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

Percentage Accurate: 97.6% → 97.6%

Time: 8.3s

Alternatives: 10

Speedup: 1.0×

• 25.4% 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: 97.6% 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: 97.6% 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 97.0%

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

2. Final simplification 97.0%

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

Alternative 2: 63.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot z\\ t_2 := \frac{x}{y} \cdot \left(-t\right)\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+73}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-55}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+98} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+203}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) z)) (t_2 (* (/ x y) (- t))))
   (if (<= (/ x y) -2e+73)
     t_2
     (if (<= (/ x y) -5e-144)
       t_1
       (if (<= (/ x y) 1e-55)
         t
         (if (or (<= (/ x y) 5e+98) (not (<= (/ x y) 4e+203))) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * z;
	double t_2 = (x / y) * -t;
	double tmp;
	if ((x / y) <= -2e+73) {
		tmp = t_2;
	} else if ((x / y) <= -5e-144) {
		tmp = t_1;
	} else if ((x / y) <= 1e-55) {
		tmp = t;
	} else if (((x / y) <= 5e+98) || !((x / y) <= 4e+203)) {
		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 = (x / y) * z
    t_2 = (x / y) * -t
    if ((x / y) <= (-2d+73)) then
        tmp = t_2
    else if ((x / y) <= (-5d-144)) then
        tmp = t_1
    else if ((x / y) <= 1d-55) then
        tmp = t
    else if (((x / y) <= 5d+98) .or. (.not. ((x / y) <= 4d+203))) 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 = (x / y) * z;
	double t_2 = (x / y) * -t;
	double tmp;
	if ((x / y) <= -2e+73) {
		tmp = t_2;
	} else if ((x / y) <= -5e-144) {
		tmp = t_1;
	} else if ((x / y) <= 1e-55) {
		tmp = t;
	} else if (((x / y) <= 5e+98) || !((x / y) <= 4e+203)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * z
	t_2 = (x / y) * -t
	tmp = 0
	if (x / y) <= -2e+73:
		tmp = t_2
	elif (x / y) <= -5e-144:
		tmp = t_1
	elif (x / y) <= 1e-55:
		tmp = t
	elif ((x / y) <= 5e+98) or not ((x / y) <= 4e+203):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * z)
	t_2 = Float64(Float64(x / y) * Float64(-t))
	tmp = 0.0
	if (Float64(x / y) <= -2e+73)
		tmp = t_2;
	elseif (Float64(x / y) <= -5e-144)
		tmp = t_1;
	elseif (Float64(x / y) <= 1e-55)
		tmp = t;
	elseif ((Float64(x / y) <= 5e+98) || !(Float64(x / y) <= 4e+203))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * z;
	t_2 = (x / y) * -t;
	tmp = 0.0;
	if ((x / y) <= -2e+73)
		tmp = t_2;
	elseif ((x / y) <= -5e-144)
		tmp = t_1;
	elseif ((x / y) <= 1e-55)
		tmp = t;
	elseif (((x / y) <= 5e+98) || ~(((x / y) <= 4e+203)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e+73], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], -5e-144], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 1e-55], t, If[Or[LessEqual[N[(x / y), $MachinePrecision], 5e+98], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4e+203]], $MachinePrecision]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.99999999999999997e73 or 4.9999999999999998e98 < (/.f64 x y) < 4e203

   1. Initial program 94.5%

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

   2. Taylor expanded in z around 0 67.3%

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

      1. mul-1-neg 67.3%

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

      2. associate-/l* 69.0%

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

   4. Simplified 69.0%

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

      1. +-commutative 69.0%

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

      2. unsub-neg 69.0%

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

      3. associate-/r/ 65.7%

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

   6. Applied egg-rr 65.7%

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

   7. Taylor expanded in y around 0 67.3%

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

      1. mul-1-neg 67.3%

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

      2. associate-*l/ 65.7%

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

      3. distribute-rgt-neg-out 65.7%

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

      4. associate-*l/ 67.3%

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

      5. associate-*r/ 69.1%

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

   9. Simplified 69.1%

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

   if -1.99999999999999997e73 < (/.f64 x y) < -4.9999999999999998e-144 or 9.99999999999999995e-56 < (/.f64 x y) < 4.9999999999999998e98 or 4e203 < (/.f64 x y)

   1. Initial program 97.3%

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

      1. *-commutative 97.3%

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

      2. clear-num 97.1%

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

      3. un-div-inv 97.3%

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

   3. Applied egg-rr 97.3%

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

   4. Taylor expanded in y around 0 89.9%

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

   5. Taylor expanded in x around -inf 73.0%

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

   6. Taylor expanded in z around inf 50.6%

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

      1. associate-*l/ 60.2%

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

      2. *-commutative 60.2%

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

   8. Simplified 60.2%

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

   if -4.9999999999999998e-144 < (/.f64 x y) < 9.99999999999999995e-56

   1. Initial program 98.1%

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

   2. Taylor expanded in x around 0 83.9%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+73}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-144}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-55}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+98} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+203}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \]

Alternative 3: 73.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot z\\ t_2 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{+19}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+102}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) z)) (t_2 (* t (- 1.0 (/ x y)))))
   (if (<= z -4.6e+72)
     t_1
     (if (<= z -6e+51)
       t_2
       (if (<= z -1.62e+19) (/ (* x z) y) (if (<= z 6.2e+102) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * z;
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (z <= -4.6e+72) {
		tmp = t_1;
	} else if (z <= -6e+51) {
		tmp = t_2;
	} else if (z <= -1.62e+19) {
		tmp = (x * z) / y;
	} else if (z <= 6.2e+102) {
		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 / y) * z
    t_2 = t * (1.0d0 - (x / y))
    if (z <= (-4.6d+72)) then
        tmp = t_1
    else if (z <= (-6d+51)) then
        tmp = t_2
    else if (z <= (-1.62d+19)) then
        tmp = (x * z) / y
    else if (z <= 6.2d+102) 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 / y) * z;
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (z <= -4.6e+72) {
		tmp = t_1;
	} else if (z <= -6e+51) {
		tmp = t_2;
	} else if (z <= -1.62e+19) {
		tmp = (x * z) / y;
	} else if (z <= 6.2e+102) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * z
	t_2 = t * (1.0 - (x / y))
	tmp = 0
	if z <= -4.6e+72:
		tmp = t_1
	elif z <= -6e+51:
		tmp = t_2
	elif z <= -1.62e+19:
		tmp = (x * z) / y
	elif z <= 6.2e+102:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * z)
	t_2 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (z <= -4.6e+72)
		tmp = t_1;
	elseif (z <= -6e+51)
		tmp = t_2;
	elseif (z <= -1.62e+19)
		tmp = Float64(Float64(x * z) / y);
	elseif (z <= 6.2e+102)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * z;
	t_2 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (z <= -4.6e+72)
		tmp = t_1;
	elseif (z <= -6e+51)
		tmp = t_2;
	elseif (z <= -1.62e+19)
		tmp = (x * z) / y;
	elseif (z <= 6.2e+102)
		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 / y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e+72], t$95$1, If[LessEqual[z, -6e+51], t$95$2, If[LessEqual[z, -1.62e+19], N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 6.2e+102], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6e72 or 6.19999999999999973e102 < z

   1. Initial program 98.0%

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

      1. *-commutative 98.0%

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

      2. clear-num 96.0%

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

      3. un-div-inv 96.1%

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

   3. Applied egg-rr 96.1%

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

   4. Taylor expanded in y around 0 90.3%

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

   5. Taylor expanded in x around -inf 70.1%

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

   6. Taylor expanded in z around inf 66.7%

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

      1. associate-*l/ 73.7%

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

      2. *-commutative 73.7%

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

   8. Simplified 73.7%

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

   if -4.6e72 < z < -6e51 or -1.62e19 < z < 6.19999999999999973e102

   1. Initial program 96.4%

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

   2. Taylor expanded in z around 0 80.7%

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

      1. mul-1-neg 80.7%

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

      2. unsub-neg 80.7%

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

      3. *-commutative 80.7%

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

      4. associate-*l/ 82.0%

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

      5. cancel-sign-sub-inv 82.0%

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

      6. *-lft-identity 82.0%

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

      7. mul-1-neg 82.0%

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

      8. distribute-rgt-in 82.0%

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

      9. mul-1-neg 82.0%

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

      10. unsub-neg 82.0%

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

   4. Simplified 82.0%

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

   if -6e51 < z < -1.62e19

   1. Initial program 99.1%

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

      1. *-commutative 99.1%

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

      2. clear-num 99.1%

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

      3. un-div-inv 99.4%

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

   3. Applied egg-rr 99.4%

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

   4. Taylor expanded in y around 0 99.4%

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

   5. Taylor expanded in x around -inf 92.3%

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

   6. Taylor expanded in z around inf 92.3%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+72}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{+19}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+102}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \]

Alternative 4: 93.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+55} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e+55) (not (<= (/ x y) 2e-10)))
   (/ (* x (- z t)) y)
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+55) || !((x / y) <= 2e-10)) {
		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) <= (-5d+55)) .or. (.not. ((x / y) <= 2d-10))) 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) <= -5e+55) || !((x / y) <= 2e-10)) {
		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) <= -5e+55) or not ((x / y) <= 2e-10):
		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) <= -5e+55) || !(Float64(x / y) <= 2e-10))
		tmp = Float64(Float64(x * 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) <= -5e+55) || ~(((x / y) <= 2e-10)))
		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], -5e+55], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-10]], $MachinePrecision]], N[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.00000000000000046e55 or 2.00000000000000007e-10 < (/.f64 x y)

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

      2. clear-num 94.8%

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

      3. un-div-inv 95.1%

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

   3. Applied egg-rr 95.1%

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

   4. Taylor expanded in y around 0 96.5%

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

   5. Taylor expanded in x around -inf 95.6%

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

   if -5.00000000000000046e55 < (/.f64 x y) < 2.00000000000000007e-10

   1. Initial program 98.7%

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

   2. Taylor expanded in z around inf 88.8%

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

      1. associate-*l/ 94.8%

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

      2. *-commutative 94.8%

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

   4. Simplified 94.8%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+55} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]

Alternative 5: 93.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z - t\right)\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+55}:\\ \;\;\;\;\frac{1}{y} \cdot t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-10}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- z t))))
   (if (<= (/ x y) -5e+55)
     (* (/ 1.0 y) t_1)
     (if (<= (/ x y) 2e-10) (+ t (* (/ x y) z)) (/ t_1 y)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z - t);
	double tmp;
	if ((x / y) <= -5e+55) {
		tmp = (1.0 / y) * t_1;
	} else if ((x / y) <= 2e-10) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t_1 / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z - t)
    if ((x / y) <= (-5d+55)) then
        tmp = (1.0d0 / y) * t_1
    else if ((x / y) <= 2d-10) then
        tmp = t + ((x / y) * z)
    else
        tmp = t_1 / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z - t);
	double tmp;
	if ((x / y) <= -5e+55) {
		tmp = (1.0 / y) * t_1;
	} else if ((x / y) <= 2e-10) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t_1 / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z - t)
	tmp = 0
	if (x / y) <= -5e+55:
		tmp = (1.0 / y) * t_1
	elif (x / y) <= 2e-10:
		tmp = t + ((x / y) * z)
	else:
		tmp = t_1 / y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z - t))
	tmp = 0.0
	if (Float64(x / y) <= -5e+55)
		tmp = Float64(Float64(1.0 / y) * t_1);
	elseif (Float64(x / y) <= 2e-10)
		tmp = Float64(t + Float64(Float64(x / y) * z));
	else
		tmp = Float64(t_1 / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z - t);
	tmp = 0.0;
	if ((x / y) <= -5e+55)
		tmp = (1.0 / y) * t_1;
	elseif ((x / y) <= 2e-10)
		tmp = t + ((x / y) * z);
	else
		tmp = t_1 / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -5e+55], N[(N[(1.0 / y), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e-10], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5.00000000000000046e55

   1. Initial program 93.4%

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

      1. *-commutative 93.4%

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

      2. clear-num 93.2%

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

      3. un-div-inv 93.8%

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

   3. Applied egg-rr 93.8%

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

   4. Taylor expanded in y around 0 99.7%

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

   5. Taylor expanded in x around -inf 99.7%

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

      1. clear-num 99.6%

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

      2. associate-/r/ 99.7%

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

   7. Applied egg-rr 99.7%

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

   if -5.00000000000000046e55 < (/.f64 x y) < 2.00000000000000007e-10

   1. Initial program 98.7%

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

   2. Taylor expanded in z around inf 88.8%

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

      1. associate-*l/ 94.8%

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

      2. *-commutative 94.8%

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

   4. Simplified 94.8%

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

   if 2.00000000000000007e-10 < (/.f64 x y)

   1. Initial program 95.8%

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

      1. *-commutative 95.8%

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

      2. clear-num 95.8%

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

      3. un-div-inv 95.9%

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

   3. Applied egg-rr 95.9%

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

   4. Taylor expanded in y around 0 94.5%

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

   5. Taylor expanded in x around -inf 93.0%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+55}:\\ \;\;\;\;\frac{1}{y} \cdot \left(x \cdot \left(z - t\right)\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-10}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \end{array} \]

Alternative 6: 63.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-144} \lor \neg \left(\frac{x}{y} \leq 10^{-55}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e-144) (not (<= (/ x y) 1e-55))) (* (/ x y) z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e-144) || !((x / y) <= 1e-55)) {
		tmp = (x / y) * 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 (((x / y) <= (-5d-144)) .or. (.not. ((x / y) <= 1d-55))) then
        tmp = (x / y) * 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 (((x / y) <= -5e-144) || !((x / y) <= 1e-55)) {
		tmp = (x / y) * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e-144) or not ((x / y) <= 1e-55):
		tmp = (x / y) * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e-144) || !(Float64(x / y) <= 1e-55))
		tmp = Float64(Float64(x / y) * z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5e-144) || ~(((x / y) <= 1e-55)))
		tmp = (x / y) * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e-144], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e-55]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.9999999999999998e-144 or 9.99999999999999995e-56 < (/.f64 x y)

   1. Initial program 96.4%

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

      1. *-commutative 96.4%

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

      2. clear-num 96.2%

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

      3. un-div-inv 96.5%

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

   3. Applied egg-rr 96.5%

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

   4. Taylor expanded in y around 0 92.6%

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

   5. Taylor expanded in x around -inf 81.3%

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

   6. Taylor expanded in z around inf 48.4%

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

      1. associate-*l/ 54.2%

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

      2. *-commutative 54.2%

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

   8. Simplified 54.2%

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

   if -4.9999999999999998e-144 < (/.f64 x y) < 9.99999999999999995e-56

   1. Initial program 98.1%

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

   2. Taylor expanded in x around 0 83.9%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-144} \lor \neg \left(\frac{x}{y} \leq 10^{-55}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 82.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-138} \lor \neg \left(z \leq 2.7 \cdot 10^{+69}\right):\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.2e-138) (not (<= z 2.7e+69)))
   (+ t (* x (/ z y)))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.2e-138) || !(z <= 2.7e+69)) {
		tmp = t + (x * (z / y));
	} else {
		tmp = t * (1.0 - (x / 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 ((z <= (-5.2d-138)) .or. (.not. (z <= 2.7d+69))) then
        tmp = t + (x * (z / y))
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.2e-138) || !(z <= 2.7e+69)) {
		tmp = t + (x * (z / y));
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.2e-138) or not (z <= 2.7e+69):
		tmp = t + (x * (z / y))
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.2e-138) || !(z <= 2.7e+69))
		tmp = Float64(t + Float64(x * Float64(z / y)));
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.2e-138) || ~((z <= 2.7e+69)))
		tmp = t + (x * (z / y));
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.2e-138], N[Not[LessEqual[z, 2.7e+69]], $MachinePrecision]], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2e-138 or 2.6999999999999998e69 < z

   1. Initial program 97.9%

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

      1. *-commutative 97.9%

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

      2. clear-num 96.6%

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

      3. un-div-inv 96.8%

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

   3. Applied egg-rr 96.8%

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

   4. Taylor expanded in z around inf 85.7%

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

      1. associate-*r/ 85.8%

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

   6. Simplified 85.8%

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

   if -5.2e-138 < z < 2.6999999999999998e69

   1. Initial program 96.0%

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

   2. Taylor expanded in z around 0 85.4%

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

      1. mul-1-neg 85.4%

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

      2. unsub-neg 85.4%

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

      3. *-commutative 85.4%

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

      4. associate-*l/ 87.1%

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

      5. cancel-sign-sub-inv 87.1%

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

      6. *-lft-identity 87.1%

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

      7. mul-1-neg 87.1%

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

      8. distribute-rgt-in 87.1%

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

      9. mul-1-neg 87.1%

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

      10. unsub-neg 87.1%

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

   4. Simplified 87.1%

      \[\leadsto \color{blue}{t \cdot \left(1 - \frac{x}{y}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-138} \lor \neg \left(z \leq 2.7 \cdot 10^{+69}\right):\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 8: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-138} \lor \neg \left(z \leq 2.5 \cdot 10^{+73}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.2e-138) (not (<= z 2.5e+73)))
   (+ t (* (/ x y) z))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.2e-138) || !(z <= 2.5e+73)) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t * (1.0 - (x / 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 ((z <= (-5.2d-138)) .or. (.not. (z <= 2.5d+73))) then
        tmp = t + ((x / y) * z)
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.2e-138) || !(z <= 2.5e+73)) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.2e-138) or not (z <= 2.5e+73):
		tmp = t + ((x / y) * z)
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.2e-138) || !(z <= 2.5e+73))
		tmp = Float64(t + Float64(Float64(x / y) * z));
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.2e-138) || ~((z <= 2.5e+73)))
		tmp = t + ((x / y) * z);
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.2e-138], N[Not[LessEqual[z, 2.5e+73]], $MachinePrecision]], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2e-138 or 2.49999999999999988e73 < z

   1. Initial program 97.9%

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

   2. Taylor expanded in z around inf 85.7%

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

      1. associate-*l/ 90.7%

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

      2. *-commutative 90.7%

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

   4. Simplified 90.7%

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

   if -5.2e-138 < z < 2.49999999999999988e73

   1. Initial program 96.0%

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

   2. Taylor expanded in z around 0 85.4%

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

      1. mul-1-neg 85.4%

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

      2. unsub-neg 85.4%

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

      3. *-commutative 85.4%

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

      4. associate-*l/ 87.1%

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

      5. cancel-sign-sub-inv 87.1%

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

      6. *-lft-identity 87.1%

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

      7. mul-1-neg 87.1%

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

      8. distribute-rgt-in 87.1%

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

      9. mul-1-neg 87.1%

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

      10. unsub-neg 87.1%

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

   4. Simplified 87.1%

      \[\leadsto \color{blue}{t \cdot \left(1 - \frac{x}{y}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-138} \lor \neg \left(z \leq 2.5 \cdot 10^{+73}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 9: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.52 \cdot 10^{-138}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.52e-138)
   (+ t (/ z (/ y x)))
   (if (<= z 2.7e+69) (* t (- 1.0 (/ x y))) (+ t (* (/ x y) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.52e-138) {
		tmp = t + (z / (y / x));
	} else if (z <= 2.7e+69) {
		tmp = t * (1.0 - (x / 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 (z <= (-2.52d-138)) then
        tmp = t + (z / (y / x))
    else if (z <= 2.7d+69) then
        tmp = t * (1.0d0 - (x / 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 (z <= -2.52e-138) {
		tmp = t + (z / (y / x));
	} else if (z <= 2.7e+69) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.52e-138:
		tmp = t + (z / (y / x))
	elif z <= 2.7e+69:
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.52e-138)
		tmp = Float64(t + Float64(z / Float64(y / x)));
	elseif (z <= 2.7e+69)
		tmp = Float64(t * Float64(1.0 - Float64(x / 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 (z <= -2.52e-138)
		tmp = t + (z / (y / x));
	elseif (z <= 2.7e+69)
		tmp = t * (1.0 - (x / y));
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.52e-138], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e+69], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5199999999999999e-138

   1. Initial program 97.5%

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

      1. *-commutative 97.5%

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

      2. clear-num 97.4%

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

      3. un-div-inv 97.7%

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

   3. Applied egg-rr 97.7%

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

   4. Taylor expanded in z around inf 82.4%

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

      1. associate-*r/ 81.4%

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

   6. Simplified 81.4%

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

      1. associate-*r/ 82.4%

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

      2. *-commutative 82.4%

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

      3. associate-/l* 85.9%

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

   8. Applied egg-rr 85.9%

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

   if -2.5199999999999999e-138 < z < 2.6999999999999998e69

   1. Initial program 96.0%

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

   2. Taylor expanded in z around 0 85.4%

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

      1. mul-1-neg 85.4%

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

      2. unsub-neg 85.4%

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

      3. *-commutative 85.4%

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

      4. associate-*l/ 87.1%

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

      5. cancel-sign-sub-inv 87.1%

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

      6. *-lft-identity 87.1%

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

      7. mul-1-neg 87.1%

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

      8. distribute-rgt-in 87.1%

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

      9. mul-1-neg 87.1%

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

      10. unsub-neg 87.1%

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

   4. Simplified 87.1%

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

   if 2.6999999999999998e69 < z

   1. Initial program 98.6%

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

   2. Taylor expanded in z around inf 90.8%

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

      1. associate-*l/ 98.6%

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

      2. *-commutative 98.6%

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

   4. Simplified 98.6%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.52 \cdot 10^{-138}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]

Alternative 10: 38.4% 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 97.0%

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

2. Taylor expanded in x around 0 37.7%

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

3. Final simplification 37.7%

   \[\leadsto t \]

Developer target: 97.6% accurate, 0.7× 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 2023318 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (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))