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

Percentage Accurate: 96.8% → 96.8%

Time: 12.0s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

Alternative 2: 74.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z} \cdot t\\ t_2 := \left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-60}:\\ \;\;\;\;\frac{x}{z - y} \cdot t\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+35}:\\ \;\;\;\;\frac{\left(-y\right) \cdot t}{z - y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+207}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ (- x y) z) t)) (t_2 (* (- 1.0 (/ x y)) t)))
   (if (<= y -1.25e+32)
     t_2
     (if (<= y -1.3e-196)
       t_1
       (if (<= y 1.65e-60)
         (* (/ x (- z y)) t)
         (if (<= y 3e+35)
           (/ (* (- y) t) (- z y))
           (if (<= y 7e+47)
             t_1
             (if (<= y 5.6e+207) t_2 (/ t (- 1.0 (/ z y)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x - y) / z) * t;
	double t_2 = (1.0 - (x / y)) * t;
	double tmp;
	if (y <= -1.25e+32) {
		tmp = t_2;
	} else if (y <= -1.3e-196) {
		tmp = t_1;
	} else if (y <= 1.65e-60) {
		tmp = (x / (z - y)) * t;
	} else if (y <= 3e+35) {
		tmp = (-y * t) / (z - y);
	} else if (y <= 7e+47) {
		tmp = t_1;
	} else if (y <= 5.6e+207) {
		tmp = t_2;
	} else {
		tmp = t / (1.0 - (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x - y) / z) * t
    t_2 = (1.0d0 - (x / y)) * t
    if (y <= (-1.25d+32)) then
        tmp = t_2
    else if (y <= (-1.3d-196)) then
        tmp = t_1
    else if (y <= 1.65d-60) then
        tmp = (x / (z - y)) * t
    else if (y <= 3d+35) then
        tmp = (-y * t) / (z - y)
    else if (y <= 7d+47) then
        tmp = t_1
    else if (y <= 5.6d+207) then
        tmp = t_2
    else
        tmp = t / (1.0d0 - (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((x - y) / z) * t;
	double t_2 = (1.0 - (x / y)) * t;
	double tmp;
	if (y <= -1.25e+32) {
		tmp = t_2;
	} else if (y <= -1.3e-196) {
		tmp = t_1;
	} else if (y <= 1.65e-60) {
		tmp = (x / (z - y)) * t;
	} else if (y <= 3e+35) {
		tmp = (-y * t) / (z - y);
	} else if (y <= 7e+47) {
		tmp = t_1;
	} else if (y <= 5.6e+207) {
		tmp = t_2;
	} else {
		tmp = t / (1.0 - (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x - y) / z) * t
	t_2 = (1.0 - (x / y)) * t
	tmp = 0
	if y <= -1.25e+32:
		tmp = t_2
	elif y <= -1.3e-196:
		tmp = t_1
	elif y <= 1.65e-60:
		tmp = (x / (z - y)) * t
	elif y <= 3e+35:
		tmp = (-y * t) / (z - y)
	elif y <= 7e+47:
		tmp = t_1
	elif y <= 5.6e+207:
		tmp = t_2
	else:
		tmp = t / (1.0 - (z / y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x - y) / z) * t)
	t_2 = Float64(Float64(1.0 - Float64(x / y)) * t)
	tmp = 0.0
	if (y <= -1.25e+32)
		tmp = t_2;
	elseif (y <= -1.3e-196)
		tmp = t_1;
	elseif (y <= 1.65e-60)
		tmp = Float64(Float64(x / Float64(z - y)) * t);
	elseif (y <= 3e+35)
		tmp = Float64(Float64(Float64(-y) * t) / Float64(z - y));
	elseif (y <= 7e+47)
		tmp = t_1;
	elseif (y <= 5.6e+207)
		tmp = t_2;
	else
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x - y) / z) * t;
	t_2 = (1.0 - (x / y)) * t;
	tmp = 0.0;
	if (y <= -1.25e+32)
		tmp = t_2;
	elseif (y <= -1.3e-196)
		tmp = t_1;
	elseif (y <= 1.65e-60)
		tmp = (x / (z - y)) * t;
	elseif (y <= 3e+35)
		tmp = (-y * t) / (z - y);
	elseif (y <= 7e+47)
		tmp = t_1;
	elseif (y <= 5.6e+207)
		tmp = t_2;
	else
		tmp = t / (1.0 - (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[y, -1.25e+32], t$95$2, If[LessEqual[y, -1.3e-196], t$95$1, If[LessEqual[y, 1.65e-60], N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 3e+35], N[(N[((-y) * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+47], t$95$1, If[LessEqual[y, 5.6e+207], t$95$2, N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.2499999999999999e32 or 7.00000000000000031e47 < y < 5.60000000000000022e207

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.2499999999999999e32 < y < -1.2999999999999999e-196 or 2.99999999999999991e35 < y < 7.00000000000000031e47

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.2999999999999999e-196 < y < 1.6499999999999999e-60

   1. Initial program 93.6%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1.6499999999999999e-60 < y < 2.99999999999999991e35

   1. Initial program 96.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 5.60000000000000022e207 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 3: 74.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z} \cdot t\\ t_2 := \left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.56 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{z - y} \cdot t\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+39}:\\ \;\;\;\;\frac{y}{\frac{y - z}{t}}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+212}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ (- x y) z) t)) (t_2 (* (- 1.0 (/ x y)) t)))
   (if (<= y -1.2e+34)
     t_2
     (if (<= y -1.4e-195)
       t_1
       (if (<= y 1.56e-59)
         (* (/ x (- z y)) t)
         (if (<= y 2.75e+39)
           (/ y (/ (- y z) t))
           (if (<= y 4.6e+48)
             t_1
             (if (<= y 1.25e+212) t_2 (/ t (- 1.0 (/ z y)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x - y) / z) * t;
	double t_2 = (1.0 - (x / y)) * t;
	double tmp;
	if (y <= -1.2e+34) {
		tmp = t_2;
	} else if (y <= -1.4e-195) {
		tmp = t_1;
	} else if (y <= 1.56e-59) {
		tmp = (x / (z - y)) * t;
	} else if (y <= 2.75e+39) {
		tmp = y / ((y - z) / t);
	} else if (y <= 4.6e+48) {
		tmp = t_1;
	} else if (y <= 1.25e+212) {
		tmp = t_2;
	} else {
		tmp = t / (1.0 - (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x - y) / z) * t
    t_2 = (1.0d0 - (x / y)) * t
    if (y <= (-1.2d+34)) then
        tmp = t_2
    else if (y <= (-1.4d-195)) then
        tmp = t_1
    else if (y <= 1.56d-59) then
        tmp = (x / (z - y)) * t
    else if (y <= 2.75d+39) then
        tmp = y / ((y - z) / t)
    else if (y <= 4.6d+48) then
        tmp = t_1
    else if (y <= 1.25d+212) then
        tmp = t_2
    else
        tmp = t / (1.0d0 - (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((x - y) / z) * t;
	double t_2 = (1.0 - (x / y)) * t;
	double tmp;
	if (y <= -1.2e+34) {
		tmp = t_2;
	} else if (y <= -1.4e-195) {
		tmp = t_1;
	} else if (y <= 1.56e-59) {
		tmp = (x / (z - y)) * t;
	} else if (y <= 2.75e+39) {
		tmp = y / ((y - z) / t);
	} else if (y <= 4.6e+48) {
		tmp = t_1;
	} else if (y <= 1.25e+212) {
		tmp = t_2;
	} else {
		tmp = t / (1.0 - (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x - y) / z) * t
	t_2 = (1.0 - (x / y)) * t
	tmp = 0
	if y <= -1.2e+34:
		tmp = t_2
	elif y <= -1.4e-195:
		tmp = t_1
	elif y <= 1.56e-59:
		tmp = (x / (z - y)) * t
	elif y <= 2.75e+39:
		tmp = y / ((y - z) / t)
	elif y <= 4.6e+48:
		tmp = t_1
	elif y <= 1.25e+212:
		tmp = t_2
	else:
		tmp = t / (1.0 - (z / y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x - y) / z) * t)
	t_2 = Float64(Float64(1.0 - Float64(x / y)) * t)
	tmp = 0.0
	if (y <= -1.2e+34)
		tmp = t_2;
	elseif (y <= -1.4e-195)
		tmp = t_1;
	elseif (y <= 1.56e-59)
		tmp = Float64(Float64(x / Float64(z - y)) * t);
	elseif (y <= 2.75e+39)
		tmp = Float64(y / Float64(Float64(y - z) / t));
	elseif (y <= 4.6e+48)
		tmp = t_1;
	elseif (y <= 1.25e+212)
		tmp = t_2;
	else
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x - y) / z) * t;
	t_2 = (1.0 - (x / y)) * t;
	tmp = 0.0;
	if (y <= -1.2e+34)
		tmp = t_2;
	elseif (y <= -1.4e-195)
		tmp = t_1;
	elseif (y <= 1.56e-59)
		tmp = (x / (z - y)) * t;
	elseif (y <= 2.75e+39)
		tmp = y / ((y - z) / t);
	elseif (y <= 4.6e+48)
		tmp = t_1;
	elseif (y <= 1.25e+212)
		tmp = t_2;
	else
		tmp = t / (1.0 - (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[y, -1.2e+34], t$95$2, If[LessEqual[y, -1.4e-195], t$95$1, If[LessEqual[y, 1.56e-59], N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 2.75e+39], N[(y / N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+48], t$95$1, If[LessEqual[y, 1.25e+212], t$95$2, N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.19999999999999993e34 or 4.6e48 < y < 1.24999999999999998e212

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.19999999999999993e34 < y < -1.40000000000000002e-195 or 2.7499999999999999e39 < y < 4.6e48

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.40000000000000002e-195 < y < 1.5600000000000001e-59

   1. Initial program 93.6%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1.5600000000000001e-59 < y < 2.7499999999999999e39

   1. Initial program 96.8%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if 1.24999999999999998e212 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 4: 74.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{z} \cdot \left(x - y\right)\\ t_2 := \left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-198}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.35 \cdot 10^{-177}:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ t z) (- x y))) (t_2 (* (- 1.0 (/ x y)) t)))
   (if (<= y -6.5e+34)
     t_2
     (if (<= y -8.6e-198)
       t_1
       (if (<= y 3.35e-177)
         (* (/ t (- z y)) x)
         (if (<= y 5.5e-38) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t / z) * (x - y);
	double t_2 = (1.0 - (x / y)) * t;
	double tmp;
	if (y <= -6.5e+34) {
		tmp = t_2;
	} else if (y <= -8.6e-198) {
		tmp = t_1;
	} else if (y <= 3.35e-177) {
		tmp = (t / (z - y)) * x;
	} else if (y <= 5.5e-38) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t / z) * (x - y)
    t_2 = (1.0d0 - (x / y)) * t
    if (y <= (-6.5d+34)) then
        tmp = t_2
    else if (y <= (-8.6d-198)) then
        tmp = t_1
    else if (y <= 3.35d-177) then
        tmp = (t / (z - y)) * x
    else if (y <= 5.5d-38) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t / z) * (x - y);
	double t_2 = (1.0 - (x / y)) * t;
	double tmp;
	if (y <= -6.5e+34) {
		tmp = t_2;
	} else if (y <= -8.6e-198) {
		tmp = t_1;
	} else if (y <= 3.35e-177) {
		tmp = (t / (z - y)) * x;
	} else if (y <= 5.5e-38) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t / z) * (x - y)
	t_2 = (1.0 - (x / y)) * t
	tmp = 0
	if y <= -6.5e+34:
		tmp = t_2
	elif y <= -8.6e-198:
		tmp = t_1
	elif y <= 3.35e-177:
		tmp = (t / (z - y)) * x
	elif y <= 5.5e-38:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t / z) * Float64(x - y))
	t_2 = Float64(Float64(1.0 - Float64(x / y)) * t)
	tmp = 0.0
	if (y <= -6.5e+34)
		tmp = t_2;
	elseif (y <= -8.6e-198)
		tmp = t_1;
	elseif (y <= 3.35e-177)
		tmp = Float64(Float64(t / Float64(z - y)) * x);
	elseif (y <= 5.5e-38)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t / z) * (x - y);
	t_2 = (1.0 - (x / y)) * t;
	tmp = 0.0;
	if (y <= -6.5e+34)
		tmp = t_2;
	elseif (y <= -8.6e-198)
		tmp = t_1;
	elseif (y <= 3.35e-177)
		tmp = (t / (z - y)) * x;
	elseif (y <= 5.5e-38)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t / z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[y, -6.5e+34], t$95$2, If[LessEqual[y, -8.6e-198], t$95$1, If[LessEqual[y, 3.35e-177], N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 5.5e-38], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.50000000000000017e34 or 5.50000000000000005e-38 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -6.50000000000000017e34 < y < -8.6000000000000007e-198 or 3.35e-177 < y < 5.50000000000000005e-38

   1. Initial program 96.7%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -8.6000000000000007e-198 < y < 3.35e-177

   1. Initial program 92.7%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 75.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+36}:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-197}:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.65e+36)
   (* (- 1.0 (/ x y)) t)
   (if (<= y -1.15e-197)
     (* (/ (- x y) z) t)
     (if (<= y 2.7e-38) (* (/ x (- z y)) t) (/ t (/ (- y z) y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65e+36) {
		tmp = (1.0 - (x / y)) * t;
	} else if (y <= -1.15e-197) {
		tmp = ((x - y) / z) * t;
	} else if (y <= 2.7e-38) {
		tmp = (x / (z - y)) * t;
	} else {
		tmp = t / ((y - z) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.65d+36)) then
        tmp = (1.0d0 - (x / y)) * t
    else if (y <= (-1.15d-197)) then
        tmp = ((x - y) / z) * t
    else if (y <= 2.7d-38) then
        tmp = (x / (z - y)) * t
    else
        tmp = t / ((y - z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65e+36) {
		tmp = (1.0 - (x / y)) * t;
	} else if (y <= -1.15e-197) {
		tmp = ((x - y) / z) * t;
	} else if (y <= 2.7e-38) {
		tmp = (x / (z - y)) * t;
	} else {
		tmp = t / ((y - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.65e+36:
		tmp = (1.0 - (x / y)) * t
	elif y <= -1.15e-197:
		tmp = ((x - y) / z) * t
	elif y <= 2.7e-38:
		tmp = (x / (z - y)) * t
	else:
		tmp = t / ((y - z) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.65e+36)
		tmp = Float64(Float64(1.0 - Float64(x / y)) * t);
	elseif (y <= -1.15e-197)
		tmp = Float64(Float64(Float64(x - y) / z) * t);
	elseif (y <= 2.7e-38)
		tmp = Float64(Float64(x / Float64(z - y)) * t);
	else
		tmp = Float64(t / Float64(Float64(y - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.65e+36)
		tmp = (1.0 - (x / y)) * t;
	elseif (y <= -1.15e-197)
		tmp = ((x - y) / z) * t;
	elseif (y <= 2.7e-38)
		tmp = (x / (z - y)) * t;
	else
		tmp = t / ((y - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.65e+36], N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, -1.15e-197], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 2.7e-38], N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(t / N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.6499999999999999e36

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.6499999999999999e36 < y < -1.15e-197

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.15e-197 < y < 2.70000000000000005e-38

   1. Initial program 93.3%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 2.70000000000000005e-38 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 6: 75.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+32}:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-195}:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9.8e+32)
   (* (- 1.0 (/ x y)) t)
   (if (<= y -3.4e-195)
     (* (/ (- x y) z) t)
     (if (<= y 5.2e-38) (* (/ x (- z y)) t) (/ t (- 1.0 (/ z y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.8e+32) {
		tmp = (1.0 - (x / y)) * t;
	} else if (y <= -3.4e-195) {
		tmp = ((x - y) / z) * t;
	} else if (y <= 5.2e-38) {
		tmp = (x / (z - y)) * t;
	} else {
		tmp = t / (1.0 - (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-9.8d+32)) then
        tmp = (1.0d0 - (x / y)) * t
    else if (y <= (-3.4d-195)) then
        tmp = ((x - y) / z) * t
    else if (y <= 5.2d-38) then
        tmp = (x / (z - y)) * t
    else
        tmp = t / (1.0d0 - (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.8e+32) {
		tmp = (1.0 - (x / y)) * t;
	} else if (y <= -3.4e-195) {
		tmp = ((x - y) / z) * t;
	} else if (y <= 5.2e-38) {
		tmp = (x / (z - y)) * t;
	} else {
		tmp = t / (1.0 - (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9.8e+32:
		tmp = (1.0 - (x / y)) * t
	elif y <= -3.4e-195:
		tmp = ((x - y) / z) * t
	elif y <= 5.2e-38:
		tmp = (x / (z - y)) * t
	else:
		tmp = t / (1.0 - (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9.8e+32)
		tmp = Float64(Float64(1.0 - Float64(x / y)) * t);
	elseif (y <= -3.4e-195)
		tmp = Float64(Float64(Float64(x - y) / z) * t);
	elseif (y <= 5.2e-38)
		tmp = Float64(Float64(x / Float64(z - y)) * t);
	else
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -9.8e+32)
		tmp = (1.0 - (x / y)) * t;
	elseif (y <= -3.4e-195)
		tmp = ((x - y) / z) * t;
	elseif (y <= 5.2e-38)
		tmp = (x / (z - y)) * t;
	else
		tmp = t / (1.0 - (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9.8e+32], N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, -3.4e-195], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 5.2e-38], N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.8000000000000003e32

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -9.8000000000000003e32 < y < -3.40000000000000001e-195

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -3.40000000000000001e-195 < y < 5.20000000000000022e-38

   1. Initial program 93.3%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 5.20000000000000022e-38 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 7: 75.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-197}:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- 1.0 (/ x y)) t)))
   (if (<= y -2.1e+32)
     t_1
     (if (<= y -1.15e-197)
       (* (/ (- x y) z) t)
       (if (<= y 8.2e-39) (* (/ x (- z y)) t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (1.0 - (x / y)) * t;
	double tmp;
	if (y <= -2.1e+32) {
		tmp = t_1;
	} else if (y <= -1.15e-197) {
		tmp = ((x - y) / z) * t;
	} else if (y <= 8.2e-39) {
		tmp = (x / (z - y)) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (1.0d0 - (x / y)) * t
    if (y <= (-2.1d+32)) then
        tmp = t_1
    else if (y <= (-1.15d-197)) then
        tmp = ((x - y) / z) * t
    else if (y <= 8.2d-39) then
        tmp = (x / (z - y)) * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (1.0 - (x / y)) * t;
	double tmp;
	if (y <= -2.1e+32) {
		tmp = t_1;
	} else if (y <= -1.15e-197) {
		tmp = ((x - y) / z) * t;
	} else if (y <= 8.2e-39) {
		tmp = (x / (z - y)) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (1.0 - (x / y)) * t
	tmp = 0
	if y <= -2.1e+32:
		tmp = t_1
	elif y <= -1.15e-197:
		tmp = ((x - y) / z) * t
	elif y <= 8.2e-39:
		tmp = (x / (z - y)) * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(1.0 - Float64(x / y)) * t)
	tmp = 0.0
	if (y <= -2.1e+32)
		tmp = t_1;
	elseif (y <= -1.15e-197)
		tmp = Float64(Float64(Float64(x - y) / z) * t);
	elseif (y <= 8.2e-39)
		tmp = Float64(Float64(x / Float64(z - y)) * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (1.0 - (x / y)) * t;
	tmp = 0.0;
	if (y <= -2.1e+32)
		tmp = t_1;
	elseif (y <= -1.15e-197)
		tmp = ((x - y) / z) * t;
	elseif (y <= 8.2e-39)
		tmp = (x / (z - y)) * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[y, -2.1e+32], t$95$1, If[LessEqual[y, -1.15e-197], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 8.2e-39], N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1000000000000001e32 or 8.2e-39 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -2.1000000000000001e32 < y < -1.15e-197

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.15e-197 < y < 8.2e-39

   1. Initial program 93.3%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 89.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+186}:\\ \;\;\;\;\frac{t}{z - y} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (- 1.0 (/ z y)))))
   (if (<= y -7.5e+160)
     t_1
     (if (<= y 1.6e+186) (* (/ t (- z y)) (- x y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -7.5e+160) {
		tmp = t_1;
	} else if (y <= 1.6e+186) {
		tmp = (t / (z - y)) * (x - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (1.0d0 - (z / y))
    if (y <= (-7.5d+160)) then
        tmp = t_1
    else if (y <= 1.6d+186) then
        tmp = (t / (z - y)) * (x - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -7.5e+160) {
		tmp = t_1;
	} else if (y <= 1.6e+186) {
		tmp = (t / (z - y)) * (x - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (1.0 - (z / y))
	tmp = 0
	if y <= -7.5e+160:
		tmp = t_1
	elif y <= 1.6e+186:
		tmp = (t / (z - y)) * (x - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(1.0 - Float64(z / y)))
	tmp = 0.0
	if (y <= -7.5e+160)
		tmp = t_1;
	elseif (y <= 1.6e+186)
		tmp = Float64(Float64(t / Float64(z - y)) * Float64(x - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (1.0 - (z / y));
	tmp = 0.0;
	if (y <= -7.5e+160)
		tmp = t_1;
	elseif (y <= 1.6e+186)
		tmp = (t / (z - y)) * (x - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.5e+160], t$95$1, If[LessEqual[y, 1.6e+186], N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.50000000000000028e160 or 1.6e186 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -7.50000000000000028e160 < y < 1.6e186

   1. Initial program 96.5%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 74.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{if}\;y \leq -2.85 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-41}:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- 1.0 (/ x y)) t)))
   (if (<= y -2.85e+32) t_1 (if (<= y 1.8e-41) (* (/ t z) (- x y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (1.0 - (x / y)) * t;
	double tmp;
	if (y <= -2.85e+32) {
		tmp = t_1;
	} else if (y <= 1.8e-41) {
		tmp = (t / z) * (x - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (1.0d0 - (x / y)) * t
    if (y <= (-2.85d+32)) then
        tmp = t_1
    else if (y <= 1.8d-41) then
        tmp = (t / z) * (x - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (1.0 - (x / y)) * t;
	double tmp;
	if (y <= -2.85e+32) {
		tmp = t_1;
	} else if (y <= 1.8e-41) {
		tmp = (t / z) * (x - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (1.0 - (x / y)) * t
	tmp = 0
	if y <= -2.85e+32:
		tmp = t_1
	elif y <= 1.8e-41:
		tmp = (t / z) * (x - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(1.0 - Float64(x / y)) * t)
	tmp = 0.0
	if (y <= -2.85e+32)
		tmp = t_1;
	elseif (y <= 1.8e-41)
		tmp = Float64(Float64(t / z) * Float64(x - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (1.0 - (x / y)) * t;
	tmp = 0.0;
	if (y <= -2.85e+32)
		tmp = t_1;
	elseif (y <= 1.8e-41)
		tmp = (t / z) * (x - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[y, -2.85e+32], t$95$1, If[LessEqual[y, 1.8e-41], N[(N[(t / z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.85e32 or 1.8e-41 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -2.85e32 < y < 1.8e-41

   1. Initial program 95.0%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 71.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{-48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-42}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- 1.0 (/ x y)) t)))
   (if (<= y -1.65e-48) t_1 (if (<= y 1.22e-42) (/ t (/ z x)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (1.0 - (x / y)) * t;
	double tmp;
	if (y <= -1.65e-48) {
		tmp = t_1;
	} else if (y <= 1.22e-42) {
		tmp = t / (z / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (1.0d0 - (x / y)) * t
    if (y <= (-1.65d-48)) then
        tmp = t_1
    else if (y <= 1.22d-42) then
        tmp = t / (z / x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (1.0 - (x / y)) * t;
	double tmp;
	if (y <= -1.65e-48) {
		tmp = t_1;
	} else if (y <= 1.22e-42) {
		tmp = t / (z / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (1.0 - (x / y)) * t
	tmp = 0
	if y <= -1.65e-48:
		tmp = t_1
	elif y <= 1.22e-42:
		tmp = t / (z / x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(1.0 - Float64(x / y)) * t)
	tmp = 0.0
	if (y <= -1.65e-48)
		tmp = t_1;
	elseif (y <= 1.22e-42)
		tmp = Float64(t / Float64(z / x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (1.0 - (x / y)) * t;
	tmp = 0.0;
	if (y <= -1.65e-48)
		tmp = t_1;
	elseif (y <= 1.22e-42)
		tmp = t / (z / x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[y, -1.65e-48], t$95$1, If[LessEqual[y, 1.22e-42], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.65e-48 or 1.22000000000000007e-42 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.65e-48 < y < 1.22000000000000007e-42

   1. Initial program 94.2%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 61.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+64}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.8e+64) t (if (<= y 2.4e-38) (* (/ x z) t) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.8e+64) {
		tmp = t;
	} else if (y <= 2.4e-38) {
		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) :: tmp
    if (y <= (-8.8d+64)) then
        tmp = t
    else if (y <= 2.4d-38) 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 tmp;
	if (y <= -8.8e+64) {
		tmp = t;
	} else if (y <= 2.4e-38) {
		tmp = (x / z) * t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.8e+64:
		tmp = t
	elif y <= 2.4e-38:
		tmp = (x / z) * t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.8e+64)
		tmp = t;
	elseif (y <= 2.4e-38)
		tmp = Float64(Float64(x / z) * t);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8.8e+64)
		tmp = t;
	elseif (y <= 2.4e-38)
		tmp = (x / z) * t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.8e+64], t, If[LessEqual[y, 2.4e-38], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -8.80000000000000007e64 or 2.40000000000000022e-38 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -8.80000000000000007e64 < y < 2.40000000000000022e-38

   1. Initial program 95.2%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 60.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+64}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-51}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8e+64) t (if (<= y 3.9e-51) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8e+64) {
		tmp = t;
	} else if (y <= 3.9e-51) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-8d+64)) then
        tmp = t
    else if (y <= 3.9d-51) then
        tmp = x * (t / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8e+64) {
		tmp = t;
	} else if (y <= 3.9e-51) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8e+64:
		tmp = t
	elif y <= 3.9e-51:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8e+64)
		tmp = t;
	elseif (y <= 3.9e-51)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8e+64)
		tmp = t;
	elseif (y <= 3.9e-51)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8e+64], t, If[LessEqual[y, 3.9e-51], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -8.00000000000000017e64 or 3.8999999999999997e-51 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -8.00000000000000017e64 < y < 3.8999999999999997e-51

   1. Initial program 95.2%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 34.8% 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 97.3%

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

3. Taylor expanded in y around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Developer target: 96.9% 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 2024110 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (/ t (/ (- z y) (- x y)))

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