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

Percentage Accurate: 97.0% → 97.4%

Time: 11.3s

Alternatives: 15

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 -1e+89) (* x (/ t (- z y))) (* t_1 t))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -1e+89) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t_1 * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= (-1d+89)) then
        tmp = x * (t / (z - y))
    else
        tmp = t_1 * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -1e+89) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t_1 * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= -1e+89:
		tmp = x * (t / (z - y))
	else:
		tmp = t_1 * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= -1e+89)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = Float64(t_1 * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= -1e+89)
		tmp = x * (t / (z - y));
	else
		tmp = t_1 * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+89], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -9.99999999999999995e88

   1. Initial program 76.9%

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

      1. associate-*l/ 99.6%

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

      2. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 99.6%

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

      1. associate-*l/ 99.9%

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

      2. *-commutative 99.9%

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

   6. Simplified 99.9%

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

   if -9.99999999999999995e88 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 98.1%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -1 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \end{array} \]

Alternative 2: 64.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z - y}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+171}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+55}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-25}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+14} \lor \neg \left(y \leq 4.2 \cdot 10^{+87}\right) \land y \leq 2.15 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t (- z y)))))
   (if (<= y -3.8e+171)
     t
     (if (<= y -1.7e+79)
       t_1
       (if (<= y -4.5e+55)
         t
         (if (<= y -6.2e-25)
           (* t (/ x z))
           (if (<= y -9e-29)
             t
             (if (or (<= y 6e+14) (and (not (<= y 4.2e+87)) (<= y 2.15e+126)))
               t_1
               t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / (z - y));
	double tmp;
	if (y <= -3.8e+171) {
		tmp = t;
	} else if (y <= -1.7e+79) {
		tmp = t_1;
	} else if (y <= -4.5e+55) {
		tmp = t;
	} else if (y <= -6.2e-25) {
		tmp = t * (x / z);
	} else if (y <= -9e-29) {
		tmp = t;
	} else if ((y <= 6e+14) || (!(y <= 4.2e+87) && (y <= 2.15e+126))) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t / (z - y))
    if (y <= (-3.8d+171)) then
        tmp = t
    else if (y <= (-1.7d+79)) then
        tmp = t_1
    else if (y <= (-4.5d+55)) then
        tmp = t
    else if (y <= (-6.2d-25)) then
        tmp = t * (x / z)
    else if (y <= (-9d-29)) then
        tmp = t
    else if ((y <= 6d+14) .or. (.not. (y <= 4.2d+87)) .and. (y <= 2.15d+126)) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / (z - y));
	double tmp;
	if (y <= -3.8e+171) {
		tmp = t;
	} else if (y <= -1.7e+79) {
		tmp = t_1;
	} else if (y <= -4.5e+55) {
		tmp = t;
	} else if (y <= -6.2e-25) {
		tmp = t * (x / z);
	} else if (y <= -9e-29) {
		tmp = t;
	} else if ((y <= 6e+14) || (!(y <= 4.2e+87) && (y <= 2.15e+126))) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / (z - y))
	tmp = 0
	if y <= -3.8e+171:
		tmp = t
	elif y <= -1.7e+79:
		tmp = t_1
	elif y <= -4.5e+55:
		tmp = t
	elif y <= -6.2e-25:
		tmp = t * (x / z)
	elif y <= -9e-29:
		tmp = t
	elif (y <= 6e+14) or (not (y <= 4.2e+87) and (y <= 2.15e+126)):
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / Float64(z - y)))
	tmp = 0.0
	if (y <= -3.8e+171)
		tmp = t;
	elseif (y <= -1.7e+79)
		tmp = t_1;
	elseif (y <= -4.5e+55)
		tmp = t;
	elseif (y <= -6.2e-25)
		tmp = Float64(t * Float64(x / z));
	elseif (y <= -9e-29)
		tmp = t;
	elseif ((y <= 6e+14) || (!(y <= 4.2e+87) && (y <= 2.15e+126)))
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / (z - y));
	tmp = 0.0;
	if (y <= -3.8e+171)
		tmp = t;
	elseif (y <= -1.7e+79)
		tmp = t_1;
	elseif (y <= -4.5e+55)
		tmp = t;
	elseif (y <= -6.2e-25)
		tmp = t * (x / z);
	elseif (y <= -9e-29)
		tmp = t;
	elseif ((y <= 6e+14) || (~((y <= 4.2e+87)) && (y <= 2.15e+126)))
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e+171], t, If[LessEqual[y, -1.7e+79], t$95$1, If[LessEqual[y, -4.5e+55], t, If[LessEqual[y, -6.2e-25], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9e-29], t, If[Or[LessEqual[y, 6e+14], And[N[Not[LessEqual[y, 4.2e+87]], $MachinePrecision], LessEqual[y, 2.15e+126]]], t$95$1, t]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8000000000000002e171 or -1.70000000000000016e79 < y < -4.49999999999999998e55 or -6.19999999999999989e-25 < y < -8.9999999999999996e-29 or 6e14 < y < 4.2e87 or 2.1500000000000001e126 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 74.9%

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

      2. associate-*r/ 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in y around inf 73.2%

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

   if -3.8000000000000002e171 < y < -1.70000000000000016e79 or -8.9999999999999996e-29 < y < 6e14 or 4.2e87 < y < 2.1500000000000001e126

   1. Initial program 93.4%

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

      1. associate-*l/ 85.8%

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

      2. associate-*r/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in x around inf 71.9%

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

      1. associate-*l/ 78.3%

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

      2. *-commutative 78.3%

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

   6. Simplified 78.3%

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

   if -4.49999999999999998e55 < y < -6.19999999999999989e-25

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 46.3%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+171}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+55}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-25}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+14} \lor \neg \left(y \leq 4.2 \cdot 10^{+87}\right) \land y \leq 2.15 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 3: 58.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{-x}{y}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+171}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+55}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-25}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-30}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 28000:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- x) y))))
   (if (<= y -3.8e+171)
     t
     (if (<= y -5.1e+73)
       t_1
       (if (<= y -1.75e+55)
         t
         (if (<= y -6.8e-25)
           (* t (/ x z))
           (if (<= y -3.6e-30)
             t
             (if (<= y -4.1e-70)
               t_1
               (if (<= y 28000.0) (/ x (/ z t)) t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (-x / y);
	double tmp;
	if (y <= -3.8e+171) {
		tmp = t;
	} else if (y <= -5.1e+73) {
		tmp = t_1;
	} else if (y <= -1.75e+55) {
		tmp = t;
	} else if (y <= -6.8e-25) {
		tmp = t * (x / z);
	} else if (y <= -3.6e-30) {
		tmp = t;
	} else if (y <= -4.1e-70) {
		tmp = t_1;
	} else if (y <= 28000.0) {
		tmp = x / (z / t);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (-x / y)
    if (y <= (-3.8d+171)) then
        tmp = t
    else if (y <= (-5.1d+73)) then
        tmp = t_1
    else if (y <= (-1.75d+55)) then
        tmp = t
    else if (y <= (-6.8d-25)) then
        tmp = t * (x / z)
    else if (y <= (-3.6d-30)) then
        tmp = t
    else if (y <= (-4.1d-70)) then
        tmp = t_1
    else if (y <= 28000.0d0) then
        tmp = x / (z / t)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (-x / y);
	double tmp;
	if (y <= -3.8e+171) {
		tmp = t;
	} else if (y <= -5.1e+73) {
		tmp = t_1;
	} else if (y <= -1.75e+55) {
		tmp = t;
	} else if (y <= -6.8e-25) {
		tmp = t * (x / z);
	} else if (y <= -3.6e-30) {
		tmp = t;
	} else if (y <= -4.1e-70) {
		tmp = t_1;
	} else if (y <= 28000.0) {
		tmp = x / (z / t);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (-x / y)
	tmp = 0
	if y <= -3.8e+171:
		tmp = t
	elif y <= -5.1e+73:
		tmp = t_1
	elif y <= -1.75e+55:
		tmp = t
	elif y <= -6.8e-25:
		tmp = t * (x / z)
	elif y <= -3.6e-30:
		tmp = t
	elif y <= -4.1e-70:
		tmp = t_1
	elif y <= 28000.0:
		tmp = x / (z / t)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(-x) / y))
	tmp = 0.0
	if (y <= -3.8e+171)
		tmp = t;
	elseif (y <= -5.1e+73)
		tmp = t_1;
	elseif (y <= -1.75e+55)
		tmp = t;
	elseif (y <= -6.8e-25)
		tmp = Float64(t * Float64(x / z));
	elseif (y <= -3.6e-30)
		tmp = t;
	elseif (y <= -4.1e-70)
		tmp = t_1;
	elseif (y <= 28000.0)
		tmp = Float64(x / Float64(z / t));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (-x / y);
	tmp = 0.0;
	if (y <= -3.8e+171)
		tmp = t;
	elseif (y <= -5.1e+73)
		tmp = t_1;
	elseif (y <= -1.75e+55)
		tmp = t;
	elseif (y <= -6.8e-25)
		tmp = t * (x / z);
	elseif (y <= -3.6e-30)
		tmp = t;
	elseif (y <= -4.1e-70)
		tmp = t_1;
	elseif (y <= 28000.0)
		tmp = x / (z / t);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[((-x) / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e+171], t, If[LessEqual[y, -5.1e+73], t$95$1, If[LessEqual[y, -1.75e+55], t, If[LessEqual[y, -6.8e-25], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.6e-30], t, If[LessEqual[y, -4.1e-70], t$95$1, If[LessEqual[y, 28000.0], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], t]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.8000000000000002e171 or -5.10000000000000024e73 < y < -1.75000000000000005e55 or -6.80000000000000003e-25 < y < -3.6000000000000003e-30 or 28000 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 75.1%

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

      2. associate-*r/ 79.5%

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

   3. Simplified 79.5%

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

   4. Taylor expanded in y around inf 68.5%

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

   if -3.8000000000000002e171 < y < -5.10000000000000024e73 or -3.6000000000000003e-30 < y < -4.09999999999999977e-70

   1. Initial program 99.8%

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

      1. associate-*l/ 79.4%

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

      2. associate-*r/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in x around inf 57.4%

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

      1. associate-*l/ 66.0%

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

      2. *-commutative 66.0%

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

   6. Simplified 66.0%

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

   7. Taylor expanded in z around 0 58.6%

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

      1. associate-*r/ 58.6%

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

      2. neg-mul-1 58.6%

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

   9. Simplified 58.6%

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

   10. Taylor expanded in x around 0 50.0%

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

       1. mul-1-neg 50.0%

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

       2. associate-*r/ 61.5%

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

       3. distribute-rgt-neg-in 61.5%

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

   12. Simplified 61.5%

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

   if -1.75000000000000005e55 < y < -6.80000000000000003e-25

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 46.3%

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

   if -4.09999999999999977e-70 < y < 28000

   1. Initial program 91.0%

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

   2. Taylor expanded in y around 0 66.7%

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

      1. associate-*l/ 64.1%

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

      2. associate-/l* 69.0%

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

   4. Applied egg-rr 69.0%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+171}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+55}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-25}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-30}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-70}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;y \leq 28000:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 58.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{-x}{y}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+171}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{+41}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-25}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.8:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- x) y))))
   (if (<= y -3.8e+171)
     t
     (if (<= y -4.7e+139)
       t_1
       (if (<= y -4.3e+41)
         (* t (/ (- y) z))
         (if (<= y -6e-25)
           (* t (/ x z))
           (if (<= y -8.8e-29)
             t
             (if (<= y -1e-69) t_1 (if (<= y 2.8) (/ x (/ z t)) t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (-x / y);
	double tmp;
	if (y <= -3.8e+171) {
		tmp = t;
	} else if (y <= -4.7e+139) {
		tmp = t_1;
	} else if (y <= -4.3e+41) {
		tmp = t * (-y / z);
	} else if (y <= -6e-25) {
		tmp = t * (x / z);
	} else if (y <= -8.8e-29) {
		tmp = t;
	} else if (y <= -1e-69) {
		tmp = t_1;
	} else if (y <= 2.8) {
		tmp = x / (z / t);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (-x / y)
    if (y <= (-3.8d+171)) then
        tmp = t
    else if (y <= (-4.7d+139)) then
        tmp = t_1
    else if (y <= (-4.3d+41)) then
        tmp = t * (-y / z)
    else if (y <= (-6d-25)) then
        tmp = t * (x / z)
    else if (y <= (-8.8d-29)) then
        tmp = t
    else if (y <= (-1d-69)) then
        tmp = t_1
    else if (y <= 2.8d0) then
        tmp = x / (z / t)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (-x / y);
	double tmp;
	if (y <= -3.8e+171) {
		tmp = t;
	} else if (y <= -4.7e+139) {
		tmp = t_1;
	} else if (y <= -4.3e+41) {
		tmp = t * (-y / z);
	} else if (y <= -6e-25) {
		tmp = t * (x / z);
	} else if (y <= -8.8e-29) {
		tmp = t;
	} else if (y <= -1e-69) {
		tmp = t_1;
	} else if (y <= 2.8) {
		tmp = x / (z / t);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (-x / y)
	tmp = 0
	if y <= -3.8e+171:
		tmp = t
	elif y <= -4.7e+139:
		tmp = t_1
	elif y <= -4.3e+41:
		tmp = t * (-y / z)
	elif y <= -6e-25:
		tmp = t * (x / z)
	elif y <= -8.8e-29:
		tmp = t
	elif y <= -1e-69:
		tmp = t_1
	elif y <= 2.8:
		tmp = x / (z / t)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(-x) / y))
	tmp = 0.0
	if (y <= -3.8e+171)
		tmp = t;
	elseif (y <= -4.7e+139)
		tmp = t_1;
	elseif (y <= -4.3e+41)
		tmp = Float64(t * Float64(Float64(-y) / z));
	elseif (y <= -6e-25)
		tmp = Float64(t * Float64(x / z));
	elseif (y <= -8.8e-29)
		tmp = t;
	elseif (y <= -1e-69)
		tmp = t_1;
	elseif (y <= 2.8)
		tmp = Float64(x / Float64(z / t));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (-x / y);
	tmp = 0.0;
	if (y <= -3.8e+171)
		tmp = t;
	elseif (y <= -4.7e+139)
		tmp = t_1;
	elseif (y <= -4.3e+41)
		tmp = t * (-y / z);
	elseif (y <= -6e-25)
		tmp = t * (x / z);
	elseif (y <= -8.8e-29)
		tmp = t;
	elseif (y <= -1e-69)
		tmp = t_1;
	elseif (y <= 2.8)
		tmp = x / (z / t);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[((-x) / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e+171], t, If[LessEqual[y, -4.7e+139], t$95$1, If[LessEqual[y, -4.3e+41], N[(t * N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6e-25], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.8e-29], t, If[LessEqual[y, -1e-69], t$95$1, If[LessEqual[y, 2.8], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], t]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.8000000000000002e171 or -5.9999999999999995e-25 < y < -8.79999999999999961e-29 or 2.7999999999999998 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 73.5%

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

      2. associate-*r/ 78.1%

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

   3. Simplified 78.1%

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

   4. Taylor expanded in y around inf 68.6%

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

   if -3.8000000000000002e171 < y < -4.7000000000000001e139 or -8.79999999999999961e-29 < y < -9.9999999999999996e-70

   1. Initial program 99.9%

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

      1. associate-*l/ 86.5%

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

      2. associate-*r/ 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in x around inf 66.6%

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

      1. associate-*l/ 75.5%

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

      2. *-commutative 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in z around 0 73.4%

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

      1. associate-*r/ 73.4%

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

      2. neg-mul-1 73.4%

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

   9. Simplified 73.4%

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

   10. Taylor expanded in x around 0 64.5%

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

       1. mul-1-neg 64.5%

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

       2. associate-*r/ 78.0%

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

       3. distribute-rgt-neg-in 78.0%

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

   12. Simplified 78.0%

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

   if -4.7000000000000001e139 < y < -4.30000000000000024e41

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 66.2%

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

      1. neg-mul-1 66.2%

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

      2. distribute-neg-frac 66.2%

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

   4. Simplified 66.2%

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

   5. Taylor expanded in y around 0 42.8%

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

      1. mul-1-neg 42.8%

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

      2. distribute-neg-frac 42.8%

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

   7. Simplified 42.8%

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

   if -4.30000000000000024e41 < y < -5.9999999999999995e-25

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 48.4%

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

   if -9.9999999999999996e-70 < y < 2.7999999999999998

   1. Initial program 91.0%

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

   2. Taylor expanded in y around 0 66.7%

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

      1. associate-*l/ 64.1%

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

      2. associate-/l* 69.0%

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

   4. Applied egg-rr 69.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{t}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+171}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{+139}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{+41}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-25}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-69}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;y \leq 2.8:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 58.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{-x}{y}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+171}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{+141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{+41}:\\ \;\;\;\;\frac{t}{\frac{-z}{y}}\\ \mathbf{elif}\;y \leq -6.3 \cdot 10^{-25}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-35}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.01:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- x) y))))
   (if (<= y -3.8e+171)
     t
     (if (<= y -2.65e+141)
       t_1
       (if (<= y -2.65e+41)
         (/ t (/ (- z) y))
         (if (<= y -6.3e-25)
           (* t (/ x z))
           (if (<= y -8e-35)
             t
             (if (<= y -1.7e-70) t_1 (if (<= y 0.01) (/ x (/ z t)) t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (-x / y);
	double tmp;
	if (y <= -3.8e+171) {
		tmp = t;
	} else if (y <= -2.65e+141) {
		tmp = t_1;
	} else if (y <= -2.65e+41) {
		tmp = t / (-z / y);
	} else if (y <= -6.3e-25) {
		tmp = t * (x / z);
	} else if (y <= -8e-35) {
		tmp = t;
	} else if (y <= -1.7e-70) {
		tmp = t_1;
	} else if (y <= 0.01) {
		tmp = x / (z / t);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (-x / y)
    if (y <= (-3.8d+171)) then
        tmp = t
    else if (y <= (-2.65d+141)) then
        tmp = t_1
    else if (y <= (-2.65d+41)) then
        tmp = t / (-z / y)
    else if (y <= (-6.3d-25)) then
        tmp = t * (x / z)
    else if (y <= (-8d-35)) then
        tmp = t
    else if (y <= (-1.7d-70)) then
        tmp = t_1
    else if (y <= 0.01d0) then
        tmp = x / (z / t)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (-x / y);
	double tmp;
	if (y <= -3.8e+171) {
		tmp = t;
	} else if (y <= -2.65e+141) {
		tmp = t_1;
	} else if (y <= -2.65e+41) {
		tmp = t / (-z / y);
	} else if (y <= -6.3e-25) {
		tmp = t * (x / z);
	} else if (y <= -8e-35) {
		tmp = t;
	} else if (y <= -1.7e-70) {
		tmp = t_1;
	} else if (y <= 0.01) {
		tmp = x / (z / t);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (-x / y)
	tmp = 0
	if y <= -3.8e+171:
		tmp = t
	elif y <= -2.65e+141:
		tmp = t_1
	elif y <= -2.65e+41:
		tmp = t / (-z / y)
	elif y <= -6.3e-25:
		tmp = t * (x / z)
	elif y <= -8e-35:
		tmp = t
	elif y <= -1.7e-70:
		tmp = t_1
	elif y <= 0.01:
		tmp = x / (z / t)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(-x) / y))
	tmp = 0.0
	if (y <= -3.8e+171)
		tmp = t;
	elseif (y <= -2.65e+141)
		tmp = t_1;
	elseif (y <= -2.65e+41)
		tmp = Float64(t / Float64(Float64(-z) / y));
	elseif (y <= -6.3e-25)
		tmp = Float64(t * Float64(x / z));
	elseif (y <= -8e-35)
		tmp = t;
	elseif (y <= -1.7e-70)
		tmp = t_1;
	elseif (y <= 0.01)
		tmp = Float64(x / Float64(z / t));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (-x / y);
	tmp = 0.0;
	if (y <= -3.8e+171)
		tmp = t;
	elseif (y <= -2.65e+141)
		tmp = t_1;
	elseif (y <= -2.65e+41)
		tmp = t / (-z / y);
	elseif (y <= -6.3e-25)
		tmp = t * (x / z);
	elseif (y <= -8e-35)
		tmp = t;
	elseif (y <= -1.7e-70)
		tmp = t_1;
	elseif (y <= 0.01)
		tmp = x / (z / t);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[((-x) / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e+171], t, If[LessEqual[y, -2.65e+141], t$95$1, If[LessEqual[y, -2.65e+41], N[(t / N[((-z) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.3e-25], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8e-35], t, If[LessEqual[y, -1.7e-70], t$95$1, If[LessEqual[y, 0.01], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], t]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.8000000000000002e171 or -6.29999999999999961e-25 < y < -8.00000000000000006e-35 or 0.0100000000000000002 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 73.5%

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

      2. associate-*r/ 78.1%

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

   3. Simplified 78.1%

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

   4. Taylor expanded in y around inf 68.6%

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

   if -3.8000000000000002e171 < y < -2.65e141 or -8.00000000000000006e-35 < y < -1.69999999999999998e-70

   1. Initial program 99.9%

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

      1. associate-*l/ 86.5%

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

      2. associate-*r/ 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in x around inf 66.6%

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

      1. associate-*l/ 75.5%

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

      2. *-commutative 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in z around 0 73.4%

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

      1. associate-*r/ 73.4%

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

      2. neg-mul-1 73.4%

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

   9. Simplified 73.4%

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

   10. Taylor expanded in x around 0 64.5%

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

       1. mul-1-neg 64.5%

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

       2. associate-*r/ 78.0%

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

       3. distribute-rgt-neg-in 78.0%

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

   12. Simplified 78.0%

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

   if -2.65e141 < y < -2.6499999999999998e41

   1. Initial program 99.7%

      \[\frac{x - y}{z - y} \cdot t \]
   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/ 85.7%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in z around inf 56.6%

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

      1. associate-/l* 66.4%

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

   6. Simplified 66.4%

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

   7. Taylor expanded in x around 0 42.9%

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

      1. associate-*r/ 42.9%

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

      2. neg-mul-1 42.9%

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

   9. Simplified 42.9%

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

   if -2.6499999999999998e41 < y < -6.29999999999999961e-25

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 48.4%

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

   if -1.69999999999999998e-70 < y < 0.0100000000000000002

   1. Initial program 91.0%

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

   2. Taylor expanded in y around 0 66.7%

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

      1. associate-*l/ 64.1%

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

      2. associate-/l* 69.0%

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

   4. Applied egg-rr 69.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{t}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+171}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{+141}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{+41}:\\ \;\;\;\;\frac{t}{\frac{-z}{y}}\\ \mathbf{elif}\;y \leq -6.3 \cdot 10^{-25}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-35}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-70}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;y \leq 0.01:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6: 67.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+171}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 60000000000000:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+82}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x (- z y)))))
   (if (<= y -3.8e+171)
     t
     (if (<= y -4.4e-63)
       t_1
       (if (<= y 60000000000000.0)
         (* x (/ t (- z y)))
         (if (<= y 8.2e+82) t (if (<= y 5.6e+126) t_1 t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / (z - y));
	double tmp;
	if (y <= -3.8e+171) {
		tmp = t;
	} else if (y <= -4.4e-63) {
		tmp = t_1;
	} else if (y <= 60000000000000.0) {
		tmp = x * (t / (z - y));
	} else if (y <= 8.2e+82) {
		tmp = t;
	} else if (y <= 5.6e+126) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (x / (z - y))
    if (y <= (-3.8d+171)) then
        tmp = t
    else if (y <= (-4.4d-63)) then
        tmp = t_1
    else if (y <= 60000000000000.0d0) then
        tmp = x * (t / (z - y))
    else if (y <= 8.2d+82) then
        tmp = t
    else if (y <= 5.6d+126) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (x / (z - y));
	double tmp;
	if (y <= -3.8e+171) {
		tmp = t;
	} else if (y <= -4.4e-63) {
		tmp = t_1;
	} else if (y <= 60000000000000.0) {
		tmp = x * (t / (z - y));
	} else if (y <= 8.2e+82) {
		tmp = t;
	} else if (y <= 5.6e+126) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / (z - y))
	tmp = 0
	if y <= -3.8e+171:
		tmp = t
	elif y <= -4.4e-63:
		tmp = t_1
	elif y <= 60000000000000.0:
		tmp = x * (t / (z - y))
	elif y <= 8.2e+82:
		tmp = t
	elif y <= 5.6e+126:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (y <= -3.8e+171)
		tmp = t;
	elseif (y <= -4.4e-63)
		tmp = t_1;
	elseif (y <= 60000000000000.0)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 8.2e+82)
		tmp = t;
	elseif (y <= 5.6e+126)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / (z - y));
	tmp = 0.0;
	if (y <= -3.8e+171)
		tmp = t;
	elseif (y <= -4.4e-63)
		tmp = t_1;
	elseif (y <= 60000000000000.0)
		tmp = x * (t / (z - y));
	elseif (y <= 8.2e+82)
		tmp = t;
	elseif (y <= 5.6e+126)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e+171], t, If[LessEqual[y, -4.4e-63], t$95$1, If[LessEqual[y, 60000000000000.0], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e+82], t, If[LessEqual[y, 5.6e+126], t$95$1, t]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8000000000000002e171 or 6e13 < y < 8.1999999999999999e82 or 5.60000000000000018e126 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 71.1%

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

      2. associate-*r/ 75.4%

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

   3. Simplified 75.4%

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

   4. Taylor expanded in y around inf 74.8%

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

   if -3.8000000000000002e171 < y < -4.3999999999999999e-63 or 8.1999999999999999e82 < y < 5.60000000000000018e126

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 56.4%

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

   if -4.3999999999999999e-63 < y < 6e13

   1. Initial program 91.3%

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

      1. associate-*l/ 88.8%

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

      2. associate-*r/ 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in x around inf 77.5%

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

      1. associate-*l/ 81.9%

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

      2. *-commutative 81.9%

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

   6. Simplified 81.9%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+171}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-63}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 60000000000000:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+82}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+126}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 60.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{+55}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-45}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-228}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 30000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x z))))
   (if (<= y -5.4e+55)
     t
     (if (<= y -8.5e-25)
       t_1
       (if (<= y -8.4e-45)
         t
         (if (<= y 4.4e-228)
           (/ x (/ z t))
           (if (<= y 30000000000.0) t_1 t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / z);
	double tmp;
	if (y <= -5.4e+55) {
		tmp = t;
	} else if (y <= -8.5e-25) {
		tmp = t_1;
	} else if (y <= -8.4e-45) {
		tmp = t;
	} else if (y <= 4.4e-228) {
		tmp = x / (z / t);
	} else if (y <= 30000000000.0) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (x / z)
    if (y <= (-5.4d+55)) then
        tmp = t
    else if (y <= (-8.5d-25)) then
        tmp = t_1
    else if (y <= (-8.4d-45)) then
        tmp = t
    else if (y <= 4.4d-228) then
        tmp = x / (z / t)
    else if (y <= 30000000000.0d0) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (x / z);
	double tmp;
	if (y <= -5.4e+55) {
		tmp = t;
	} else if (y <= -8.5e-25) {
		tmp = t_1;
	} else if (y <= -8.4e-45) {
		tmp = t;
	} else if (y <= 4.4e-228) {
		tmp = x / (z / t);
	} else if (y <= 30000000000.0) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / z)
	tmp = 0
	if y <= -5.4e+55:
		tmp = t
	elif y <= -8.5e-25:
		tmp = t_1
	elif y <= -8.4e-45:
		tmp = t
	elif y <= 4.4e-228:
		tmp = x / (z / t)
	elif y <= 30000000000.0:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / z))
	tmp = 0.0
	if (y <= -5.4e+55)
		tmp = t;
	elseif (y <= -8.5e-25)
		tmp = t_1;
	elseif (y <= -8.4e-45)
		tmp = t;
	elseif (y <= 4.4e-228)
		tmp = Float64(x / Float64(z / t));
	elseif (y <= 30000000000.0)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / z);
	tmp = 0.0;
	if (y <= -5.4e+55)
		tmp = t;
	elseif (y <= -8.5e-25)
		tmp = t_1;
	elseif (y <= -8.4e-45)
		tmp = t;
	elseif (y <= 4.4e-228)
		tmp = x / (z / t);
	elseif (y <= 30000000000.0)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.4e+55], t, If[LessEqual[y, -8.5e-25], t$95$1, If[LessEqual[y, -8.4e-45], t, If[LessEqual[y, 4.4e-228], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 30000000000.0], t$95$1, t]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.39999999999999954e55 or -8.49999999999999981e-25 < y < -8.3999999999999998e-45 or 3e10 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 74.4%

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

      2. associate-*r/ 81.0%

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

   3. Simplified 81.0%

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

   4. Taylor expanded in y around inf 59.4%

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

   if -5.39999999999999954e55 < y < -8.49999999999999981e-25 or 4.4000000000000001e-228 < y < 3e10

   1. Initial program 95.5%

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

   2. Taylor expanded in y around 0 58.5%

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

   if -8.3999999999999998e-45 < y < 4.4000000000000001e-228

   1. Initial program 90.1%

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

   2. Taylor expanded in y around 0 65.2%

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

      1. associate-*l/ 69.6%

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

      2. associate-/l* 71.9%

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

   4. Applied egg-rr 71.9%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+55}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-25}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-45}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-228}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 30000000000:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 60.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -3.05 \cdot 10^{+55}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-63}:\\ \;\;\;\;\frac{y}{\frac{y}{t}}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-189}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 460000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x z))))
   (if (<= y -3.05e+55)
     t
     (if (<= y -1.1e-24)
       t_1
       (if (<= y -7e-63)
         (/ y (/ y t))
         (if (<= y 1.45e-189)
           (/ x (/ z t))
           (if (<= y 460000000000.0) t_1 t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / z);
	double tmp;
	if (y <= -3.05e+55) {
		tmp = t;
	} else if (y <= -1.1e-24) {
		tmp = t_1;
	} else if (y <= -7e-63) {
		tmp = y / (y / t);
	} else if (y <= 1.45e-189) {
		tmp = x / (z / t);
	} else if (y <= 460000000000.0) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (x / z)
    if (y <= (-3.05d+55)) then
        tmp = t
    else if (y <= (-1.1d-24)) then
        tmp = t_1
    else if (y <= (-7d-63)) then
        tmp = y / (y / t)
    else if (y <= 1.45d-189) then
        tmp = x / (z / t)
    else if (y <= 460000000000.0d0) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (x / z);
	double tmp;
	if (y <= -3.05e+55) {
		tmp = t;
	} else if (y <= -1.1e-24) {
		tmp = t_1;
	} else if (y <= -7e-63) {
		tmp = y / (y / t);
	} else if (y <= 1.45e-189) {
		tmp = x / (z / t);
	} else if (y <= 460000000000.0) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / z)
	tmp = 0
	if y <= -3.05e+55:
		tmp = t
	elif y <= -1.1e-24:
		tmp = t_1
	elif y <= -7e-63:
		tmp = y / (y / t)
	elif y <= 1.45e-189:
		tmp = x / (z / t)
	elif y <= 460000000000.0:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / z))
	tmp = 0.0
	if (y <= -3.05e+55)
		tmp = t;
	elseif (y <= -1.1e-24)
		tmp = t_1;
	elseif (y <= -7e-63)
		tmp = Float64(y / Float64(y / t));
	elseif (y <= 1.45e-189)
		tmp = Float64(x / Float64(z / t));
	elseif (y <= 460000000000.0)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / z);
	tmp = 0.0;
	if (y <= -3.05e+55)
		tmp = t;
	elseif (y <= -1.1e-24)
		tmp = t_1;
	elseif (y <= -7e-63)
		tmp = y / (y / t);
	elseif (y <= 1.45e-189)
		tmp = x / (z / t);
	elseif (y <= 460000000000.0)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.05e+55], t, If[LessEqual[y, -1.1e-24], t$95$1, If[LessEqual[y, -7e-63], N[(y / N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e-189], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 460000000000.0], t$95$1, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.0500000000000001e55 or 4.6e11 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 73.5%

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

      2. associate-*r/ 80.4%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in y around inf 59.3%

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

   if -3.0500000000000001e55 < y < -1.10000000000000001e-24 or 1.45e-189 < y < 4.6e11

   1. Initial program 96.6%

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

   2. Taylor expanded in y around 0 56.6%

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

   if -1.10000000000000001e-24 < y < -7.00000000000000006e-63

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 27.2%

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

      1. neg-mul-1 27.2%

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

      2. distribute-neg-frac 27.2%

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

   4. Simplified 27.2%

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

      1. associate-*l/ 27.2%

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

      2. associate-/l* 36.2%

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

      3. add-sqr-sqrt 36.1%

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

      4. sqrt-unprod 36.2%

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

      5. sqr-neg 36.2%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 3.6%

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

      8. frac-2neg 3.6%

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

      9. add-sqr-sqrt 3.6%

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

      10. sqrt-unprod 3.6%

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

      11. sqr-neg 3.6%

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

      12. sqrt-unprod 0.0%

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

      13. add-sqr-sqrt 36.2%

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

      14. distribute-neg-frac 36.2%

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

      15. sub-neg 36.2%

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

      16. distribute-neg-in 36.2%

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

      17. remove-double-neg 36.2%

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

   6. Applied egg-rr 36.2%

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

   7. Taylor expanded in z around 0 36.2%

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

   if -7.00000000000000006e-63 < y < 1.45e-189

   1. Initial program 89.1%

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

   2. Taylor expanded in y around 0 69.9%

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

      1. associate-*l/ 71.3%

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

      2. associate-/l* 74.8%

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

   4. Applied egg-rr 74.8%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.05 \cdot 10^{+55}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-24}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-63}:\\ \;\;\;\;\frac{y}{\frac{y}{t}}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-189}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 460000000000:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{+81}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-31} \lor \neg \left(y \leq 820\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))))
   (if (<= y -3.8e+171)
     t_1
     (if (<= y -7.6e+81)
       (* t (/ x (- z y)))
       (if (or (<= y -1.15e-31) (not (<= y 820.0)))
         t_1
         (* x (/ t (- z y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -3.8e+171) {
		tmp = t_1;
	} else if (y <= -7.6e+81) {
		tmp = t * (x / (z - y));
	} else if ((y <= -1.15e-31) || !(y <= 820.0)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (y - z))
    if (y <= (-3.8d+171)) then
        tmp = t_1
    else if (y <= (-7.6d+81)) then
        tmp = t * (x / (z - y))
    else if ((y <= (-1.15d-31)) .or. (.not. (y <= 820.0d0))) then
        tmp = t_1
    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 t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -3.8e+171) {
		tmp = t_1;
	} else if (y <= -7.6e+81) {
		tmp = t * (x / (z - y));
	} else if ((y <= -1.15e-31) || !(y <= 820.0)) {
		tmp = t_1;
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	tmp = 0
	if y <= -3.8e+171:
		tmp = t_1
	elif y <= -7.6e+81:
		tmp = t * (x / (z - y))
	elif (y <= -1.15e-31) or not (y <= 820.0):
		tmp = t_1
	else:
		tmp = x * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (y <= -3.8e+171)
		tmp = t_1;
	elseif (y <= -7.6e+81)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif ((y <= -1.15e-31) || !(y <= 820.0))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	tmp = 0.0;
	if (y <= -3.8e+171)
		tmp = t_1;
	elseif (y <= -7.6e+81)
		tmp = t * (x / (z - y));
	elseif ((y <= -1.15e-31) || ~((y <= 820.0)))
		tmp = t_1;
	else
		tmp = x * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e+171], t$95$1, If[LessEqual[y, -7.6e+81], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.15e-31], N[Not[LessEqual[y, 820.0]], $MachinePrecision]], t$95$1, N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8000000000000002e171 or -7.599999999999999e81 < y < -1.1499999999999999e-31 or 820 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 82.4%

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

      1. neg-mul-1 82.4%

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

      2. distribute-neg-frac 82.4%

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

   4. Simplified 82.4%

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

      1. associate-*l/ 63.6%

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

      2. associate-/l* 68.5%

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

      3. add-sqr-sqrt 30.2%

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

      4. sqrt-unprod 18.5%

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

      5. sqr-neg 18.5%

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

      6. sqrt-unprod 2.8%

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

      7. add-sqr-sqrt 5.0%

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

      8. frac-2neg 5.0%

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

      9. add-sqr-sqrt 2.1%

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

      10. sqrt-unprod 23.8%

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

      11. sqr-neg 23.8%

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

      12. sqrt-unprod 37.9%

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

      13. add-sqr-sqrt 68.5%

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

      14. distribute-neg-frac 68.5%

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

      15. sub-neg 68.5%

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

      16. distribute-neg-in 68.5%

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

      17. remove-double-neg 68.5%

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

   6. Applied egg-rr 68.5%

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

      1. associate-/r/ 82.4%

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

      2. +-commutative 82.4%

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

      3. unsub-neg 82.4%

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

   8. Simplified 82.4%

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

   if -3.8000000000000002e171 < y < -7.599999999999999e81

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 63.2%

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

   if -1.1499999999999999e-31 < y < 820

   1. Initial program 91.8%

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

      1. associate-*l/ 89.4%

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

      2. associate-*r/ 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in x around inf 78.8%

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

      1. associate-*l/ 82.9%

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

      2. *-commutative 82.9%

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

   6. Simplified 82.9%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{+81}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-31} \lor \neg \left(y \leq 820\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]

Alternative 10: 74.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+138}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-35} \lor \neg \left(y \leq 10500000000000\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.7e+138)
   (- t (* t (/ x y)))
   (if (or (<= y -2.25e-35) (not (<= y 10500000000000.0)))
     (* t (/ y (- y z)))
     (* x (/ t (- z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.7e+138) {
		tmp = t - (t * (x / y));
	} else if ((y <= -2.25e-35) || !(y <= 10500000000000.0)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.7d+138)) then
        tmp = t - (t * (x / y))
    else if ((y <= (-2.25d-35)) .or. (.not. (y <= 10500000000000.0d0))) then
        tmp = t * (y / (y - z))
    else
        tmp = x * (t / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.7e+138) {
		tmp = t - (t * (x / y));
	} else if ((y <= -2.25e-35) || !(y <= 10500000000000.0)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.7e+138:
		tmp = t - (t * (x / y))
	elif (y <= -2.25e-35) or not (y <= 10500000000000.0):
		tmp = t * (y / (y - z))
	else:
		tmp = x * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.7e+138)
		tmp = Float64(t - Float64(t * Float64(x / y)));
	elseif ((y <= -2.25e-35) || !(y <= 10500000000000.0))
		tmp = Float64(t * Float64(y / Float64(y - z)));
	else
		tmp = Float64(x * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.7e+138)
		tmp = t - (t * (x / y));
	elseif ((y <= -2.25e-35) || ~((y <= 10500000000000.0)))
		tmp = t * (y / (y - z));
	else
		tmp = x * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.7e+138], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -2.25e-35], N[Not[LessEqual[y, 10500000000000.0]], $MachinePrecision]], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.70000000000000009e138

   1. Initial program 99.9%

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

      1. associate-*l/ 67.6%

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

      2. associate-*r/ 69.7%

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

   3. Simplified 69.7%

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

      1. *-commutative 69.7%

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

      2. sub-neg 69.7%

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

      3. distribute-lft-in 69.7%

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

      4. fma-def 69.7%

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

   5. Applied egg-rr 69.7%

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

   6. Taylor expanded in z around 0 73.2%

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

      1. mul-1-neg 73.2%

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

      2. associate-/l* 86.1%

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

      3. unsub-neg 86.1%

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

      4. associate-/l* 73.2%

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

      5. associate-*r/ 86.1%

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

   8. Simplified 86.1%

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

   if -2.70000000000000009e138 < y < -2.25000000000000005e-35 or 1.05e13 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 77.1%

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

      1. neg-mul-1 77.1%

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

      2. distribute-neg-frac 77.1%

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

   4. Simplified 77.1%

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

      1. associate-*l/ 63.1%

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

      2. associate-/l* 70.4%

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

      3. add-sqr-sqrt 23.3%

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

      4. sqrt-unprod 26.5%

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

      5. sqr-neg 26.5%

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

      6. sqrt-unprod 3.5%

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

      7. add-sqr-sqrt 5.4%

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

      8. frac-2neg 5.4%

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

      9. add-sqr-sqrt 1.9%

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

      10. sqrt-unprod 29.6%

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

      11. sqr-neg 29.6%

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

      12. sqrt-unprod 46.7%

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

      13. add-sqr-sqrt 70.4%

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

      14. distribute-neg-frac 70.4%

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

      15. sub-neg 70.4%

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

      16. distribute-neg-in 70.4%

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

      17. remove-double-neg 70.4%

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

   6. Applied egg-rr 70.4%

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

      1. associate-/r/ 77.1%

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

      2. +-commutative 77.1%

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

      3. unsub-neg 77.1%

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

   8. Simplified 77.1%

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

   if -2.25000000000000005e-35 < y < 1.05e13

   1. Initial program 91.8%

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

      1. associate-*l/ 89.4%

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

      2. associate-*r/ 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in x around inf 78.8%

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

      1. associate-*l/ 82.9%

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

      2. *-commutative 82.9%

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

   6. Simplified 82.9%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+138}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-35} \lor \neg \left(y \leq 10500000000000\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]

Alternative 11: 72.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+138}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-11}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq 2100000000:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.45e+138)
   (- t (* t (/ x y)))
   (if (<= y -3.2e-11)
     (/ t (/ z (- x y)))
     (if (<= y 2100000000.0) (* x (/ t (- z y))) (* t (/ y (- y z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e+138) {
		tmp = t - (t * (x / y));
	} else if (y <= -3.2e-11) {
		tmp = t / (z / (x - y));
	} else if (y <= 2100000000.0) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.45d+138)) then
        tmp = t - (t * (x / y))
    else if (y <= (-3.2d-11)) then
        tmp = t / (z / (x - y))
    else if (y <= 2100000000.0d0) then
        tmp = x * (t / (z - y))
    else
        tmp = t * (y / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e+138) {
		tmp = t - (t * (x / y));
	} else if (y <= -3.2e-11) {
		tmp = t / (z / (x - y));
	} else if (y <= 2100000000.0) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.45e+138:
		tmp = t - (t * (x / y))
	elif y <= -3.2e-11:
		tmp = t / (z / (x - y))
	elif y <= 2100000000.0:
		tmp = x * (t / (z - y))
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.45e+138)
		tmp = Float64(t - Float64(t * Float64(x / y)));
	elseif (y <= -3.2e-11)
		tmp = Float64(t / Float64(z / Float64(x - y)));
	elseif (y <= 2100000000.0)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = Float64(t * Float64(y / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.45e+138)
		tmp = t - (t * (x / y));
	elseif (y <= -3.2e-11)
		tmp = t / (z / (x - y));
	elseif (y <= 2100000000.0)
		tmp = x * (t / (z - y));
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.45e+138], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.2e-11], N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2100000000.0], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.45000000000000005e138

   1. Initial program 99.9%

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

      1. associate-*l/ 67.6%

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

      2. associate-*r/ 69.7%

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

   3. Simplified 69.7%

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

      1. *-commutative 69.7%

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

      2. sub-neg 69.7%

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

      3. distribute-lft-in 69.7%

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

      4. fma-def 69.7%

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

   5. Applied egg-rr 69.7%

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

   6. Taylor expanded in z around 0 73.2%

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

      1. mul-1-neg 73.2%

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

      2. associate-/l* 86.1%

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

      3. unsub-neg 86.1%

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

      4. associate-/l* 73.2%

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

      5. associate-*r/ 86.1%

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

   8. Simplified 86.1%

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

   if -1.45000000000000005e138 < y < -3.19999999999999994e-11

   1. Initial program 99.7%

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

      1. associate-*l/ 87.9%

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

      2. associate-*r/ 82.0%

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

   3. Simplified 82.0%

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

   4. Taylor expanded in z around inf 63.9%

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

      1. associate-/l* 69.9%

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

   6. Simplified 69.9%

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

   if -3.19999999999999994e-11 < y < 2.1e9

   1. Initial program 92.2%

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

      1. associate-*l/ 89.8%

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

      2. associate-*r/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in x around inf 77.3%

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

      1. associate-*l/ 81.3%

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

      2. *-commutative 81.3%

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

   6. Simplified 81.3%

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

   if 2.1e9 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 87.9%

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

      1. neg-mul-1 87.9%

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

      2. distribute-neg-frac 87.9%

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

   4. Simplified 87.9%

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

      1. associate-*l/ 68.1%

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

      2. associate-/l* 78.3%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 5.1%

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

      5. sqr-neg 5.1%

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

      6. sqrt-unprod 5.8%

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

      7. add-sqr-sqrt 5.8%

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

      8. frac-2neg 5.8%

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

      9. add-sqr-sqrt 0.0%

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

      10. sqrt-unprod 46.0%

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

      11. sqr-neg 46.0%

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

      12. sqrt-unprod 77.8%

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

      13. add-sqr-sqrt 78.3%

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

      14. distribute-neg-frac 78.3%

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

      15. sub-neg 78.3%

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

      16. distribute-neg-in 78.3%

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

      17. remove-double-neg 78.3%

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

   6. Applied egg-rr 78.3%

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

      1. associate-/r/ 87.9%

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

      2. +-commutative 87.9%

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

      3. unsub-neg 87.9%

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

   8. Simplified 87.9%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+138}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-11}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq 2100000000:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]

Alternative 12: 90.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+171} \lor \neg \left(y \leq 2.8 \cdot 10^{+124}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.4e+171) (not (<= y 2.8e+124)))
   (* t (/ y (- y z)))
   (* (- x y) (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.4e+171) || !(y <= 2.8e+124)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.4d+171)) .or. (.not. (y <= 2.8d+124))) then
        tmp = t * (y / (y - z))
    else
        tmp = (x - y) * (t / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.4e+171) || !(y <= 2.8e+124)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.4e+171) or not (y <= 2.8e+124):
		tmp = t * (y / (y - z))
	else:
		tmp = (x - y) * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.4e+171) || !(y <= 2.8e+124))
		tmp = Float64(t * Float64(y / Float64(y - z)));
	else
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.4e+171) || ~((y <= 2.8e+124)))
		tmp = t * (y / (y - z));
	else
		tmp = (x - y) * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.4e+171], N[Not[LessEqual[y, 2.8e+124]], $MachinePrecision]], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.3999999999999999e171 or 2.8e124 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 91.0%

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

      1. neg-mul-1 91.0%

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

      2. distribute-neg-frac 91.0%

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

   4. Simplified 91.0%

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

      1. associate-*l/ 57.5%

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

      2. associate-/l* 67.3%

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

      3. add-sqr-sqrt 26.7%

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

      4. sqrt-unprod 3.0%

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

      5. sqr-neg 3.0%

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

      6. sqrt-unprod 2.5%

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

      7. add-sqr-sqrt 4.1%

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

      8. frac-2neg 4.1%

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

      9. add-sqr-sqrt 1.6%

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

      10. sqrt-unprod 12.3%

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

      11. sqr-neg 12.3%

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

      12. sqrt-unprod 40.2%

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

      13. add-sqr-sqrt 67.3%

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

      14. distribute-neg-frac 67.3%

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

      15. sub-neg 67.3%

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

      16. distribute-neg-in 67.3%

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

      17. remove-double-neg 67.3%

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

   6. Applied egg-rr 67.3%

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

      1. associate-/r/ 91.0%

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

      2. +-commutative 91.0%

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

      3. unsub-neg 91.0%

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

   8. Simplified 91.0%

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

   if -4.3999999999999999e171 < y < 2.8e124

   1. Initial program 94.9%

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

      1. associate-*l/ 88.9%

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

      2. associate-*r/ 92.6%

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

   3. Simplified 92.6%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+171} \lor \neg \left(y \leq 2.8 \cdot 10^{+124}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \]

Alternative 13: 61.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+55}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 11200000:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.7e+55) t (if (<= y 11200000.0) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.7e+55) {
		tmp = t;
	} else if (y <= 11200000.0) {
		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 <= (-2.7d+55)) then
        tmp = t
    else if (y <= 11200000.0d0) 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 <= -2.7e+55) {
		tmp = t;
	} else if (y <= 11200000.0) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.7e+55:
		tmp = t
	elif y <= 11200000.0:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.7e+55)
		tmp = t;
	elseif (y <= 11200000.0)
		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 <= -2.7e+55)
		tmp = t;
	elseif (y <= 11200000.0)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.7e+55], t, If[LessEqual[y, 11200000.0], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.69999999999999977e55 or 1.12e7 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 73.5%

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

      2. associate-*r/ 80.4%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in y around inf 59.3%

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

   if -2.69999999999999977e55 < y < 1.12e7

   1. Initial program 93.0%

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

   2. Taylor expanded in y around 0 60.2%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+55}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 11200000:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 61.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+55}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7000000000:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.8e+55) t (if (<= y 7000000000.0) (/ t (/ z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.8e+55) {
		tmp = t;
	} else if (y <= 7000000000.0) {
		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 <= (-1.8d+55)) then
        tmp = t
    else if (y <= 7000000000.0d0) 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 <= -1.8e+55) {
		tmp = t;
	} else if (y <= 7000000000.0) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.8e+55:
		tmp = t
	elif y <= 7000000000.0:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.8e+55)
		tmp = t;
	elseif (y <= 7000000000.0)
		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 <= -1.8e+55)
		tmp = t;
	elseif (y <= 7000000000.0)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.8e+55], t, If[LessEqual[y, 7000000000.0], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.79999999999999994e55 or 7e9 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 73.5%

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

      2. associate-*r/ 80.4%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in y around inf 59.3%

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

   if -1.79999999999999994e55 < y < 7e9

   1. Initial program 93.0%

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

      1. associate-*l/ 90.8%

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

      2. associate-*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 y around 0 58.2%

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

      1. associate-/l* 60.8%

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

   6. Simplified 60.8%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+55}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7000000000:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15: 35.0% 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 96.2%

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

   1. associate-*l/ 82.8%

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

   2. associate-*r/ 87.4%

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

3. Simplified 87.4%

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

4. Taylor expanded in y around inf 34.7%

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

5. Final simplification 34.7%

   \[\leadsto t \]

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 2023257 
(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))