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

Percentage Accurate: 96.9% → 96.9%

Time: 9.8s

Alternatives: 14

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: 96.9% 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: 96.9% 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 96.3%

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

3. Final simplification 96.3%

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

Alternative 2: 66.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x - y}{z}\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+144}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -25000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-55}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 0.002:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- x y) z))))
   (if (<= y -4.6e+144)
     t
     (if (<= y -1.8e+17)
       t_1
       (if (<= y -25000.0)
         t
         (if (<= y -1.3e-55)
           (* (- x y) (/ t z))
           (if (<= y 0.002)
             (* x (/ t (- z y)))
             (if (<= y 1.2e+50) t_1 t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double tmp;
	if (y <= -4.6e+144) {
		tmp = t;
	} else if (y <= -1.8e+17) {
		tmp = t_1;
	} else if (y <= -25000.0) {
		tmp = t;
	} else if (y <= -1.3e-55) {
		tmp = (x - y) * (t / z);
	} else if (y <= 0.002) {
		tmp = x * (t / (z - y));
	} else if (y <= 1.2e+50) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * ((x - y) / z)
    if (y <= (-4.6d+144)) then
        tmp = t
    else if (y <= (-1.8d+17)) then
        tmp = t_1
    else if (y <= (-25000.0d0)) then
        tmp = t
    else if (y <= (-1.3d-55)) then
        tmp = (x - y) * (t / z)
    else if (y <= 0.002d0) then
        tmp = x * (t / (z - y))
    else if (y <= 1.2d+50) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double tmp;
	if (y <= -4.6e+144) {
		tmp = t;
	} else if (y <= -1.8e+17) {
		tmp = t_1;
	} else if (y <= -25000.0) {
		tmp = t;
	} else if (y <= -1.3e-55) {
		tmp = (x - y) * (t / z);
	} else if (y <= 0.002) {
		tmp = x * (t / (z - y));
	} else if (y <= 1.2e+50) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((x - y) / z)
	tmp = 0
	if y <= -4.6e+144:
		tmp = t
	elif y <= -1.8e+17:
		tmp = t_1
	elif y <= -25000.0:
		tmp = t
	elif y <= -1.3e-55:
		tmp = (x - y) * (t / z)
	elif y <= 0.002:
		tmp = x * (t / (z - y))
	elif y <= 1.2e+50:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(x - y) / z))
	tmp = 0.0
	if (y <= -4.6e+144)
		tmp = t;
	elseif (y <= -1.8e+17)
		tmp = t_1;
	elseif (y <= -25000.0)
		tmp = t;
	elseif (y <= -1.3e-55)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 0.002)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 1.2e+50)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((x - y) / z);
	tmp = 0.0;
	if (y <= -4.6e+144)
		tmp = t;
	elseif (y <= -1.8e+17)
		tmp = t_1;
	elseif (y <= -25000.0)
		tmp = t;
	elseif (y <= -1.3e-55)
		tmp = (x - y) * (t / z);
	elseif (y <= 0.002)
		tmp = x * (t / (z - y));
	elseif (y <= 1.2e+50)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.6e+144], t, If[LessEqual[y, -1.8e+17], t$95$1, If[LessEqual[y, -25000.0], t, If[LessEqual[y, -1.3e-55], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.002], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+50], t$95$1, t]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.6000000000000003e144 or -1.8e17 < y < -25000 or 1.2000000000000001e50 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 71.2%

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

      2. associate-/l* 74.2%

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

   3. Simplified 74.2%

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

   5. Taylor expanded in y around inf 73.3%

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

   if -4.6000000000000003e144 < y < -1.8e17 or 2e-3 < y < 1.2000000000000001e50

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 63.6%

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

   if -25000 < y < -1.2999999999999999e-55

   1. Initial program 99.5%

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

      1. associate-*l/ 92.2%

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

      2. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 67.6%

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

      1. *-commutative 67.6%

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

      2. associate-/l* 75.3%

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

   7. Simplified 75.3%

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

   if -1.2999999999999999e-55 < y < 2e-3

   1. Initial program 92.8%

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

      1. associate-*l/ 88.7%

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

      2. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

      1. clear-num 94.5%

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

      2. un-div-inv 94.6%

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

   6. Applied egg-rr 94.6%

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

   7. Taylor expanded in x around inf 77.9%

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

      1. *-commutative 77.9%

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

      2. associate-*r/ 83.2%

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

   9. Simplified 83.2%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+144}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -25000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-55}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 0.002:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z - y}\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+121}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-22}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 11000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+64}:\\ \;\;\;\;\frac{t}{\frac{-y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t (- z y)))))
   (if (<= y -4.8e+121)
     t
     (if (<= y -2.1e+15)
       t_1
       (if (<= y -2.8e-22)
         t
         (if (<= y 11000000.0)
           t_1
           (if (<= y 3.1e+43)
             (* t (/ y (- z)))
             (if (<= y 1.2e+64) (/ t (/ (- y) x)) t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / (z - y));
	double tmp;
	if (y <= -4.8e+121) {
		tmp = t;
	} else if (y <= -2.1e+15) {
		tmp = t_1;
	} else if (y <= -2.8e-22) {
		tmp = t;
	} else if (y <= 11000000.0) {
		tmp = t_1;
	} else if (y <= 3.1e+43) {
		tmp = t * (y / -z);
	} else if (y <= 1.2e+64) {
		tmp = t / (-y / 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) :: t_1
    real(8) :: tmp
    t_1 = x * (t / (z - y))
    if (y <= (-4.8d+121)) then
        tmp = t
    else if (y <= (-2.1d+15)) then
        tmp = t_1
    else if (y <= (-2.8d-22)) then
        tmp = t
    else if (y <= 11000000.0d0) then
        tmp = t_1
    else if (y <= 3.1d+43) then
        tmp = t * (y / -z)
    else if (y <= 1.2d+64) then
        tmp = t / (-y / x)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / (z - y));
	double tmp;
	if (y <= -4.8e+121) {
		tmp = t;
	} else if (y <= -2.1e+15) {
		tmp = t_1;
	} else if (y <= -2.8e-22) {
		tmp = t;
	} else if (y <= 11000000.0) {
		tmp = t_1;
	} else if (y <= 3.1e+43) {
		tmp = t * (y / -z);
	} else if (y <= 1.2e+64) {
		tmp = t / (-y / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / (z - y))
	tmp = 0
	if y <= -4.8e+121:
		tmp = t
	elif y <= -2.1e+15:
		tmp = t_1
	elif y <= -2.8e-22:
		tmp = t
	elif y <= 11000000.0:
		tmp = t_1
	elif y <= 3.1e+43:
		tmp = t * (y / -z)
	elif y <= 1.2e+64:
		tmp = t / (-y / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / Float64(z - y)))
	tmp = 0.0
	if (y <= -4.8e+121)
		tmp = t;
	elseif (y <= -2.1e+15)
		tmp = t_1;
	elseif (y <= -2.8e-22)
		tmp = t;
	elseif (y <= 11000000.0)
		tmp = t_1;
	elseif (y <= 3.1e+43)
		tmp = Float64(t * Float64(y / Float64(-z)));
	elseif (y <= 1.2e+64)
		tmp = Float64(t / Float64(Float64(-y) / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / (z - y));
	tmp = 0.0;
	if (y <= -4.8e+121)
		tmp = t;
	elseif (y <= -2.1e+15)
		tmp = t_1;
	elseif (y <= -2.8e-22)
		tmp = t;
	elseif (y <= 11000000.0)
		tmp = t_1;
	elseif (y <= 3.1e+43)
		tmp = t * (y / -z);
	elseif (y <= 1.2e+64)
		tmp = t / (-y / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e+121], t, If[LessEqual[y, -2.1e+15], t$95$1, If[LessEqual[y, -2.8e-22], t, If[LessEqual[y, 11000000.0], t$95$1, If[LessEqual[y, 3.1e+43], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+64], N[(t / N[((-y) / x), $MachinePrecision]), $MachinePrecision], t]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.8e121 or -2.1e15 < y < -2.79999999999999995e-22 or 1.2e64 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 70.8%

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

      2. associate-/l* 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in y around inf 72.3%

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

   if -4.8e121 < y < -2.1e15 or -2.79999999999999995e-22 < y < 1.1e7

   1. Initial program 94.2%

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

      1. associate-*l/ 88.6%

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

      2. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

      1. clear-num 93.1%

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

      2. un-div-inv 93.3%

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

   6. Applied egg-rr 93.3%

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

   7. Taylor expanded in x around inf 72.5%

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

      1. *-commutative 72.5%

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

      2. associate-*r/ 77.9%

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

   9. Simplified 77.9%

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

   if 1.1e7 < y < 3.1000000000000002e43

   1. Initial program 99.7%

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

      1. associate-*l/ 90.8%

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

      2. associate-/l* 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in z around inf 64.5%

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

      1. *-commutative 64.5%

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

      2. associate-/l* 65.0%

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

   7. Simplified 65.0%

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

   8. Taylor expanded in x around 0 56.3%

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

      1. mul-1-neg 56.3%

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

      2. associate-/l* 65.2%

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

      3. distribute-rgt-neg-in 65.2%

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

      4. distribute-frac-neg2 65.2%

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

   10. Simplified 65.2%

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

   if 3.1000000000000002e43 < y < 1.2e64

   1. Initial program 99.7%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 99.2%

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

   3. Simplified 99.2%

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

      1. associate-*r/ 99.7%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. clear-num 99.7%

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

      5. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 66.9%

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

   8. Taylor expanded in z around 0 66.9%

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

      1. neg-mul-1 66.9%

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

      2. distribute-neg-frac 66.9%

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

   10. Simplified 66.9%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+121}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-22}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 11000000:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+64}:\\ \;\;\;\;\frac{t}{\frac{-y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{if}\;y \leq -5 \cdot 10^{+144}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-22}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.00185:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+65}:\\ \;\;\;\;\frac{t}{\frac{-y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x y) (/ t z))))
   (if (<= y -5e+144)
     t
     (if (<= y -1.95e+17)
       t_1
       (if (<= y -2.6e-22)
         t
         (if (<= y 0.00185)
           (* x (/ t (- z y)))
           (if (<= y 4.2e+43)
             t_1
             (if (<= y 2.4e+65) (/ t (/ (- y) x)) t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) * (t / z);
	double tmp;
	if (y <= -5e+144) {
		tmp = t;
	} else if (y <= -1.95e+17) {
		tmp = t_1;
	} else if (y <= -2.6e-22) {
		tmp = t;
	} else if (y <= 0.00185) {
		tmp = x * (t / (z - y));
	} else if (y <= 4.2e+43) {
		tmp = t_1;
	} else if (y <= 2.4e+65) {
		tmp = t / (-y / 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) :: t_1
    real(8) :: tmp
    t_1 = (x - y) * (t / z)
    if (y <= (-5d+144)) then
        tmp = t
    else if (y <= (-1.95d+17)) then
        tmp = t_1
    else if (y <= (-2.6d-22)) then
        tmp = t
    else if (y <= 0.00185d0) then
        tmp = x * (t / (z - y))
    else if (y <= 4.2d+43) then
        tmp = t_1
    else if (y <= 2.4d+65) then
        tmp = t / (-y / x)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) * (t / z);
	double tmp;
	if (y <= -5e+144) {
		tmp = t;
	} else if (y <= -1.95e+17) {
		tmp = t_1;
	} else if (y <= -2.6e-22) {
		tmp = t;
	} else if (y <= 0.00185) {
		tmp = x * (t / (z - y));
	} else if (y <= 4.2e+43) {
		tmp = t_1;
	} else if (y <= 2.4e+65) {
		tmp = t / (-y / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) * (t / z)
	tmp = 0
	if y <= -5e+144:
		tmp = t
	elif y <= -1.95e+17:
		tmp = t_1
	elif y <= -2.6e-22:
		tmp = t
	elif y <= 0.00185:
		tmp = x * (t / (z - y))
	elif y <= 4.2e+43:
		tmp = t_1
	elif y <= 2.4e+65:
		tmp = t / (-y / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) * Float64(t / z))
	tmp = 0.0
	if (y <= -5e+144)
		tmp = t;
	elseif (y <= -1.95e+17)
		tmp = t_1;
	elseif (y <= -2.6e-22)
		tmp = t;
	elseif (y <= 0.00185)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 4.2e+43)
		tmp = t_1;
	elseif (y <= 2.4e+65)
		tmp = Float64(t / Float64(Float64(-y) / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) * (t / z);
	tmp = 0.0;
	if (y <= -5e+144)
		tmp = t;
	elseif (y <= -1.95e+17)
		tmp = t_1;
	elseif (y <= -2.6e-22)
		tmp = t;
	elseif (y <= 0.00185)
		tmp = x * (t / (z - y));
	elseif (y <= 4.2e+43)
		tmp = t_1;
	elseif (y <= 2.4e+65)
		tmp = t / (-y / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e+144], t, If[LessEqual[y, -1.95e+17], t$95$1, If[LessEqual[y, -2.6e-22], t, If[LessEqual[y, 0.00185], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+43], t$95$1, If[LessEqual[y, 2.4e+65], N[(t / N[((-y) / x), $MachinePrecision]), $MachinePrecision], t]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.9999999999999999e144 or -1.95e17 < y < -2.6e-22 or 2.4000000000000002e65 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 69.7%

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

      2. associate-/l* 72.9%

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

   3. Simplified 72.9%

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

   5. Taylor expanded in y around inf 74.7%

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

   if -4.9999999999999999e144 < y < -1.95e17 or 0.0018500000000000001 < y < 4.20000000000000003e43

   1. Initial program 99.7%

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

      1. associate-*l/ 89.0%

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

      2. associate-/l* 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in z around inf 57.4%

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

      1. *-commutative 57.4%

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

      2. associate-/l* 57.3%

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

   7. Simplified 57.3%

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

   if -2.6e-22 < y < 0.0018500000000000001

   1. Initial program 93.3%

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

      1. associate-*l/ 88.9%

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

      2. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

      1. clear-num 94.9%

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

      2. un-div-inv 95.0%

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

   6. Applied egg-rr 95.0%

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

   7. Taylor expanded in x around inf 75.8%

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

      1. *-commutative 75.8%

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

      2. associate-*r/ 81.4%

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

   9. Simplified 81.4%

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

   if 4.20000000000000003e43 < y < 2.4000000000000002e65

   1. Initial program 99.7%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 99.2%

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

   3. Simplified 99.2%

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

      1. associate-*r/ 99.7%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. clear-num 99.7%

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

      5. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 66.9%

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

   8. Taylor expanded in z around 0 66.9%

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

      1. neg-mul-1 66.9%

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

      2. distribute-neg-frac 66.9%

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

   10. Simplified 66.9%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+144}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{+17}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-22}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.00185:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+43}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+65}:\\ \;\;\;\;\frac{t}{\frac{-y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x - y}{z}\\ t_2 := t - x \cdot \frac{t}{y}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+144}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 0.0022:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- x y) z))) (t_2 (- t (* x (/ t y)))))
   (if (<= y -5.5e+144)
     t_2
     (if (<= y -1.2e+62)
       t_1
       (if (<= y -3.5e-23)
         t_2
         (if (<= y 0.0022)
           (* x (/ t (- z y)))
           (if (<= y 6.4e+43) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t - (x * (t / y));
	double tmp;
	if (y <= -5.5e+144) {
		tmp = t_2;
	} else if (y <= -1.2e+62) {
		tmp = t_1;
	} else if (y <= -3.5e-23) {
		tmp = t_2;
	} else if (y <= 0.0022) {
		tmp = x * (t / (z - y));
	} else if (y <= 6.4e+43) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = t * ((x - y) / z)
    t_2 = t - (x * (t / y))
    if (y <= (-5.5d+144)) then
        tmp = t_2
    else if (y <= (-1.2d+62)) then
        tmp = t_1
    else if (y <= (-3.5d-23)) then
        tmp = t_2
    else if (y <= 0.0022d0) then
        tmp = x * (t / (z - y))
    else if (y <= 6.4d+43) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t - (x * (t / y));
	double tmp;
	if (y <= -5.5e+144) {
		tmp = t_2;
	} else if (y <= -1.2e+62) {
		tmp = t_1;
	} else if (y <= -3.5e-23) {
		tmp = t_2;
	} else if (y <= 0.0022) {
		tmp = x * (t / (z - y));
	} else if (y <= 6.4e+43) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((x - y) / z)
	t_2 = t - (x * (t / y))
	tmp = 0
	if y <= -5.5e+144:
		tmp = t_2
	elif y <= -1.2e+62:
		tmp = t_1
	elif y <= -3.5e-23:
		tmp = t_2
	elif y <= 0.0022:
		tmp = x * (t / (z - y))
	elif y <= 6.4e+43:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(x - y) / z))
	t_2 = Float64(t - Float64(x * Float64(t / y)))
	tmp = 0.0
	if (y <= -5.5e+144)
		tmp = t_2;
	elseif (y <= -1.2e+62)
		tmp = t_1;
	elseif (y <= -3.5e-23)
		tmp = t_2;
	elseif (y <= 0.0022)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 6.4e+43)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((x - y) / z);
	t_2 = t - (x * (t / y));
	tmp = 0.0;
	if (y <= -5.5e+144)
		tmp = t_2;
	elseif (y <= -1.2e+62)
		tmp = t_1;
	elseif (y <= -3.5e-23)
		tmp = t_2;
	elseif (y <= 0.0022)
		tmp = x * (t / (z - y));
	elseif (y <= 6.4e+43)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+144], t$95$2, If[LessEqual[y, -1.2e+62], t$95$1, If[LessEqual[y, -3.5e-23], t$95$2, If[LessEqual[y, 0.0022], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e+43], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.50000000000000022e144 or -1.2e62 < y < -3.49999999999999993e-23 or 6.40000000000000029e43 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 73.1%

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

      2. associate-/l* 76.4%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in z around 0 63.0%

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

      1. associate-*r/ 63.0%

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

      2. mul-1-neg 63.0%

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

      3. distribute-lft-neg-out 63.0%

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

      4. *-commutative 63.0%

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

   7. Simplified 63.0%

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

   8. Taylor expanded in x around 0 77.7%

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

      1. mul-1-neg 77.7%

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

      2. unsub-neg 77.7%

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

   10. Simplified 77.7%

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

       1. *-commutative 77.7%

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

       2. associate-/l* 82.9%

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

   12. Applied egg-rr 82.9%

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

   if -5.50000000000000022e144 < y < -1.2e62 or 0.00220000000000000013 < y < 6.40000000000000029e43

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 74.5%

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

   if -3.49999999999999993e-23 < y < 0.00220000000000000013

   1. Initial program 93.3%

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

      1. associate-*l/ 88.8%

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

      2. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

      1. clear-num 94.9%

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

      2. un-div-inv 95.0%

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

   6. Applied egg-rr 95.0%

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

   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/ 81.7%

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

   9. Simplified 81.7%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+144}:\\ \;\;\;\;t - x \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-23}:\\ \;\;\;\;t - x \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 0.0022:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x - y}{z}\\ t_2 := t - t \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+144}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 0.00165:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- x y) z))) (t_2 (- t (* t (/ x y)))))
   (if (<= y -4.6e+144)
     t_2
     (if (<= y -1.2e+62)
       t_1
       (if (<= y -2.4e-25)
         t_2
         (if (<= y 0.00165)
           (* x (/ t (- z y)))
           (if (<= y 9.5e+41) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t - (t * (x / y));
	double tmp;
	if (y <= -4.6e+144) {
		tmp = t_2;
	} else if (y <= -1.2e+62) {
		tmp = t_1;
	} else if (y <= -2.4e-25) {
		tmp = t_2;
	} else if (y <= 0.00165) {
		tmp = x * (t / (z - y));
	} else if (y <= 9.5e+41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = t * ((x - y) / z)
    t_2 = t - (t * (x / y))
    if (y <= (-4.6d+144)) then
        tmp = t_2
    else if (y <= (-1.2d+62)) then
        tmp = t_1
    else if (y <= (-2.4d-25)) then
        tmp = t_2
    else if (y <= 0.00165d0) then
        tmp = x * (t / (z - y))
    else if (y <= 9.5d+41) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t - (t * (x / y));
	double tmp;
	if (y <= -4.6e+144) {
		tmp = t_2;
	} else if (y <= -1.2e+62) {
		tmp = t_1;
	} else if (y <= -2.4e-25) {
		tmp = t_2;
	} else if (y <= 0.00165) {
		tmp = x * (t / (z - y));
	} else if (y <= 9.5e+41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((x - y) / z)
	t_2 = t - (t * (x / y))
	tmp = 0
	if y <= -4.6e+144:
		tmp = t_2
	elif y <= -1.2e+62:
		tmp = t_1
	elif y <= -2.4e-25:
		tmp = t_2
	elif y <= 0.00165:
		tmp = x * (t / (z - y))
	elif y <= 9.5e+41:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(x - y) / z))
	t_2 = Float64(t - Float64(t * Float64(x / y)))
	tmp = 0.0
	if (y <= -4.6e+144)
		tmp = t_2;
	elseif (y <= -1.2e+62)
		tmp = t_1;
	elseif (y <= -2.4e-25)
		tmp = t_2;
	elseif (y <= 0.00165)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 9.5e+41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((x - y) / z);
	t_2 = t - (t * (x / y));
	tmp = 0.0;
	if (y <= -4.6e+144)
		tmp = t_2;
	elseif (y <= -1.2e+62)
		tmp = t_1;
	elseif (y <= -2.4e-25)
		tmp = t_2;
	elseif (y <= 0.00165)
		tmp = x * (t / (z - y));
	elseif (y <= 9.5e+41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.6e+144], t$95$2, If[LessEqual[y, -1.2e+62], t$95$1, If[LessEqual[y, -2.4e-25], t$95$2, If[LessEqual[y, 0.00165], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e+41], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.6000000000000003e144 or -1.2e62 < y < -2.40000000000000009e-25 or 9.4999999999999996e41 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 73.1%

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

      2. associate-/l* 76.4%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in z around 0 63.0%

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

      1. associate-*r/ 63.0%

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

      2. mul-1-neg 63.0%

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

      3. distribute-lft-neg-out 63.0%

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

      4. *-commutative 63.0%

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

   7. Simplified 63.0%

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

   8. Taylor expanded in x around 0 77.7%

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

      1. mul-1-neg 77.7%

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

      2. unsub-neg 77.7%

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

   10. Simplified 77.7%

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

       1. associate-/l* 87.8%

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

       2. *-commutative 87.8%

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

   12. Applied egg-rr 87.8%

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

   if -4.6000000000000003e144 < y < -1.2e62 or 0.00165 < y < 9.4999999999999996e41

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 74.5%

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

   if -2.40000000000000009e-25 < y < 0.00165

   1. Initial program 93.3%

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

      1. associate-*l/ 88.8%

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

      2. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

      1. clear-num 94.9%

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

      2. un-div-inv 95.0%

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

   6. Applied egg-rr 95.0%

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

   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/ 81.7%

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

   9. Simplified 81.7%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+144}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-25}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 0.00165:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+41}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{z}{x - y}}\\ t_2 := t - t \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+144}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 0.00165:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (/ z (- x y)))) (t_2 (- t (* t (/ x y)))))
   (if (<= y -4.6e+144)
     t_2
     (if (<= y -5.2e+61)
       t_1
       (if (<= y -1.02e-26)
         t_2
         (if (<= y 0.00165)
           (* x (/ t (- z y)))
           (if (<= y 3.1e+42) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (z / (x - y));
	double t_2 = t - (t * (x / y));
	double tmp;
	if (y <= -4.6e+144) {
		tmp = t_2;
	} else if (y <= -5.2e+61) {
		tmp = t_1;
	} else if (y <= -1.02e-26) {
		tmp = t_2;
	} else if (y <= 0.00165) {
		tmp = x * (t / (z - y));
	} else if (y <= 3.1e+42) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = t / (z / (x - y))
    t_2 = t - (t * (x / y))
    if (y <= (-4.6d+144)) then
        tmp = t_2
    else if (y <= (-5.2d+61)) then
        tmp = t_1
    else if (y <= (-1.02d-26)) then
        tmp = t_2
    else if (y <= 0.00165d0) then
        tmp = x * (t / (z - y))
    else if (y <= 3.1d+42) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t / (z / (x - y));
	double t_2 = t - (t * (x / y));
	double tmp;
	if (y <= -4.6e+144) {
		tmp = t_2;
	} else if (y <= -5.2e+61) {
		tmp = t_1;
	} else if (y <= -1.02e-26) {
		tmp = t_2;
	} else if (y <= 0.00165) {
		tmp = x * (t / (z - y));
	} else if (y <= 3.1e+42) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (z / (x - y))
	t_2 = t - (t * (x / y))
	tmp = 0
	if y <= -4.6e+144:
		tmp = t_2
	elif y <= -5.2e+61:
		tmp = t_1
	elif y <= -1.02e-26:
		tmp = t_2
	elif y <= 0.00165:
		tmp = x * (t / (z - y))
	elif y <= 3.1e+42:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(z / Float64(x - y)))
	t_2 = Float64(t - Float64(t * Float64(x / y)))
	tmp = 0.0
	if (y <= -4.6e+144)
		tmp = t_2;
	elseif (y <= -5.2e+61)
		tmp = t_1;
	elseif (y <= -1.02e-26)
		tmp = t_2;
	elseif (y <= 0.00165)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 3.1e+42)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (z / (x - y));
	t_2 = t - (t * (x / y));
	tmp = 0.0;
	if (y <= -4.6e+144)
		tmp = t_2;
	elseif (y <= -5.2e+61)
		tmp = t_1;
	elseif (y <= -1.02e-26)
		tmp = t_2;
	elseif (y <= 0.00165)
		tmp = x * (t / (z - y));
	elseif (y <= 3.1e+42)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.6e+144], t$95$2, If[LessEqual[y, -5.2e+61], t$95$1, If[LessEqual[y, -1.02e-26], t$95$2, If[LessEqual[y, 0.00165], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e+42], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.6000000000000003e144 or -5.19999999999999945e61 < y < -1.02e-26 or 3.1000000000000002e42 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 73.1%

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

      2. associate-/l* 76.4%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in z around 0 63.0%

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

      1. associate-*r/ 63.0%

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

      2. mul-1-neg 63.0%

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

      3. distribute-lft-neg-out 63.0%

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

      4. *-commutative 63.0%

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

   7. Simplified 63.0%

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

   8. Taylor expanded in x around 0 77.7%

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

      1. mul-1-neg 77.7%

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

      2. unsub-neg 77.7%

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

   10. Simplified 77.7%

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

       1. associate-/l* 87.8%

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

       2. *-commutative 87.8%

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

   12. Applied egg-rr 87.8%

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

   if -4.6000000000000003e144 < y < -5.19999999999999945e61 or 0.00165 < y < 3.1000000000000002e42

   1. Initial program 99.6%

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

      1. associate-*l/ 92.1%

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

      2. associate-/l* 86.6%

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

   3. Simplified 86.6%

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

      1. associate-*r/ 92.1%

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

      2. associate-*l/ 99.6%

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

      3. *-commutative 99.6%

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

      4. clear-num 99.3%

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

      5. un-div-inv 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in z around inf 74.6%

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

   if -1.02e-26 < y < 0.00165

   1. Initial program 93.3%

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

      1. associate-*l/ 88.8%

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

      2. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

      1. clear-num 94.9%

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

      2. un-div-inv 95.0%

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

   6. Applied egg-rr 95.0%

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

   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/ 81.7%

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

   9. Simplified 81.7%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+144}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+61}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-26}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 0.00165:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+42}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - t \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+62}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.00176:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+45}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- t (* t (/ x y)))))
   (if (<= y -4.6e+144)
     t_1
     (if (<= y -1.2e+62)
       (/ (* (- x y) t) z)
       (if (<= y -1.5e-23)
         t_1
         (if (<= y 0.00176)
           (* x (/ t (- z y)))
           (if (<= y 5.4e+45) (/ t (/ z (- x y))) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t - (t * (x / y));
	double tmp;
	if (y <= -4.6e+144) {
		tmp = t_1;
	} else if (y <= -1.2e+62) {
		tmp = ((x - y) * t) / z;
	} else if (y <= -1.5e-23) {
		tmp = t_1;
	} else if (y <= 0.00176) {
		tmp = x * (t / (z - y));
	} else if (y <= 5.4e+45) {
		tmp = t / (z / (x - y));
	} else {
		tmp = t_1;
	}
	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 - (t * (x / y))
    if (y <= (-4.6d+144)) then
        tmp = t_1
    else if (y <= (-1.2d+62)) then
        tmp = ((x - y) * t) / z
    else if (y <= (-1.5d-23)) then
        tmp = t_1
    else if (y <= 0.00176d0) then
        tmp = x * (t / (z - y))
    else if (y <= 5.4d+45) then
        tmp = t / (z / (x - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t - (t * (x / y));
	double tmp;
	if (y <= -4.6e+144) {
		tmp = t_1;
	} else if (y <= -1.2e+62) {
		tmp = ((x - y) * t) / z;
	} else if (y <= -1.5e-23) {
		tmp = t_1;
	} else if (y <= 0.00176) {
		tmp = x * (t / (z - y));
	} else if (y <= 5.4e+45) {
		tmp = t / (z / (x - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t - (t * (x / y))
	tmp = 0
	if y <= -4.6e+144:
		tmp = t_1
	elif y <= -1.2e+62:
		tmp = ((x - y) * t) / z
	elif y <= -1.5e-23:
		tmp = t_1
	elif y <= 0.00176:
		tmp = x * (t / (z - y))
	elif y <= 5.4e+45:
		tmp = t / (z / (x - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t - Float64(t * Float64(x / y)))
	tmp = 0.0
	if (y <= -4.6e+144)
		tmp = t_1;
	elseif (y <= -1.2e+62)
		tmp = Float64(Float64(Float64(x - y) * t) / z);
	elseif (y <= -1.5e-23)
		tmp = t_1;
	elseif (y <= 0.00176)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 5.4e+45)
		tmp = Float64(t / Float64(z / Float64(x - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t - (t * (x / y));
	tmp = 0.0;
	if (y <= -4.6e+144)
		tmp = t_1;
	elseif (y <= -1.2e+62)
		tmp = ((x - y) * t) / z;
	elseif (y <= -1.5e-23)
		tmp = t_1;
	elseif (y <= 0.00176)
		tmp = x * (t / (z - y));
	elseif (y <= 5.4e+45)
		tmp = t / (z / (x - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.6e+144], t$95$1, If[LessEqual[y, -1.2e+62], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -1.5e-23], t$95$1, If[LessEqual[y, 0.00176], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e+45], N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.6000000000000003e144 or -1.2e62 < y < -1.50000000000000001e-23 or 5.39999999999999968e45 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 73.1%

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

      2. associate-/l* 76.4%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in z around 0 63.0%

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

      1. associate-*r/ 63.0%

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

      2. mul-1-neg 63.0%

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

      3. distribute-lft-neg-out 63.0%

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

      4. *-commutative 63.0%

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

   7. Simplified 63.0%

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

   8. Taylor expanded in x around 0 77.7%

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

      1. mul-1-neg 77.7%

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

      2. unsub-neg 77.7%

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

   10. Simplified 77.7%

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

       1. associate-/l* 87.8%

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

       2. *-commutative 87.8%

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

   12. Applied egg-rr 87.8%

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

   if -4.6000000000000003e144 < y < -1.2e62

   1. Initial program 99.4%

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

      1. associate-*l/ 99.8%

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

      2. associate-/l* 76.5%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in z around inf 81.6%

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

   if -1.50000000000000001e-23 < y < 0.00176000000000000006

   1. Initial program 93.3%

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

      1. associate-*l/ 88.8%

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

      2. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

      1. clear-num 94.9%

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

      2. un-div-inv 95.0%

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

   6. Applied egg-rr 95.0%

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

   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/ 81.7%

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

   9. Simplified 81.7%

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

   if 0.00176000000000000006 < y < 5.39999999999999968e45

   1. Initial program 99.7%

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

      1. associate-*l/ 88.5%

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

      2. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

      1. associate-*r/ 88.5%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. clear-num 99.5%

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

      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 z around inf 71.4%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+144}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+62}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-23}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 0.00176:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+45}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - t \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -4.7 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{+59}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8200000:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+48}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- t (* t (/ x y)))))
   (if (<= y -4.7e+144)
     t_1
     (if (<= y -1.95e+59)
       (/ (* (- x y) t) z)
       (if (<= y -2.2e-24)
         t_1
         (if (<= y 8200000.0)
           (* x (/ t (- z y)))
           (if (<= y 2.55e+48) (* y (/ t (- y z))) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t - (t * (x / y));
	double tmp;
	if (y <= -4.7e+144) {
		tmp = t_1;
	} else if (y <= -1.95e+59) {
		tmp = ((x - y) * t) / z;
	} else if (y <= -2.2e-24) {
		tmp = t_1;
	} else if (y <= 8200000.0) {
		tmp = x * (t / (z - y));
	} else if (y <= 2.55e+48) {
		tmp = y * (t / (y - z));
	} else {
		tmp = t_1;
	}
	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 - (t * (x / y))
    if (y <= (-4.7d+144)) then
        tmp = t_1
    else if (y <= (-1.95d+59)) then
        tmp = ((x - y) * t) / z
    else if (y <= (-2.2d-24)) then
        tmp = t_1
    else if (y <= 8200000.0d0) then
        tmp = x * (t / (z - y))
    else if (y <= 2.55d+48) then
        tmp = y * (t / (y - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t - (t * (x / y));
	double tmp;
	if (y <= -4.7e+144) {
		tmp = t_1;
	} else if (y <= -1.95e+59) {
		tmp = ((x - y) * t) / z;
	} else if (y <= -2.2e-24) {
		tmp = t_1;
	} else if (y <= 8200000.0) {
		tmp = x * (t / (z - y));
	} else if (y <= 2.55e+48) {
		tmp = y * (t / (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t - (t * (x / y))
	tmp = 0
	if y <= -4.7e+144:
		tmp = t_1
	elif y <= -1.95e+59:
		tmp = ((x - y) * t) / z
	elif y <= -2.2e-24:
		tmp = t_1
	elif y <= 8200000.0:
		tmp = x * (t / (z - y))
	elif y <= 2.55e+48:
		tmp = y * (t / (y - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t - Float64(t * Float64(x / y)))
	tmp = 0.0
	if (y <= -4.7e+144)
		tmp = t_1;
	elseif (y <= -1.95e+59)
		tmp = Float64(Float64(Float64(x - y) * t) / z);
	elseif (y <= -2.2e-24)
		tmp = t_1;
	elseif (y <= 8200000.0)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 2.55e+48)
		tmp = Float64(y * Float64(t / Float64(y - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t - (t * (x / y));
	tmp = 0.0;
	if (y <= -4.7e+144)
		tmp = t_1;
	elseif (y <= -1.95e+59)
		tmp = ((x - y) * t) / z;
	elseif (y <= -2.2e-24)
		tmp = t_1;
	elseif (y <= 8200000.0)
		tmp = x * (t / (z - y));
	elseif (y <= 2.55e+48)
		tmp = y * (t / (y - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.7e+144], t$95$1, If[LessEqual[y, -1.95e+59], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -2.2e-24], t$95$1, If[LessEqual[y, 8200000.0], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.55e+48], N[(y * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.7000000000000002e144 or -1.95000000000000011e59 < y < -2.20000000000000002e-24 or 2.5499999999999999e48 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 73.1%

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

      2. associate-/l* 76.4%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in z around 0 63.0%

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

      1. associate-*r/ 63.0%

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

      2. mul-1-neg 63.0%

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

      3. distribute-lft-neg-out 63.0%

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

      4. *-commutative 63.0%

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

   7. Simplified 63.0%

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

   8. Taylor expanded in x around 0 77.7%

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

      1. mul-1-neg 77.7%

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

      2. unsub-neg 77.7%

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

   10. Simplified 77.7%

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

       1. associate-/l* 87.8%

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

       2. *-commutative 87.8%

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

   12. Applied egg-rr 87.8%

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

   if -4.7000000000000002e144 < y < -1.95000000000000011e59

   1. Initial program 99.4%

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

      1. associate-*l/ 99.8%

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

      2. associate-/l* 76.5%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in z around inf 81.6%

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

   if -2.20000000000000002e-24 < y < 8.2e6

   1. Initial program 93.5%

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

      1. associate-*l/ 88.6%

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

      2. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

      1. clear-num 94.9%

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

      2. un-div-inv 95.1%

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

   6. Applied egg-rr 95.1%

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

   7. Taylor expanded in x around inf 74.9%

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

      1. *-commutative 74.9%

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

      2. associate-*r/ 80.9%

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

   9. Simplified 80.9%

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

   if 8.2e6 < y < 2.5499999999999999e48

   1. Initial program 99.7%

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

      1. associate-*l/ 90.8%

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

      2. associate-/l* 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in x around 0 73.7%

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

      1. mul-1-neg 73.7%

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

      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%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+144}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{+59}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-24}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 8200000:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+48}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+121}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-22}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.75e+121)
   t
   (if (<= y -1.5e+18)
     (* t (/ x (- z y)))
     (if (<= y -2.8e-22) t (if (<= y 2.55e+65) (* x (/ t (- z y))) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.75e+121) {
		tmp = t;
	} else if (y <= -1.5e+18) {
		tmp = t * (x / (z - y));
	} else if (y <= -2.8e-22) {
		tmp = t;
	} else if (y <= 2.55e+65) {
		tmp = x * (t / (z - y));
	} 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 <= (-1.75d+121)) then
        tmp = t
    else if (y <= (-1.5d+18)) then
        tmp = t * (x / (z - y))
    else if (y <= (-2.8d-22)) then
        tmp = t
    else if (y <= 2.55d+65) then
        tmp = x * (t / (z - y))
    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 <= -1.75e+121) {
		tmp = t;
	} else if (y <= -1.5e+18) {
		tmp = t * (x / (z - y));
	} else if (y <= -2.8e-22) {
		tmp = t;
	} else if (y <= 2.55e+65) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.75e+121:
		tmp = t
	elif y <= -1.5e+18:
		tmp = t * (x / (z - y))
	elif y <= -2.8e-22:
		tmp = t
	elif y <= 2.55e+65:
		tmp = x * (t / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.75e+121)
		tmp = t;
	elseif (y <= -1.5e+18)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (y <= -2.8e-22)
		tmp = t;
	elseif (y <= 2.55e+65)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.75e+121)
		tmp = t;
	elseif (y <= -1.5e+18)
		tmp = t * (x / (z - y));
	elseif (y <= -2.8e-22)
		tmp = t;
	elseif (y <= 2.55e+65)
		tmp = x * (t / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.75e+121], t, If[LessEqual[y, -1.5e+18], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.8e-22], t, If[LessEqual[y, 2.55e+65], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.75e121 or -1.5e18 < y < -2.79999999999999995e-22 or 2.54999999999999994e65 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 70.8%

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

      2. associate-/l* 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in y around inf 72.3%

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

   if -1.75e121 < y < -1.5e18

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 64.2%

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

   if -2.79999999999999995e-22 < y < 2.54999999999999994e65

   1. Initial program 94.2%

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

      1. associate-*l/ 89.2%

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

      2. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

      1. clear-num 94.2%

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

      2. un-div-inv 94.4%

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

   6. Applied egg-rr 94.4%

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

   7. Taylor expanded in x around inf 71.3%

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

      1. *-commutative 71.3%

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

      2. associate-*r/ 75.8%

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

   9. Simplified 75.8%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+121}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-22}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-28}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.35:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.5e-28)
   t
   (if (<= y 0.35) (* x (/ t z)) (if (<= y 1.7e+50) (* t (/ y (- z))) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.5e-28) {
		tmp = t;
	} else if (y <= 0.35) {
		tmp = x * (t / z);
	} else if (y <= 1.7e+50) {
		tmp = t * (y / -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 <= (-8.5d-28)) then
        tmp = t
    else if (y <= 0.35d0) then
        tmp = x * (t / z)
    else if (y <= 1.7d+50) then
        tmp = t * (y / -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 <= -8.5e-28) {
		tmp = t;
	} else if (y <= 0.35) {
		tmp = x * (t / z);
	} else if (y <= 1.7e+50) {
		tmp = t * (y / -z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.5e-28:
		tmp = t
	elif y <= 0.35:
		tmp = x * (t / z)
	elif y <= 1.7e+50:
		tmp = t * (y / -z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.5e-28)
		tmp = t;
	elseif (y <= 0.35)
		tmp = Float64(x * Float64(t / z));
	elseif (y <= 1.7e+50)
		tmp = Float64(t * Float64(y / Float64(-z)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8.5e-28)
		tmp = t;
	elseif (y <= 0.35)
		tmp = x * (t / z);
	elseif (y <= 1.7e+50)
		tmp = t * (y / -z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.5e-28], t, If[LessEqual[y, 0.35], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+50], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.49999999999999925e-28 or 1.6999999999999999e50 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 75.2%

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

      2. associate-/l* 76.4%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in y around inf 62.1%

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

   if -8.49999999999999925e-28 < y < 0.34999999999999998

   1. Initial program 93.3%

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

      1. associate-*l/ 88.2%

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

      2. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in y around 0 63.1%

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

      1. *-commutative 63.1%

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

      2. associate-/l* 69.1%

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

   7. Simplified 69.1%

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

   if 0.34999999999999998 < y < 1.6999999999999999e50

   1. Initial program 99.7%

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

      1. associate-*l/ 93.7%

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

      2. associate-/l* 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in z around inf 63.7%

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

      1. *-commutative 63.7%

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

      2. associate-/l* 63.4%

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

   7. Simplified 63.4%

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

   8. Taylor expanded in x around 0 52.0%

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

      1. mul-1-neg 52.0%

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

      2. associate-/l* 58.1%

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

      3. distribute-rgt-neg-in 58.1%

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

      4. distribute-frac-neg2 58.1%

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

   10. Simplified 58.1%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-28}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.35:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 89.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+192} \lor \neg \left(y \leq 6 \cdot 10^{+114}\right):\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9e+192) (not (<= y 6e+114)))
   (- t (* t (/ x y)))
   (* (- x y) (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9e+192) || !(y <= 6e+114)) {
		tmp = t - (t * (x / y));
	} else {
		tmp = (x - y) * (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 <= (-9d+192)) .or. (.not. (y <= 6d+114))) then
        tmp = t - (t * (x / y))
    else
        tmp = (x - y) * (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 <= -9e+192) || !(y <= 6e+114)) {
		tmp = t - (t * (x / y));
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9e+192) or not (y <= 6e+114):
		tmp = t - (t * (x / y))
	else:
		tmp = (x - y) * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9e+192) || !(y <= 6e+114))
		tmp = Float64(t - Float64(t * Float64(x / y)));
	else
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -9e+192) || ~((y <= 6e+114)))
		tmp = t - (t * (x / y));
	else
		tmp = (x - y) * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9e+192], N[Not[LessEqual[y, 6e+114]], $MachinePrecision]], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9e192 or 6.0000000000000001e114 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 67.8%

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

      2. associate-/l* 68.9%

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

   3. Simplified 68.9%

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

   5. Taylor expanded in z around 0 64.6%

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

      1. associate-*r/ 64.6%

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

      2. mul-1-neg 64.6%

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

      3. distribute-lft-neg-out 64.6%

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

      4. *-commutative 64.6%

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

   7. Simplified 64.6%

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

   8. Taylor expanded in x around 0 81.9%

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

      1. mul-1-neg 81.9%

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

      2. unsub-neg 81.9%

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

   10. Simplified 81.9%

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

       1. associate-/l* 95.0%

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

       2. *-commutative 95.0%

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

   12. Applied egg-rr 95.0%

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

   if -9e192 < y < 6.0000000000000001e114

   1. Initial program 95.3%

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

      1. associate-*l/ 87.9%

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

      2. associate-/l* 93.5%

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

   3. Simplified 93.5%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+192} \lor \neg \left(y \leq 6 \cdot 10^{+114}\right):\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-27}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 21000000000:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.5e-27) t (if (<= y 21000000000.0) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.5e-27) {
		tmp = t;
	} else if (y <= 21000000000.0) {
		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 <= (-1.5d-27)) then
        tmp = t
    else if (y <= 21000000000.0d0) 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 <= -1.5e-27) {
		tmp = t;
	} else if (y <= 21000000000.0) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.5e-27:
		tmp = t
	elif y <= 21000000000.0:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.5e-27)
		tmp = t;
	elseif (y <= 21000000000.0)
		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 <= -1.5e-27)
		tmp = t;
	elseif (y <= 21000000000.0)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.5e-27], t, If[LessEqual[y, 21000000000.0], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5000000000000001e-27 or 2.1e10 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 76.3%

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

      2. associate-/l* 77.1%

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

   3. Simplified 77.1%

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

   5. Taylor expanded in y around inf 59.2%

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

   if -1.5000000000000001e-27 < y < 2.1e10

   1. Initial program 93.6%

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

      1. associate-*l/ 88.8%

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

      2. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in y around 0 62.1%

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

      1. *-commutative 62.1%

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

      2. associate-/l* 67.7%

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

   7. Simplified 67.7%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-27}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 21000000000:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 34.9% 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 96.3%

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

   1. associate-*l/ 83.3%

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

   2. associate-/l* 87.8%

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

3. Simplified 87.8%

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

5. Taylor expanded in y around inf 31.5%

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

6. Final simplification 31.5%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 96.8% 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 2024066 
(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))