Numeric.Interval.Internal:bisect from intervals-0.7.1, A

Percentage Accurate: 100.0% → 100.0%

Time: 1.1s

Alternatives: 3

Speedup: 1.5×

Specification

Math

\[x + \frac{y - x}{2} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (+ x (/ (- y x) 2.0)))

C

double code(double x, double y) {
	return x + ((y - x) / 2.0);
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + ((y - x) / 2.0d0)
end function

Java

public static double code(double x, double y) {
	return x + ((y - x) / 2.0);
}

Python

def code(x, y):
	return x + ((y - x) / 2.0)

Julia

function code(x, y)
	return Float64(x + Float64(Float64(y - x) / 2.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x + ((y - x) / 2.0);
end

Wolfram

code[x_, y_] := N[(x + N[(N[(y - x), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	x + ((y - x) / (2))
END code

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[x + \frac{y - x}{2} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (+ x (/ (- y x) 2.0)))

C

double code(double x, double y) {
	return x + ((y - x) / 2.0);
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + ((y - x) / 2.0d0)
end function

Java

public static double code(double x, double y) {
	return x + ((y - x) / 2.0);
}

Python

def code(x, y):
	return x + ((y - x) / 2.0)

Julia

function code(x, y)
	return Float64(x + Float64(Float64(y - x) / 2.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x + ((y - x) / 2.0);
end

Wolfram

code[x_, y_] := N[(x + N[(N[(y - x), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	x + ((y - x) / (2))
END code

Alternative 1: 100.0% accurate, 1.5× speedup

Math

\[\left(y + x\right) \cdot 0.5 \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (* (+ y x) 0.5))

C

double code(double x, double y) {
	return (y + x) * 0.5;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (y + x) * 0.5d0
end function

Java

public static double code(double x, double y) {
	return (y + x) * 0.5;
}

Python

def code(x, y):
	return (y + x) * 0.5

Julia

function code(x, y)
	return Float64(Float64(y + x) * 0.5)
end

MATLAB

function tmp = code(x, y)
	tmp = (y + x) * 0.5;
end

Wolfram

code[x_, y_] := N[(N[(y + x), $MachinePrecision] * 0.5), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	(y + x) * (5e-1)
END code

Derivation

1. Initial program 100.0%

   \[x + \frac{y - x}{2} \]

2. Taylor expanded in x around 0

   \[\leadsto \frac{1}{2} \cdot x + \frac{1}{2} \cdot y \]
3. Step-by-step derivation

4. Applied rewrites 100.0%

   \[\leadsto \mathsf{fma}\left(0.5, x, 0.5 \cdot y\right) \]
5. Step-by-step derivation

6. Applied rewrites 100.0%

   \[\leadsto \left(y + x\right) \cdot 0.5 \]
7. Add Preprocessing

Alternative 2: 74.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -3.7736488112764267 \cdot 10^{+33}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{elif}\;y \leq 2.426229654520916 \cdot 10^{+48}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= y -3.7736488112764267e+33)
  (* y 0.5)
  (if (<= y 2.426229654520916e+48) (* 0.5 x) (* y 0.5))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.7736488112764267e+33) {
		tmp = y * 0.5;
	} else if (y <= 2.426229654520916e+48) {
		tmp = 0.5 * x;
	} else {
		tmp = y * 0.5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-3.7736488112764267d+33)) then
        tmp = y * 0.5d0
    else if (y <= 2.426229654520916d+48) then
        tmp = 0.5d0 * x
    else
        tmp = y * 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3.7736488112764267e+33) {
		tmp = y * 0.5;
	} else if (y <= 2.426229654520916e+48) {
		tmp = 0.5 * x;
	} else {
		tmp = y * 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.7736488112764267e+33:
		tmp = y * 0.5
	elif y <= 2.426229654520916e+48:
		tmp = 0.5 * x
	else:
		tmp = y * 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.7736488112764267e+33)
		tmp = Float64(y * 0.5);
	elseif (y <= 2.426229654520916e+48)
		tmp = Float64(0.5 * x);
	else
		tmp = Float64(y * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.7736488112764267e+33)
		tmp = y * 0.5;
	elseif (y <= 2.426229654520916e+48)
		tmp = 0.5 * x;
	else
		tmp = y * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.7736488112764267e+33], N[(y * 0.5), $MachinePrecision], If[LessEqual[y, 2.426229654520916e+48], N[(0.5 * x), $MachinePrecision], N[(y * 0.5), $MachinePrecision]]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp_1 = IF (y <= (2426229654520915891643607200729785382101422440448)) THEN ((5e-1) * x) ELSE (y * (5e-1)) ENDIF IN
	LET tmp = IF (y <= (-3773648811276426676203284156383232)) THEN (y * (5e-1)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -3.7736488112764267e33 or 2.4262296545209159e48 < y

   1. Initial program 100.0%

      \[x + \frac{y - x}{2} \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{2} \cdot x + \frac{1}{2} \cdot y \]
   3. Step-by-step derivation

   4. Applied rewrites 100.0%

      \[\leadsto \mathsf{fma}\left(0.5, x, 0.5 \cdot y\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 100.0%

      \[\leadsto \left(y + x\right) \cdot 0.5 \]

   7. Taylor expanded in x around 0

      \[\leadsto y \cdot 0.5 \]
   8. Step-by-step derivation

   9. Applied rewrites 50.2%

      \[\leadsto y \cdot 0.5 \]

   if -3.7736488112764267e33 < y < 2.4262296545209159e48

   1. Initial program 100.0%

      \[x + \frac{y - x}{2} \]

   2. Taylor expanded in x around inf

      \[\leadsto \frac{1}{2} \cdot x \]
   3. Step-by-step derivation

   4. Applied rewrites 51.3%

      \[\leadsto 0.5 \cdot x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 51.3% accurate, 2.5× speedup

Math

\[0.5 \cdot x \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (* 0.5 x))

C

double code(double x, double y) {
	return 0.5 * x;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.5d0 * x
end function

Java

public static double code(double x, double y) {
	return 0.5 * x;
}

Python

def code(x, y):
	return 0.5 * x

Julia

function code(x, y)
	return Float64(0.5 * x)
end

MATLAB

function tmp = code(x, y)
	tmp = 0.5 * x;
end

Wolfram

code[x_, y_] := N[(0.5 * x), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	(5e-1) * x
END code

Derivation

1. Initial program 100.0%

   \[x + \frac{y - x}{2} \]

2. Taylor expanded in x around inf

   \[\leadsto \frac{1}{2} \cdot x \]
3. Step-by-step derivation

4. Applied rewrites 51.3%

   \[\leadsto 0.5 \cdot x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y)
  :name "Numeric.Interval.Internal:bisect from intervals-0.7.1, A"
  :precision binary64
  (+ x (/ (- y x) 2.0)))