Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A

Percentage Accurate: 99.9% → 99.9%

Time: 13.5s

Alternatives: 4

Speedup: 1.0×

• 26.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(1 - x \cdot y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* x (- 1.0 (* x y))))

C

double code(double x, double y) {
	return x * (1.0 - (x * y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (1.0d0 - (x * y))
end function

Java

public static double code(double x, double y) {
	return x * (1.0 - (x * y));
}

Python

def code(x, y):
	return x * (1.0 - (x * y))

Julia

function code(x, y)
	return Float64(x * Float64(1.0 - Float64(x * y)))
end

MATLAB

function tmp = code(x, y)
	tmp = x * (1.0 - (x * y));
end

Wolfram

code[x_, y_] := N[(x * N[(1.0 - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - x \cdot y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* x (- 1.0 (* x y))))

C

double code(double x, double y) {
	return x * (1.0 - (x * y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (1.0d0 - (x * y))
end function

Java

public static double code(double x, double y) {
	return x * (1.0 - (x * y));
}

Python

def code(x, y):
	return x * (1.0 - (x * y))

Julia

function code(x, y)
	return Float64(x * Float64(1.0 - Float64(x * y)))
end

MATLAB

function tmp = code(x, y)
	tmp = x * (1.0 - (x * y));
end

Wolfram

code[x_, y_] := N[(x * N[(1.0 - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (- x (* x (* x y))))

C

double code(double x, double y) {
	return x - (x * (x * y));
}

Fortran

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

Java

public static double code(double x, double y) {
	return x - (x * (x * y));
}

Python

def code(x, y):
	return x - (x * (x * y))

Julia

function code(x, y)
	return Float64(x - Float64(x * Float64(x * y)))
end

MATLAB

function tmp = code(x, y)
	tmp = x - (x * (x * y));
end

Wolfram

code[x_, y_] := N[(x - N[(x * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot \left(1 - x \cdot y\right) \]
2. Add Preprocessing

4. Applied egg-rr 0

   \[\leadsto expr\]
5. Add Preprocessing

Alternative 2: 73.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-x \cdot y\right) \cdot x\\ \mathbf{if}\;y \leq -2.36 \cdot 10^{+83}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -3.35 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-147}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (- (* x y)) x)))
   (if (<= y -2.36e+83)
     t_0
     (if (<= y -3.35e-93)
       x
       (if (<= y -5.2e-147) t_0 (if (<= y 1.45e+20) x t_0))))))

C

double code(double x, double y) {
	double t_0 = -(x * y) * x;
	double tmp;
	if (y <= -2.36e+83) {
		tmp = t_0;
	} else if (y <= -3.35e-93) {
		tmp = x;
	} else if (y <= -5.2e-147) {
		tmp = t_0;
	} else if (y <= 1.45e+20) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -(x * y) * x
    if (y <= (-2.36d+83)) then
        tmp = t_0
    else if (y <= (-3.35d-93)) then
        tmp = x
    else if (y <= (-5.2d-147)) then
        tmp = t_0
    else if (y <= 1.45d+20) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = -(x * y) * x;
	double tmp;
	if (y <= -2.36e+83) {
		tmp = t_0;
	} else if (y <= -3.35e-93) {
		tmp = x;
	} else if (y <= -5.2e-147) {
		tmp = t_0;
	} else if (y <= 1.45e+20) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = -(x * y) * x
	tmp = 0
	if y <= -2.36e+83:
		tmp = t_0
	elif y <= -3.35e-93:
		tmp = x
	elif y <= -5.2e-147:
		tmp = t_0
	elif y <= 1.45e+20:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(-Float64(x * y)) * x)
	tmp = 0.0
	if (y <= -2.36e+83)
		tmp = t_0;
	elseif (y <= -3.35e-93)
		tmp = x;
	elseif (y <= -5.2e-147)
		tmp = t_0;
	elseif (y <= 1.45e+20)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = -(x * y) * x;
	tmp = 0.0;
	if (y <= -2.36e+83)
		tmp = t_0;
	elseif (y <= -3.35e-93)
		tmp = x;
	elseif (y <= -5.2e-147)
		tmp = t_0;
	elseif (y <= 1.45e+20)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[((-N[(x * y), $MachinePrecision]) * x), $MachinePrecision]}, If[LessEqual[y, -2.36e+83], t$95$0, If[LessEqual[y, -3.35e-93], x, If[LessEqual[y, -5.2e-147], t$95$0, If[LessEqual[y, 1.45e+20], x, t$95$0]]]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3599999999999999e83 or -3.34999999999999987e-93 < y < -5.1999999999999997e-147 or 1.45e20 < y

   1. Initial program 99.8%

      \[x \cdot \left(1 - x \cdot y\right) \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   9. Simplified 0

      \[\leadsto expr\]

   11. Applied egg-rr 0

       \[\leadsto expr\]

   if -2.3599999999999999e83 < y < -3.34999999999999987e-93 or -5.1999999999999997e-147 < y < 1.45e20

   1. Initial program 100.0%

      \[x \cdot \left(1 - x \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - x \cdot y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* x (- 1.0 (* x y))))

C

double code(double x, double y) {
	return x * (1.0 - (x * y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (1.0d0 - (x * y))
end function

Java

public static double code(double x, double y) {
	return x * (1.0 - (x * y));
}

Python

def code(x, y):
	return x * (1.0 - (x * y))

Julia

function code(x, y)
	return Float64(x * Float64(1.0 - Float64(x * y)))
end

MATLAB

function tmp = code(x, y)
	tmp = x * (1.0 - (x * y));
end

Wolfram

code[x_, y_] := N[(x * N[(1.0 - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot \left(1 - x \cdot y\right) \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 4: 50.0% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 x)

C

double code(double x, double y) {
	return x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x
end function

Java

public static double code(double x, double y) {
	return x;
}

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

function tmp = code(x, y)
	tmp = x;
end

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 99.9%

   \[x \cdot \left(1 - x \cdot y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024110 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1.0 (* x y))))