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

Percentage Accurate: 97.1% → 97.0%

Time: 10.5s

Alternatives: 13

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: 97.1% 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

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

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 96.9%

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

   1. associate-*l/ 81.0%

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

   2. associate-*r/ 85.6%

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

3. Simplified 85.6%

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

   1. associate-*r/ 81.0%

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

   2. associate-*l/ 96.9%

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

   3. *-commutative 96.9%

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

   4. clear-num 96.8%

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

   5. un-div-inv 97.1%

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

5. Applied egg-rr 97.1%

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

6. Final simplification 97.1%

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

Alternative 2: 65.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+150}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.00155 \lor \neg \left(y \leq 1.55 \cdot 10^{+86}\right) \land y \leq 3.9 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.1e+150)
   t
   (if (or (<= y 0.00155) (and (not (<= y 1.55e+86)) (<= y 3.9e+126)))
     (* x (/ t (- z y)))
     t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.1e+150) {
		tmp = t;
	} else if ((y <= 0.00155) || (!(y <= 1.55e+86) && (y <= 3.9e+126))) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.1d+150)) then
        tmp = t
    else if ((y <= 0.00155d0) .or. (.not. (y <= 1.55d+86)) .and. (y <= 3.9d+126)) then
        tmp = x * (t / (z - y))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.1e+150) {
		tmp = t;
	} else if ((y <= 0.00155) || (!(y <= 1.55e+86) && (y <= 3.9e+126))) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.1e+150:
		tmp = t
	elif (y <= 0.00155) or (not (y <= 1.55e+86) and (y <= 3.9e+126)):
		tmp = x * (t / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.1e+150)
		tmp = t;
	elseif ((y <= 0.00155) || (!(y <= 1.55e+86) && (y <= 3.9e+126)))
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.1e+150)
		tmp = t;
	elseif ((y <= 0.00155) || (~((y <= 1.55e+86)) && (y <= 3.9e+126)))
		tmp = x * (t / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.1e+150], t, If[Or[LessEqual[y, 0.00155], And[N[Not[LessEqual[y, 1.55e+86]], $MachinePrecision], LessEqual[y, 3.9e+126]]], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -5.1000000000000001e150 or 0.00154999999999999995 < y < 1.5500000000000001e86 or 3.89999999999999993e126 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 66.0%

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

      2. associate-*r/ 70.8%

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

   3. Simplified 70.8%

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

   4. Taylor expanded in y around inf 75.2%

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

   if -5.1000000000000001e150 < y < 0.00154999999999999995 or 1.5500000000000001e86 < y < 3.89999999999999993e126

   1. Initial program 95.4%

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

      1. associate-*l/ 88.6%

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

      2. associate-*r/ 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in x around inf 70.7%

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

      1. associate-*l/ 76.3%

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

      2. *-commutative 76.3%

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

   6. Simplified 76.3%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+150}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.00155 \lor \neg \left(y \leq 1.55 \cdot 10^{+86}\right) \land y \leq 3.9 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 3: 65.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+150}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.00155:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+85}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+121}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.5e+150)
   t
   (if (<= y 0.00155)
     (* x (/ t (- z y)))
     (if (<= y 5.6e+85) t (if (<= y 1.8e+121) (* t (/ x (- z y))) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e+150) {
		tmp = t;
	} else if (y <= 0.00155) {
		tmp = x * (t / (z - y));
	} else if (y <= 5.6e+85) {
		tmp = t;
	} else if (y <= 1.8e+121) {
		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 <= (-7.5d+150)) then
        tmp = t
    else if (y <= 0.00155d0) then
        tmp = x * (t / (z - y))
    else if (y <= 5.6d+85) then
        tmp = t
    else if (y <= 1.8d+121) 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 <= -7.5e+150) {
		tmp = t;
	} else if (y <= 0.00155) {
		tmp = x * (t / (z - y));
	} else if (y <= 5.6e+85) {
		tmp = t;
	} else if (y <= 1.8e+121) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.5e+150:
		tmp = t
	elif y <= 0.00155:
		tmp = x * (t / (z - y))
	elif y <= 5.6e+85:
		tmp = t
	elif y <= 1.8e+121:
		tmp = t * (x / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.5e+150)
		tmp = t;
	elseif (y <= 0.00155)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 5.6e+85)
		tmp = t;
	elseif (y <= 1.8e+121)
		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 <= -7.5e+150)
		tmp = t;
	elseif (y <= 0.00155)
		tmp = x * (t / (z - y));
	elseif (y <= 5.6e+85)
		tmp = t;
	elseif (y <= 1.8e+121)
		tmp = t * (x / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.5e+150], t, If[LessEqual[y, 0.00155], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e+85], t, If[LessEqual[y, 1.8e+121], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.4999999999999998e150 or 0.00154999999999999995 < y < 5.5999999999999998e85 or 1.79999999999999991e121 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 66.0%

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

      2. associate-*r/ 70.8%

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

   3. Simplified 70.8%

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

   4. Taylor expanded in y around inf 75.2%

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

   if -7.4999999999999998e150 < y < 0.00154999999999999995

   1. Initial program 95.1%

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

      1. associate-*l/ 89.2%

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

      2. associate-*r/ 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in x around inf 71.5%

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

      1. associate-*l/ 76.4%

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

      2. *-commutative 76.4%

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

   6. Simplified 76.4%

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

   if 5.5999999999999998e85 < y < 1.79999999999999991e121

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 77.9%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+150}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.00155:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+85}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+121}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 65.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+152}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.00155:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+85}:\\ \;\;\;\;t + \frac{t}{\frac{y}{z}}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+117}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.45e+152)
   t
   (if (<= y 0.00155)
     (* x (/ t (- z y)))
     (if (<= y 5.2e+85)
       (+ t (/ t (/ y z)))
       (if (<= y 6.5e+117) (* t (/ x (- z y))) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e+152) {
		tmp = t;
	} else if (y <= 0.00155) {
		tmp = x * (t / (z - y));
	} else if (y <= 5.2e+85) {
		tmp = t + (t / (y / z));
	} else if (y <= 6.5e+117) {
		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 <= (-1.45d+152)) then
        tmp = t
    else if (y <= 0.00155d0) then
        tmp = x * (t / (z - y))
    else if (y <= 5.2d+85) then
        tmp = t + (t / (y / z))
    else if (y <= 6.5d+117) 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 <= -1.45e+152) {
		tmp = t;
	} else if (y <= 0.00155) {
		tmp = x * (t / (z - y));
	} else if (y <= 5.2e+85) {
		tmp = t + (t / (y / z));
	} else if (y <= 6.5e+117) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.45e+152:
		tmp = t
	elif y <= 0.00155:
		tmp = x * (t / (z - y))
	elif y <= 5.2e+85:
		tmp = t + (t / (y / z))
	elif y <= 6.5e+117:
		tmp = t * (x / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.45e+152)
		tmp = t;
	elseif (y <= 0.00155)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 5.2e+85)
		tmp = Float64(t + Float64(t / Float64(y / z)));
	elseif (y <= 6.5e+117)
		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 <= -1.45e+152)
		tmp = t;
	elseif (y <= 0.00155)
		tmp = x * (t / (z - y));
	elseif (y <= 5.2e+85)
		tmp = t + (t / (y / z));
	elseif (y <= 6.5e+117)
		tmp = t * (x / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.45e+152], t, If[LessEqual[y, 0.00155], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+85], N[(t + N[(t / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+117], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.4499999999999999e152 or 6.5000000000000004e117 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 60.9%

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

      2. associate-*r/ 64.2%

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

   3. Simplified 64.2%

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

   4. Taylor expanded in y around inf 76.5%

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

   if -1.4499999999999999e152 < y < 0.00154999999999999995

   1. Initial program 95.1%

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

      1. associate-*l/ 89.2%

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

      2. associate-*r/ 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in x around inf 71.5%

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

      1. associate-*l/ 76.4%

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

      2. *-commutative 76.4%

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

   6. Simplified 76.4%

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

   if 0.00154999999999999995 < y < 5.20000000000000021e85

   1. Initial program 99.6%

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

      1. associate-*l/ 88.3%

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

      2. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 81.7%

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

      1. associate--l+ 81.7%

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

      2. distribute-lft-out-- 81.7%

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

      3. div-sub 81.7%

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

      4. mul-1-neg 81.7%

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

      5. unsub-neg 81.7%

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

      6. distribute-lft-out-- 81.7%

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

   6. Simplified 81.7%

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

   7. Taylor expanded in x around 0 70.3%

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

      1. sub-neg 70.3%

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

      2. mul-1-neg 70.3%

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

      3. remove-double-neg 70.3%

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

      4. associate-/l* 70.3%

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

   9. Simplified 70.3%

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

   if 5.20000000000000021e85 < y < 6.5000000000000004e117

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 77.9%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+152}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.00155:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+85}:\\ \;\;\;\;t + \frac{t}{\frac{y}{z}}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+117}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 61.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.00013:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+95}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+114}:\\ \;\;\;\;-\frac{t}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.8e+37)
   t
   (if (<= y 0.00013)
     (/ t (/ z x))
     (if (<= y 6e+95) t (if (<= y 2e+114) (- (* (/ t y) x)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e+37) {
		tmp = t;
	} else if (y <= 0.00013) {
		tmp = t / (z / x);
	} else if (y <= 6e+95) {
		tmp = t;
	} else if (y <= 2e+114) {
		tmp = -((t / y) * x);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.8d+37)) then
        tmp = t
    else if (y <= 0.00013d0) then
        tmp = t / (z / x)
    else if (y <= 6d+95) then
        tmp = t
    else if (y <= 2d+114) then
        tmp = -((t / y) * x)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e+37) {
		tmp = t;
	} else if (y <= 0.00013) {
		tmp = t / (z / x);
	} else if (y <= 6e+95) {
		tmp = t;
	} else if (y <= 2e+114) {
		tmp = -((t / y) * x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.8e+37:
		tmp = t
	elif y <= 0.00013:
		tmp = t / (z / x)
	elif y <= 6e+95:
		tmp = t
	elif y <= 2e+114:
		tmp = -((t / y) * x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.8e+37)
		tmp = t;
	elseif (y <= 0.00013)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= 6e+95)
		tmp = t;
	elseif (y <= 2e+114)
		tmp = Float64(-Float64(Float64(t / y) * x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.8e+37)
		tmp = t;
	elseif (y <= 0.00013)
		tmp = t / (z / x);
	elseif (y <= 6e+95)
		tmp = t;
	elseif (y <= 2e+114)
		tmp = -((t / y) * x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.8e+37], t, If[LessEqual[y, 0.00013], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+95], t, If[LessEqual[y, 2e+114], (-N[(N[(t / y), $MachinePrecision] * x), $MachinePrecision]), t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.79999999999999957e37 or 1.29999999999999989e-4 < y < 5.99999999999999982e95 or 2e114 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 68.5%

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

      2. associate-*r/ 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in y around inf 66.9%

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

   if -5.79999999999999957e37 < y < 1.29999999999999989e-4

   1. Initial program 94.6%

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

      1. associate-*l/ 90.4%

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

      2. associate-*r/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in y around 0 66.6%

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

      1. associate-/l* 70.6%

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

   6. Simplified 70.6%

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

   if 5.99999999999999982e95 < y < 2e114

   1. Initial program 99.6%

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

      1. associate-*l/ 76.3%

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

      2. associate-*r/ 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in x around inf 51.6%

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

      1. associate-*l/ 71.5%

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

      2. *-commutative 71.5%

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

   6. Simplified 71.5%

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

   7. Taylor expanded in z around 0 71.4%

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

      1. associate-*r/ 71.4%

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

      2. neg-mul-1 71.4%

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

   9. Simplified 71.4%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.00013:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+95}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+114}:\\ \;\;\;\;-\frac{t}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6: 89.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+129}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+199}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot \frac{y}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.9e+129)
   (- t (/ t (/ y x)))
   (if (<= y 2.5e+199) (* (- x y) (/ t (- z y))) (* (- t) (/ y (- z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.9e+129) {
		tmp = t - (t / (y / x));
	} else if (y <= 2.5e+199) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = -t * (y / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.9d+129)) then
        tmp = t - (t / (y / x))
    else if (y <= 2.5d+199) then
        tmp = (x - y) * (t / (z - y))
    else
        tmp = -t * (y / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.9e+129) {
		tmp = t - (t / (y / x));
	} else if (y <= 2.5e+199) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = -t * (y / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.9e+129:
		tmp = t - (t / (y / x))
	elif y <= 2.5e+199:
		tmp = (x - y) * (t / (z - y))
	else:
		tmp = -t * (y / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.9e+129)
		tmp = Float64(t - Float64(t / Float64(y / x)));
	elseif (y <= 2.5e+199)
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	else
		tmp = Float64(Float64(-t) * Float64(y / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.9e+129)
		tmp = t - (t / (y / x));
	elseif (y <= 2.5e+199)
		tmp = (x - y) * (t / (z - y));
	else
		tmp = -t * (y / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.9e+129], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+199], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-t) * N[(y / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.90000000000000003e129

   1. Initial program 99.9%

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

      1. associate-*l/ 69.2%

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

      2. associate-*r/ 61.4%

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

   3. Simplified 61.4%

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

   4. Taylor expanded in y around inf 74.5%

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

      1. associate--l+ 74.5%

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

      2. distribute-lft-out-- 74.5%

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

      3. div-sub 74.5%

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

      4. mul-1-neg 74.5%

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

      5. unsub-neg 74.5%

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

      6. distribute-lft-out-- 74.6%

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

   6. Simplified 74.6%

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

   7. Taylor expanded in x around inf 77.8%

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

      1. associate-/l* 90.2%

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

   9. Simplified 90.2%

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

   if -1.90000000000000003e129 < y < 2.4999999999999999e199

   1. Initial program 95.9%

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

      1. associate-*l/ 86.9%

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

      2. associate-*r/ 93.7%

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

   3. Simplified 93.7%

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

   if 2.4999999999999999e199 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 93.0%

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

      1. neg-mul-1 93.0%

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

      2. distribute-neg-frac 93.0%

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

   4. Simplified 93.0%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+129}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+199}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot \frac{y}{z - y}\\ \end{array} \]

Alternative 7: 74.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+39} \lor \neg \left(y \leq 0.0012\right):\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.1e+39) (not (<= y 0.0012)))
   (- t (/ t (/ y x)))
   (* x (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.1e+39) || !(y <= 0.0012)) {
		tmp = t - (t / (y / x));
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.1d+39)) .or. (.not. (y <= 0.0012d0))) then
        tmp = t - (t / (y / x))
    else
        tmp = x * (t / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.1e+39) || !(y <= 0.0012)) {
		tmp = t - (t / (y / x));
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.1e+39) or not (y <= 0.0012):
		tmp = t - (t / (y / x))
	else:
		tmp = x * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.1e+39) || !(y <= 0.0012))
		tmp = Float64(t - Float64(t / Float64(y / x)));
	else
		tmp = Float64(x * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.1e+39) || ~((y <= 0.0012)))
		tmp = t - (t / (y / x));
	else
		tmp = x * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.1e+39], N[Not[LessEqual[y, 0.0012]], $MachinePrecision]], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1000000000000001e39 or 0.00119999999999999989 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 69.1%

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

      2. associate-*r/ 74.3%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in y around inf 71.7%

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

      1. associate--l+ 71.7%

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

      2. distribute-lft-out-- 71.7%

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

      3. div-sub 71.7%

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

      4. mul-1-neg 71.7%

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

      5. unsub-neg 71.7%

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

      6. distribute-lft-out-- 71.7%

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

   6. Simplified 71.7%

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

   7. Taylor expanded in x around inf 73.5%

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

      1. associate-/l* 81.0%

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

   9. Simplified 81.0%

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

   if -1.1000000000000001e39 < y < 0.00119999999999999989

   1. Initial program 94.6%

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

      1. associate-*l/ 90.4%

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

      2. associate-*r/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in x around inf 77.2%

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

      1. associate-*l/ 81.4%

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

      2. *-commutative 81.4%

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

   6. Simplified 81.4%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+39} \lor \neg \left(y \leq 0.0012\right):\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]

Alternative 8: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+37} \lor \neg \left(y \leq 0.0014\right):\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z - y}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8e+37) (not (<= y 0.0014)))
   (- t (/ t (/ y x)))
   (/ x (/ (- z y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8e+37) || !(y <= 0.0014)) {
		tmp = t - (t / (y / x));
	} else {
		tmp = x / ((z - y) / 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 <= (-8d+37)) .or. (.not. (y <= 0.0014d0))) then
        tmp = t - (t / (y / x))
    else
        tmp = x / ((z - y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8e+37) || !(y <= 0.0014)) {
		tmp = t - (t / (y / x));
	} else {
		tmp = x / ((z - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -8e+37) or not (y <= 0.0014):
		tmp = t - (t / (y / x))
	else:
		tmp = x / ((z - y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -8e+37) || !(y <= 0.0014))
		tmp = Float64(t - Float64(t / Float64(y / x)));
	else
		tmp = Float64(x / Float64(Float64(z - y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -8e+37) || ~((y <= 0.0014)))
		tmp = t - (t / (y / x));
	else
		tmp = x / ((z - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -8e+37], N[Not[LessEqual[y, 0.0014]], $MachinePrecision]], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.99999999999999963e37 or 0.00139999999999999999 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 69.1%

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

      2. associate-*r/ 74.3%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in y around inf 71.7%

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

      1. associate--l+ 71.7%

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

      2. distribute-lft-out-- 71.7%

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

      3. div-sub 71.7%

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

      4. mul-1-neg 71.7%

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

      5. unsub-neg 71.7%

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

      6. distribute-lft-out-- 71.7%

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

   6. Simplified 71.7%

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

   7. Taylor expanded in x around inf 73.5%

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

      1. associate-/l* 81.0%

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

   9. Simplified 81.0%

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

   if -7.99999999999999963e37 < y < 0.00139999999999999999

   1. Initial program 94.6%

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

      1. associate-*l/ 90.4%

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

      2. associate-*r/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in x around inf 77.2%

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

      1. associate-*l/ 81.4%

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

      2. *-commutative 81.4%

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

   6. Simplified 81.4%

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

      1. clear-num 81.4%

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

      2. un-div-inv 81.8%

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

   8. Applied egg-rr 81.8%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+37} \lor \neg \left(y \leq 0.0014\right):\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z - y}{t}}\\ \end{array} \]

Alternative 9: 60.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+36}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.00095:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.4e+36) t (if (<= y 0.00095) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.4e+36) {
		tmp = t;
	} else if (y <= 0.00095) {
		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 <= (-6.4d+36)) then
        tmp = t
    else if (y <= 0.00095d0) 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 <= -6.4e+36) {
		tmp = t;
	} else if (y <= 0.00095) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.4e+36:
		tmp = t
	elif y <= 0.00095:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.4e+36)
		tmp = t;
	elseif (y <= 0.00095)
		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 <= -6.4e+36)
		tmp = t;
	elseif (y <= 0.00095)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.4e+36], t, If[LessEqual[y, 0.00095], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -6.3999999999999998e36 or 9.49999999999999998e-4 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 69.1%

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

      2. associate-*r/ 74.3%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in y around inf 63.3%

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

   if -6.3999999999999998e36 < y < 9.49999999999999998e-4

   1. Initial program 94.6%

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

      1. associate-*l/ 90.4%

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

      2. associate-*r/ 94.5%

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

   3. Simplified 94.5%

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

      1. associate-*r/ 90.4%

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

      2. associate-*l/ 94.6%

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

      3. *-commutative 94.6%

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

      4. clear-num 94.4%

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

      5. un-div-inv 95.0%

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

   5. Applied egg-rr 95.0%

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

   6. Taylor expanded in y around 0 66.6%

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

      1. associate-/l* 70.6%

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

      2. associate-/r/ 69.4%

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

   8. Simplified 69.4%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+36}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.00095:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10: 61.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+36}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-5}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9.5e+36) t (if (<= y 1.15e-5) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.5e+36) {
		tmp = t;
	} else if (y <= 1.15e-5) {
		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 <= (-9.5d+36)) then
        tmp = t
    else if (y <= 1.15d-5) 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 <= -9.5e+36) {
		tmp = t;
	} else if (y <= 1.15e-5) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9.5e+36:
		tmp = t
	elif y <= 1.15e-5:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9.5e+36)
		tmp = t;
	elseif (y <= 1.15e-5)
		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 <= -9.5e+36)
		tmp = t;
	elseif (y <= 1.15e-5)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9.5e+36], t, If[LessEqual[y, 1.15e-5], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -9.49999999999999974e36 or 1.15e-5 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 69.1%

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

      2. associate-*r/ 74.3%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in y around inf 63.3%

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

   if -9.49999999999999974e36 < y < 1.15e-5

   1. Initial program 94.6%

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

   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 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+36}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-5}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11: 61.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+40}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.00085:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.1e+40) t (if (<= y 0.00085) (/ t (/ z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.1e+40) {
		tmp = t;
	} else if (y <= 0.00085) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.1d+40)) then
        tmp = t
    else if (y <= 0.00085d0) then
        tmp = t / (z / x)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.1e+40) {
		tmp = t;
	} else if (y <= 0.00085) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.1e+40:
		tmp = t
	elif y <= 0.00085:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.1e+40)
		tmp = t;
	elseif (y <= 0.00085)
		tmp = Float64(t / Float64(z / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.1e+40)
		tmp = t;
	elseif (y <= 0.00085)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.1e+40], t, If[LessEqual[y, 0.00085], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0999999999999999e40 or 8.49999999999999953e-4 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 69.1%

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

      2. associate-*r/ 74.3%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in y around inf 63.3%

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

   if -1.0999999999999999e40 < y < 8.49999999999999953e-4

   1. Initial program 94.6%

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

      1. associate-*l/ 90.4%

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

      2. associate-*r/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in y around 0 66.6%

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

      1. associate-/l* 70.6%

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

   6. Simplified 70.6%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+40}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.00085:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 97.1% 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 96.9%

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

2. Final simplification 96.9%

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

Alternative 13: 35.6% 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 96.9%

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

   1. associate-*l/ 81.0%

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

   2. associate-*r/ 85.6%

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

3. Simplified 85.6%

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

4. Taylor expanded in y around inf 33.2%

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

5. Final simplification 33.2%

   \[\leadsto t \]

Developer target: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023176 
(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))