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

Percentage Accurate: 97.7% → 97.7%

Time: 6.9s

Alternatives: 12

Speedup: 1.0×

• 25.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x}{y} \cdot \left(z - t\right) + t \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \cdot \left(z - t\right) + t \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{x}{y}, z - t, t\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.4%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]
2. Step-by-step derivation

   1. fma-define 98.4%

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

3. Simplified 98.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{y}, z - t, t\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 71.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot z}{y}\\ t_2 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.000195:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+127}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x z) y)) (t_2 (* t (- 1.0 (/ x y)))))
   (if (<= z -4.2e+130)
     t_1
     (if (<= z 0.000195)
       t_2
       (if (<= z 1.25e+76) (* x (/ z y)) (if (<= z 7.6e+127) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * z) / y;
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (z <= -4.2e+130) {
		tmp = t_1;
	} else if (z <= 0.000195) {
		tmp = t_2;
	} else if (z <= 1.25e+76) {
		tmp = x * (z / y);
	} else if (z <= 7.6e+127) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (x * z) / y
    t_2 = t * (1.0d0 - (x / y))
    if (z <= (-4.2d+130)) then
        tmp = t_1
    else if (z <= 0.000195d0) then
        tmp = t_2
    else if (z <= 1.25d+76) then
        tmp = x * (z / y)
    else if (z <= 7.6d+127) then
        tmp = t_2
    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 = (x * z) / y;
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (z <= -4.2e+130) {
		tmp = t_1;
	} else if (z <= 0.000195) {
		tmp = t_2;
	} else if (z <= 1.25e+76) {
		tmp = x * (z / y);
	} else if (z <= 7.6e+127) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * z) / y
	t_2 = t * (1.0 - (x / y))
	tmp = 0
	if z <= -4.2e+130:
		tmp = t_1
	elif z <= 0.000195:
		tmp = t_2
	elif z <= 1.25e+76:
		tmp = x * (z / y)
	elif z <= 7.6e+127:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * z) / y)
	t_2 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (z <= -4.2e+130)
		tmp = t_1;
	elseif (z <= 0.000195)
		tmp = t_2;
	elseif (z <= 1.25e+76)
		tmp = Float64(x * Float64(z / y));
	elseif (z <= 7.6e+127)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * z) / y;
	t_2 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (z <= -4.2e+130)
		tmp = t_1;
	elseif (z <= 0.000195)
		tmp = t_2;
	elseif (z <= 1.25e+76)
		tmp = x * (z / y);
	elseif (z <= 7.6e+127)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+130], t$95$1, If[LessEqual[z, 0.000195], t$95$2, If[LessEqual[z, 1.25e+76], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.6e+127], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.19999999999999981e130 or 7.59999999999999961e127 < z

   1. Initial program 98.7%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 76.6%

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

      1. associate--l+ 76.6%

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

      2. div-sub 79.1%

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

   5. Simplified 79.1%

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

   6. Taylor expanded in t around 0 69.0%

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

      1. *-commutative 69.0%

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

      2. associate-*l/ 75.9%

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

   8. Applied egg-rr 75.9%

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

   if -4.19999999999999981e130 < z < 1.94999999999999996e-4 or 1.24999999999999998e76 < z < 7.59999999999999961e127

   1. Initial program 98.2%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 74.8%

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

      1. mul-1-neg 74.8%

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

      2. unsub-neg 74.8%

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

      3. *-rgt-identity 74.8%

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

      4. associate-/l* 77.7%

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

      5. distribute-lft-out-- 77.7%

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

   5. Simplified 77.7%

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

   if 1.94999999999999996e-4 < z < 1.24999999999999998e76

   1. Initial program 99.4%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 94.2%

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

      1. associate--l+ 94.2%

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

      2. div-sub 94.3%

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

   5. Simplified 94.3%

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

   6. Taylor expanded in t around 0 73.2%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+130}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{elif}\;z \leq 0.000195:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+127}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot z}{y}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+74}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-87}:\\ \;\;\;\;\frac{x \cdot t}{x}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x z) y)))
   (if (<= y -9.5e+74)
     t
     (if (<= y -1.3e-70)
       t_1
       (if (<= y -4.5e-87) (/ (* x t) x) (if (<= y 4.4e+127) t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * z) / y;
	double tmp;
	if (y <= -9.5e+74) {
		tmp = t;
	} else if (y <= -1.3e-70) {
		tmp = t_1;
	} else if (y <= -4.5e-87) {
		tmp = (x * t) / x;
	} else if (y <= 4.4e+127) {
		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 * z) / y
    if (y <= (-9.5d+74)) then
        tmp = t
    else if (y <= (-1.3d-70)) then
        tmp = t_1
    else if (y <= (-4.5d-87)) then
        tmp = (x * t) / x
    else if (y <= 4.4d+127) 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 * z) / y;
	double tmp;
	if (y <= -9.5e+74) {
		tmp = t;
	} else if (y <= -1.3e-70) {
		tmp = t_1;
	} else if (y <= -4.5e-87) {
		tmp = (x * t) / x;
	} else if (y <= 4.4e+127) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * z) / y
	tmp = 0
	if y <= -9.5e+74:
		tmp = t
	elif y <= -1.3e-70:
		tmp = t_1
	elif y <= -4.5e-87:
		tmp = (x * t) / x
	elif y <= 4.4e+127:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * z) / y)
	tmp = 0.0
	if (y <= -9.5e+74)
		tmp = t;
	elseif (y <= -1.3e-70)
		tmp = t_1;
	elseif (y <= -4.5e-87)
		tmp = Float64(Float64(x * t) / x);
	elseif (y <= 4.4e+127)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * z) / y;
	tmp = 0.0;
	if (y <= -9.5e+74)
		tmp = t;
	elseif (y <= -1.3e-70)
		tmp = t_1;
	elseif (y <= -4.5e-87)
		tmp = (x * t) / x;
	elseif (y <= 4.4e+127)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -9.5e+74], t, If[LessEqual[y, -1.3e-70], t$95$1, If[LessEqual[y, -4.5e-87], N[(N[(x * t), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[y, 4.4e+127], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.5000000000000006e74 or 4.4000000000000003e127 < y

   1. Initial program 98.8%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 62.1%

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

   if -9.5000000000000006e74 < y < -1.30000000000000001e-70 or -4.49999999999999958e-87 < y < 4.4000000000000003e127

   1. Initial program 98.1%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 80.1%

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

      1. associate--l+ 80.1%

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

      2. div-sub 82.0%

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

   5. Simplified 82.0%

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

   6. Taylor expanded in t around 0 55.1%

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

      1. *-commutative 55.1%

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

      2. associate-*l/ 62.6%

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

   8. Applied egg-rr 62.6%

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

   if -1.30000000000000001e-70 < y < -4.49999999999999958e-87

   1. Initial program 99.8%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 86.3%

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

      1. associate--l+ 86.3%

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

      2. div-sub 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in x around 0 31.2%

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

      1. associate-*r/ 71.9%

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

   8. Applied egg-rr 71.9%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+74}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-70}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-87}:\\ \;\;\;\;\frac{x \cdot t}{x}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+127}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -50000000000:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-14}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y} \cdot \left(x \cdot \left(z - t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -50000000000.0)
   (* x (/ (- z t) y))
   (if (<= (/ x y) 1e-14) (+ t (* (/ x y) z)) (* (/ 1.0 y) (* x (- z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -50000000000.0) {
		tmp = x * ((z - t) / y);
	} else if ((x / y) <= 1e-14) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = (1.0 / y) * (x * (z - 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 ((x / y) <= (-50000000000.0d0)) then
        tmp = x * ((z - t) / y)
    else if ((x / y) <= 1d-14) then
        tmp = t + ((x / y) * z)
    else
        tmp = (1.0d0 / y) * (x * (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -50000000000.0) {
		tmp = x * ((z - t) / y);
	} else if ((x / y) <= 1e-14) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = (1.0 / y) * (x * (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -50000000000.0:
		tmp = x * ((z - t) / y)
	elif (x / y) <= 1e-14:
		tmp = t + ((x / y) * z)
	else:
		tmp = (1.0 / y) * (x * (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -50000000000.0)
		tmp = Float64(x * Float64(Float64(z - t) / y));
	elseif (Float64(x / y) <= 1e-14)
		tmp = Float64(t + Float64(Float64(x / y) * z));
	else
		tmp = Float64(Float64(1.0 / y) * Float64(x * Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -50000000000.0)
		tmp = x * ((z - t) / y);
	elseif ((x / y) <= 1e-14)
		tmp = t + ((x / y) * z);
	else
		tmp = (1.0 / y) * (x * (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -50000000000.0], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-14], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / y), $MachinePrecision] * N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5e10

   1. Initial program 98.5%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 92.6%

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

      1. associate--l+ 92.6%

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

      2. div-sub 92.7%

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

   5. Simplified 92.7%

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

   6. Taylor expanded in x around inf 92.2%

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

      1. div-sub 92.3%

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

   8. Simplified 92.3%

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

   if -5e10 < (/.f64 x y) < 9.99999999999999999e-15

   1. Initial program 99.1%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 94.8%

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

      1. associate-/l* 90.1%

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

   5. Simplified 90.1%

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

      1. clear-num 90.1%

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

      2. un-div-inv 90.5%

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

   7. Applied egg-rr 90.5%

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

      1. associate-/r/ 98.9%

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

   9. Applied egg-rr 98.9%

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

   if 9.99999999999999999e-15 < (/.f64 x y)

   1. Initial program 97.1%

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

      1. *-commutative 97.1%

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

      2. clear-num 97.0%

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

      3. un-div-inv 97.0%

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

   4. Applied egg-rr 97.0%

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

   5. Taylor expanded in y around 0 95.7%

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

   6. Taylor expanded in x around -inf 95.0%

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

      1. clear-num 94.9%

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

      2. associate-/r/ 95.0%

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

   8. Applied egg-rr 95.0%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -50000000000:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-14}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y} \cdot \left(x \cdot \left(z - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -50000000000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -50000000000.0) (not (<= (/ x y) 5e-22)))
   (* x (/ (- z t) y))
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -50000000000.0) || !((x / y) <= 5e-22)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t + ((x / 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 (((x / y) <= (-50000000000.0d0)) .or. (.not. ((x / y) <= 5d-22))) then
        tmp = x * ((z - t) / y)
    else
        tmp = t + ((x / y) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -50000000000.0) || !((x / y) <= 5e-22)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -50000000000.0) or not ((x / y) <= 5e-22):
		tmp = x * ((z - t) / y)
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -50000000000.0) || !(Float64(x / y) <= 5e-22))
		tmp = Float64(x * Float64(Float64(z - t) / y));
	else
		tmp = Float64(t + Float64(Float64(x / y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -50000000000.0) || ~(((x / y) <= 5e-22)))
		tmp = x * ((z - t) / y);
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -50000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e-22]], $MachinePrecision]], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5e10 or 4.99999999999999954e-22 < (/.f64 x y)

   1. Initial program 97.8%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 91.4%

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

      1. associate--l+ 91.4%

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

      2. div-sub 93.6%

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

   5. Simplified 93.6%

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

   6. Taylor expanded in x around inf 90.4%

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

      1. div-sub 92.6%

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

   8. Simplified 92.6%

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

   if -5e10 < (/.f64 x y) < 4.99999999999999954e-22

   1. Initial program 99.1%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 95.5%

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

      1. associate-/l* 90.0%

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

   5. Simplified 90.0%

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

      1. clear-num 90.0%

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

      2. un-div-inv 90.4%

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

   7. Applied egg-rr 90.4%

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

      1. associate-/r/ 98.9%

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

   9. Applied egg-rr 98.9%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -50000000000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-10} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e-10) (not (<= (/ x y) 5e-22)))
   (* x (/ (- z t) y))
   (+ t (* x (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e-10) || !((x / y) <= 5e-22)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-1d-10)) .or. (.not. ((x / y) <= 5d-22))) then
        tmp = x * ((z - t) / y)
    else
        tmp = t + (x * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e-10) || !((x / y) <= 5e-22)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e-10) or not ((x / y) <= 5e-22):
		tmp = x * ((z - t) / y)
	else:
		tmp = t + (x * (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e-10) || !(Float64(x / y) <= 5e-22))
		tmp = Float64(x * Float64(Float64(z - t) / y));
	else
		tmp = Float64(t + Float64(x * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1e-10) || ~(((x / y) <= 5e-22)))
		tmp = x * ((z - t) / y);
	else
		tmp = t + (x * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e-10], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e-22]], $MachinePrecision]], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.00000000000000004e-10 or 4.99999999999999954e-22 < (/.f64 x y)

   1. Initial program 97.9%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 90.9%

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

      1. associate--l+ 90.9%

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

      2. div-sub 93.1%

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

   5. Simplified 93.1%

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

   6. Taylor expanded in x around inf 90.0%

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

      1. div-sub 92.1%

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

   8. Simplified 92.1%

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

   if -1.00000000000000004e-10 < (/.f64 x y) < 4.99999999999999954e-22

   1. Initial program 99.0%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 97.0%

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

      1. associate-/l* 90.5%

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

   5. Simplified 90.5%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-10} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-35} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-66}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e-35) (not (<= (/ x y) 5e-66))) (* x (/ (- z t) y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e-35) || !((x / y) <= 5e-66)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2d-35)) .or. (.not. ((x / y) <= 5d-66))) then
        tmp = x * ((z - t) / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e-35) || !((x / y) <= 5e-66)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e-35) or not ((x / y) <= 5e-66):
		tmp = x * ((z - t) / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e-35) || !(Float64(x / y) <= 5e-66))
		tmp = Float64(x * Float64(Float64(z - t) / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2e-35) || ~(((x / y) <= 5e-66)))
		tmp = x * ((z - t) / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e-35], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e-66]], $MachinePrecision]], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2.00000000000000002e-35 or 4.99999999999999962e-66 < (/.f64 x y)

   1. Initial program 98.0%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 88.2%

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

      1. associate--l+ 88.2%

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

      2. div-sub 90.2%

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

   5. Simplified 90.2%

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

   6. Taylor expanded in x around inf 85.6%

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

      1. div-sub 87.5%

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

   8. Simplified 87.5%

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

   if -2.00000000000000002e-35 < (/.f64 x y) < 4.99999999999999962e-66

   1. Initial program 98.9%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 74.8%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-35} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-66}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 94.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -50000000000:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-14}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -50000000000.0)
   (* x (/ (- z t) y))
   (if (<= (/ x y) 1e-14) (+ t (* (/ x y) z)) (/ (* x (- z t)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -50000000000.0) {
		tmp = x * ((z - t) / y);
	} else if ((x / y) <= 1e-14) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = (x * (z - t)) / 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 ((x / y) <= (-50000000000.0d0)) then
        tmp = x * ((z - t) / y)
    else if ((x / y) <= 1d-14) then
        tmp = t + ((x / y) * z)
    else
        tmp = (x * (z - t)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -50000000000.0) {
		tmp = x * ((z - t) / y);
	} else if ((x / y) <= 1e-14) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = (x * (z - t)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -50000000000.0:
		tmp = x * ((z - t) / y)
	elif (x / y) <= 1e-14:
		tmp = t + ((x / y) * z)
	else:
		tmp = (x * (z - t)) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -50000000000.0)
		tmp = Float64(x * Float64(Float64(z - t) / y));
	elseif (Float64(x / y) <= 1e-14)
		tmp = Float64(t + Float64(Float64(x / y) * z));
	else
		tmp = Float64(Float64(x * Float64(z - t)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -50000000000.0)
		tmp = x * ((z - t) / y);
	elseif ((x / y) <= 1e-14)
		tmp = t + ((x / y) * z);
	else
		tmp = (x * (z - t)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -50000000000.0], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-14], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5e10

   1. Initial program 98.5%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 92.6%

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

      1. associate--l+ 92.6%

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

      2. div-sub 92.7%

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

   5. Simplified 92.7%

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

   6. Taylor expanded in x around inf 92.2%

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

      1. div-sub 92.3%

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

   8. Simplified 92.3%

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

   if -5e10 < (/.f64 x y) < 9.99999999999999999e-15

   1. Initial program 99.1%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 94.8%

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

      1. associate-/l* 90.1%

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

   5. Simplified 90.1%

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

      1. clear-num 90.1%

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

      2. un-div-inv 90.5%

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

   7. Applied egg-rr 90.5%

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

      1. associate-/r/ 98.9%

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

   9. Applied egg-rr 98.9%

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

   if 9.99999999999999999e-15 < (/.f64 x y)

   1. Initial program 97.1%

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

      1. *-commutative 97.1%

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

      2. clear-num 97.0%

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

      3. un-div-inv 97.0%

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

   4. Applied egg-rr 97.0%

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

   5. Taylor expanded in y around 0 95.7%

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

   6. Taylor expanded in x around -inf 95.0%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -50000000000:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-14}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-75} \lor \neg \left(x \leq 1.3 \cdot 10^{+25}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5e-75) (not (<= x 1.3e+25))) (* x (/ z y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5e-75) || !(x <= 1.3e+25)) {
		tmp = x * (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-5d-75)) .or. (.not. (x <= 1.3d+25))) then
        tmp = x * (z / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5e-75) || !(x <= 1.3e+25)) {
		tmp = x * (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5e-75) or not (x <= 1.3e+25):
		tmp = x * (z / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5e-75) || !(x <= 1.3e+25))
		tmp = Float64(x * Float64(z / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5e-75) || ~((x <= 1.3e+25)))
		tmp = x * (z / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5e-75], N[Not[LessEqual[x, 1.3e+25]], $MachinePrecision]], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if x < -4.99999999999999979e-75 or 1.2999999999999999e25 < x

   1. Initial program 98.1%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 93.6%

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

      1. associate--l+ 93.6%

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

      2. div-sub 95.5%

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

   5. Simplified 95.5%

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

   6. Taylor expanded in t around 0 60.1%

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

   if -4.99999999999999979e-75 < x < 1.2999999999999999e25

   1. Initial program 98.9%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 59.9%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-75} \lor \neg \left(x \leq 1.3 \cdot 10^{+25}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-75}:\\ \;\;\;\;\frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+25}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.5e-75) (/ x (/ y z)) (if (<= x 1.3e+25) t (* x (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.5e-75) {
		tmp = x / (y / z);
	} else if (x <= 1.3e+25) {
		tmp = t;
	} else {
		tmp = x * (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-4.5d-75)) then
        tmp = x / (y / z)
    else if (x <= 1.3d+25) then
        tmp = t
    else
        tmp = x * (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.5e-75) {
		tmp = x / (y / z);
	} else if (x <= 1.3e+25) {
		tmp = t;
	} else {
		tmp = x * (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.5e-75:
		tmp = x / (y / z)
	elif x <= 1.3e+25:
		tmp = t
	else:
		tmp = x * (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.5e-75)
		tmp = Float64(x / Float64(y / z));
	elseif (x <= 1.3e+25)
		tmp = t;
	else
		tmp = Float64(x * Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.5e-75)
		tmp = x / (y / z);
	elseif (x <= 1.3e+25)
		tmp = t;
	else
		tmp = x * (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.5e-75], N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e+25], t, N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5000000000000003e-75

   1. Initial program 98.8%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 92.5%

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

      1. associate--l+ 92.5%

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

      2. div-sub 94.6%

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

   5. Simplified 94.6%

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

   6. Taylor expanded in t around 0 58.4%

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

      1. clear-num 73.9%

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

      2. un-div-inv 74.0%

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

   8. Applied egg-rr 58.5%

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

   if -4.5000000000000003e-75 < x < 1.2999999999999999e25

   1. Initial program 98.9%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 59.9%

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

   if 1.2999999999999999e25 < x

   1. Initial program 96.9%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 95.3%

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

      1. associate--l+ 95.3%

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

      2. div-sub 96.8%

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

   5. Simplified 96.8%

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

   6. Taylor expanded in t around 0 62.6%

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

Alternative 11: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ t + \frac{x}{y} \cdot \left(z - t\right) \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]
2. Add Preprocessing

3. Final simplification 98.4%

   \[\leadsto t + \frac{x}{y} \cdot \left(z - t\right) \]
4. Add Preprocessing

Alternative 12: 38.7% 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 98.4%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]
2. Add Preprocessing

3. Taylor expanded in x around 0 32.3%

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

Developer target: 97.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* (/ x y) (- z t)) t)))
   (if (< z 2.759456554562692e-282)
     t_1
     (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / 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 = ((x / y) * (z - t)) + t
    if (z < 2.759456554562692d-282) then
        tmp = t_1
    else if (z < 2.326994450874436d-110) then
        tmp = (x * ((z - t) / 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 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x / y) * (z - t)) + t
	tmp = 0
	if z < 2.759456554562692e-282:
		tmp = t_1
	elif z < 2.326994450874436e-110:
		tmp = (x * ((z - t) / y)) + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x / y) * Float64(z - t)) + t)
	tmp = 0.0
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = Float64(Float64(x * Float64(Float64(z - t) / y)) + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x / y) * (z - t)) + t;
	tmp = 0.0;
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = (x * ((z - t) / y)) + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]}, If[Less[z, 2.759456554562692e-282], t$95$1, If[Less[z, 2.326994450874436e-110], N[(N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024101 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

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