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

Percentage Accurate: 97.5% → 97.5%

Time: 5.5s

Alternatives: 10

Speedup: 1.0×

• 25.3% 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: 97.5% 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: 97.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.7%

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

3. Final simplification 98.7%

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

Alternative 2: 93.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -20:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-6}:\\ \;\;\;\;\frac{z \cdot x}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* (- z t) x) y)))
   (if (<= (/ x y) -20.0) t_1 (if (<= (/ x y) 1e-6) (+ (/ (* z x) y) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((z - t) * x) / y;
	double tmp;
	if ((x / y) <= -20.0) {
		tmp = t_1;
	} else if ((x / y) <= 1e-6) {
		tmp = ((z * x) / 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 = ((z - t) * x) / y
    if ((x / y) <= (-20.0d0)) then
        tmp = t_1
    else if ((x / y) <= 1d-6) then
        tmp = ((z * x) / 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 = ((z - t) * x) / y;
	double tmp;
	if ((x / y) <= -20.0) {
		tmp = t_1;
	} else if ((x / y) <= 1e-6) {
		tmp = ((z * x) / y) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((z - t) * x) / y
	tmp = 0
	if (x / y) <= -20.0:
		tmp = t_1
	elif (x / y) <= 1e-6:
		tmp = ((z * x) / y) + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(z - t) * x) / y)
	tmp = 0.0
	if (Float64(x / y) <= -20.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 1e-6)
		tmp = Float64(Float64(Float64(z * x) / y) + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((z - t) * x) / y;
	tmp = 0.0;
	if ((x / y) <= -20.0)
		tmp = t_1;
	elseif ((x / y) <= 1e-6)
		tmp = ((z * x) / y) + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -20.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 1e-6], N[(N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -20 or 9.99999999999999955e-7 < (/.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

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 89.4

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

   5. Applied rewrites 89.4%

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

   if -20 < (/.f64 x y) < 9.99999999999999955e-7

   1. Initial program 99.8%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. lower-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 91.4

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

   4. Applied rewrites 91.4%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 95.4

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

   7. Applied rewrites 95.4%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -20:\\ \;\;\;\;\frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-6}:\\ \;\;\;\;\frac{z \cdot x}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, -t, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* (- z t) x) y)))
   (if (<= (/ x y) -2e-17)
     t_1
     (if (<= (/ x y) 1e+19) (fma (/ x y) (- t) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((z - t) * x) / y;
	double tmp;
	if ((x / y) <= -2e-17) {
		tmp = t_1;
	} else if ((x / y) <= 1e+19) {
		tmp = fma((x / y), -t, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(z - t) * x) / y)
	tmp = 0.0
	if (Float64(x / y) <= -2e-17)
		tmp = t_1;
	elseif (Float64(x / y) <= 1e+19)
		tmp = fma(Float64(x / y), Float64(-t), t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e-17], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 1e+19], N[(N[(x / y), $MachinePrecision] * (-t) + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2.00000000000000014e-17 or 1e19 < (/.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

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 90.7

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

   5. Applied rewrites 90.7%

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

   if -2.00000000000000014e-17 < (/.f64 x y) < 1e19

   1. Initial program 99.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.1

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

   4. Applied rewrites 99.1%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*l/ N/A

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

      4. associate-*l* N/A

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

      5. associate-*r/ N/A

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

      6. associate-*l/ N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-/.f64 69.0

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

   7. Applied rewrites 69.0%

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

   9. Applied rewrites 69.0%

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

   11. Applied rewrites 76.6%

       \[\leadsto \mathsf{fma}\left(\frac{x}{y}, \color{blue}{-t}, t\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 83.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+19}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* (- z t) x) y)))
   (if (<= (/ x y) -2e-17)
     t_1
     (if (<= (/ x y) 1e+19) (- t (* t (/ x y))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((z - t) * x) / y;
	double tmp;
	if ((x / y) <= -2e-17) {
		tmp = t_1;
	} else if ((x / y) <= 1e+19) {
		tmp = t - (t * (x / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((z - t) * x) / y
    if ((x / y) <= (-2d-17)) then
        tmp = t_1
    else if ((x / y) <= 1d+19) then
        tmp = t - (t * (x / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((z - t) * x) / y;
	double tmp;
	if ((x / y) <= -2e-17) {
		tmp = t_1;
	} else if ((x / y) <= 1e+19) {
		tmp = t - (t * (x / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((z - t) * x) / y
	tmp = 0
	if (x / y) <= -2e-17:
		tmp = t_1
	elif (x / y) <= 1e+19:
		tmp = t - (t * (x / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(z - t) * x) / y)
	tmp = 0.0
	if (Float64(x / y) <= -2e-17)
		tmp = t_1;
	elseif (Float64(x / y) <= 1e+19)
		tmp = Float64(t - Float64(t * Float64(x / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((z - t) * x) / y;
	tmp = 0.0;
	if ((x / y) <= -2e-17)
		tmp = t_1;
	elseif ((x / y) <= 1e+19)
		tmp = t - (t * (x / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e-17], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 1e+19], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2.00000000000000014e-17 or 1e19 < (/.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

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 90.7

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

   5. Applied rewrites 90.7%

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

   if -2.00000000000000014e-17 < (/.f64 x y) < 1e19

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 76.6

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

   5. Applied rewrites 76.6%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-17}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+19}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - t \cdot \frac{x}{y}\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-173}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- t (* t (/ x y)))))
   (if (<= t -1.7e+33) t_1 (if (<= t 2.75e-173) (* z (/ x y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t - (t * (x / y));
	double tmp;
	if (t <= -1.7e+33) {
		tmp = t_1;
	} else if (t <= 2.75e-173) {
		tmp = z * (x / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - (t * (x / y))
    if (t <= (-1.7d+33)) then
        tmp = t_1
    else if (t <= 2.75d-173) then
        tmp = z * (x / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t - (t * (x / y));
	double tmp;
	if (t <= -1.7e+33) {
		tmp = t_1;
	} else if (t <= 2.75e-173) {
		tmp = z * (x / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t - (t * (x / y))
	tmp = 0
	if t <= -1.7e+33:
		tmp = t_1
	elif t <= 2.75e-173:
		tmp = z * (x / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t - Float64(t * Float64(x / y)))
	tmp = 0.0
	if (t <= -1.7e+33)
		tmp = t_1;
	elseif (t <= 2.75e-173)
		tmp = Float64(z * Float64(x / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t - (t * (x / y));
	tmp = 0.0;
	if (t <= -1.7e+33)
		tmp = t_1;
	elseif (t <= 2.75e-173)
		tmp = z * (x / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e+33], t$95$1, If[LessEqual[t, 2.75e-173], N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.7e33 or 2.75000000000000011e-173 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 89.0

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

   5. Applied rewrites 89.0%

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

   if -1.7e33 < t < 2.75000000000000011e-173

   1. Initial program 97.1%

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

   3. Taylor expanded in z around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 71.2

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

   5. Applied rewrites 71.2%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+33}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-173}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{y}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-28}:\\ \;\;\;\;\left(-t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ x y))))
   (if (<= z -3.1e-22) t_1 (if (<= z 9e-28) (* (- t) (/ x y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x / y);
	double tmp;
	if (z <= -3.1e-22) {
		tmp = t_1;
	} else if (z <= 9e-28) {
		tmp = -t * (x / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x / y)
    if (z <= (-3.1d-22)) then
        tmp = t_1
    else if (z <= 9d-28) then
        tmp = -t * (x / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x / y);
	double tmp;
	if (z <= -3.1e-22) {
		tmp = t_1;
	} else if (z <= 9e-28) {
		tmp = -t * (x / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x / y)
	tmp = 0
	if z <= -3.1e-22:
		tmp = t_1
	elif z <= 9e-28:
		tmp = -t * (x / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x / y))
	tmp = 0.0
	if (z <= -3.1e-22)
		tmp = t_1;
	elseif (z <= 9e-28)
		tmp = Float64(Float64(-t) * Float64(x / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x / y);
	tmp = 0.0;
	if (z <= -3.1e-22)
		tmp = t_1;
	elseif (z <= 9e-28)
		tmp = -t * (x / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e-22], t$95$1, If[LessEqual[z, 9e-28], N[((-t) * N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.10000000000000013e-22 or 8.9999999999999996e-28 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 66.6

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

   5. Applied rewrites 66.6%

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

   if -3.10000000000000013e-22 < z < 8.9999999999999996e-28

   1. Initial program 97.7%

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

   3. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 55.3

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

   5. Applied rewrites 55.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 43.8%

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

   10. Applied rewrites 48.1%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-22}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-28}:\\ \;\;\;\;\left(-t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 46.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+33}:\\ \;\;\;\;\frac{-t}{y} \cdot x\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-92}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-t\right) \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.7e+33)
   (* (/ (- t) y) x)
   (if (<= t 9.5e-92) (* z (/ x y)) (/ (* (- t) x) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.7e+33) {
		tmp = (-t / y) * x;
	} else if (t <= 9.5e-92) {
		tmp = z * (x / y);
	} else {
		tmp = (-t * 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 (t <= (-1.7d+33)) then
        tmp = (-t / y) * x
    else if (t <= 9.5d-92) then
        tmp = z * (x / y)
    else
        tmp = (-t * x) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.7e+33) {
		tmp = (-t / y) * x;
	} else if (t <= 9.5e-92) {
		tmp = z * (x / y);
	} else {
		tmp = (-t * x) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.7e+33:
		tmp = (-t / y) * x
	elif t <= 9.5e-92:
		tmp = z * (x / y)
	else:
		tmp = (-t * x) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.7e+33)
		tmp = Float64(Float64(Float64(-t) / y) * x);
	elseif (t <= 9.5e-92)
		tmp = Float64(z * Float64(x / y));
	else
		tmp = Float64(Float64(Float64(-t) * x) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.7e+33)
		tmp = (-t / y) * x;
	elseif (t <= 9.5e-92)
		tmp = z * (x / y);
	else
		tmp = (-t * x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.7e+33], N[(N[((-t) / y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, 9.5e-92], N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[((-t) * x), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.7e33

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 49.9

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

   5. Applied rewrites 49.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 44.9%

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

   10. Applied rewrites 50.0%

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

   if -1.7e33 < t < 9.49999999999999946e-92

   1. Initial program 97.4%

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

   3. Taylor expanded in z around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 67.9

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

   5. Applied rewrites 67.9%

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

   if 9.49999999999999946e-92 < t

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 50.5

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

   5. Applied rewrites 50.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 43.1%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+33}:\\ \;\;\;\;\frac{-t}{y} \cdot x\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-92}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-t\right) \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{y}\\ \mathbf{if}\;z \leq -6.7 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-28}:\\ \;\;\;\;\frac{-t}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ x y))))
   (if (<= z -6.7e-38) t_1 (if (<= z 8.8e-28) (* (/ (- t) y) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x / y);
	double tmp;
	if (z <= -6.7e-38) {
		tmp = t_1;
	} else if (z <= 8.8e-28) {
		tmp = (-t / y) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x / y)
    if (z <= (-6.7d-38)) then
        tmp = t_1
    else if (z <= 8.8d-28) then
        tmp = (-t / y) * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x / y);
	double tmp;
	if (z <= -6.7e-38) {
		tmp = t_1;
	} else if (z <= 8.8e-28) {
		tmp = (-t / y) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x / y)
	tmp = 0
	if z <= -6.7e-38:
		tmp = t_1
	elif z <= 8.8e-28:
		tmp = (-t / y) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x / y))
	tmp = 0.0
	if (z <= -6.7e-38)
		tmp = t_1;
	elseif (z <= 8.8e-28)
		tmp = Float64(Float64(Float64(-t) / y) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x / y);
	tmp = 0.0;
	if (z <= -6.7e-38)
		tmp = t_1;
	elseif (z <= 8.8e-28)
		tmp = (-t / y) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.7e-38], t$95$1, If[LessEqual[z, 8.8e-28], N[(N[((-t) / y), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.7000000000000004e-38 or 8.79999999999999984e-28 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 65.2

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

   5. Applied rewrites 65.2%

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

   if -6.7000000000000004e-38 < z < 8.79999999999999984e-28

   1. Initial program 97.6%

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

   3. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 53.9

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

   5. Applied rewrites 53.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 43.5%

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

   10. Applied rewrites 44.9%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.7 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-28}:\\ \;\;\;\;\frac{-t}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 4.8 \cdot 10^{+113}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{y}, x, t\right)\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 4.8e+113) (fma (/ (- z t) y) x t) (- t (* t (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 4.8e+113) {
		tmp = fma(((z - t) / y), x, t);
	} else {
		tmp = t - (t * (x / y));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 4.8e+113)
		tmp = fma(Float64(Float64(z - t) / y), x, t);
	else
		tmp = Float64(t - Float64(t * Float64(x / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 4.8e+113], N[(N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision] * x + t), $MachinePrecision], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 4.79999999999999966e113

   1. Initial program 98.5%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 95.2

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

   4. Applied rewrites 95.2%

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

   if 4.79999999999999966e113 < t

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 99.8

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

   5. Applied rewrites 99.8%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 4.8 \cdot 10^{+113}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{y}, x, t\right)\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 41.2% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.7%

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

3. Taylor expanded in z around inf

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

   1. associate-*l/ N/A

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

   2. lower-*.f64 N/A

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

   3. lower-/.f64 41.0

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

5. Applied rewrites 41.0%

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

6. Final simplification 41.0%

   \[\leadsto z \cdot \frac{x}{y} \]
7. Add Preprocessing

Developer Target 1: 97.1% 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 2024294 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z 689864138640673/250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* (/ x y) (- z t)) t) (if (< z 581748612718609/25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t))))

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