot x}{t}\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-191}:\\ \;\;\;\;\frac{-z}{\frac{t}{y - x}}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))))
   (if (<= a -3.1)
     t_1
     (if (<= a -1.85e-76)
       (+ y (/ (* z x) t))
       (if (<= a -5.6e-191)
         (/ (- z) (/ t (- y x)))
         (if (<= a 1.3e-40) (* y (- 1.0 (/ z t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (a <= -3.1) {
		tmp = t_1;
	} else if (a <= -1.85e-76) {
		tmp = y + ((z * x) / t);
	} else if (a <= -5.6e-191) {
		tmp = -z / (t / (y - x));
	} else if (a <= 1.3e-40) {
		tmp = y * (1.0 - (z / t));
	} 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 + (z * (y / a))
    if (a <= (-3.1d0)) then
        tmp = t_1
    else if (a <= (-1.85d-76)) then
        tmp = y + ((z * x) / t)
    else if (a <= (-5.6d-191)) then
        tmp = -z / (t / (y - x))
    else if (a <= 1.3d-40) then
        tmp = y * (1.0d0 - (z / t))
    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 + (z * (y / a));
	double tmp;
	if (a <= -3.1) {
		tmp = t_1;
	} else if (a <= -1.85e-76) {
		tmp = y + ((z * x) / t);
	} else if (a <= -5.6e-191) {
		tmp = -z / (t / (y - x));
	} else if (a <= 1.3e-40) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	tmp = 0
	if a <= -3.1:
		tmp = t_1
	elif a <= -1.85e-76:
		tmp = y + ((z * x) / t)
	elif a <= -5.6e-191:
		tmp = -z / (t / (y - x))
	elif a <= 1.3e-40:
		tmp = y * (1.0 - (z / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	tmp = 0.0
	if (a <= -3.1)
		tmp = t_1;
	elseif (a <= -1.85e-76)
		tmp = Float64(y + Float64(Float64(z * x) / t));
	elseif (a <= -5.6e-191)
		tmp = Float64(Float64(-z) / Float64(t / Float64(y - x)));
	elseif (a <= 1.3e-40)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	tmp = 0.0;
	if (a <= -3.1)
		tmp = t_1;
	elseif (a <= -1.85e-76)
		tmp = y + ((z * x) / t);
	elseif (a <= -5.6e-191)
		tmp = -z / (t / (y - x));
	elseif (a <= 1.3e-40)
		tmp = y * (1.0 - (z / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.1], t$95$1, If[LessEqual[a, -1.85e-76], N[(y + N[(N[(z * x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.6e-191], N[((-z) / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e-40], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.10000000000000009 or 1.3000000000000001e-40 < a

   1. Initial program 67.3%

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

      1. associate-/l* 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in t around 0 69.4%

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

   5. Taylor expanded in y around inf 53.6%

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

      1. associate-/l* 59.1%

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

      2. associate-/r/ 58.3%

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

   7. Simplified 58.3%

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

   if -3.10000000000000009 < a < -1.85000000000000006e-76

   1. Initial program 75.3%

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

      1. associate-/l* 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in t around inf 64.5%

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

      1. sub-neg 64.5%

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

      2. +-commutative 64.5%

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

      3. mul-1-neg 64.5%

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

      4. unsub-neg 64.5%

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

      5. associate-/l* 64.4%

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

      6. mul-1-neg 64.4%

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

      7. remove-double-neg 64.4%

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

      8. associate-/l* 64.4%

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

   6. Simplified 64.4%

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

   7. Taylor expanded in a around 0 64.4%

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

   8. Taylor expanded in y around 0 59.8%

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

      1. associate-*r/ 59.8%

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

      2. associate-*r* 59.8%

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

      3. mul-1-neg 59.8%

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

   10. Simplified 59.8%

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

   if -1.85000000000000006e-76 < a < -5.60000000000000023e-191

   1. Initial program 72.1%

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

      1. associate-/l* 74.5%

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

   3. Simplified 74.5%

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

   4. Taylor expanded in t around inf 77.7%

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

      1. sub-neg 77.7%

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

      2. +-commutative 77.7%

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

      3. mul-1-neg 77.7%

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

      4. unsub-neg 77.7%

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

      5. associate-/l* 81.0%

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

      6. mul-1-neg 81.0%

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

      7. remove-double-neg 81.0%

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

      8. associate-/l* 80.9%

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

   6. Simplified 80.9%

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

      1. associate-+l- 80.9%

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

      2. sub-div 84.8%

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

   8. Applied egg-rr 84.8%

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

   9. Taylor expanded in z around -inf 63.6%

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

       1. mul-1-neg 63.6%

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

       2. associate-*r/ 66.9%

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

       3. *-commutative 66.9%

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

       4. associate-/r/ 67.0%

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

       5. distribute-neg-frac 67.0%

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

   11. Simplified 67.0%

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

   if -5.60000000000000023e-191 < a < 1.3000000000000001e-40

   1. Initial program 73.6%

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

      1. associate-/l* 81.5%

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

   3. Simplified 81.5%

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

   4. Taylor expanded in t around inf 73.9%

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

      1. sub-neg 73.9%

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

      2. +-commutative 73.9%

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

      3. mul-1-neg 73.9%

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

      4. unsub-neg 73.9%

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

      5. associate-/l* 75.4%

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

      6. mul-1-neg 75.4%

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

      7. remove-double-neg 75.4%

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

      8. associate-/l* 68.4%

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

   6. Simplified 68.4%

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

   7. Taylor expanded in a around 0 73.7%

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

   8. Taylor expanded in y around inf 61.3%

      \[\leadsto \color{blue}{\left(1 - \frac{z}{t}\right) \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-76}:\\ \;\;\;\;y + \frac{z \cdot x}{t}\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-191}:\\ \;\;\;\;\frac{-z}{\frac{t}{y - x}}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 10: 60.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-33}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ z (/ a (- y x))))))
   (if (<= x -1.45e-6)
     t_1
     (if (<= x 2.85e-33)
       (* y (/ (- z t) (- a t)))
       (if (<= x 2e+154) t_1 (* z (/ (- y x) (- a t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double tmp;
	if (x <= -1.45e-6) {
		tmp = t_1;
	} else if (x <= 2.85e-33) {
		tmp = y * ((z - t) / (a - t));
	} else if (x <= 2e+154) {
		tmp = t_1;
	} else {
		tmp = z * ((y - x) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / (a / (y - x)))
    if (x <= (-1.45d-6)) then
        tmp = t_1
    else if (x <= 2.85d-33) then
        tmp = y * ((z - t) / (a - t))
    else if (x <= 2d+154) then
        tmp = t_1
    else
        tmp = z * ((y - x) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double tmp;
	if (x <= -1.45e-6) {
		tmp = t_1;
	} else if (x <= 2.85e-33) {
		tmp = y * ((z - t) / (a - t));
	} else if (x <= 2e+154) {
		tmp = t_1;
	} else {
		tmp = z * ((y - x) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z / (a / (y - x)))
	tmp = 0
	if x <= -1.45e-6:
		tmp = t_1
	elif x <= 2.85e-33:
		tmp = y * ((z - t) / (a - t))
	elif x <= 2e+154:
		tmp = t_1
	else:
		tmp = z * ((y - x) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z / Float64(a / Float64(y - x))))
	tmp = 0.0
	if (x <= -1.45e-6)
		tmp = t_1;
	elseif (x <= 2.85e-33)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (x <= 2e+154)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z / (a / (y - x)));
	tmp = 0.0;
	if (x <= -1.45e-6)
		tmp = t_1;
	elseif (x <= 2.85e-33)
		tmp = y * ((z - t) / (a - t));
	elseif (x <= 2e+154)
		tmp = t_1;
	else
		tmp = z * ((y - x) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.45e-6], t$95$1, If[LessEqual[x, 2.85e-33], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e+154], t$95$1, N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4500000000000001e-6 or 2.85000000000000013e-33 < x < 2.00000000000000007e154

   1. Initial program 67.9%

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

      1. associate-/l* 80.2%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in t around 0 57.3%

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

      1. +-commutative 57.3%

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

      2. *-commutative 57.3%

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

      3. associate-/l* 63.3%

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

   6. Simplified 63.3%

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

   if -1.4500000000000001e-6 < x < 2.85000000000000013e-33

   1. Initial program 78.9%

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

      1. associate-/l* 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in x around 0 64.8%

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

      1. associate-*r/ 78.2%

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

   6. Simplified 78.2%

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

   if 2.00000000000000007e154 < x

   1. Initial program 53.0%

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

      1. associate-/l* 76.0%

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

   3. Simplified 76.0%

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

   4. Taylor expanded in z around inf 64.2%

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

      1. div-sub 64.2%

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

   6. Simplified 64.2%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-6}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-33}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+154}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 11: 61.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00018:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-33}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+153}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -0.00018)
   (+ x (/ (- y x) (/ a z)))
   (if (<= x 2.8e-33)
     (* y (/ (- z t) (- a t)))
     (if (<= x 6.4e+153)
       (+ x (/ z (/ a (- y x))))
       (* z (/ (- y x) (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -0.00018) {
		tmp = x + ((y - x) / (a / z));
	} else if (x <= 2.8e-33) {
		tmp = y * ((z - t) / (a - t));
	} else if (x <= 6.4e+153) {
		tmp = x + (z / (a / (y - x)));
	} else {
		tmp = z * ((y - x) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-0.00018d0)) then
        tmp = x + ((y - x) / (a / z))
    else if (x <= 2.8d-33) then
        tmp = y * ((z - t) / (a - t))
    else if (x <= 6.4d+153) then
        tmp = x + (z / (a / (y - x)))
    else
        tmp = z * ((y - x) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -0.00018) {
		tmp = x + ((y - x) / (a / z));
	} else if (x <= 2.8e-33) {
		tmp = y * ((z - t) / (a - t));
	} else if (x <= 6.4e+153) {
		tmp = x + (z / (a / (y - x)));
	} else {
		tmp = z * ((y - x) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -0.00018:
		tmp = x + ((y - x) / (a / z))
	elif x <= 2.8e-33:
		tmp = y * ((z - t) / (a - t))
	elif x <= 6.4e+153:
		tmp = x + (z / (a / (y - x)))
	else:
		tmp = z * ((y - x) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -0.00018)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (x <= 2.8e-33)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (x <= 6.4e+153)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	else
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -0.00018)
		tmp = x + ((y - x) / (a / z));
	elseif (x <= 2.8e-33)
		tmp = y * ((z - t) / (a - t));
	elseif (x <= 6.4e+153)
		tmp = x + (z / (a / (y - x)));
	else
		tmp = z * ((y - x) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -0.00018], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e-33], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.4e+153], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.80000000000000011e-4

   1. Initial program 65.0%

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

      1. associate-/l* 81.9%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in t around 0 65.7%

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

   if -1.80000000000000011e-4 < x < 2.8e-33

   1. Initial program 78.9%

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

      1. associate-/l* 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in x around 0 64.8%

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

      1. associate-*r/ 78.2%

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

   6. Simplified 78.2%

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

   if 2.8e-33 < x < 6.4000000000000003e153

   1. Initial program 71.8%

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

      1. associate-/l* 77.9%

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

   3. Simplified 77.9%

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

   4. Taylor expanded in t around 0 60.3%

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

      1. +-commutative 60.3%

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

      2. *-commutative 60.3%

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

      3. associate-/l* 62.4%

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

   6. Simplified 62.4%

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

   if 6.4000000000000003e153 < x

   1. Initial program 53.0%

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

      1. associate-/l* 76.0%

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

   3. Simplified 76.0%

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

   4. Taylor expanded in z around inf 64.2%

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

      1. div-sub 64.2%

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

   6. Simplified 64.2%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.00018:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-33}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+153}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 12: 64.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+43} \lor \neg \left(x \leq 1.6 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -2.2e+43) (not (<= x 1.6e-22)))
   (* x (+ (/ (- t z) (- a t)) 1.0))
   (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.2e+43) || !(x <= 1.6e-22)) {
		tmp = x * (((t - z) / (a - t)) + 1.0);
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-2.2d+43)) .or. (.not. (x <= 1.6d-22))) then
        tmp = x * (((t - z) / (a - t)) + 1.0d0)
    else
        tmp = y * ((z - t) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.2e+43) || !(x <= 1.6e-22)) {
		tmp = x * (((t - z) / (a - t)) + 1.0);
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -2.2e+43) or not (x <= 1.6e-22):
		tmp = x * (((t - z) / (a - t)) + 1.0)
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -2.2e+43) || !(x <= 1.6e-22))
		tmp = Float64(x * Float64(Float64(Float64(t - z) / Float64(a - t)) + 1.0));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -2.2e+43) || ~((x <= 1.6e-22)))
		tmp = x * (((t - z) / (a - t)) + 1.0);
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -2.2e+43], N[Not[LessEqual[x, 1.6e-22]], $MachinePrecision]], N[(x * N[(N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.20000000000000001e43 or 1.59999999999999994e-22 < x

   1. Initial program 63.4%

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

      1. associate-/l* 78.6%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in x around inf 66.8%

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

      1. mul-1-neg 66.8%

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

      2. unsub-neg 66.8%

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

   6. Simplified 66.8%

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

   if -2.20000000000000001e43 < x < 1.59999999999999994e-22

   1. Initial program 77.8%

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

      1. associate-/l* 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in x around 0 62.7%

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

      1. associate-*r/ 76.3%

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

   6. Simplified 76.3%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+43} \lor \neg \left(x \leq 1.6 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 13: 71.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5 \lor \neg \left(a \leq 1.4 \cdot 10^{-42}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.0) (not (<= a 1.4e-42)))
   (+ x (/ (- y x) (/ a (- z t))))
   (+ y (/ (* z (- x y)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.0) || !(a <= 1.4e-42)) {
		tmp = x + ((y - x) / (a / (z - t)));
	} else {
		tmp = y + ((z * (x - y)) / 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 ((a <= (-5.0d0)) .or. (.not. (a <= 1.4d-42))) then
        tmp = x + ((y - x) / (a / (z - t)))
    else
        tmp = y + ((z * (x - y)) / 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 ((a <= -5.0) || !(a <= 1.4e-42)) {
		tmp = x + ((y - x) / (a / (z - t)));
	} else {
		tmp = y + ((z * (x - y)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.0) or not (a <= 1.4e-42):
		tmp = x + ((y - x) / (a / (z - t)))
	else:
		tmp = y + ((z * (x - y)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.0) || !(a <= 1.4e-42))
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / Float64(z - t))));
	else
		tmp = Float64(y + Float64(Float64(z * Float64(x - y)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.0) || ~((a <= 1.4e-42)))
		tmp = x + ((y - x) / (a / (z - t)));
	else
		tmp = y + ((z * (x - y)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.0], N[Not[LessEqual[a, 1.4e-42]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5 or 1.39999999999999999e-42 < a

   1. Initial program 67.0%

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

      1. associate-/l* 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in a around inf 76.0%

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

   if -5 < a < 1.39999999999999999e-42

   1. Initial program 73.8%

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

      1. associate-/l* 80.4%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in t around inf 73.5%

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

      1. sub-neg 73.5%

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

      2. +-commutative 73.5%

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

      3. mul-1-neg 73.5%

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

      4. unsub-neg 73.5%

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

      5. associate-/l* 75.1%

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

      6. mul-1-neg 75.1%

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

      7. remove-double-neg 75.1%

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

      8. associate-/l* 70.8%

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

   6. Simplified 70.8%

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

   7. Taylor expanded in a around 0 73.2%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \lor \neg \left(a \leq 1.4 \cdot 10^{-42}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right)}{t}\\ \end{array} \]

Alternative 14: 73.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.7 \lor \neg \left(a \leq 1.4 \cdot 10^{-40}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.7) (not (<= a 1.4e-40)))
   (+ x (/ (- y x) (/ a (- z t))))
   (+ y (/ (* (- z a) (- x y)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.7) || !(a <= 1.4e-40)) {
		tmp = x + ((y - x) / (a / (z - t)));
	} else {
		tmp = y + (((z - a) * (x - y)) / 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 ((a <= (-3.7d0)) .or. (.not. (a <= 1.4d-40))) then
        tmp = x + ((y - x) / (a / (z - t)))
    else
        tmp = y + (((z - a) * (x - y)) / 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 ((a <= -3.7) || !(a <= 1.4e-40)) {
		tmp = x + ((y - x) / (a / (z - t)));
	} else {
		tmp = y + (((z - a) * (x - y)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.7) or not (a <= 1.4e-40):
		tmp = x + ((y - x) / (a / (z - t)))
	else:
		tmp = y + (((z - a) * (x - y)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.7) || !(a <= 1.4e-40))
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / Float64(z - t))));
	else
		tmp = Float64(y + Float64(Float64(Float64(z - a) * Float64(x - y)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.7) || ~((a <= 1.4e-40)))
		tmp = x + ((y - x) / (a / (z - t)));
	else
		tmp = y + (((z - a) * (x - y)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.7], N[Not[LessEqual[a, 1.4e-40]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(N[(z - a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.7000000000000002 or 1.4e-40 < a

   1. Initial program 67.0%

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

      1. associate-/l* 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in a around inf 76.0%

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

   if -3.7000000000000002 < a < 1.4e-40

   1. Initial program 73.8%

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

      1. associate-/l* 80.4%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in t around -inf 76.0%

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

      1. mul-1-neg 76.0%

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

      2. unsub-neg 76.0%

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

      3. div-sub 73.5%

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

      4. *-commutative 73.5%

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

      5. div-sub 76.0%

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

      6. distribute-rgt-out-- 76.0%

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

   6. Simplified 76.0%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \lor \neg \left(a \leq 1.4 \cdot 10^{-40}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \end{array} \]

Alternative 15: 75.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.76 \lor \neg \left(t \leq 4.5 \cdot 10^{+55}\right):\\ \;\;\;\;y + \frac{a - z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -0.76) (not (<= t 4.5e+55)))
   (+ y (/ (- a z) (/ t (- y x))))
   (+ x (/ (- y x) (/ a (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -0.76) || !(t <= 4.5e+55)) {
		tmp = y + ((a - z) / (t / (y - x)));
	} else {
		tmp = x + ((y - x) / (a / (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 ((t <= (-0.76d0)) .or. (.not. (t <= 4.5d+55))) then
        tmp = y + ((a - z) / (t / (y - x)))
    else
        tmp = x + ((y - x) / (a / (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 ((t <= -0.76) || !(t <= 4.5e+55)) {
		tmp = y + ((a - z) / (t / (y - x)));
	} else {
		tmp = x + ((y - x) / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -0.76) or not (t <= 4.5e+55):
		tmp = y + ((a - z) / (t / (y - x)))
	else:
		tmp = x + ((y - x) / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -0.76) || !(t <= 4.5e+55))
		tmp = Float64(y + Float64(Float64(a - z) / Float64(t / Float64(y - x))));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -0.76) || ~((t <= 4.5e+55)))
		tmp = y + ((a - z) / (t / (y - x)));
	else
		tmp = x + ((y - x) / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -0.76], N[Not[LessEqual[t, 4.5e+55]], $MachinePrecision]], N[(y + N[(N[(a - z), $MachinePrecision] / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.76000000000000001 or 4.49999999999999998e55 < t

   1. Initial program 45.3%

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

      1. associate-/l* 68.9%

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

   3. Simplified 68.9%

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

   4. Taylor expanded in t around inf 60.6%

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

      1. sub-neg 60.6%

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

      2. +-commutative 60.6%

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

      3. mul-1-neg 60.6%

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

      4. unsub-neg 60.6%

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

      5. associate-/l* 66.5%

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

      6. mul-1-neg 66.5%

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

      7. remove-double-neg 66.5%

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

      8. associate-/l* 76.8%

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

   6. Simplified 76.8%

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

      1. associate-+l- 76.8%

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

      2. sub-div 76.9%

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

   8. Applied egg-rr 76.9%

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

   if -0.76000000000000001 < t < 4.49999999999999998e55

   1. Initial program 89.8%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in a around inf 81.5%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.76 \lor \neg \left(t \leq 4.5 \cdot 10^{+55}\right):\\ \;\;\;\;y + \frac{a - z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 16: 59.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-33}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6e+45)
   (* x (- 1.0 (/ z a)))
   (if (<= x 2.9e-33) (* y (/ (- z t) (- a t))) (* z (/ (- y x) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6e+45) {
		tmp = x * (1.0 - (z / a));
	} else if (x <= 2.9e-33) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = z * ((y - x) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-6d+45)) then
        tmp = x * (1.0d0 - (z / a))
    else if (x <= 2.9d-33) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = z * ((y - x) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6e+45) {
		tmp = x * (1.0 - (z / a));
	} else if (x <= 2.9e-33) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = z * ((y - x) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -6e+45:
		tmp = x * (1.0 - (z / a))
	elif x <= 2.9e-33:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = z * ((y - x) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6e+45)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (x <= 2.9e-33)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -6e+45)
		tmp = x * (1.0 - (z / a));
	elseif (x <= 2.9e-33)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = z * ((y - x) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6e+45], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.9e-33], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.00000000000000021e45

   1. Initial program 64.5%

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

      1. associate-/l* 82.6%

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

   3. Simplified 82.6%

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

   4. Taylor expanded in x around inf 71.8%

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

      1. mul-1-neg 71.8%

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

      2. unsub-neg 71.8%

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

   6. Simplified 71.8%

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

   7. Taylor expanded in t around 0 62.7%

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

   if -6.00000000000000021e45 < x < 2.90000000000000003e-33

   1. Initial program 78.0%

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

      1. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in x around 0 63.4%

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

      1. associate-*r/ 76.6%

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

   6. Simplified 76.6%

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

   if 2.90000000000000003e-33 < x

   1. Initial program 63.0%

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

      1. associate-/l* 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in z around inf 55.0%

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

      1. div-sub 55.0%

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

   6. Simplified 55.0%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-33}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 17: 30.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-54} \lor \neg \left(z \leq 4.8 \cdot 10^{+130}\right):\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.6e+64)
   (* y (/ z a))
   (if (or (<= z -7.5e-54) (not (<= z 4.8e+130))) (* x (/ z t)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.6e+64) {
		tmp = y * (z / a);
	} else if ((z <= -7.5e-54) || !(z <= 4.8e+130)) {
		tmp = x * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.6d+64)) then
        tmp = y * (z / a)
    else if ((z <= (-7.5d-54)) .or. (.not. (z <= 4.8d+130))) then
        tmp = x * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.6e+64) {
		tmp = y * (z / a);
	} else if ((z <= -7.5e-54) || !(z <= 4.8e+130)) {
		tmp = x * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.6e+64:
		tmp = y * (z / a)
	elif (z <= -7.5e-54) or not (z <= 4.8e+130):
		tmp = x * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.6e+64)
		tmp = Float64(y * Float64(z / a));
	elseif ((z <= -7.5e-54) || !(z <= 4.8e+130))
		tmp = Float64(x * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.6e+64)
		tmp = y * (z / a);
	elseif ((z <= -7.5e-54) || ~((z <= 4.8e+130)))
		tmp = x * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.6e+64], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -7.5e-54], N[Not[LessEqual[z, 4.8e+130]], $MachinePrecision]], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if z < -5.60000000000000047e64

   1. Initial program 81.3%

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

      1. associate-/l* 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in x around 0 51.0%

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

      1. associate-*r/ 60.2%

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

   6. Simplified 60.2%

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

   7. Taylor expanded in t around 0 44.0%

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

   if -5.60000000000000047e64 < z < -7.5000000000000005e-54 or 4.80000000000000048e130 < z

   1. Initial program 63.8%

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

      1. associate-/l* 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in x around inf 47.1%

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

      1. mul-1-neg 47.1%

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

      2. unsub-neg 47.1%

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

   6. Simplified 47.1%

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

   7. Taylor expanded in a around 0 40.5%

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

   if -7.5000000000000005e-54 < z < 4.80000000000000048e130

   1. Initial program 69.1%

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

      1. associate-/l* 81.7%

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

   3. Simplified 81.7%

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

   4. Taylor expanded in a around inf 35.6%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-54} \lor \neg \left(z \leq 4.8 \cdot 10^{+130}\right):\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 33.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-29} \lor \neg \left(y \leq 3.6 \cdot 10^{+22}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2e-29) (not (<= y 3.6e+22))) (* y (/ (- z t) a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2e-29) || !(y <= 3.6e+22)) {
		tmp = y * ((z - t) / a);
	} 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 ((y <= (-2d-29)) .or. (.not. (y <= 3.6d+22))) then
        tmp = y * ((z - t) / a)
    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 ((y <= -2e-29) || !(y <= 3.6e+22)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2e-29) or not (y <= 3.6e+22):
		tmp = y * ((z - t) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2e-29) || !(y <= 3.6e+22))
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2e-29) || ~((y <= 3.6e+22)))
		tmp = y * ((z - t) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2e-29], N[Not[LessEqual[y, 3.6e+22]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.99999999999999989e-29 or 3.6e22 < y

   1. Initial program 69.7%

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

      1. associate-/l* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in x around 0 54.8%

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

      1. associate-*r/ 74.1%

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

   6. Simplified 74.1%

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

   7. Taylor expanded in a around inf 43.2%

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

   if -1.99999999999999989e-29 < y < 3.6e22

   1. Initial program 70.7%

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

      1. associate-/l* 76.9%

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

   3. Simplified 76.9%

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

   4. Taylor expanded in a around inf 36.5%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-29} \lor \neg \left(y \leq 3.6 \cdot 10^{+22}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 40.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+108} \lor \neg \left(y \leq 6.2 \cdot 10^{+31}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -8.2e+108) (not (<= y 6.2e+31)))
   (* y (/ (- z t) a))
   (* x (- 1.0 (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -8.2e+108) || !(y <= 6.2e+31)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-8.2d+108)) .or. (.not. (y <= 6.2d+31))) then
        tmp = y * ((z - t) / a)
    else
        tmp = x * (1.0d0 - (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -8.2e+108) || !(y <= 6.2e+31)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -8.2e+108) or not (y <= 6.2e+31):
		tmp = y * ((z - t) / a)
	else:
		tmp = x * (1.0 - (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -8.2e+108) || !(y <= 6.2e+31))
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -8.2e+108) || ~((y <= 6.2e+31)))
		tmp = y * ((z - t) / a);
	else
		tmp = x * (1.0 - (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -8.2e+108], N[Not[LessEqual[y, 6.2e+31]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.1999999999999998e108 or 6.2000000000000004e31 < y

   1. Initial program 66.9%

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

      1. associate-/l* 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in x around 0 52.6%

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

      1. associate-*r/ 76.6%

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

   6. Simplified 76.6%

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

   7. Taylor expanded in a around inf 47.8%

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

   if -8.1999999999999998e108 < y < 6.2000000000000004e31

   1. Initial program 72.3%

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

      1. associate-/l* 78.7%

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

   3. Simplified 78.7%

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

   4. Taylor expanded in x around inf 58.1%

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

      1. mul-1-neg 58.1%

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

      2. unsub-neg 58.1%

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

   6. Simplified 58.1%

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

   7. Taylor expanded in t around 0 49.1%

      \[\leadsto \color{blue}{\left(1 - \frac{z}{a}\right)} \cdot x \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+108} \lor \neg \left(y \leq 6.2 \cdot 10^{+31}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]

Alternative 20: 52.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -300 \lor \neg \left(a \leq 3 \cdot 10^{-33}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -300.0) (not (<= a 3e-33)))
   (* x (- 1.0 (/ z a)))
   (* y (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -300.0) || !(a <= 3e-33)) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y * (1.0 - (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 ((a <= (-300.0d0)) .or. (.not. (a <= 3d-33))) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = y * (1.0d0 - (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 ((a <= -300.0) || !(a <= 3e-33)) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -300.0) or not (a <= 3e-33):
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -300.0) || !(a <= 3e-33))
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -300.0) || ~((a <= 3e-33)))
		tmp = x * (1.0 - (z / a));
	else
		tmp = y * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -300.0], N[Not[LessEqual[a, 3e-33]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -300 or 3.0000000000000002e-33 < a

   1. Initial program 66.8%

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

      1. associate-/l* 87.9%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in x around inf 54.7%

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

      1. mul-1-neg 54.7%

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

      2. unsub-neg 54.7%

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

   6. Simplified 54.7%

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

   7. Taylor expanded in t around 0 51.4%

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

   if -300 < a < 3.0000000000000002e-33

   1. Initial program 74.0%

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

      1. associate-/l* 80.6%

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

   3. Simplified 80.6%

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

   4. Taylor expanded in t around inf 72.8%

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

      1. sub-neg 72.8%

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

      2. +-commutative 72.8%

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

      3. mul-1-neg 72.8%

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

      4. unsub-neg 72.8%

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

      5. associate-/l* 74.4%

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

      6. mul-1-neg 74.4%

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

      7. remove-double-neg 74.4%

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

      8. associate-/l* 70.2%

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

   6. Simplified 70.2%

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

   7. Taylor expanded in a around 0 72.7%

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

   8. Taylor expanded in y around inf 56.0%

      \[\leadsto \color{blue}{\left(1 - \frac{z}{t}\right) \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -300 \lor \neg \left(a \leq 3 \cdot 10^{-33}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 21: 55.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-13} \lor \neg \left(a \leq 3.6 \cdot 10^{-38}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.6e-13) (not (<= a 3.6e-38)))
   (+ x (* z (/ y a)))
   (* y (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.6e-13) || !(a <= 3.6e-38)) {
		tmp = x + (z * (y / a));
	} else {
		tmp = y * (1.0 - (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 ((a <= (-5.6d-13)) .or. (.not. (a <= 3.6d-38))) then
        tmp = x + (z * (y / a))
    else
        tmp = y * (1.0d0 - (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 ((a <= -5.6e-13) || !(a <= 3.6e-38)) {
		tmp = x + (z * (y / a));
	} else {
		tmp = y * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.6e-13) or not (a <= 3.6e-38):
		tmp = x + (z * (y / a))
	else:
		tmp = y * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.6e-13) || !(a <= 3.6e-38))
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.6e-13) || ~((a <= 3.6e-38)))
		tmp = x + (z * (y / a));
	else
		tmp = y * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.6e-13], N[Not[LessEqual[a, 3.6e-38]], $MachinePrecision]], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.6000000000000004e-13 or 3.6000000000000001e-38 < a

   1. Initial program 67.5%

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

      1. associate-/l* 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in t around 0 69.0%

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

   5. Taylor expanded in y around inf 53.3%

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

      1. associate-/l* 58.8%

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

      2. associate-/r/ 57.9%

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

   7. Simplified 57.9%

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

   if -5.6000000000000004e-13 < a < 3.6000000000000001e-38

   1. Initial program 73.3%

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

      1. associate-/l* 80.1%

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

   3. Simplified 80.1%

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

   4. Taylor expanded in t around inf 73.0%

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

      1. sub-neg 73.0%

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

      2. +-commutative 73.0%

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

      3. mul-1-neg 73.0%

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

      4. unsub-neg 73.0%

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

      5. associate-/l* 74.6%

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

      6. mul-1-neg 74.6%

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

      7. remove-double-neg 74.6%

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

      8. associate-/l* 70.3%

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

   6. Simplified 70.3%

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

   7. Taylor expanded in a around 0 72.8%

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

   8. Taylor expanded in y around inf 56.5%

      \[\leadsto \color{blue}{\left(1 - \frac{z}{t}\right) \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-13} \lor \neg \left(a \leq 3.6 \cdot 10^{-38}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 22: 38.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+88}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+92}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.5e+88) y (if (<= t 3.4e+92) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.5e+88) {
		tmp = y;
	} else if (t <= 3.4e+92) {
		tmp = x;
	} else {
		tmp = y;
	}
	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 <= (-5.5d+88)) then
        tmp = y
    else if (t <= 3.4d+92) then
        tmp = x
    else
        tmp = y
    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 <= -5.5e+88) {
		tmp = y;
	} else if (t <= 3.4e+92) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.5e+88:
		tmp = y
	elif t <= 3.4e+92:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.5e+88)
		tmp = y;
	elseif (t <= 3.4e+92)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.5e+88)
		tmp = y;
	elseif (t <= 3.4e+92)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.5e+88], y, If[LessEqual[t, 3.4e+92], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -5.5e88 or 3.3999999999999998e92 < t

   1. Initial program 36.9%

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

      1. associate-/l* 61.5%

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

   3. Simplified 61.5%

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

   4. Taylor expanded in t around inf 46.8%

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

   if -5.5e88 < t < 3.3999999999999998e92

   1. Initial program 84.7%

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

      1. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in a around inf 32.2%

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

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+88}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+92}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 23: 25.0% accurate, 13.0× 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 70.2%

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

   1. associate-/l* 84.5%

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

3. Simplified 84.5%

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

4. Taylor expanded in a around inf 25.0%

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

5. Final simplification 25.0%

   \[\leadsto x \]

Developer target: 86.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - 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 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - 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 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	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 - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023257 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

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