Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.5% → 99.7%

Time: 1.5s

Alternatives: 5

Speedup: 1.0×

Specification

Math

\[\frac{x \cdot 100}{x + y} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (/ (* x 100.0) (+ x y)))

C

double code(double x, double y) {
	return (x * 100.0) / (x + y);
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * 100.0d0) / (x + y)
end function

Java

public static double code(double x, double y) {
	return (x * 100.0) / (x + y);
}

Python

def code(x, y):
	return (x * 100.0) / (x + y)

Julia

function code(x, y)
	return Float64(Float64(x * 100.0) / Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x * 100.0) / (x + y);
end

Wolfram

code[x_, y_] := N[(N[(x * 100.0), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	(x * (100)) / (x + y)
END code

Initial Program: 99.5% accurate, 1.0× speedup

Math

\[\frac{x \cdot 100}{x + y} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (/ (* x 100.0) (+ x y)))

C

double code(double x, double y) {
	return (x * 100.0) / (x + y);
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * 100.0d0) / (x + y)
end function

Java

public static double code(double x, double y) {
	return (x * 100.0) / (x + y);
}

Python

def code(x, y):
	return (x * 100.0) / (x + y)

Julia

function code(x, y)
	return Float64(Float64(x * 100.0) / Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x * 100.0) / (x + y);
end

Wolfram

code[x_, y_] := N[(N[(x * 100.0), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	(x * (100)) / (x + y)
END code

Alternative 1: 99.5% accurate, 1.0× speedup

Math

\[x \cdot \frac{100}{y + x} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (* x (/ 100.0 (+ y x))))

C

double code(double x, double y) {
	return x * (100.0 / (y + x));
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (100.0d0 / (y + x))
end function

Java

public static double code(double x, double y) {
	return x * (100.0 / (y + x));
}

Python

def code(x, y):
	return x * (100.0 / (y + x))

Julia

function code(x, y)
	return Float64(x * Float64(100.0 / Float64(y + x)))
end

MATLAB

function tmp = code(x, y)
	tmp = x * (100.0 / (y + x));
end

Wolfram

code[x_, y_] := N[(x * N[(100.0 / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	x * ((100) / (y + x))
END code

Derivation

1. Initial program 99.5%

   \[\frac{x \cdot 100}{x + y} \]
2. Step-by-step derivation

3. Applied rewrites 99.7%

   \[\leadsto x \cdot \frac{100}{y + x} \]
4. Add Preprocessing

Alternative 2: 97.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot 100}{x + y} \leq 10^{-15}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= (/ (* x 100.0) (+ x y)) 1e-15) (* x (/ 100.0 y)) 100.0))

C

double code(double x, double y) {
	double tmp;
	if (((x * 100.0) / (x + y)) <= 1e-15) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	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 (((x * 100.0d0) / (x + y)) <= 1d-15) then
        tmp = x * (100.0d0 / y)
    else
        tmp = 100.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((x * 100.0) / (x + y)) <= 1e-15) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((x * 100.0) / (x + y)) <= 1e-15:
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(x * 100.0) / Float64(x + y)) <= 1e-15)
		tmp = Float64(x * Float64(100.0 / y));
	else
		tmp = 100.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((x * 100.0) / (x + y)) <= 1e-15)
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(x * 100.0), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], 1e-15], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp = IF (((x * (100)) / (x + y)) <= (100000000000000007770539987666107923830718560119501514549256171449087560176849365234375e-101)) THEN (x * ((100) / y)) ELSE (100) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x #s(literal 100 binary64)) (+.f64 x y)) < 1.0000000000000001e-15

   1. Initial program 99.5%

      \[\frac{x \cdot 100}{x + y} \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{x \cdot 100}{y} \]
   3. Step-by-step derivation

   4. Applied rewrites 50.7%

      \[\leadsto \frac{x \cdot 100}{y} \]
   5. Step-by-step derivation

   6. Applied rewrites 50.7%

      \[\leadsto x \cdot \frac{100}{y} \]

   if 1.0000000000000001e-15 < (/.f64 (*.f64 x #s(literal 100 binary64)) (+.f64 x y))

   1. Initial program 99.5%

      \[\frac{x \cdot 100}{x + y} \]

   2. Taylor expanded in x around inf

      \[\leadsto 100 \]
   3. Step-by-step derivation

   4. Applied rewrites 50.7%

      \[\leadsto 100 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 97.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot 100}{x + y} \leq 10^{-15}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= (/ (* x 100.0) (+ x y)) 1e-15) (* 100.0 (/ x y)) 100.0))

C

double code(double x, double y) {
	double tmp;
	if (((x * 100.0) / (x + y)) <= 1e-15) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	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 (((x * 100.0d0) / (x + y)) <= 1d-15) then
        tmp = 100.0d0 * (x / y)
    else
        tmp = 100.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((x * 100.0) / (x + y)) <= 1e-15) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((x * 100.0) / (x + y)) <= 1e-15:
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(x * 100.0) / Float64(x + y)) <= 1e-15)
		tmp = Float64(100.0 * Float64(x / y));
	else
		tmp = 100.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((x * 100.0) / (x + y)) <= 1e-15)
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(x * 100.0), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], 1e-15], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp = IF (((x * (100)) / (x + y)) <= (100000000000000007770539987666107923830718560119501514549256171449087560176849365234375e-101)) THEN ((100) * (x / y)) ELSE (100) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x #s(literal 100 binary64)) (+.f64 x y)) < 1.0000000000000001e-15

   1. Initial program 99.5%

      \[\frac{x \cdot 100}{x + y} \]

   2. Taylor expanded in x around 0

      \[\leadsto 100 \cdot \frac{x}{y} \]
   3. Step-by-step derivation

   4. Applied rewrites 50.6%

      \[\leadsto 100 \cdot \frac{x}{y} \]

   if 1.0000000000000001e-15 < (/.f64 (*.f64 x #s(literal 100 binary64)) (+.f64 x y))

   1. Initial program 99.5%

      \[\frac{x \cdot 100}{x + y} \]

   2. Taylor expanded in x around inf

      \[\leadsto 100 \]
   3. Step-by-step derivation

   4. Applied rewrites 50.7%

      \[\leadsto 100 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 50.7% accurate, 10.4× speedup

Math

\[100 \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  100.0)

C

double code(double x, double y) {
	return 100.0;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 100.0d0
end function

Java

public static double code(double x, double y) {
	return 100.0;
}

Python

def code(x, y):
	return 100.0

Julia

function code(x, y)
	return 100.0
end

MATLAB

function tmp = code(x, y)
	tmp = 100.0;
end

Wolfram

code[x_, y_] := 100.0

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	100
END code

Derivation

1. Initial program 99.5%

   \[\frac{x \cdot 100}{x + y} \]

2. Taylor expanded in x around inf

   \[\leadsto 100 \]
3. Step-by-step derivation

4. Applied rewrites 50.7%

   \[\leadsto 100 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"
  :precision binary64
  (/ (* x 100.0) (+ x y)))