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

Percentage Accurate: 97.0% → 97.0%

Time: 7.5s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.8%

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

2. Final simplification 96.8%

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

Alternative 2: 73.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - x}{y}\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5200000:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-85} \lor \neg \left(y \leq 1.9 \cdot 10^{-16}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- y x) y))))
   (if (<= y -1.8e+68)
     t_1
     (if (<= y -5200000.0)
       (* t (/ (- x y) z))
       (if (or (<= y -1.25e-85) (not (<= y 1.9e-16)))
         t_1
         (* t (/ x (- z y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((y - x) / y);
	double tmp;
	if (y <= -1.8e+68) {
		tmp = t_1;
	} else if (y <= -5200000.0) {
		tmp = t * ((x - y) / z);
	} else if ((y <= -1.25e-85) || !(y <= 1.9e-16)) {
		tmp = t_1;
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - x) / y)
    if (y <= (-1.8d+68)) then
        tmp = t_1
    else if (y <= (-5200000.0d0)) then
        tmp = t * ((x - y) / z)
    else if ((y <= (-1.25d-85)) .or. (.not. (y <= 1.9d-16))) then
        tmp = t_1
    else
        tmp = t * (x / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * ((y - x) / y);
	double tmp;
	if (y <= -1.8e+68) {
		tmp = t_1;
	} else if (y <= -5200000.0) {
		tmp = t * ((x - y) / z);
	} else if ((y <= -1.25e-85) || !(y <= 1.9e-16)) {
		tmp = t_1;
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((y - x) / y)
	tmp = 0
	if y <= -1.8e+68:
		tmp = t_1
	elif y <= -5200000.0:
		tmp = t * ((x - y) / z)
	elif (y <= -1.25e-85) or not (y <= 1.9e-16):
		tmp = t_1
	else:
		tmp = t * (x / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(y - x) / y))
	tmp = 0.0
	if (y <= -1.8e+68)
		tmp = t_1;
	elseif (y <= -5200000.0)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif ((y <= -1.25e-85) || !(y <= 1.9e-16))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(x / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((y - x) / y);
	tmp = 0.0;
	if (y <= -1.8e+68)
		tmp = t_1;
	elseif (y <= -5200000.0)
		tmp = t * ((x - y) / z);
	elseif ((y <= -1.25e-85) || ~((y <= 1.9e-16)))
		tmp = t_1;
	else
		tmp = t * (x / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+68], t$95$1, If[LessEqual[y, -5200000.0], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.25e-85], N[Not[LessEqual[y, 1.9e-16]], $MachinePrecision]], t$95$1, N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7999999999999999e68 or -5.2e6 < y < -1.25e-85 or 1.90000000000000006e-16 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 79.1%

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

      2. *-commutative 79.1%

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

      3. associate-*l/ 74.9%

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

   3. Simplified 74.9%

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

   4. Taylor expanded in z around 0 66.2%

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

      1. associate-*r/ 66.2%

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

      2. neg-mul-1 66.2%

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

      3. distribute-rgt-neg-in 66.2%

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

      4. associate-/l* 84.3%

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

      5. neg-sub0 84.3%

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

      6. associate--r- 84.3%

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

      7. neg-sub0 84.3%

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

   6. Simplified 84.3%

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

   7. Taylor expanded in t around 0 66.2%

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

      1. associate-/l* 84.3%

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

   9. Simplified 84.3%

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

       1. clear-num 84.2%

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

       2. associate-/r/ 84.3%

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

       3. clear-num 84.3%

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

   11. Applied egg-rr 84.3%

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

   if -1.7999999999999999e68 < y < -5.2e6

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 85.2%

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

   if -1.25e-85 < y < 1.90000000000000006e-16

   1. Initial program 92.4%

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

   2. Taylor expanded in x around inf 86.0%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq -5200000:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-85} \lor \neg \left(y \leq 1.9 \cdot 10^{-16}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]

Alternative 3: 73.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{y}{y - x}}\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1300000:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (/ y (- y x)))))
   (if (<= y -1.8e+68)
     t_1
     (if (<= y -1300000.0)
       (* t (/ (- x y) z))
       (if (<= y -1.16e-85)
         t_1
         (if (<= y 4.5e-16) (* t (/ x (- z y))) (* t (/ (- y x) y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (y / (y - x));
	double tmp;
	if (y <= -1.8e+68) {
		tmp = t_1;
	} else if (y <= -1300000.0) {
		tmp = t * ((x - y) / z);
	} else if (y <= -1.16e-85) {
		tmp = t_1;
	} else if (y <= 4.5e-16) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t * ((y - x) / 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) :: t_1
    real(8) :: tmp
    t_1 = t / (y / (y - x))
    if (y <= (-1.8d+68)) then
        tmp = t_1
    else if (y <= (-1300000.0d0)) then
        tmp = t * ((x - y) / z)
    else if (y <= (-1.16d-85)) then
        tmp = t_1
    else if (y <= 4.5d-16) then
        tmp = t * (x / (z - y))
    else
        tmp = t * ((y - x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t / (y / (y - x));
	double tmp;
	if (y <= -1.8e+68) {
		tmp = t_1;
	} else if (y <= -1300000.0) {
		tmp = t * ((x - y) / z);
	} else if (y <= -1.16e-85) {
		tmp = t_1;
	} else if (y <= 4.5e-16) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t * ((y - x) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (y / (y - x))
	tmp = 0
	if y <= -1.8e+68:
		tmp = t_1
	elif y <= -1300000.0:
		tmp = t * ((x - y) / z)
	elif y <= -1.16e-85:
		tmp = t_1
	elif y <= 4.5e-16:
		tmp = t * (x / (z - y))
	else:
		tmp = t * ((y - x) / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(y / Float64(y - x)))
	tmp = 0.0
	if (y <= -1.8e+68)
		tmp = t_1;
	elseif (y <= -1300000.0)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (y <= -1.16e-85)
		tmp = t_1;
	elseif (y <= 4.5e-16)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = Float64(t * Float64(Float64(y - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (y / (y - x));
	tmp = 0.0;
	if (y <= -1.8e+68)
		tmp = t_1;
	elseif (y <= -1300000.0)
		tmp = t * ((x - y) / z);
	elseif (y <= -1.16e-85)
		tmp = t_1;
	elseif (y <= 4.5e-16)
		tmp = t * (x / (z - y));
	else
		tmp = t * ((y - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(y / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+68], t$95$1, If[LessEqual[y, -1300000.0], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.16e-85], t$95$1, If[LessEqual[y, 4.5e-16], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.7999999999999999e68 or -1.3e6 < y < -1.16e-85

   1. Initial program 99.9%

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

      1. associate-*l/ 73.8%

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

      2. *-commutative 73.8%

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

      3. associate-*l/ 76.2%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in z around 0 63.7%

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

      1. associate-*r/ 63.7%

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

      2. neg-mul-1 63.7%

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

      3. distribute-rgt-neg-in 63.7%

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

      4. associate-/l* 87.2%

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

      5. neg-sub0 87.2%

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

      6. associate--r- 87.2%

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

      7. neg-sub0 87.2%

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

   6. Simplified 87.2%

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

   7. Taylor expanded in t around 0 63.7%

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

      1. associate-/l* 87.2%

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

   9. Simplified 87.2%

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

   if -1.7999999999999999e68 < y < -1.3e6

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 85.2%

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

   if -1.16e-85 < y < 4.5000000000000002e-16

   1. Initial program 92.4%

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

   2. Taylor expanded in x around inf 86.0%

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

   if 4.5000000000000002e-16 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 84.6%

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

      2. *-commutative 84.6%

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

      3. associate-*l/ 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in z around 0 68.8%

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

      1. associate-*r/ 68.8%

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

      2. neg-mul-1 68.8%

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

      3. distribute-rgt-neg-in 68.8%

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

      4. associate-/l* 81.3%

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

      5. neg-sub0 81.3%

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

      6. associate--r- 81.3%

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

      7. neg-sub0 81.3%

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

   6. Simplified 81.3%

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

   7. Taylor expanded in t around 0 68.8%

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

      1. associate-/l* 81.3%

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

   9. Simplified 81.3%

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

       1. clear-num 81.1%

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

       2. associate-/r/ 81.3%

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

       3. clear-num 81.3%

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

   11. Applied egg-rr 81.3%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+68}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;y \leq -1300000:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-85}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]

Alternative 4: 73.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{y}{y - x}}\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -0.0013:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-17}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (/ y (- y x)))))
   (if (<= y -1.8e+68)
     t_1
     (if (<= y -0.0013)
       (/ t (/ z (- x y)))
       (if (<= y -1.25e-85)
         t_1
         (if (<= y 4.6e-17) (* t (/ x (- z y))) (* t (/ (- y x) y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (y / (y - x));
	double tmp;
	if (y <= -1.8e+68) {
		tmp = t_1;
	} else if (y <= -0.0013) {
		tmp = t / (z / (x - y));
	} else if (y <= -1.25e-85) {
		tmp = t_1;
	} else if (y <= 4.6e-17) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t * ((y - x) / 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) :: t_1
    real(8) :: tmp
    t_1 = t / (y / (y - x))
    if (y <= (-1.8d+68)) then
        tmp = t_1
    else if (y <= (-0.0013d0)) then
        tmp = t / (z / (x - y))
    else if (y <= (-1.25d-85)) then
        tmp = t_1
    else if (y <= 4.6d-17) then
        tmp = t * (x / (z - y))
    else
        tmp = t * ((y - x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t / (y / (y - x));
	double tmp;
	if (y <= -1.8e+68) {
		tmp = t_1;
	} else if (y <= -0.0013) {
		tmp = t / (z / (x - y));
	} else if (y <= -1.25e-85) {
		tmp = t_1;
	} else if (y <= 4.6e-17) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t * ((y - x) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (y / (y - x))
	tmp = 0
	if y <= -1.8e+68:
		tmp = t_1
	elif y <= -0.0013:
		tmp = t / (z / (x - y))
	elif y <= -1.25e-85:
		tmp = t_1
	elif y <= 4.6e-17:
		tmp = t * (x / (z - y))
	else:
		tmp = t * ((y - x) / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(y / Float64(y - x)))
	tmp = 0.0
	if (y <= -1.8e+68)
		tmp = t_1;
	elseif (y <= -0.0013)
		tmp = Float64(t / Float64(z / Float64(x - y)));
	elseif (y <= -1.25e-85)
		tmp = t_1;
	elseif (y <= 4.6e-17)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = Float64(t * Float64(Float64(y - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (y / (y - x));
	tmp = 0.0;
	if (y <= -1.8e+68)
		tmp = t_1;
	elseif (y <= -0.0013)
		tmp = t / (z / (x - y));
	elseif (y <= -1.25e-85)
		tmp = t_1;
	elseif (y <= 4.6e-17)
		tmp = t * (x / (z - y));
	else
		tmp = t * ((y - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(y / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+68], t$95$1, If[LessEqual[y, -0.0013], N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.25e-85], t$95$1, If[LessEqual[y, 4.6e-17], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.7999999999999999e68 or -0.0012999999999999999 < y < -1.25e-85

   1. Initial program 99.9%

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

      1. associate-*l/ 73.8%

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

      2. *-commutative 73.8%

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

      3. associate-*l/ 76.2%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in z around 0 63.7%

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

      1. associate-*r/ 63.7%

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

      2. neg-mul-1 63.7%

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

      3. distribute-rgt-neg-in 63.7%

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

      4. associate-/l* 87.2%

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

      5. neg-sub0 87.2%

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

      6. associate--r- 87.2%

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

      7. neg-sub0 87.2%

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

   6. Simplified 87.2%

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

   7. Taylor expanded in t around 0 63.7%

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

      1. associate-/l* 87.2%

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

   9. Simplified 87.2%

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

   if -1.7999999999999999e68 < y < -0.0012999999999999999

   1. Initial program 99.9%

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

      1. associate-*l/ 85.0%

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

      2. *-commutative 85.0%

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

      3. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around inf 70.5%

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

      1. associate-/l* 85.4%

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

   6. Simplified 85.4%

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

   if -1.25e-85 < y < 4.60000000000000018e-17

   1. Initial program 92.4%

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

   2. Taylor expanded in x around inf 86.0%

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

   if 4.60000000000000018e-17 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 84.6%

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

      2. *-commutative 84.6%

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

      3. associate-*l/ 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in z around 0 68.8%

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

      1. associate-*r/ 68.8%

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

      2. neg-mul-1 68.8%

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

      3. distribute-rgt-neg-in 68.8%

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

      4. associate-/l* 81.3%

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

      5. neg-sub0 81.3%

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

      6. associate--r- 81.3%

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

      7. neg-sub0 81.3%

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

   6. Simplified 81.3%

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

   7. Taylor expanded in t around 0 68.8%

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

      1. associate-/l* 81.3%

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

   9. Simplified 81.3%

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

       1. clear-num 81.1%

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

       2. associate-/r/ 81.3%

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

       3. clear-num 81.3%

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

   11. Applied egg-rr 81.3%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+68}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;y \leq -0.0013:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-85}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-17}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]

Alternative 5: 90.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+135} \lor \neg \left(y \leq 1.95 \cdot 10^{+192}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.4e+135) (not (<= y 1.95e+192)))
   (* t (/ (- y x) y))
   (* (- x y) (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.4e+135) || !(y <= 1.95e+192)) {
		tmp = t * ((y - 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 <= (-3.4d+135)) .or. (.not. (y <= 1.95d+192))) then
        tmp = t * ((y - 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 <= -3.4e+135) || !(y <= 1.95e+192)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.4e+135) or not (y <= 1.95e+192):
		tmp = t * ((y - x) / y)
	else:
		tmp = (x - y) * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.4e+135) || !(y <= 1.95e+192))
		tmp = Float64(t * Float64(Float64(y - 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 <= -3.4e+135) || ~((y <= 1.95e+192)))
		tmp = t * ((y - x) / y);
	else
		tmp = (x - y) * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.4e+135], N[Not[LessEqual[y, 1.95e+192]], $MachinePrecision]], N[(t * N[(N[(y - x), $MachinePrecision] / y), $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 < -3.4000000000000001e135 or 1.9499999999999999e192 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 72.7%

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

      2. *-commutative 72.7%

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

      3. associate-*l/ 52.3%

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

   3. Simplified 52.3%

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

   4. Taylor expanded in z around 0 67.8%

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

      1. associate-*r/ 67.8%

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

      2. neg-mul-1 67.8%

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

      3. distribute-rgt-neg-in 67.8%

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

      4. associate-/l* 91.8%

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

      5. neg-sub0 91.8%

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

      6. associate--r- 91.8%

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

      7. neg-sub0 91.8%

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

   6. Simplified 91.8%

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

   7. Taylor expanded in t around 0 67.8%

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

      1. associate-/l* 91.8%

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

   9. Simplified 91.8%

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

       1. clear-num 91.6%

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

       2. associate-/r/ 91.8%

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

       3. clear-num 91.8%

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

   11. Applied egg-rr 91.8%

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

   if -3.4000000000000001e135 < y < 1.9499999999999999e192

   1. Initial program 95.9%

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

      1. associate-*l/ 87.0%

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

      2. *-commutative 87.0%

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

      3. associate-*l/ 92.1%

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

   3. Simplified 92.1%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+135} \lor \neg \left(y \leq 1.95 \cdot 10^{+192}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \]

Alternative 6: 65.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+68}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-16}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.8e+68) t (if (<= y 7e-16) (* (- x y) (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.8e+68) {
		tmp = t;
	} else if (y <= 7e-16) {
		tmp = (x - y) * (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 <= (-1.8d+68)) then
        tmp = t
    else if (y <= 7d-16) then
        tmp = (x - y) * (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 <= -1.8e+68) {
		tmp = t;
	} else if (y <= 7e-16) {
		tmp = (x - y) * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.8e+68:
		tmp = t
	elif y <= 7e-16:
		tmp = (x - y) * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.8e+68)
		tmp = t;
	elseif (y <= 7e-16)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.8e+68)
		tmp = t;
	elseif (y <= 7e-16)
		tmp = (x - y) * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.8e+68], t, If[LessEqual[y, 7e-16], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7999999999999999e68 or 7.00000000000000035e-16 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 77.3%

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

      2. *-commutative 77.3%

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

      3. associate-*l/ 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in y around inf 69.1%

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

   if -1.7999999999999999e68 < y < 7.00000000000000035e-16

   1. Initial program 93.9%

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

      1. associate-*l/ 89.7%

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

      2. *-commutative 89.7%

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

      3. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in z around inf 73.1%

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

      1. associate-/l* 76.0%

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

      2. associate-/r/ 73.6%

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

   6. Simplified 73.6%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+68}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-16}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 67.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.14:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.1e+69) t (if (<= y 0.14) (* t (/ x (- z y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.1e+69) {
		tmp = t;
	} else if (y <= 0.14) {
		tmp = t * (x / (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 <= (-2.1d+69)) then
        tmp = t
    else if (y <= 0.14d0) then
        tmp = t * (x / (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 <= -2.1e+69) {
		tmp = t;
	} else if (y <= 0.14) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.1e+69:
		tmp = t
	elif y <= 0.14:
		tmp = t * (x / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.1e+69)
		tmp = t;
	elseif (y <= 0.14)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.1e+69)
		tmp = t;
	elseif (y <= 0.14)
		tmp = t * (x / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.1e+69], t, If[LessEqual[y, 0.14], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.10000000000000015e69 or 0.14000000000000001 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 76.6%

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

      2. *-commutative 76.6%

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

      3. associate-*l/ 72.1%

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

   3. Simplified 72.1%

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

   4. Taylor expanded in y around inf 70.5%

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

   if -2.10000000000000015e69 < y < 0.14000000000000001

   1. Initial program 94.1%

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

   2. Taylor expanded in x around inf 80.7%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.14:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 59.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 10^{-16}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.1e+69) t (if (<= y 1e-16) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.1e+69) {
		tmp = t;
	} else if (y <= 1e-16) {
		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 <= (-4.1d+69)) then
        tmp = t
    else if (y <= 1d-16) 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 <= -4.1e+69) {
		tmp = t;
	} else if (y <= 1e-16) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.1e+69:
		tmp = t
	elif y <= 1e-16:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.1e+69)
		tmp = t;
	elseif (y <= 1e-16)
		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 <= -4.1e+69)
		tmp = t;
	elseif (y <= 1e-16)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.1e+69], t, If[LessEqual[y, 1e-16], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -4.0999999999999999e69 or 9.9999999999999998e-17 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 77.3%

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

      2. *-commutative 77.3%

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

      3. associate-*l/ 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in y around inf 69.1%

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

   if -4.0999999999999999e69 < y < 9.9999999999999998e-17

   1. Initial program 93.9%

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

      1. associate-*l/ 89.7%

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

      2. *-commutative 89.7%

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

      3. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in y around 0 66.5%

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

      1. associate-/l* 70.1%

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

      2. associate-/r/ 66.2%

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

   6. Simplified 66.2%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 10^{-16}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9: 60.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+68}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.8e+68) t (if (<= y 2.5e-16) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.8e+68) {
		tmp = t;
	} else if (y <= 2.5e-16) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.8d+68)) then
        tmp = t
    else if (y <= 2.5d-16) then
        tmp = t * (x / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.8e+68) {
		tmp = t;
	} else if (y <= 2.5e-16) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.8e+68:
		tmp = t
	elif y <= 2.5e-16:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.8e+68)
		tmp = t;
	elseif (y <= 2.5e-16)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.8e+68)
		tmp = t;
	elseif (y <= 2.5e-16)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.8e+68], t, If[LessEqual[y, 2.5e-16], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7999999999999999e68 or 2.5000000000000002e-16 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 77.3%

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

      2. *-commutative 77.3%

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

      3. associate-*l/ 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in y around inf 69.1%

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

   if -1.7999999999999999e68 < y < 2.5000000000000002e-16

   1. Initial program 93.9%

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

   2. Taylor expanded in y around 0 70.1%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+68}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10: 35.5% 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 96.8%

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

   1. associate-*l/ 83.7%

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

   2. *-commutative 83.7%

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

   3. associate-*l/ 82.9%

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

3. Simplified 82.9%

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

4. Taylor expanded in y around inf 38.6%

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

5. Final simplification 38.6%

   \[\leadsto t \]

Developer target: 97.1% 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 2023320 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

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