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

Percentage Accurate: 97.5% → 97.5%

Time: 7.5s

Alternatives: 7

Speedup: 1.1×

• 25.2% 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, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.1%

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

   1. accelerator-lowering-fma.f64 N/A

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

   2. /-lowering-/.f64 N/A

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

   3. --lowering--.f64 97.1

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

4. Applied egg-rr 97.1%

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

Alternative 2: 95.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{if}\;\frac{x}{y} \leq -6 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 0.005:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) (- z t))))
   (if (<= (/ x y) -6e+19) t_1 (if (<= (/ x y) 0.005) (fma (/ x y) z t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * (z - t);
	double tmp;
	if ((x / y) <= -6e+19) {
		tmp = t_1;
	} else if ((x / y) <= 0.005) {
		tmp = fma((x / y), z, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * Float64(z - t))
	tmp = 0.0
	if (Float64(x / y) <= -6e+19)
		tmp = t_1;
	elseif (Float64(x / y) <= 0.005)
		tmp = fma(Float64(x / y), z, t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -6e+19], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 0.005], N[(N[(x / y), $MachinePrecision] * z + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -6e19 or 0.0050000000000000001 < (/.f64 x y)

   1. Initial program 96.7%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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. /-lowering-/.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. --lowering--.f64 91.1

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

   5. Simplified 91.1%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. --lowering--.f64 95.4

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

   7. Applied egg-rr 95.4%

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

   if -6e19 < (/.f64 x y) < 0.0050000000000000001

   1. Initial program 97.6%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 95.8%

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. /-lowering-/.f64 95.8

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

   7. Applied egg-rr 95.8%

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

Alternative 3: 64.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot z\\ \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 0.005:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) z)))
   (if (<= (/ x y) -4e-89) t_1 (if (<= (/ x y) 0.005) t t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * z;
	double tmp;
	if ((x / y) <= -4e-89) {
		tmp = t_1;
	} else if ((x / y) <= 0.005) {
		tmp = 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
    if ((x / y) <= (-4d-89)) then
        tmp = t_1
    else if ((x / y) <= 0.005d0) then
        tmp = 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;
	double tmp;
	if ((x / y) <= -4e-89) {
		tmp = t_1;
	} else if ((x / y) <= 0.005) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * z
	tmp = 0
	if (x / y) <= -4e-89:
		tmp = t_1
	elif (x / y) <= 0.005:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * z)
	tmp = 0.0
	if (Float64(x / y) <= -4e-89)
		tmp = t_1;
	elseif (Float64(x / y) <= 0.005)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * z;
	tmp = 0.0;
	if ((x / y) <= -4e-89)
		tmp = t_1;
	elseif ((x / y) <= 0.005)
		tmp = t;
	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]}, If[LessEqual[N[(x / y), $MachinePrecision], -4e-89], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 0.005], t, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.00000000000000015e-89 or 0.0050000000000000001 < (/.f64 x y)

   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. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 49.0

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

   5. Simplified 49.0%

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

      1. associate-*l/ N/A

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

      2. div-inv N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. associate-*l/ N/A

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

      6. *-lft-identity N/A

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

      7. /-lowering-/.f64 57.3

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

   7. Applied egg-rr 57.3%

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

   if -4.00000000000000015e-89 < (/.f64 x y) < 0.0050000000000000001

   1. Initial program 97.2%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Simplified 78.5%

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

Alternative 4: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+79}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e+79) (* (/ x y) (- t)) (fma (/ x y) z t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+79) {
		tmp = (x / y) * -t;
	} else {
		tmp = fma((x / y), z, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e+79)
		tmp = Float64(Float64(x / y) * Float64(-t));
	else
		tmp = fma(Float64(x / y), z, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e+79], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * z + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.99999999999999993e79

   1. Initial program 94.7%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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. --lowering--.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. *-lowering-*.f64 68.4

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

   5. Simplified 68.4%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. neg-mul-1 N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. *-lowering-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. neg-lowering-neg.f64 68.4

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

   8. Simplified 68.4%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. frac-2neg N/A

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

      5. remove-double-neg N/A

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

      6. /-lowering-/.f64 N/A

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

      7. neg-lowering-neg.f64 73.3

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

   10. Applied egg-rr 73.3%

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

   if -1.99999999999999993e79 < (/.f64 x y)

   1. Initial program 97.5%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 82.0%

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. /-lowering-/.f64 82.0

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

   7. Applied egg-rr 82.0%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+79}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e+79) (* x (/ (- t) y)) (fma (/ x y) z t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+79) {
		tmp = x * (-t / y);
	} else {
		tmp = fma((x / y), z, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e+79)
		tmp = Float64(x * Float64(Float64(-t) / y));
	else
		tmp = fma(Float64(x / y), z, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e+79], N[(x * N[((-t) / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * z + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.99999999999999993e79

   1. Initial program 94.7%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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. --lowering--.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. *-lowering-*.f64 68.4

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

   5. Simplified 68.4%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. neg-mul-1 N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. *-lowering-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. neg-lowering-neg.f64 68.4

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

   8. Simplified 68.4%

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

      1. distribute-rgt-neg-out N/A

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

      2. distribute-lft-neg-in N/A

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

      3. associate-*l/ N/A

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

      4. *-lowering-*.f64 N/A

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

      5. distribute-frac-neg N/A

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

      6. distribute-frac-neg2 N/A

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

      7. /-lowering-/.f64 N/A

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

      8. neg-lowering-neg.f64 68.5

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

   10. Applied egg-rr 68.5%

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

   if -1.99999999999999993e79 < (/.f64 x y)

   1. Initial program 97.5%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 82.0%

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. /-lowering-/.f64 82.0

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

   7. Applied egg-rr 82.0%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.7% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.1%

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

3. Taylor expanded in z around inf

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

5. Simplified 76.4%

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

   1. accelerator-lowering-fma.f64 N/A

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

   2. /-lowering-/.f64 76.4

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

7. Applied egg-rr 76.4%

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

Alternative 7: 38.0% accurate, 23.0× 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 97.1%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{t} \]
4. Step-by-step derivation

5. Simplified 37.7%

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

Developer Target 1: 97.3% 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 2024199 
(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))