exact-inv-half-inv-exp

Percentage Accurate: 100.0% → 100.0%

Time: 1.3min

Alternatives: 7

Speedup: 1.0×

• could not determine a ground truth

  1. Ce = -382630830.6065868

Specification

Math

\[\frac{0.5}{e^{2 \cdot Ce}} \]

FPCore

(FPCore (Ce)
  :precision binary64
  :pre TRUE
  (/ 0.5 (exp (* 2.0 Ce))))

C

double code(double Ce) {
	return 0.5 / exp((2.0 * Ce));
}

Fortran

real(8) function code(ce)
use fmin_fmax_functions
    real(8), intent (in) :: ce
    code = 0.5d0 / exp((2.0d0 * ce))
end function

Java

public static double code(double Ce) {
	return 0.5 / Math.exp((2.0 * Ce));
}

Python

def code(Ce):
	return 0.5 / math.exp((2.0 * Ce))

Julia

function code(Ce)
	return Float64(0.5 / exp(Float64(2.0 * Ce)))
end

MATLAB

function tmp = code(Ce)
	tmp = 0.5 / exp((2.0 * Ce));
end

Wolfram

code[Ce_] := N[(0.5 / N[Exp[N[(2.0 * Ce), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

ReFlow

f(Ce):
	Ce in [-inf, +inf]
code: THEORY
BEGIN
f(Ce: real): real =
	(5e-1) / (exp(((2) * Ce)))
END code

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\frac{0.5}{e^{2 \cdot Ce}} \]

FPCore

(FPCore (Ce)
  :precision binary64
  :pre TRUE
  (/ 0.5 (exp (* 2.0 Ce))))

C

double code(double Ce) {
	return 0.5 / exp((2.0 * Ce));
}

Fortran

real(8) function code(ce)
use fmin_fmax_functions
    real(8), intent (in) :: ce
    code = 0.5d0 / exp((2.0d0 * ce))
end function

Java

public static double code(double Ce) {
	return 0.5 / Math.exp((2.0 * Ce));
}

Python

def code(Ce):
	return 0.5 / math.exp((2.0 * Ce))

Julia

function code(Ce)
	return Float64(0.5 / exp(Float64(2.0 * Ce)))
end

MATLAB

function tmp = code(Ce)
	tmp = 0.5 / exp((2.0 * Ce));
end

Wolfram

code[Ce_] := N[(0.5 / N[Exp[N[(2.0 * Ce), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

ReFlow

f(Ce):
	Ce in [-inf, +inf]
code: THEORY
BEGIN
f(Ce: real): real =
	(5e-1) / (exp(((2) * Ce)))
END code

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[e^{-2 \cdot Ce} \cdot 0.5 \]

FPCore

(FPCore (Ce)
  :precision binary64
  :pre TRUE
  (* (exp (* -2.0 Ce)) 0.5))

C

double code(double Ce) {
	return exp((-2.0 * Ce)) * 0.5;
}

Fortran

real(8) function code(ce)
use fmin_fmax_functions
    real(8), intent (in) :: ce
    code = exp(((-2.0d0) * ce)) * 0.5d0
end function

Java

public static double code(double Ce) {
	return Math.exp((-2.0 * Ce)) * 0.5;
}

Python

def code(Ce):
	return math.exp((-2.0 * Ce)) * 0.5

Julia

function code(Ce)
	return Float64(exp(Float64(-2.0 * Ce)) * 0.5)
end

MATLAB

function tmp = code(Ce)
	tmp = exp((-2.0 * Ce)) * 0.5;
end

Wolfram

code[Ce_] := N[(N[Exp[N[(-2.0 * Ce), $MachinePrecision]], $MachinePrecision] * 0.5), $MachinePrecision]

ReFlow

f(Ce):
	Ce in [-inf, +inf]
code: THEORY
BEGIN
f(Ce: real): real =
	(exp(((-2) * Ce))) * (5e-1)
END code

Derivation

1. Initial program 100.0%

   \[\frac{0.5}{e^{2 \cdot Ce}} \]

3. Applied rewrites 100.0%

   \[\leadsto e^{-2 \cdot Ce} \cdot 0.5 \]
4. Add Preprocessing

Alternative 2: 98.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;2 \cdot Ce \leq 0.2:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-0.6666666666666666, Ce, 1\right), Ce \cdot Ce, 0.5\right) - Ce\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

FPCore

(FPCore (Ce)
  :precision binary64
  :pre TRUE
  (if (<= (* 2.0 Ce) 0.2)
  (- (fma (fma -0.6666666666666666 Ce 1.0) (* Ce Ce) 0.5) Ce)
  0.0))

C

double code(double Ce) {
	double tmp;
	if ((2.0 * Ce) <= 0.2) {
		tmp = fma(fma(-0.6666666666666666, Ce, 1.0), (Ce * Ce), 0.5) - Ce;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Julia

function code(Ce)
	tmp = 0.0
	if (Float64(2.0 * Ce) <= 0.2)
		tmp = Float64(fma(fma(-0.6666666666666666, Ce, 1.0), Float64(Ce * Ce), 0.5) - Ce);
	else
		tmp = 0.0;
	end
	return tmp
end

Wolfram

code[Ce_] := If[LessEqual[N[(2.0 * Ce), $MachinePrecision], 0.2], N[(N[(N[(-0.6666666666666666 * Ce + 1.0), $MachinePrecision] * N[(Ce * Ce), $MachinePrecision] + 0.5), $MachinePrecision] - Ce), $MachinePrecision], 0.0]

ReFlow

f(Ce):
	Ce in [-inf, +inf]
code: THEORY
BEGIN
f(Ce: real): real =
	LET tmp = IF (((2) * Ce) <= (200000000000000011102230246251565404236316680908203125e-54)) THEN ((((((-66666666666666662965923251249478198587894439697265625e-53) * Ce) + (1)) * (Ce * Ce)) + (5e-1)) - Ce) ELSE (0) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 2 binary64) Ce) < 0.20000000000000001

   1. Initial program 100.0%

      \[\frac{0.5}{e^{2 \cdot Ce}} \]

   2. Taylor expanded in Ce around 0

      \[\leadsto \frac{1}{2} + Ce \cdot \left(Ce \cdot \left(1 + \frac{-2}{3} \cdot Ce\right) - 1\right) \]

   4. Applied rewrites 67.0%

      \[\leadsto 0.5 + Ce \cdot \left(Ce \cdot \left(1 + -0.6666666666666666 \cdot Ce\right) - 1\right) \]

   6. Applied rewrites 67.0%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-0.6666666666666666, Ce, 1\right), Ce \cdot Ce, 0.5\right) - Ce \]

   if 0.20000000000000001 < (*.f64 #s(literal 2 binary64) Ce)

   1. Initial program 100.0%

      \[\frac{0.5}{e^{2 \cdot Ce}} \]

   2. Taylor expanded in Ce around 0

      \[\leadsto \frac{1}{2} \]

   4. Applied rewrites 66.2%

      \[\leadsto 0.5 \]

   5. Taylor expanded in undef-var around zero

      \[\leadsto 0 \]

   7. Applied rewrites 34.3%

      \[\leadsto 0 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 98.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;2 \cdot Ce \leq 0.2:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-0.6666666666666666, Ce, 1\right), Ce, -1\right), Ce, 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

FPCore

(FPCore (Ce)
  :precision binary64
  :pre TRUE
  (if (<= (* 2.0 Ce) 0.2)
  (fma (fma (fma -0.6666666666666666 Ce 1.0) Ce -1.0) Ce 0.5)
  0.0))

C

double code(double Ce) {
	double tmp;
	if ((2.0 * Ce) <= 0.2) {
		tmp = fma(fma(fma(-0.6666666666666666, Ce, 1.0), Ce, -1.0), Ce, 0.5);
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Julia

function code(Ce)
	tmp = 0.0
	if (Float64(2.0 * Ce) <= 0.2)
		tmp = fma(fma(fma(-0.6666666666666666, Ce, 1.0), Ce, -1.0), Ce, 0.5);
	else
		tmp = 0.0;
	end
	return tmp
end

Wolfram

code[Ce_] := If[LessEqual[N[(2.0 * Ce), $MachinePrecision], 0.2], N[(N[(N[(-0.6666666666666666 * Ce + 1.0), $MachinePrecision] * Ce + -1.0), $MachinePrecision] * Ce + 0.5), $MachinePrecision], 0.0]

ReFlow

f(Ce):
	Ce in [-inf, +inf]
code: THEORY
BEGIN
f(Ce: real): real =
	LET tmp = IF (((2) * Ce) <= (200000000000000011102230246251565404236316680908203125e-54)) THEN (((((((-66666666666666662965923251249478198587894439697265625e-53) * Ce) + (1)) * Ce) + (-1)) * Ce) + (5e-1)) ELSE (0) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 2 binary64) Ce) < 0.20000000000000001

   1. Initial program 100.0%

      \[\frac{0.5}{e^{2 \cdot Ce}} \]

   2. Taylor expanded in Ce around 0

      \[\leadsto \frac{1}{2} + Ce \cdot \left(Ce \cdot \left(1 + \frac{-2}{3} \cdot Ce\right) - 1\right) \]

   4. Applied rewrites 67.0%

      \[\leadsto 0.5 + Ce \cdot \left(Ce \cdot \left(1 + -0.6666666666666666 \cdot Ce\right) - 1\right) \]

   6. Applied rewrites 67.0%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-0.6666666666666666, Ce, 1\right), Ce, -1\right), Ce, 0.5\right) \]

   if 0.20000000000000001 < (*.f64 #s(literal 2 binary64) Ce)

   1. Initial program 100.0%

      \[\frac{0.5}{e^{2 \cdot Ce}} \]

   2. Taylor expanded in Ce around 0

      \[\leadsto \frac{1}{2} \]

   4. Applied rewrites 66.2%

      \[\leadsto 0.5 \]

   5. Taylor expanded in undef-var around zero

      \[\leadsto 0 \]

   7. Applied rewrites 34.3%

      \[\leadsto 0 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 98.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;2 \cdot Ce \leq 0.2:\\ \;\;\;\;\mathsf{fma}\left(Ce, Ce, 0.5 - Ce\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

FPCore

(FPCore (Ce)
  :precision binary64
  :pre TRUE
  (if (<= (* 2.0 Ce) 0.2) (fma Ce Ce (- 0.5 Ce)) 0.0))

C

double code(double Ce) {
	double tmp;
	if ((2.0 * Ce) <= 0.2) {
		tmp = fma(Ce, Ce, (0.5 - Ce));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Julia

function code(Ce)
	tmp = 0.0
	if (Float64(2.0 * Ce) <= 0.2)
		tmp = fma(Ce, Ce, Float64(0.5 - Ce));
	else
		tmp = 0.0;
	end
	return tmp
end

Wolfram

code[Ce_] := If[LessEqual[N[(2.0 * Ce), $MachinePrecision], 0.2], N[(Ce * Ce + N[(0.5 - Ce), $MachinePrecision]), $MachinePrecision], 0.0]

ReFlow

f(Ce):
	Ce in [-inf, +inf]
code: THEORY
BEGIN
f(Ce: real): real =
	LET tmp = IF (((2) * Ce) <= (200000000000000011102230246251565404236316680908203125e-54)) THEN ((Ce * Ce) + ((5e-1) - Ce)) ELSE (0) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 2 binary64) Ce) < 0.20000000000000001

   1. Initial program 100.0%

      \[\frac{0.5}{e^{2 \cdot Ce}} \]

   2. Taylor expanded in Ce around 0

      \[\leadsto \frac{1}{2} + Ce \cdot \left(Ce - 1\right) \]

   4. Applied rewrites 66.9%

      \[\leadsto 0.5 + Ce \cdot \left(Ce - 1\right) \]

   6. Applied rewrites 66.9%

      \[\leadsto \mathsf{fma}\left(Ce, Ce, 0.5 - Ce\right) \]

   if 0.20000000000000001 < (*.f64 #s(literal 2 binary64) Ce)

   1. Initial program 100.0%

      \[\frac{0.5}{e^{2 \cdot Ce}} \]

   2. Taylor expanded in Ce around 0

      \[\leadsto \frac{1}{2} \]

   4. Applied rewrites 66.2%

      \[\leadsto 0.5 \]

   5. Taylor expanded in undef-var around zero

      \[\leadsto 0 \]

   7. Applied rewrites 34.3%

      \[\leadsto 0 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 98.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;2 \cdot Ce \leq 0.2:\\ \;\;\;\;0.5 - Ce\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

FPCore

(FPCore (Ce)
  :precision binary64
  :pre TRUE
  (if (<= (* 2.0 Ce) 0.2) (- 0.5 Ce) 0.0))

C

double code(double Ce) {
	double tmp;
	if ((2.0 * Ce) <= 0.2) {
		tmp = 0.5 - Ce;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(ce)
use fmin_fmax_functions
    real(8), intent (in) :: ce
    real(8) :: tmp
    if ((2.0d0 * ce) <= 0.2d0) then
        tmp = 0.5d0 - ce
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double Ce) {
	double tmp;
	if ((2.0 * Ce) <= 0.2) {
		tmp = 0.5 - Ce;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(Ce):
	tmp = 0
	if (2.0 * Ce) <= 0.2:
		tmp = 0.5 - Ce
	else:
		tmp = 0.0
	return tmp

Julia

function code(Ce)
	tmp = 0.0
	if (Float64(2.0 * Ce) <= 0.2)
		tmp = Float64(0.5 - Ce);
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(Ce)
	tmp = 0.0;
	if ((2.0 * Ce) <= 0.2)
		tmp = 0.5 - Ce;
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[Ce_] := If[LessEqual[N[(2.0 * Ce), $MachinePrecision], 0.2], N[(0.5 - Ce), $MachinePrecision], 0.0]

ReFlow

f(Ce):
	Ce in [-inf, +inf]
code: THEORY
BEGIN
f(Ce: real): real =
	LET tmp = IF (((2) * Ce) <= (200000000000000011102230246251565404236316680908203125e-54)) THEN ((5e-1) - Ce) ELSE (0) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 2 binary64) Ce) < 0.20000000000000001

   1. Initial program 100.0%

      \[\frac{0.5}{e^{2 \cdot Ce}} \]

   2. Taylor expanded in Ce around 0

      \[\leadsto \frac{1}{2} + -1 \cdot Ce \]

   4. Applied rewrites 66.7%

      \[\leadsto 0.5 + -1 \cdot Ce \]

   6. Applied rewrites 66.7%

      \[\leadsto 0.5 - Ce \]

   if 0.20000000000000001 < (*.f64 #s(literal 2 binary64) Ce)

   1. Initial program 100.0%

      \[\frac{0.5}{e^{2 \cdot Ce}} \]

   2. Taylor expanded in Ce around 0

      \[\leadsto \frac{1}{2} \]

   4. Applied rewrites 66.2%

      \[\leadsto 0.5 \]

   5. Taylor expanded in undef-var around zero

      \[\leadsto 0 \]

   7. Applied rewrites 34.3%

      \[\leadsto 0 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 97.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;2 \cdot Ce \leq 169.95083588869068:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

FPCore

(FPCore (Ce)
  :precision binary64
  :pre TRUE
  (if (<= (* 2.0 Ce) 169.95083588869068) 0.5 0.0))

C

double code(double Ce) {
	double tmp;
	if ((2.0 * Ce) <= 169.95083588869068) {
		tmp = 0.5;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(ce)
use fmin_fmax_functions
    real(8), intent (in) :: ce
    real(8) :: tmp
    if ((2.0d0 * ce) <= 169.95083588869068d0) then
        tmp = 0.5d0
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double Ce) {
	double tmp;
	if ((2.0 * Ce) <= 169.95083588869068) {
		tmp = 0.5;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(Ce):
	tmp = 0
	if (2.0 * Ce) <= 169.95083588869068:
		tmp = 0.5
	else:
		tmp = 0.0
	return tmp

Julia

function code(Ce)
	tmp = 0.0
	if (Float64(2.0 * Ce) <= 169.95083588869068)
		tmp = 0.5;
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(Ce)
	tmp = 0.0;
	if ((2.0 * Ce) <= 169.95083588869068)
		tmp = 0.5;
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[Ce_] := If[LessEqual[N[(2.0 * Ce), $MachinePrecision], 169.95083588869068], 0.5, 0.0]

ReFlow

f(Ce):
	Ce in [-inf, +inf]
code: THEORY
BEGIN
f(Ce: real): real =
	LET tmp = IF (((2) * Ce) <= (1699508358886906762563739903271198272705078125e-43)) THEN (5e-1) ELSE (0) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 2 binary64) Ce) < 169.95083588869068

   1. Initial program 100.0%

      \[\frac{0.5}{e^{2 \cdot Ce}} \]

   2. Taylor expanded in Ce around 0

      \[\leadsto \frac{1}{2} \]

   4. Applied rewrites 66.2%

      \[\leadsto 0.5 \]

   if 169.95083588869068 < (*.f64 #s(literal 2 binary64) Ce)

   1. Initial program 100.0%

      \[\frac{0.5}{e^{2 \cdot Ce}} \]

   2. Taylor expanded in Ce around 0

      \[\leadsto \frac{1}{2} \]

   4. Applied rewrites 66.2%

      \[\leadsto 0.5 \]

   5. Taylor expanded in undef-var around zero

      \[\leadsto 0 \]

   7. Applied rewrites 34.3%

      \[\leadsto 0 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 66.2% accurate, 18.8× speedup

Math

\[0.5 \]

FPCore

(FPCore (Ce)
  :precision binary64
  :pre TRUE
  0.5)

C

double code(double Ce) {
	return 0.5;
}

Fortran

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

Java

public static double code(double Ce) {
	return 0.5;
}

Python

def code(Ce):
	return 0.5

Julia

function code(Ce)
	return 0.5
end

MATLAB

function tmp = code(Ce)
	tmp = 0.5;
end

Wolfram

code[Ce_] := 0.5

ReFlow

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

Derivation

1. Initial program 100.0%

   \[\frac{0.5}{e^{2 \cdot Ce}} \]

2. Taylor expanded in Ce around 0

   \[\leadsto \frac{1}{2} \]

4. Applied rewrites 66.2%

   \[\leadsto 0.5 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2026050 +o generate:egglog
(FPCore (Ce)
  :name "exact-inv-half-inv-exp"
  :precision binary64
  (/ 0.5 (exp (* 2.0 Ce))))