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

Percentage Accurate: 97.7% → 97.8%

Time: 6.2s

Alternatives: 8

Speedup: 1.1×

• 24.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]
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 97.1

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

4. Applied rewrites 97.1%

   \[\leadsto \color{blue}{\frac{z - t}{\frac{y}{x}}} + t \]
5. Add Preprocessing

Alternative 2: 94.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{y} \cdot x\\ \mathbf{if}\;\frac{x}{y} \leq -100000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 0.02:\\ \;\;\;\;\frac{x}{y} \cdot z + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ (- z t) y) x)))
   (if (<= (/ x y) -100000000.0)
     t_1
     (if (<= (/ x y) 0.02) (+ (* (/ x y) z) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((z - t) / y) * x;
	double tmp;
	if ((x / y) <= -100000000.0) {
		tmp = t_1;
	} else if ((x / y) <= 0.02) {
		tmp = ((x / y) * z) + 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) / y) * x
    if ((x / y) <= (-100000000.0d0)) then
        tmp = t_1
    else if ((x / y) <= 0.02d0) then
        tmp = ((x / y) * z) + 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) / y) * x;
	double tmp;
	if ((x / y) <= -100000000.0) {
		tmp = t_1;
	} else if ((x / y) <= 0.02) {
		tmp = ((x / y) * z) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((z - t) / y) * x
	tmp = 0
	if (x / y) <= -100000000.0:
		tmp = t_1
	elif (x / y) <= 0.02:
		tmp = ((x / y) * z) + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(z - t) / y) * x)
	tmp = 0.0
	if (Float64(x / y) <= -100000000.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 0.02)
		tmp = Float64(Float64(Float64(x / y) * z) + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((z - t) / y) * x;
	tmp = 0.0;
	if ((x / y) <= -100000000.0)
		tmp = t_1;
	elseif ((x / y) <= 0.02)
		tmp = ((x / y) * z) + 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] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -100000000.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 0.02], N[(N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e8 or 0.0200000000000000004 < (/.f64 x y)

   1. Initial program 96.8%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 91.8

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

   5. Applied rewrites 91.8%

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

   7. Applied rewrites 93.7%

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

   if -1e8 < (/.f64 x y) < 0.0200000000000000004

   1. Initial program 97.0%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 97.0

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

   4. Applied rewrites 97.0%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 90.6

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

   7. Applied rewrites 90.6%

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

   9. Applied rewrites 93.8%

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

Alternative 3: 93.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{y} \cdot x\\ \mathbf{if}\;\frac{x}{y} \leq -0.5:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-10}:\\ \;\;\;\;\frac{x \cdot z}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ (- z t) y) x)))
   (if (<= (/ x y) -0.5) t_1 (if (<= (/ x y) 2e-10) (+ (/ (* x z) y) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((z - t) / y) * x;
	double tmp;
	if ((x / y) <= -0.5) {
		tmp = t_1;
	} else if ((x / y) <= 2e-10) {
		tmp = ((x * z) / y) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((z - t) / y) * x
    if ((x / y) <= (-0.5d0)) then
        tmp = t_1
    else if ((x / y) <= 2d-10) then
        tmp = ((x * z) / y) + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((z - t) / y) * x;
	double tmp;
	if ((x / y) <= -0.5) {
		tmp = t_1;
	} else if ((x / y) <= 2e-10) {
		tmp = ((x * z) / y) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((z - t) / y) * x
	tmp = 0
	if (x / y) <= -0.5:
		tmp = t_1
	elif (x / y) <= 2e-10:
		tmp = ((x * z) / y) + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(z - t) / y) * x)
	tmp = 0.0
	if (Float64(x / y) <= -0.5)
		tmp = t_1;
	elseif (Float64(x / y) <= 2e-10)
		tmp = Float64(Float64(Float64(x * z) / y) + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((z - t) / y) * x;
	tmp = 0.0;
	if ((x / y) <= -0.5)
		tmp = t_1;
	elseif ((x / y) <= 2e-10)
		tmp = ((x * z) / y) + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -0.5], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 2e-10], N[(N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -0.5 or 2.00000000000000007e-10 < (/.f64 x y)

   1. Initial program 96.9%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 89.9

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

   5. Applied rewrites 89.9%

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

   7. Applied rewrites 93.5%

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

   if -0.5 < (/.f64 x y) < 2.00000000000000007e-10

   1. Initial program 96.9%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 92.5

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

   5. Applied rewrites 92.5%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.5:\\ \;\;\;\;\frac{z - t}{y} \cdot x\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-10}:\\ \;\;\;\;\frac{x \cdot z}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{y} \cdot x\\ \mathbf{if}\;\frac{x}{y} \leq -0.5:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-40}:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ (- z t) y) x)))
   (if (<= (/ x y) -0.5)
     t_1
     (if (<= (/ x y) 5e-40) (* (- 1.0 (/ x y)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((z - t) / y) * x;
	double tmp;
	if ((x / y) <= -0.5) {
		tmp = t_1;
	} else if ((x / y) <= 5e-40) {
		tmp = (1.0 - (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) / y) * x
    if ((x / y) <= (-0.5d0)) then
        tmp = t_1
    else if ((x / y) <= 5d-40) then
        tmp = (1.0d0 - (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) / y) * x;
	double tmp;
	if ((x / y) <= -0.5) {
		tmp = t_1;
	} else if ((x / y) <= 5e-40) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((z - t) / y) * x
	tmp = 0
	if (x / y) <= -0.5:
		tmp = t_1
	elif (x / y) <= 5e-40:
		tmp = (1.0 - (x / y)) * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(z - t) / y) * x)
	tmp = 0.0
	if (Float64(x / y) <= -0.5)
		tmp = t_1;
	elseif (Float64(x / y) <= 5e-40)
		tmp = Float64(Float64(1.0 - Float64(x / y)) * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((z - t) / y) * x;
	tmp = 0.0;
	if ((x / y) <= -0.5)
		tmp = t_1;
	elseif ((x / y) <= 5e-40)
		tmp = (1.0 - (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] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -0.5], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5e-40], N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -0.5 or 4.99999999999999965e-40 < (/.f64 x y)

   1. Initial program 97.1%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 88.8

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

   5. Applied rewrites 88.8%

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

   7. Applied rewrites 90.9%

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

   if -0.5 < (/.f64 x y) < 4.99999999999999965e-40

   1. Initial program 96.8%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 80.0

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

   5. Applied rewrites 80.0%

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

Alternative 5: 74.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{-107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-31}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- 1.0 (/ x y)) t)))
   (if (<= t -3.8e-107) t_1 (if (<= t 9.5e-31) (* (/ x y) z) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (1.0 - (x / y)) * t;
	double tmp;
	if (t <= -3.8e-107) {
		tmp = t_1;
	} else if (t <= 9.5e-31) {
		tmp = (x / y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (1.0d0 - (x / y)) * t
    if (t <= (-3.8d-107)) then
        tmp = t_1
    else if (t <= 9.5d-31) then
        tmp = (x / y) * z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (1.0 - (x / y)) * t;
	double tmp;
	if (t <= -3.8e-107) {
		tmp = t_1;
	} else if (t <= 9.5e-31) {
		tmp = (x / y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (1.0 - (x / y)) * t
	tmp = 0
	if t <= -3.8e-107:
		tmp = t_1
	elif t <= 9.5e-31:
		tmp = (x / y) * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(1.0 - Float64(x / y)) * t)
	tmp = 0.0
	if (t <= -3.8e-107)
		tmp = t_1;
	elseif (t <= 9.5e-31)
		tmp = Float64(Float64(x / y) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (1.0 - (x / y)) * t;
	tmp = 0.0;
	if (t <= -3.8e-107)
		tmp = t_1;
	elseif (t <= 9.5e-31)
		tmp = (x / y) * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -3.8e-107], t$95$1, If[LessEqual[t, 9.5e-31], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.8000000000000002e-107 or 9.5000000000000008e-31 < t

   1. Initial program 99.4%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 84.8

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

   5. Applied rewrites 84.8%

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

   if -3.8000000000000002e-107 < t < 9.5000000000000008e-31

   1. Initial program 93.2%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 66.6

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

   5. Applied rewrites 66.6%

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

   7. Applied rewrites 69.3%

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

Alternative 6: 50.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-t\right) \cdot \frac{x}{y}\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+96}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- t) (/ x y))))
   (if (<= t -6.5e+50) t_1 (if (<= t 7e+96) (* (/ x y) z) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -t * (x / y);
	double tmp;
	if (t <= -6.5e+50) {
		tmp = t_1;
	} else if (t <= 7e+96) {
		tmp = (x / y) * z;
	} 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 * (x / y)
    if (t <= (-6.5d+50)) then
        tmp = t_1
    else if (t <= 7d+96) then
        tmp = (x / y) * z
    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 * (x / y);
	double tmp;
	if (t <= -6.5e+50) {
		tmp = t_1;
	} else if (t <= 7e+96) {
		tmp = (x / y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -t * (x / y)
	tmp = 0
	if t <= -6.5e+50:
		tmp = t_1
	elif t <= 7e+96:
		tmp = (x / y) * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-t) * Float64(x / y))
	tmp = 0.0
	if (t <= -6.5e+50)
		tmp = t_1;
	elseif (t <= 7e+96)
		tmp = Float64(Float64(x / y) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -t * (x / y);
	tmp = 0.0;
	if (t <= -6.5e+50)
		tmp = t_1;
	elseif (t <= 7e+96)
		tmp = (x / y) * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-t) * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e+50], t$95$1, If[LessEqual[t, 7e+96], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.5000000000000003e50 or 6.9999999999999998e96 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 41.7

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

   5. Applied rewrites 41.7%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 38.0%

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

   10. Applied rewrites 41.0%

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

   if -6.5000000000000003e50 < t < 6.9999999999999998e96

   1. Initial program 95.0%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 52.4

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

   5. Applied rewrites 52.4%

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

   7. Applied rewrites 55.9%

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

Alternative 7: 97.7% 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 96.9%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]
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. lower-fma.f64 96.9

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

4. Applied rewrites 96.9%

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

Alternative 8: 40.6% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

3. Taylor expanded in t around 0

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

   1. lower-/.f64 N/A

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

   2. *-commutative N/A

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

   3. lower-*.f64 36.7

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

5. Applied rewrites 36.7%

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

7. Applied rewrites 39.7%

   \[\leadsto \color{blue}{\frac{x}{y} \cdot z} \]
8. Add Preprocessing

Developer Target 1: 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 2024255 
(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))