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

Percentage Accurate: 97.2% → 97.2%

Time: 8.6s

Alternatives: 12

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: 97.2% 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: 97.2% 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]

Derivation

1. Initial program 95.5%

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

   1. *-commutative 95.5%

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

   2. clear-num 95.0%

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

   3. un-div-inv 95.8%

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

4. Applied egg-rr 95.8%

   \[\leadsto \color{blue}{\frac{t}{\frac{z - y}{x - y}}} \]
5. Add Preprocessing

Alternative 2: 87.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{+94}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 10^{-265}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-151}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+254}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\left(--1\right) - \frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x y) (/ t (- z y)))))
   (if (<= y -5.6e+94)
     (* t (/ y (- y z)))
     (if (<= y 1e-265)
       t_1
       (if (<= y 1.65e-151)
         (/ (* t x) (- z y))
         (if (<= y 5.2e+254) t_1 (/ t (- (- -1.0) (/ z y)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) * (t / (z - y));
	double tmp;
	if (y <= -5.6e+94) {
		tmp = t * (y / (y - z));
	} else if (y <= 1e-265) {
		tmp = t_1;
	} else if (y <= 1.65e-151) {
		tmp = (t * x) / (z - y);
	} else if (y <= 5.2e+254) {
		tmp = t_1;
	} else {
		tmp = t / (-(-1.0) - (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 = (x - y) * (t / (z - y))
    if (y <= (-5.6d+94)) then
        tmp = t * (y / (y - z))
    else if (y <= 1d-265) then
        tmp = t_1
    else if (y <= 1.65d-151) then
        tmp = (t * x) / (z - y)
    else if (y <= 5.2d+254) then
        tmp = t_1
    else
        tmp = t / (-(-1.0d0) - (z / y))
    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 - y));
	double tmp;
	if (y <= -5.6e+94) {
		tmp = t * (y / (y - z));
	} else if (y <= 1e-265) {
		tmp = t_1;
	} else if (y <= 1.65e-151) {
		tmp = (t * x) / (z - y);
	} else if (y <= 5.2e+254) {
		tmp = t_1;
	} else {
		tmp = t / (-(-1.0) - (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) * (t / (z - y))
	tmp = 0
	if y <= -5.6e+94:
		tmp = t * (y / (y - z))
	elif y <= 1e-265:
		tmp = t_1
	elif y <= 1.65e-151:
		tmp = (t * x) / (z - y)
	elif y <= 5.2e+254:
		tmp = t_1
	else:
		tmp = t / (-(-1.0) - (z / y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) * Float64(t / Float64(z - y)))
	tmp = 0.0
	if (y <= -5.6e+94)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	elseif (y <= 1e-265)
		tmp = t_1;
	elseif (y <= 1.65e-151)
		tmp = Float64(Float64(t * x) / Float64(z - y));
	elseif (y <= 5.2e+254)
		tmp = t_1;
	else
		tmp = Float64(t / Float64(Float64(-(-1.0)) - Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) * (t / (z - y));
	tmp = 0.0;
	if (y <= -5.6e+94)
		tmp = t * (y / (y - z));
	elseif (y <= 1e-265)
		tmp = t_1;
	elseif (y <= 1.65e-151)
		tmp = (t * x) / (z - y);
	elseif (y <= 5.2e+254)
		tmp = t_1;
	else
		tmp = t / (-(-1.0) - (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.6e+94], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-265], t$95$1, If[LessEqual[y, 1.65e-151], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+254], t$95$1, N[(t / N[((--1.0) - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.59999999999999997e94

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 93.3%

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

      1. neg-mul-1 93.3%

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

      2. distribute-neg-frac 93.3%

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

   5. Simplified 93.3%

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

   if -5.59999999999999997e94 < y < 9.99999999999999985e-266 or 1.6499999999999999e-151 < y < 5.2000000000000002e254

   1. Initial program 93.5%

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

   3. Taylor expanded in x around 0 90.9%

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

      1. mul-1-neg 90.9%

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

      2. associate-/l* 93.3%

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

      3. distribute-rgt-neg-in 93.3%

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

      4. associate-/l* 93.5%

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

      5. distribute-lft-in 93.5%

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

      6. +-commutative 93.5%

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

      7. sub-neg 93.5%

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

      8. div-sub 93.5%

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

      9. associate-*r/ 91.6%

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

      10. associate-*l/ 95.6%

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

   5. Simplified 95.6%

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

   if 9.99999999999999985e-266 < y < 1.6499999999999999e-151

   1. Initial program 95.0%

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

   3. Taylor expanded in x around inf 99.5%

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

   if 5.2000000000000002e254 < y

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.9%

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

      3. un-div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. div-sub 100.0%

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

      3. sub-neg 100.0%

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

      4. *-inverses 100.0%

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

      5. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+94}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 10^{-265}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-151}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+254}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\left(--1\right) - \frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(\frac{x}{-y} - -1\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.05 \cdot 10^{+63}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-265}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+35}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- (/ x (- y)) -1.0))))
   (if (<= y -7e+111)
     t_1
     (if (<= y -3.05e+63)
       (* t (/ (- x y) z))
       (if (<= y 1.85e-265)
         (* x (/ t (- z y)))
         (if (<= y 6.4e+35) (/ (* t x) (- z y)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((x / -y) - -1.0);
	double tmp;
	if (y <= -7e+111) {
		tmp = t_1;
	} else if (y <= -3.05e+63) {
		tmp = t * ((x - y) / z);
	} else if (y <= 1.85e-265) {
		tmp = x * (t / (z - y));
	} else if (y <= 6.4e+35) {
		tmp = (t * x) / (z - 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 * ((x / -y) - (-1.0d0))
    if (y <= (-7d+111)) then
        tmp = t_1
    else if (y <= (-3.05d+63)) then
        tmp = t * ((x - y) / z)
    else if (y <= 1.85d-265) then
        tmp = x * (t / (z - y))
    else if (y <= 6.4d+35) then
        tmp = (t * x) / (z - 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 * ((x / -y) - -1.0);
	double tmp;
	if (y <= -7e+111) {
		tmp = t_1;
	} else if (y <= -3.05e+63) {
		tmp = t * ((x - y) / z);
	} else if (y <= 1.85e-265) {
		tmp = x * (t / (z - y));
	} else if (y <= 6.4e+35) {
		tmp = (t * x) / (z - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((x / -y) - -1.0)
	tmp = 0
	if y <= -7e+111:
		tmp = t_1
	elif y <= -3.05e+63:
		tmp = t * ((x - y) / z)
	elif y <= 1.85e-265:
		tmp = x * (t / (z - y))
	elif y <= 6.4e+35:
		tmp = (t * x) / (z - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(x / Float64(-y)) - -1.0))
	tmp = 0.0
	if (y <= -7e+111)
		tmp = t_1;
	elseif (y <= -3.05e+63)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (y <= 1.85e-265)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 6.4e+35)
		tmp = Float64(Float64(t * x) / Float64(z - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((x / -y) - -1.0);
	tmp = 0.0;
	if (y <= -7e+111)
		tmp = t_1;
	elseif (y <= -3.05e+63)
		tmp = t * ((x - y) / z);
	elseif (y <= 1.85e-265)
		tmp = x * (t / (z - y));
	elseif (y <= 6.4e+35)
		tmp = (t * x) / (z - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(x / (-y)), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e+111], t$95$1, If[LessEqual[y, -3.05e+63], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e-265], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e+35], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.0000000000000004e111 or 6.39999999999999965e35 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 83.5%

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

      1. mul-1-neg 83.5%

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

      2. div-sub 83.5%

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

      3. sub-neg 83.5%

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

      4. *-inverses 83.5%

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

      5. metadata-eval 83.5%

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

   5. Simplified 83.5%

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

   if -7.0000000000000004e111 < y < -3.04999999999999984e63

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 80.8%

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

   if -3.04999999999999984e63 < y < 1.8499999999999999e-265

   1. Initial program 90.9%

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

   3. Taylor expanded in x around inf 74.4%

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

      1. associate-*l/ 76.7%

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

      2. associate-/l* 82.4%

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

   5. Applied egg-rr 82.4%

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

   if 1.8499999999999999e-265 < y < 6.39999999999999965e35

   1. Initial program 93.0%

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

   3. Taylor expanded in x around inf 79.7%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+111}:\\ \;\;\;\;t \cdot \left(\frac{x}{-y} - -1\right)\\ \mathbf{elif}\;y \leq -3.05 \cdot 10^{+63}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-265}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+35}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{x}{-y} - -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+46}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-265}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+34}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{x}{-y} - -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.2e+46)
   (* t (/ y (- y z)))
   (if (<= y 2.6e-265)
     (* x (/ t (- z y)))
     (if (<= y 7.8e+34) (/ (* t x) (- z y)) (* t (- (/ x (- y)) -1.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.2e+46) {
		tmp = t * (y / (y - z));
	} else if (y <= 2.6e-265) {
		tmp = x * (t / (z - y));
	} else if (y <= 7.8e+34) {
		tmp = (t * x) / (z - y);
	} else {
		tmp = t * ((x / -y) - -1.0);
	}
	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 <= (-3.2d+46)) then
        tmp = t * (y / (y - z))
    else if (y <= 2.6d-265) then
        tmp = x * (t / (z - y))
    else if (y <= 7.8d+34) then
        tmp = (t * x) / (z - y)
    else
        tmp = t * ((x / -y) - (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.2e+46) {
		tmp = t * (y / (y - z));
	} else if (y <= 2.6e-265) {
		tmp = x * (t / (z - y));
	} else if (y <= 7.8e+34) {
		tmp = (t * x) / (z - y);
	} else {
		tmp = t * ((x / -y) - -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.2e+46:
		tmp = t * (y / (y - z))
	elif y <= 2.6e-265:
		tmp = x * (t / (z - y))
	elif y <= 7.8e+34:
		tmp = (t * x) / (z - y)
	else:
		tmp = t * ((x / -y) - -1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.2e+46)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	elseif (y <= 2.6e-265)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 7.8e+34)
		tmp = Float64(Float64(t * x) / Float64(z - y));
	else
		tmp = Float64(t * Float64(Float64(x / Float64(-y)) - -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.2e+46)
		tmp = t * (y / (y - z));
	elseif (y <= 2.6e-265)
		tmp = x * (t / (z - y));
	elseif (y <= 7.8e+34)
		tmp = (t * x) / (z - y);
	else
		tmp = t * ((x / -y) - -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.2e+46], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e-265], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e+34], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(x / (-y)), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.1999999999999998e46

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 89.7%

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

      1. neg-mul-1 89.7%

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

      2. distribute-neg-frac 89.7%

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

   5. Simplified 89.7%

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

   if -3.1999999999999998e46 < y < 2.6000000000000001e-265

   1. Initial program 90.7%

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

   3. Taylor expanded in x around inf 75.0%

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

      1. associate-*l/ 77.3%

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

      2. associate-/l* 83.2%

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

   5. Applied egg-rr 83.2%

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

   if 2.6000000000000001e-265 < y < 7.80000000000000038e34

   1. Initial program 93.0%

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

   3. Taylor expanded in x around inf 79.7%

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

   if 7.80000000000000038e34 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 77.3%

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

      1. mul-1-neg 77.3%

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

      2. div-sub 77.4%

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

      3. sub-neg 77.4%

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

      4. *-inverses 77.4%

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

      5. metadata-eval 77.4%

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

   5. Simplified 77.4%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+46}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-265}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+34}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{x}{-y} - -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+46}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-265}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 10^{+36}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.8e+46)
   (* t (/ y (- y z)))
   (if (<= y 1.2e-265)
     (* x (/ t (- z y)))
     (if (<= y 1e+36) (/ (* t x) (- z y)) (/ t (/ y (- y x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.8e+46) {
		tmp = t * (y / (y - z));
	} else if (y <= 1.2e-265) {
		tmp = x * (t / (z - y));
	} else if (y <= 1e+36) {
		tmp = (t * x) / (z - y);
	} else {
		tmp = t / (y / (y - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.8d+46)) then
        tmp = t * (y / (y - z))
    else if (y <= 1.2d-265) then
        tmp = x * (t / (z - y))
    else if (y <= 1d+36) then
        tmp = (t * x) / (z - y)
    else
        tmp = t / (y / (y - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.8e+46) {
		tmp = t * (y / (y - z));
	} else if (y <= 1.2e-265) {
		tmp = x * (t / (z - y));
	} else if (y <= 1e+36) {
		tmp = (t * x) / (z - y);
	} else {
		tmp = t / (y / (y - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.8e+46:
		tmp = t * (y / (y - z))
	elif y <= 1.2e-265:
		tmp = x * (t / (z - y))
	elif y <= 1e+36:
		tmp = (t * x) / (z - y)
	else:
		tmp = t / (y / (y - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.8e+46)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	elseif (y <= 1.2e-265)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 1e+36)
		tmp = Float64(Float64(t * x) / Float64(z - y));
	else
		tmp = Float64(t / Float64(y / Float64(y - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.8e+46)
		tmp = t * (y / (y - z));
	elseif (y <= 1.2e-265)
		tmp = x * (t / (z - y));
	elseif (y <= 1e+36)
		tmp = (t * x) / (z - y);
	else
		tmp = t / (y / (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.8e+46], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e-265], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+36], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(t / N[(y / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.80000000000000018e46

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 89.7%

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

      1. neg-mul-1 89.7%

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

      2. distribute-neg-frac 89.7%

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

   5. Simplified 89.7%

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

   if -2.80000000000000018e46 < y < 1.2e-265

   1. Initial program 90.7%

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

   3. Taylor expanded in x around inf 75.0%

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

      1. associate-*l/ 77.3%

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

      2. associate-/l* 83.2%

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

   5. Applied egg-rr 83.2%

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

   if 1.2e-265 < y < 1.00000000000000004e36

   1. Initial program 93.0%

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

   3. Taylor expanded in x around inf 79.7%

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

   if 1.00000000000000004e36 < y

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. clear-num 99.7%

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

      3. un-div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around 0 77.4%

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

      1. neg-mul-1 77.4%

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

      2. distribute-neg-frac2 77.4%

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

   7. Simplified 77.4%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+46}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-265}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 10^{+36}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+114}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+36}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.05e+114)
   t
   (if (<= y -8.5e-24) (* x (/ t (- y))) (if (<= y 3.5e+36) (* t (/ x z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.05e+114) {
		tmp = t;
	} else if (y <= -8.5e-24) {
		tmp = x * (t / -y);
	} else if (y <= 3.5e+36) {
		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 <= (-2.05d+114)) then
        tmp = t
    else if (y <= (-8.5d-24)) then
        tmp = x * (t / -y)
    else if (y <= 3.5d+36) 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 <= -2.05e+114) {
		tmp = t;
	} else if (y <= -8.5e-24) {
		tmp = x * (t / -y);
	} else if (y <= 3.5e+36) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.05e+114:
		tmp = t
	elif y <= -8.5e-24:
		tmp = x * (t / -y)
	elif y <= 3.5e+36:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.05e+114)
		tmp = t;
	elseif (y <= -8.5e-24)
		tmp = Float64(x * Float64(t / Float64(-y)));
	elseif (y <= 3.5e+36)
		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 <= -2.05e+114)
		tmp = t;
	elseif (y <= -8.5e-24)
		tmp = x * (t / -y);
	elseif (y <= 3.5e+36)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.05e+114], t, If[LessEqual[y, -8.5e-24], N[(x * N[(t / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+36], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.05e114 or 3.4999999999999998e36 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 70.7%

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

   if -2.05e114 < y < -8.5000000000000002e-24

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 62.9%

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

      1. associate-*l/ 62.9%

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

      2. associate-/l* 59.0%

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

   5. Applied egg-rr 59.0%

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

   6. Taylor expanded in z around 0 51.8%

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

      1. associate-*r/ 51.8%

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

      2. neg-mul-1 51.8%

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

   8. Simplified 51.8%

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

   if -8.5000000000000002e-24 < y < 3.4999999999999998e36

   1. Initial program 91.0%

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

   3. Taylor expanded in y around 0 64.9%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+114}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+36}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+113} \lor \neg \left(y \leq 10^{+164}\right):\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.9e+113) (not (<= y 1e+164))) t (/ (* t x) (- z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.9e+113) || !(y <= 1e+164)) {
		tmp = t;
	} else {
		tmp = (t * x) / (z - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-5.9d+113)) .or. (.not. (y <= 1d+164))) then
        tmp = t
    else
        tmp = (t * x) / (z - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.9e+113) || !(y <= 1e+164)) {
		tmp = t;
	} else {
		tmp = (t * x) / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.9e+113) or not (y <= 1e+164):
		tmp = t
	else:
		tmp = (t * x) / (z - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.9e+113) || !(y <= 1e+164))
		tmp = t;
	else
		tmp = Float64(Float64(t * x) / Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5.9e+113) || ~((y <= 1e+164)))
		tmp = t;
	else
		tmp = (t * x) / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.9e+113], N[Not[LessEqual[y, 1e+164]], $MachinePrecision]], t, N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.90000000000000023e113 or 1e164 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 80.5%

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

   if -5.90000000000000023e113 < y < 1e164

   1. Initial program 93.2%

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

   3. Taylor expanded in x around inf 73.6%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+113} \lor \neg \left(y \leq 10^{+164}\right):\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+114} \lor \neg \left(y \leq 3 \cdot 10^{+163}\right):\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.4e+114) (not (<= y 3e+163))) t (* x (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.4e+114) || !(y <= 3e+163)) {
		tmp = t;
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.4d+114)) .or. (.not. (y <= 3d+163))) then
        tmp = t
    else
        tmp = x * (t / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.4e+114) || !(y <= 3e+163)) {
		tmp = t;
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.4e+114) or not (y <= 3e+163):
		tmp = t
	else:
		tmp = x * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.4e+114) || !(y <= 3e+163))
		tmp = t;
	else
		tmp = Float64(x * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.4e+114) || ~((y <= 3e+163)))
		tmp = t;
	else
		tmp = x * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.4e+114], N[Not[LessEqual[y, 3e+163]], $MachinePrecision]], t, N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4e114 or 3.00000000000000013e163 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 80.5%

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

   if -2.4e114 < y < 3.00000000000000013e163

   1. Initial program 93.2%

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

   3. Taylor expanded in x around inf 70.8%

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

      1. associate-*l/ 73.6%

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

      2. associate-/l* 73.0%

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

   5. Applied egg-rr 73.0%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+114} \lor \neg \left(y \leq 3 \cdot 10^{+163}\right):\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+101} \lor \neg \left(y \leq 1.7 \cdot 10^{+40}\right):\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.2e+101) (not (<= y 1.7e+40))) t (* t (/ x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.2e+101) || !(y <= 1.7e+40)) {
		tmp = t;
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-5.2d+101)) .or. (.not. (y <= 1.7d+40))) then
        tmp = t
    else
        tmp = t * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.2e+101) || !(y <= 1.7e+40)) {
		tmp = t;
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.2e+101) or not (y <= 1.7e+40):
		tmp = t
	else:
		tmp = t * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.2e+101) || !(y <= 1.7e+40))
		tmp = t;
	else
		tmp = Float64(t * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5.2e+101) || ~((y <= 1.7e+40)))
		tmp = t;
	else
		tmp = t * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.2e+101], N[Not[LessEqual[y, 1.7e+40]], $MachinePrecision]], t, N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.2e101 or 1.69999999999999994e40 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 68.8%

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

   if -5.2e101 < y < 1.69999999999999994e40

   1. Initial program 92.3%

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

   3. Taylor expanded in y around 0 60.6%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+101} \lor \neg \left(y \leq 1.7 \cdot 10^{+40}\right):\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+101} \lor \neg \left(y \leq 3.8 \cdot 10^{+37}\right):\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.2e+101) (not (<= y 3.8e+37))) t (* x (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.2e+101) || !(y <= 3.8e+37)) {
		tmp = t;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-5.2d+101)) .or. (.not. (y <= 3.8d+37))) then
        tmp = t
    else
        tmp = x * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.2e+101) || !(y <= 3.8e+37)) {
		tmp = t;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.2e+101) or not (y <= 3.8e+37):
		tmp = t
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.2e+101) || !(y <= 3.8e+37))
		tmp = t;
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5.2e+101) || ~((y <= 3.8e+37)))
		tmp = t;
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.2e+101], N[Not[LessEqual[y, 3.8e+37]], $MachinePrecision]], t, N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.2e101 or 3.7999999999999999e37 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 68.8%

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

   if -5.2e101 < y < 3.7999999999999999e37

   1. Initial program 92.3%

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

   3. Taylor expanded in y around 0 60.6%

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

      1. associate-*l/ 59.4%

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

      2. associate-/l* 58.0%

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

   5. Applied egg-rr 58.0%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+101} \lor \neg \left(y \leq 3.8 \cdot 10^{+37}\right):\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.5%

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

3. Final simplification 95.5%

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

Alternative 12: 35.1% 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 95.5%

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

3. Taylor expanded in y around inf 37.4%

   \[\leadsto \color{blue}{t} \]
4. Add Preprocessing

Developer target: 97.2% 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 2024096 
(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))