Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1

Percentage Accurate: 97.0% → 97.0%

Time: 8.8s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.9%

   \[\frac{x - y}{z - y} \cdot t \]
2. Add Preprocessing

3. Final simplification 97.9%

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

Alternative 2: 72.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+82} \lor \neg \left(y \leq -1.46 \cdot 10^{+28} \lor \neg \left(y \leq -1.26 \cdot 10^{-111}\right) \land y \leq 3.15 \cdot 10^{+62}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.55e+82)
         (not
          (or (<= y -1.46e+28) (and (not (<= y -1.26e-111)) (<= y 3.15e+62)))))
   (* t (/ y (- y z)))
   (* x (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.55e+82) || !((y <= -1.46e+28) || (!(y <= -1.26e-111) && (y <= 3.15e+62)))) {
		tmp = t * (y / (y - z));
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.55d+82)) .or. (.not. (y <= (-1.46d+28)) .or. (.not. (y <= (-1.26d-111))) .and. (y <= 3.15d+62))) then
        tmp = t * (y / (y - z))
    else
        tmp = x * (t / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.55e+82) || !((y <= -1.46e+28) || (!(y <= -1.26e-111) && (y <= 3.15e+62)))) {
		tmp = t * (y / (y - z));
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.55e+82) or not ((y <= -1.46e+28) or (not (y <= -1.26e-111) and (y <= 3.15e+62))):
		tmp = t * (y / (y - z))
	else:
		tmp = x * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.55e+82) || !((y <= -1.46e+28) || (!(y <= -1.26e-111) && (y <= 3.15e+62))))
		tmp = Float64(t * Float64(y / Float64(y - z)));
	else
		tmp = Float64(x * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.55e+82) || ~(((y <= -1.46e+28) || (~((y <= -1.26e-111)) && (y <= 3.15e+62)))))
		tmp = t * (y / (y - z));
	else
		tmp = x * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.55e+82], N[Not[Or[LessEqual[y, -1.46e+28], And[N[Not[LessEqual[y, -1.26e-111]], $MachinePrecision], LessEqual[y, 3.15e+62]]]], $MachinePrecision]], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.55000000000000016e82 or -1.46e28 < y < -1.26000000000000003e-111 or 3.14999999999999999e62 < y

   1. Initial program 98.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 86.0%

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

      1. neg-mul-1 86.0%

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

      2. distribute-neg-frac2 86.0%

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

      3. neg-sub0 86.0%

         \[\leadsto \frac{y}{\color{blue}{0 - \left(z - y\right)}} \cdot t \]

      4. associate--r- 86.0%

         \[\leadsto \frac{y}{\color{blue}{\left(0 - z\right) + y}} \cdot t \]

      5. neg-sub0 86.0%

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

   5. Simplified 86.0%

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

   6. Taylor expanded in t around 0 67.9%

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

      1. associate-/l* 86.0%

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

   8. Simplified 86.0%

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

   if -1.55000000000000016e82 < y < -1.46e28 or -1.26000000000000003e-111 < y < 3.14999999999999999e62

   1. Initial program 96.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 96.6%

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

      2. associate-/l* 91.5%

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

   3. Simplified 91.5%

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

      1. clear-num 91.2%

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

      2. un-div-inv 91.4%

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

   6. Applied egg-rr 91.4%

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

   7. Taylor expanded in x around inf 76.1%

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

      1. *-commutative 76.1%

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

      2. associate-*r/ 71.8%

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

   9. Simplified 71.8%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+82} \lor \neg \left(y \leq -1.46 \cdot 10^{+28} \lor \neg \left(y \leq -1.26 \cdot 10^{-111}\right) \land y \leq 3.15 \cdot 10^{+62}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+84} \lor \neg \left(y \leq -4.2 \cdot 10^{+28}\right) \land \left(y \leq -3.4 \cdot 10^{-119} \lor \neg \left(y \leq 3.15 \cdot 10^{+62}\right)\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5e+84)
         (and (not (<= y -4.2e+28))
              (or (<= y -3.4e-119) (not (<= y 3.15e+62)))))
   (* t (/ y (- y z)))
   (* t (/ x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5e+84) || (!(y <= -4.2e+28) && ((y <= -3.4e-119) || !(y <= 3.15e+62)))) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-5d+84)) .or. (.not. (y <= (-4.2d+28))) .and. (y <= (-3.4d-119)) .or. (.not. (y <= 3.15d+62))) then
        tmp = t * (y / (y - z))
    else
        tmp = t * (x / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5e+84) || (!(y <= -4.2e+28) && ((y <= -3.4e-119) || !(y <= 3.15e+62)))) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5e+84) or (not (y <= -4.2e+28) and ((y <= -3.4e-119) or not (y <= 3.15e+62))):
		tmp = t * (y / (y - z))
	else:
		tmp = t * (x / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5e+84) || (!(y <= -4.2e+28) && ((y <= -3.4e-119) || !(y <= 3.15e+62))))
		tmp = Float64(t * Float64(y / Float64(y - z)));
	else
		tmp = Float64(t * Float64(x / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5e+84) || (~((y <= -4.2e+28)) && ((y <= -3.4e-119) || ~((y <= 3.15e+62)))))
		tmp = t * (y / (y - z));
	else
		tmp = t * (x / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5e+84], And[N[Not[LessEqual[y, -4.2e+28]], $MachinePrecision], Or[LessEqual[y, -3.4e-119], N[Not[LessEqual[y, 3.15e+62]], $MachinePrecision]]]], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.0000000000000001e84 or -4.19999999999999978e28 < y < -3.40000000000000024e-119 or 3.14999999999999999e62 < y

   1. Initial program 98.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 84.5%

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

      1. neg-mul-1 84.5%

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

      2. distribute-neg-frac2 84.5%

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

      3. neg-sub0 84.5%

         \[\leadsto \frac{y}{\color{blue}{0 - \left(z - y\right)}} \cdot t \]

      4. associate--r- 84.5%

         \[\leadsto \frac{y}{\color{blue}{\left(0 - z\right) + y}} \cdot t \]

      5. neg-sub0 84.5%

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

   5. Simplified 84.5%

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

   6. Taylor expanded in t around 0 67.0%

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

      1. associate-/l* 84.5%

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

   8. Simplified 84.5%

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

   if -5.0000000000000001e84 < y < -4.19999999999999978e28 or -3.40000000000000024e-119 < y < 3.14999999999999999e62

   1. Initial program 97.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 76.9%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+84} \lor \neg \left(y \leq -4.2 \cdot 10^{+28}\right) \land \left(y \leq -3.4 \cdot 10^{-119} \lor \neg \left(y \leq 3.15 \cdot 10^{+62}\right)\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+29}:\\ \;\;\;\;\frac{x \cdot t}{-y}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-119} \lor \neg \left(y \leq 2.1 \cdot 10^{-83}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))))
   (if (<= y -2.7e+64)
     t_1
     (if (<= y -2.8e+29)
       (/ (* x t) (- y))
       (if (or (<= y -1.7e-119) (not (<= y 2.1e-83))) t_1 (/ t (/ z x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -2.7e+64) {
		tmp = t_1;
	} else if (y <= -2.8e+29) {
		tmp = (x * t) / -y;
	} else if ((y <= -1.7e-119) || !(y <= 2.1e-83)) {
		tmp = t_1;
	} else {
		tmp = t / (z / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (y - z))
    if (y <= (-2.7d+64)) then
        tmp = t_1
    else if (y <= (-2.8d+29)) then
        tmp = (x * t) / -y
    else if ((y <= (-1.7d-119)) .or. (.not. (y <= 2.1d-83))) then
        tmp = t_1
    else
        tmp = t / (z / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -2.7e+64) {
		tmp = t_1;
	} else if (y <= -2.8e+29) {
		tmp = (x * t) / -y;
	} else if ((y <= -1.7e-119) || !(y <= 2.1e-83)) {
		tmp = t_1;
	} else {
		tmp = t / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	tmp = 0
	if y <= -2.7e+64:
		tmp = t_1
	elif y <= -2.8e+29:
		tmp = (x * t) / -y
	elif (y <= -1.7e-119) or not (y <= 2.1e-83):
		tmp = t_1
	else:
		tmp = t / (z / x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (y <= -2.7e+64)
		tmp = t_1;
	elseif (y <= -2.8e+29)
		tmp = Float64(Float64(x * t) / Float64(-y));
	elseif ((y <= -1.7e-119) || !(y <= 2.1e-83))
		tmp = t_1;
	else
		tmp = Float64(t / Float64(z / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	tmp = 0.0;
	if (y <= -2.7e+64)
		tmp = t_1;
	elseif (y <= -2.8e+29)
		tmp = (x * t) / -y;
	elseif ((y <= -1.7e-119) || ~((y <= 2.1e-83)))
		tmp = t_1;
	else
		tmp = t / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e+64], t$95$1, If[LessEqual[y, -2.8e+29], N[(N[(x * t), $MachinePrecision] / (-y)), $MachinePrecision], If[Or[LessEqual[y, -1.7e-119], N[Not[LessEqual[y, 2.1e-83]], $MachinePrecision]], t$95$1, N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7e64 or -2.8e29 < y < -1.70000000000000012e-119 or 2.0999999999999999e-83 < y

   1. Initial program 98.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 76.7%

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

      1. neg-mul-1 76.7%

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

      2. distribute-neg-frac2 76.7%

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

      3. neg-sub0 76.7%

         \[\leadsto \frac{y}{\color{blue}{0 - \left(z - y\right)}} \cdot t \]

      4. associate--r- 76.7%

         \[\leadsto \frac{y}{\color{blue}{\left(0 - z\right) + y}} \cdot t \]

      5. neg-sub0 76.7%

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

   5. Simplified 76.7%

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

   6. Taylor expanded in t around 0 63.6%

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

      1. associate-/l* 76.7%

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

   8. Simplified 76.7%

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

   if -2.7e64 < y < -2.8e29

   1. Initial program 99.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 94.1%

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

   4. Taylor expanded in z around 0 94.7%

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

      1. associate-*r/ 94.7%

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

      2. associate-*r* 94.7%

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

      3. neg-mul-1 94.7%

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

      4. *-commutative 94.7%

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

   6. Simplified 94.7%

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

   if -1.70000000000000012e-119 < y < 2.0999999999999999e-83

   1. Initial program 97.3%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 97.2%

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

      2. associate-/l* 90.3%

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

   3. Simplified 90.3%

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

      1. associate-*r/ 97.2%

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

      2. associate-*l/ 97.3%

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

      3. *-commutative 97.3%

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

      4. clear-num 97.2%

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

      5. un-div-inv 97.4%

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

   6. Applied egg-rr 97.4%

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

   7. Taylor expanded in y around 0 77.9%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+64}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+29}:\\ \;\;\;\;\frac{x \cdot t}{-y}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-119} \lor \neg \left(y \leq 2.1 \cdot 10^{-83}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -1.12 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.18 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-46} \lor \neg \left(y \leq 1.3 \cdot 10^{+90}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))))
   (if (<= y -1.12e+82)
     t_1
     (if (<= y -1.18e+29)
       (* t (/ x (- z y)))
       (if (or (<= y -3.7e-46) (not (<= y 1.3e+90)))
         t_1
         (* t (/ (- x y) z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -1.12e+82) {
		tmp = t_1;
	} else if (y <= -1.18e+29) {
		tmp = t * (x / (z - y));
	} else if ((y <= -3.7e-46) || !(y <= 1.3e+90)) {
		tmp = t_1;
	} else {
		tmp = t * ((x - y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (y - z))
    if (y <= (-1.12d+82)) then
        tmp = t_1
    else if (y <= (-1.18d+29)) then
        tmp = t * (x / (z - y))
    else if ((y <= (-3.7d-46)) .or. (.not. (y <= 1.3d+90))) then
        tmp = t_1
    else
        tmp = t * ((x - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -1.12e+82) {
		tmp = t_1;
	} else if (y <= -1.18e+29) {
		tmp = t * (x / (z - y));
	} else if ((y <= -3.7e-46) || !(y <= 1.3e+90)) {
		tmp = t_1;
	} else {
		tmp = t * ((x - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	tmp = 0
	if y <= -1.12e+82:
		tmp = t_1
	elif y <= -1.18e+29:
		tmp = t * (x / (z - y))
	elif (y <= -3.7e-46) or not (y <= 1.3e+90):
		tmp = t_1
	else:
		tmp = t * ((x - y) / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (y <= -1.12e+82)
		tmp = t_1;
	elseif (y <= -1.18e+29)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif ((y <= -3.7e-46) || !(y <= 1.3e+90))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(x - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	tmp = 0.0;
	if (y <= -1.12e+82)
		tmp = t_1;
	elseif (y <= -1.18e+29)
		tmp = t * (x / (z - y));
	elseif ((y <= -3.7e-46) || ~((y <= 1.3e+90)))
		tmp = t_1;
	else
		tmp = t * ((x - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.12e+82], t$95$1, If[LessEqual[y, -1.18e+29], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -3.7e-46], N[Not[LessEqual[y, 1.3e+90]], $MachinePrecision]], t$95$1, N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.11999999999999998e82 or -1.18e29 < y < -3.69999999999999983e-46 or 1.2999999999999999e90 < y

   1. Initial program 99.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 89.0%

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

      1. neg-mul-1 89.0%

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

      2. distribute-neg-frac2 89.0%

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

      3. neg-sub0 89.0%

         \[\leadsto \frac{y}{\color{blue}{0 - \left(z - y\right)}} \cdot t \]

      4. associate--r- 89.0%

         \[\leadsto \frac{y}{\color{blue}{\left(0 - z\right) + y}} \cdot t \]

      5. neg-sub0 89.0%

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

   5. Simplified 89.0%

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

   6. Taylor expanded in t around 0 68.2%

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

      1. associate-/l* 89.0%

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

   8. Simplified 89.0%

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

   if -1.11999999999999998e82 < y < -1.18e29

   1. Initial program 99.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 94.8%

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

   if -3.69999999999999983e-46 < y < 1.2999999999999999e90

   1. Initial program 96.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 75.3%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+82}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -1.18 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-46} \lor \neg \left(y \leq 1.3 \cdot 10^{+90}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -1.34 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+28}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-47} \lor \neg \left(y \leq 1.3 \cdot 10^{+90}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))))
   (if (<= y -1.34e+82)
     t_1
     (if (<= y -3.5e+28)
       (/ t (/ (- z y) x))
       (if (or (<= y -1.35e-47) (not (<= y 1.3e+90)))
         t_1
         (* t (/ (- x y) z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -1.34e+82) {
		tmp = t_1;
	} else if (y <= -3.5e+28) {
		tmp = t / ((z - y) / x);
	} else if ((y <= -1.35e-47) || !(y <= 1.3e+90)) {
		tmp = t_1;
	} else {
		tmp = t * ((x - y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (y - z))
    if (y <= (-1.34d+82)) then
        tmp = t_1
    else if (y <= (-3.5d+28)) then
        tmp = t / ((z - y) / x)
    else if ((y <= (-1.35d-47)) .or. (.not. (y <= 1.3d+90))) then
        tmp = t_1
    else
        tmp = t * ((x - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -1.34e+82) {
		tmp = t_1;
	} else if (y <= -3.5e+28) {
		tmp = t / ((z - y) / x);
	} else if ((y <= -1.35e-47) || !(y <= 1.3e+90)) {
		tmp = t_1;
	} else {
		tmp = t * ((x - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	tmp = 0
	if y <= -1.34e+82:
		tmp = t_1
	elif y <= -3.5e+28:
		tmp = t / ((z - y) / x)
	elif (y <= -1.35e-47) or not (y <= 1.3e+90):
		tmp = t_1
	else:
		tmp = t * ((x - y) / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (y <= -1.34e+82)
		tmp = t_1;
	elseif (y <= -3.5e+28)
		tmp = Float64(t / Float64(Float64(z - y) / x));
	elseif ((y <= -1.35e-47) || !(y <= 1.3e+90))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(x - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	tmp = 0.0;
	if (y <= -1.34e+82)
		tmp = t_1;
	elseif (y <= -3.5e+28)
		tmp = t / ((z - y) / x);
	elseif ((y <= -1.35e-47) || ~((y <= 1.3e+90)))
		tmp = t_1;
	else
		tmp = t * ((x - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.34e+82], t$95$1, If[LessEqual[y, -3.5e+28], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.35e-47], N[Not[LessEqual[y, 1.3e+90]], $MachinePrecision]], t$95$1, N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.33999999999999992e82 or -3.5e28 < y < -1.3499999999999999e-47 or 1.2999999999999999e90 < y

   1. Initial program 99.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 89.0%

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

      1. neg-mul-1 89.0%

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

      2. distribute-neg-frac2 89.0%

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

      3. neg-sub0 89.0%

         \[\leadsto \frac{y}{\color{blue}{0 - \left(z - y\right)}} \cdot t \]

      4. associate--r- 89.0%

         \[\leadsto \frac{y}{\color{blue}{\left(0 - z\right) + y}} \cdot t \]

      5. neg-sub0 89.0%

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

   5. Simplified 89.0%

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

   6. Taylor expanded in t around 0 68.2%

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

      1. associate-/l* 89.0%

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

   8. Simplified 89.0%

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

   if -1.33999999999999992e82 < y < -3.5e28

   1. Initial program 99.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 100.0%

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

      2. associate-/l* 83.9%

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

   3. Simplified 83.9%

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

      1. associate-*r/ 100.0%

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

      2. associate-*l/ 99.2%

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

      3. *-commutative 99.2%

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

      4. clear-num 99.2%

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

      5. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around inf 95.6%

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

   if -1.3499999999999999e-47 < y < 1.2999999999999999e90

   1. Initial program 96.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 75.3%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.34 \cdot 10^{+82}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+28}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-47} \lor \neg \left(y \leq 1.3 \cdot 10^{+90}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{+28}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \frac{-t}{z}\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-47}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+90}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.9e+28)
   t
   (if (<= y -2.85e-37)
     (* y (/ (- t) z))
     (if (<= y -7.6e-47) t (if (<= y 1.3e+90) (/ t (/ z x)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.9e+28) {
		tmp = t;
	} else if (y <= -2.85e-37) {
		tmp = y * (-t / z);
	} else if (y <= -7.6e-47) {
		tmp = t;
	} else if (y <= 1.3e+90) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-6.9d+28)) then
        tmp = t
    else if (y <= (-2.85d-37)) then
        tmp = y * (-t / z)
    else if (y <= (-7.6d-47)) then
        tmp = t
    else if (y <= 1.3d+90) then
        tmp = t / (z / x)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.9e+28) {
		tmp = t;
	} else if (y <= -2.85e-37) {
		tmp = y * (-t / z);
	} else if (y <= -7.6e-47) {
		tmp = t;
	} else if (y <= 1.3e+90) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.9e+28:
		tmp = t
	elif y <= -2.85e-37:
		tmp = y * (-t / z)
	elif y <= -7.6e-47:
		tmp = t
	elif y <= 1.3e+90:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.9e+28)
		tmp = t;
	elseif (y <= -2.85e-37)
		tmp = Float64(y * Float64(Float64(-t) / z));
	elseif (y <= -7.6e-47)
		tmp = t;
	elseif (y <= 1.3e+90)
		tmp = Float64(t / Float64(z / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.9e+28)
		tmp = t;
	elseif (y <= -2.85e-37)
		tmp = y * (-t / z);
	elseif (y <= -7.6e-47)
		tmp = t;
	elseif (y <= 1.3e+90)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.9e+28], t, If[LessEqual[y, -2.85e-37], N[(y * N[((-t) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.6e-47], t, If[LessEqual[y, 1.3e+90], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.9e28 or -2.84999999999999987e-37 < y < -7.60000000000000029e-47 or 1.2999999999999999e90 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 75.1%

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

      2. associate-/l* 71.5%

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

   3. Simplified 71.5%

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

   5. Taylor expanded in y around inf 72.8%

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

   if -6.9e28 < y < -2.84999999999999987e-37

   1. Initial program 94.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 99.9%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 61.4%

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

      1. *-commutative 61.4%

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

      2. associate-/l* 61.4%

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

   7. Simplified 61.4%

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

   8. Taylor expanded in x around 0 60.8%

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

      1. associate-*r/ 60.8%

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

      2. neg-mul-1 60.8%

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

      3. distribute-rgt-neg-in 60.8%

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

      4. associate-*l/ 60.8%

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

   10. Simplified 60.8%

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

   if -7.60000000000000029e-47 < y < 1.2999999999999999e90

   1. Initial program 96.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 96.9%

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

      2. associate-/l* 92.2%

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

   3. Simplified 92.2%

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

      1. associate-*r/ 96.9%

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

      2. associate-*l/ 96.5%

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

      3. *-commutative 96.5%

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

      4. clear-num 96.2%

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

      5. un-div-inv 96.5%

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

   6. Applied egg-rr 96.5%

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

   7. Taylor expanded in y around 0 60.8%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{+28}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \frac{-t}{z}\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-47}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+90}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+64}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-119}:\\ \;\;\;\;y \cdot \frac{-t}{z}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+91}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.8e+64)
   t
   (if (<= y -2e+28)
     (* t (/ x (- y)))
     (if (<= y -3.5e-119)
       (* y (/ (- t) z))
       (if (<= y 2.35e+91) (/ t (/ z x)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.8e+64) {
		tmp = t;
	} else if (y <= -2e+28) {
		tmp = t * (x / -y);
	} else if (y <= -3.5e-119) {
		tmp = y * (-t / z);
	} else if (y <= 2.35e+91) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.8d+64)) then
        tmp = t
    else if (y <= (-2d+28)) then
        tmp = t * (x / -y)
    else if (y <= (-3.5d-119)) then
        tmp = y * (-t / z)
    else if (y <= 2.35d+91) then
        tmp = t / (z / x)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.8e+64) {
		tmp = t;
	} else if (y <= -2e+28) {
		tmp = t * (x / -y);
	} else if (y <= -3.5e-119) {
		tmp = y * (-t / z);
	} else if (y <= 2.35e+91) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.8e+64:
		tmp = t
	elif y <= -2e+28:
		tmp = t * (x / -y)
	elif y <= -3.5e-119:
		tmp = y * (-t / z)
	elif y <= 2.35e+91:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.8e+64)
		tmp = t;
	elseif (y <= -2e+28)
		tmp = Float64(t * Float64(x / Float64(-y)));
	elseif (y <= -3.5e-119)
		tmp = Float64(y * Float64(Float64(-t) / z));
	elseif (y <= 2.35e+91)
		tmp = Float64(t / Float64(z / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.8e+64)
		tmp = t;
	elseif (y <= -2e+28)
		tmp = t * (x / -y);
	elseif (y <= -3.5e-119)
		tmp = y * (-t / z);
	elseif (y <= 2.35e+91)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.8e+64], t, If[LessEqual[y, -2e+28], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.5e-119], N[(y * N[((-t) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.35e+91], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.80000000000000024e64 or 2.3499999999999999e91 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 72.9%

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

      2. associate-/l* 69.9%

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

   3. Simplified 69.9%

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

   5. Taylor expanded in y around inf 75.9%

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

   if -2.80000000000000024e64 < y < -1.99999999999999992e28

   1. Initial program 99.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 94.1%

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

   4. Taylor expanded in z around 0 94.1%

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

      1. associate-*r/ 94.1%

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

      2. neg-mul-1 94.1%

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

   6. Simplified 94.1%

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

   if -1.99999999999999992e28 < y < -3.5e-119

   1. Initial program 92.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 62.3%

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

      1. *-commutative 62.3%

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

      2. associate-/l* 62.4%

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

   7. Simplified 62.4%

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

   8. Taylor expanded in x around 0 51.6%

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

      1. associate-*r/ 51.6%

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

      2. neg-mul-1 51.6%

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

      3. distribute-rgt-neg-in 51.6%

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

      4. associate-*l/ 51.7%

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

   10. Simplified 51.7%

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

   if -3.5e-119 < y < 2.3499999999999999e91

   1. Initial program 97.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 96.5%

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

      2. associate-/l* 91.1%

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

   3. Simplified 91.1%

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

      1. associate-*r/ 96.5%

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

      2. associate-*l/ 97.6%

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

      3. *-commutative 97.6%

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

      4. clear-num 97.2%

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

      5. un-div-inv 97.4%

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

   6. Applied egg-rr 97.4%

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

   7. Taylor expanded in y around 0 63.1%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+64}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-119}:\\ \;\;\;\;y \cdot \frac{-t}{z}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+91}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+64}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot \left(-t\right)}{y}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-119}:\\ \;\;\;\;y \cdot \frac{-t}{z}\\ \mathbf{elif}\;y \leq 1.38 \cdot 10^{+90}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.3e+64)
   t
   (if (<= y -9.6e+28)
     (/ (* x (- t)) y)
     (if (<= y -3.2e-119)
       (* y (/ (- t) z))
       (if (<= y 1.38e+90) (/ t (/ z x)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.3e+64) {
		tmp = t;
	} else if (y <= -9.6e+28) {
		tmp = (x * -t) / y;
	} else if (y <= -3.2e-119) {
		tmp = y * (-t / z);
	} else if (y <= 1.38e+90) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.3d+64)) then
        tmp = t
    else if (y <= (-9.6d+28)) then
        tmp = (x * -t) / y
    else if (y <= (-3.2d-119)) then
        tmp = y * (-t / z)
    else if (y <= 1.38d+90) then
        tmp = t / (z / x)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.3e+64) {
		tmp = t;
	} else if (y <= -9.6e+28) {
		tmp = (x * -t) / y;
	} else if (y <= -3.2e-119) {
		tmp = y * (-t / z);
	} else if (y <= 1.38e+90) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.3e+64:
		tmp = t
	elif y <= -9.6e+28:
		tmp = (x * -t) / y
	elif y <= -3.2e-119:
		tmp = y * (-t / z)
	elif y <= 1.38e+90:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.3e+64)
		tmp = t;
	elseif (y <= -9.6e+28)
		tmp = Float64(Float64(x * Float64(-t)) / y);
	elseif (y <= -3.2e-119)
		tmp = Float64(y * Float64(Float64(-t) / z));
	elseif (y <= 1.38e+90)
		tmp = Float64(t / Float64(z / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.3e+64)
		tmp = t;
	elseif (y <= -9.6e+28)
		tmp = (x * -t) / y;
	elseif (y <= -3.2e-119)
		tmp = y * (-t / z);
	elseif (y <= 1.38e+90)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.3e+64], t, If[LessEqual[y, -9.6e+28], N[(N[(x * (-t)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -3.2e-119], N[(y * N[((-t) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.38e+90], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.29999999999999988e64 or 1.38000000000000005e90 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 72.9%

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

      2. associate-/l* 69.9%

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

   3. Simplified 69.9%

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

   5. Taylor expanded in y around inf 75.9%

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

   if -3.29999999999999988e64 < y < -9.59999999999999925e28

   1. Initial program 99.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 94.1%

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

   4. Taylor expanded in z around 0 94.7%

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

      1. associate-*r/ 94.7%

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

      2. associate-*r* 94.7%

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

      3. neg-mul-1 94.7%

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

      4. *-commutative 94.7%

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

   6. Simplified 94.7%

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

   if -9.59999999999999925e28 < y < -3.19999999999999993e-119

   1. Initial program 92.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 62.3%

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

      1. *-commutative 62.3%

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

      2. associate-/l* 62.4%

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

   7. Simplified 62.4%

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

   8. Taylor expanded in x around 0 51.6%

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

      1. associate-*r/ 51.6%

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

      2. neg-mul-1 51.6%

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

      3. distribute-rgt-neg-in 51.6%

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

      4. associate-*l/ 51.7%

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

   10. Simplified 51.7%

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

   if -3.19999999999999993e-119 < y < 1.38000000000000005e90

   1. Initial program 97.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 96.5%

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

      2. associate-/l* 91.1%

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

   3. Simplified 91.1%

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

      1. associate-*r/ 96.5%

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

      2. associate-*l/ 97.6%

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

      3. *-commutative 97.6%

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

      4. clear-num 97.2%

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

      5. un-div-inv 97.4%

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

   6. Applied egg-rr 97.4%

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

   7. Taylor expanded in y around 0 63.1%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+64}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot \left(-t\right)}{y}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-119}:\\ \;\;\;\;y \cdot \frac{-t}{z}\\ \mathbf{elif}\;y \leq 1.38 \cdot 10^{+90}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \left(\frac{x}{-y} - -1\right)\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-47} \lor \neg \left(y \leq 1.3 \cdot 10^{+90}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.4e+28)
   (* t (- (/ x (- y)) -1.0))
   (if (or (<= y -4.4e-47) (not (<= y 1.3e+90)))
     (* t (/ y (- y z)))
     (* t (/ (- x y) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.4e+28) {
		tmp = t * ((x / -y) - -1.0);
	} else if ((y <= -4.4e-47) || !(y <= 1.3e+90)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t * ((x - y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-7.4d+28)) then
        tmp = t * ((x / -y) - (-1.0d0))
    else if ((y <= (-4.4d-47)) .or. (.not. (y <= 1.3d+90))) then
        tmp = t * (y / (y - z))
    else
        tmp = t * ((x - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.4e+28) {
		tmp = t * ((x / -y) - -1.0);
	} else if ((y <= -4.4e-47) || !(y <= 1.3e+90)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t * ((x - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.4e+28:
		tmp = t * ((x / -y) - -1.0)
	elif (y <= -4.4e-47) or not (y <= 1.3e+90):
		tmp = t * (y / (y - z))
	else:
		tmp = t * ((x - y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.4e+28)
		tmp = Float64(t * Float64(Float64(x / Float64(-y)) - -1.0));
	elseif ((y <= -4.4e-47) || !(y <= 1.3e+90))
		tmp = Float64(t * Float64(y / Float64(y - z)));
	else
		tmp = Float64(t * Float64(Float64(x - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.4e+28)
		tmp = t * ((x / -y) - -1.0);
	elseif ((y <= -4.4e-47) || ~((y <= 1.3e+90)))
		tmp = t * (y / (y - z));
	else
		tmp = t * ((x - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.4e+28], N[(t * N[(N[(x / (-y)), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -4.4e-47], N[Not[LessEqual[y, 1.3e+90]], $MachinePrecision]], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.3999999999999998e28

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 87.7%

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

      1. mul-1-neg 87.7%

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

      2. div-sub 87.7%

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

      3. sub-neg 87.7%

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

      4. *-inverses 87.7%

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

      5. metadata-eval 87.7%

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

   5. Simplified 87.7%

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

   if -7.3999999999999998e28 < y < -4.40000000000000037e-47 or 1.2999999999999999e90 < y

   1. Initial program 99.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 89.5%

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

      1. neg-mul-1 89.5%

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

      2. distribute-neg-frac2 89.5%

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

      3. neg-sub0 89.5%

         \[\leadsto \frac{y}{\color{blue}{0 - \left(z - y\right)}} \cdot t \]

      4. associate--r- 89.5%

         \[\leadsto \frac{y}{\color{blue}{\left(0 - z\right) + y}} \cdot t \]

      5. neg-sub0 89.5%

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

   5. Simplified 89.5%

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

   6. Taylor expanded in t around 0 69.7%

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

      1. associate-/l* 89.5%

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

   8. Simplified 89.5%

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

   if -4.40000000000000037e-47 < y < 1.2999999999999999e90

   1. Initial program 96.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 75.3%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \left(\frac{x}{-y} - -1\right)\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-47} \lor \neg \left(y \leq 1.3 \cdot 10^{+90}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 73.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \left(\frac{x}{-y} - -1\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-45}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+90}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.45e+28)
   (* t (- (/ x (- y)) -1.0))
   (if (<= y -1.2e-45)
     (* y (/ t (- y z)))
     (if (<= y 1.3e+90) (* t (/ (- x y) z)) (* t (/ y (- y z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.45e+28) {
		tmp = t * ((x / -y) - -1.0);
	} else if (y <= -1.2e-45) {
		tmp = y * (t / (y - z));
	} else if (y <= 1.3e+90) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.45d+28)) then
        tmp = t * ((x / -y) - (-1.0d0))
    else if (y <= (-1.2d-45)) then
        tmp = y * (t / (y - z))
    else if (y <= 1.3d+90) then
        tmp = t * ((x - y) / z)
    else
        tmp = t * (y / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.45e+28) {
		tmp = t * ((x / -y) - -1.0);
	} else if (y <= -1.2e-45) {
		tmp = y * (t / (y - z));
	} else if (y <= 1.3e+90) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.45e+28:
		tmp = t * ((x / -y) - -1.0)
	elif y <= -1.2e-45:
		tmp = y * (t / (y - z))
	elif y <= 1.3e+90:
		tmp = t * ((x - y) / z)
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.45e+28)
		tmp = Float64(t * Float64(Float64(x / Float64(-y)) - -1.0));
	elseif (y <= -1.2e-45)
		tmp = Float64(y * Float64(t / Float64(y - z)));
	elseif (y <= 1.3e+90)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	else
		tmp = Float64(t * Float64(y / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.45e+28)
		tmp = t * ((x / -y) - -1.0);
	elseif (y <= -1.2e-45)
		tmp = y * (t / (y - z));
	elseif (y <= 1.3e+90)
		tmp = t * ((x - y) / z);
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.45e+28], N[(t * N[(N[(x / (-y)), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.2e-45], N[(y * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+90], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.4499999999999998e28

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 87.7%

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

      1. mul-1-neg 87.7%

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

      2. div-sub 87.7%

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

      3. sub-neg 87.7%

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

      4. *-inverses 87.7%

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

      5. metadata-eval 87.7%

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

   5. Simplified 87.7%

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

   if -2.4499999999999998e28 < y < -1.19999999999999995e-45

   1. Initial program 96.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 82.3%

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

      1. mul-1-neg 82.3%

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

      2. associate-*l/ 82.4%

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

      3. distribute-rgt-neg-out 82.4%

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

   7. Simplified 82.4%

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

   if -1.19999999999999995e-45 < y < 1.2999999999999999e90

   1. Initial program 96.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 75.3%

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

   if 1.2999999999999999e90 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 92.7%

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

      1. neg-mul-1 92.7%

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

      2. distribute-neg-frac2 92.7%

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

      3. neg-sub0 92.7%

         \[\leadsto \frac{y}{\color{blue}{0 - \left(z - y\right)}} \cdot t \]

      4. associate--r- 92.7%

         \[\leadsto \frac{y}{\color{blue}{\left(0 - z\right) + y}} \cdot t \]

      5. neg-sub0 92.7%

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

   5. Simplified 92.7%

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

   6. Taylor expanded in t around 0 65.9%

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

      1. associate-/l* 92.7%

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

   8. Simplified 92.7%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \left(\frac{x}{-y} - -1\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-45}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+90}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 89.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+152}:\\ \;\;\;\;t \cdot \left(\frac{x}{-y} - -1\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+101}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2e+152)
   (* t (- (/ x (- y)) -1.0))
   (if (<= y 1.3e+101) (* (- x y) (/ t (- z y))) (* t (/ y (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2e+152) {
		tmp = t * ((x / -y) - -1.0);
	} else if (y <= 1.3e+101) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2d+152)) then
        tmp = t * ((x / -y) - (-1.0d0))
    else if (y <= 1.3d+101) then
        tmp = (x - y) * (t / (z - y))
    else
        tmp = t * (y / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2e+152) {
		tmp = t * ((x / -y) - -1.0);
	} else if (y <= 1.3e+101) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2e+152:
		tmp = t * ((x / -y) - -1.0)
	elif y <= 1.3e+101:
		tmp = (x - y) * (t / (z - y))
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2e+152)
		tmp = Float64(t * Float64(Float64(x / Float64(-y)) - -1.0));
	elseif (y <= 1.3e+101)
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	else
		tmp = Float64(t * Float64(y / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2e+152)
		tmp = t * ((x / -y) - -1.0);
	elseif (y <= 1.3e+101)
		tmp = (x - y) * (t / (z - y));
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2e+152], N[(t * N[(N[(x / (-y)), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+101], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.0000000000000001e152

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 94.8%

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

      1. mul-1-neg 94.8%

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

      2. div-sub 94.8%

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

      3. sub-neg 94.8%

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

      4. *-inverses 94.8%

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

      5. metadata-eval 94.8%

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

   5. Simplified 94.8%

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

   if -2.0000000000000001e152 < y < 1.3e101

   1. Initial program 97.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 96.1%

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

      2. associate-/l* 91.5%

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

   3. Simplified 91.5%

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

   if 1.3e101 < y

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 95.9%

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

      1. neg-mul-1 95.9%

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

      2. distribute-neg-frac2 95.9%

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

      3. neg-sub0 95.9%

         \[\leadsto \frac{y}{\color{blue}{0 - \left(z - y\right)}} \cdot t \]

      4. associate--r- 95.9%

         \[\leadsto \frac{y}{\color{blue}{\left(0 - z\right) + y}} \cdot t \]

      5. neg-sub0 95.9%

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

   5. Simplified 95.9%

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

   6. Taylor expanded in t around 0 68.3%

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

      1. associate-/l* 95.9%

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

   8. Simplified 95.9%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+152}:\\ \;\;\;\;t \cdot \left(\frac{x}{-y} - -1\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+101}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-45}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.05e-45) t (if (<= y 1.3e+90) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e-45) {
		tmp = t;
	} else if (y <= 1.3e+90) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.05d-45)) then
        tmp = t
    else if (y <= 1.3d+90) then
        tmp = x * (t / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e-45) {
		tmp = t;
	} else if (y <= 1.3e+90) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.05e-45:
		tmp = t
	elif y <= 1.3e+90:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.05e-45)
		tmp = t;
	elseif (y <= 1.3e+90)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.05e-45)
		tmp = t;
	elseif (y <= 1.3e+90)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.05e-45], t, If[LessEqual[y, 1.3e+90], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.04999999999999998e-45 or 1.2999999999999999e90 < y

   1. Initial program 99.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 77.5%

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

      2. associate-/l* 74.3%

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

   3. Simplified 74.3%

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

   5. Taylor expanded in y around inf 67.7%

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

   if -1.04999999999999998e-45 < y < 1.2999999999999999e90

   1. Initial program 96.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 96.9%

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

      2. associate-/l* 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in y around 0 60.1%

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

      1. *-commutative 60.1%

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

      2. associate-/l* 55.5%

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

   7. Simplified 55.5%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-45}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-45}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+90}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.2e-45) t (if (<= y 1.3e+90) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.2e-45) {
		tmp = t;
	} else if (y <= 1.3e+90) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.2d-45)) then
        tmp = t
    else if (y <= 1.3d+90) then
        tmp = t * (x / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.2e-45) {
		tmp = t;
	} else if (y <= 1.3e+90) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.2e-45:
		tmp = t
	elif y <= 1.3e+90:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.2e-45)
		tmp = t;
	elseif (y <= 1.3e+90)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.2e-45)
		tmp = t;
	elseif (y <= 1.3e+90)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.2e-45], t, If[LessEqual[y, 1.3e+90], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.19999999999999995e-45 or 1.2999999999999999e90 < y

   1. Initial program 99.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 77.5%

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

      2. associate-/l* 74.3%

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

   3. Simplified 74.3%

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

   5. Taylor expanded in y around inf 67.7%

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

   if -1.19999999999999995e-45 < y < 1.2999999999999999e90

   1. Initial program 96.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 60.8%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-45}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+90}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 61.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-46}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+90}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9.8e-46) t (if (<= y 1.3e+90) (/ t (/ z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.8e-46) {
		tmp = t;
	} else if (y <= 1.3e+90) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-9.8d-46)) then
        tmp = t
    else if (y <= 1.3d+90) then
        tmp = t / (z / x)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.8e-46) {
		tmp = t;
	} else if (y <= 1.3e+90) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9.8e-46:
		tmp = t
	elif y <= 1.3e+90:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9.8e-46)
		tmp = t;
	elseif (y <= 1.3e+90)
		tmp = Float64(t / Float64(z / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -9.8e-46)
		tmp = t;
	elseif (y <= 1.3e+90)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9.8e-46], t, If[LessEqual[y, 1.3e+90], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -9.8000000000000002e-46 or 1.2999999999999999e90 < y

   1. Initial program 99.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 77.5%

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

      2. associate-/l* 74.3%

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

   3. Simplified 74.3%

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

   5. Taylor expanded in y around inf 67.7%

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

   if -9.8000000000000002e-46 < y < 1.2999999999999999e90

   1. Initial program 96.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 96.9%

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

      2. associate-/l* 92.2%

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

   3. Simplified 92.2%

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

      1. associate-*r/ 96.9%

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

      2. associate-*l/ 96.5%

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

      3. *-commutative 96.5%

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

      4. clear-num 96.2%

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

      5. un-div-inv 96.5%

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

   6. Applied egg-rr 96.5%

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

   7. Taylor expanded in y around 0 60.8%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-46}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+90}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 35.8% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.9%

   \[\frac{x - y}{z - y} \cdot t \]
2. Step-by-step derivation

   1. associate-*l/ 87.7%

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

   2. associate-/l* 83.7%

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

3. Simplified 83.7%

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

5. Taylor expanded in y around inf 39.2%

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

6. Final simplification 39.2%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024115 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (/ t (/ (- z y) (- x y)))

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