Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.7% → 79.7%

Time: 1.7s

Alternatives: 6

Speedup: 1.0×

Specification

\[\mathsf{TRUE}\left(\right)\]

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 79.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.6%

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

Alternative 2: 21.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 2 \cdot 10^{+297}:\\ \;\;\;\;x + \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (+ x (* (- y z) (/ (- t x) (- a z)))) 2e+297)
   (+ x (- y z))
   (* (- y z) (- y z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x + ((y - z) * ((t - x) / (a - z)))) <= 2e+297) {
		tmp = x + (y - z);
	} else {
		tmp = (y - z) * (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x + ((y - z) * ((t - x) / (a - z)))) <= 2d+297) then
        tmp = x + (y - z)
    else
        tmp = (y - z) * (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x + ((y - z) * ((t - x) / (a - z)))) <= 2e+297) {
		tmp = x + (y - z);
	} else {
		tmp = (y - z) * (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x + ((y - z) * ((t - x) / (a - z)))) <= 2e+297:
		tmp = x + (y - z)
	else:
		tmp = (y - z) * (y - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z)))) <= 2e+297)
		tmp = Float64(x + Float64(y - z));
	else
		tmp = Float64(Float64(y - z) * Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x + ((y - z) * ((t - x) / (a - z)))) <= 2e+297)
		tmp = x + (y - z);
	else
		tmp = (y - z) * (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e+297], N[(x + N[(y - z), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 2e297

   1. Initial program 76.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 18.4%

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

   if 2e297 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 85.7%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 85.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 1.7%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 56.7%

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

Alternative 3: 55.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+87}:\\ \;\;\;\;x + \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.5e+87) (+ x (- y z)) (* (- y z) (/ (- t x) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.5e+87) {
		tmp = x + (y - z);
	} else {
		tmp = (y - z) * ((t - x) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.5d+87)) then
        tmp = x + (y - z)
    else
        tmp = (y - z) * ((t - x) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.5e+87) {
		tmp = x + (y - z);
	} else {
		tmp = (y - z) * ((t - x) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.5e+87:
		tmp = x + (y - z)
	else:
		tmp = (y - z) * ((t - x) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.5e+87)
		tmp = Float64(x + Float64(y - z));
	else
		tmp = Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.5e+87)
		tmp = x + (y - z);
	else
		tmp = (y - z) * ((t - x) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.5e+87], N[(x + N[(y - z), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.4999999999999999e87

   1. Initial program 84.5%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 35.0%

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

   if -1.4999999999999999e87 < a

   1. Initial program 76.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 59.1%

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

Alternative 4: 17.0% accurate, 4.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.6%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 18.0%

   \[\leadsto x + \color{blue}{\left(y - z\right)} \]
6. Add Preprocessing

Alternative 5: 3.3% accurate, 7.3× speedup

Math

\[\begin{array}{l} \\ y - z \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (- y z))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(y - z), $MachinePrecision]

Derivation

1. Initial program 77.6%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 52.8%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 3.1%

   \[\leadsto y - \color{blue}{z} \]
9. Add Preprocessing

Alternative 6: 2.9% accurate, 7.3× speedup

Math

\[\begin{array}{l} \\ a - z \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (- a z))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(a - z), $MachinePrecision]

Derivation

1. Initial program 77.6%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 52.8%

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

6. Taylor expanded in x around inf

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

8. Applied rewrites 2.7%

   \[\leadsto a - \color{blue}{z} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024321 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  :pre (TRUE)
  (+ x (* (- y z) (/ (- t x) (- a z)))))