Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B

Percentage Accurate: 99.8% → 99.8%

Time: 2.1s

Alternatives: 4

Speedup: 1.4×

Specification

Math

\[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))

C

double code(double x, double y, double z) {
	return (1.0 / 2.0) * (x + (y * sqrt(z)));
}

Fortran

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (1.0d0 / 2.0d0) * (x + (y * sqrt(z)))
end function

Java

public static double code(double x, double y, double z) {
	return (1.0 / 2.0) * (x + (y * Math.sqrt(z)));
}

Python

def code(x, y, z):
	return (1.0 / 2.0) * (x + (y * math.sqrt(z)))

Julia

function code(x, y, z)
	return Float64(Float64(1.0 / 2.0) * Float64(x + Float64(y * sqrt(z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (1.0 / 2.0) * (x + (y * sqrt(z)));
end

Wolfram

code[x_, y_, z_] := N[(N[(1.0 / 2.0), $MachinePrecision] * N[(x + N[(y * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

ReFlow

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))

C

double code(double x, double y, double z) {
	return (1.0 / 2.0) * (x + (y * sqrt(z)));
}

Fortran

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (1.0d0 / 2.0d0) * (x + (y * sqrt(z)))
end function

Java

public static double code(double x, double y, double z) {
	return (1.0 / 2.0) * (x + (y * Math.sqrt(z)));
}

Python

def code(x, y, z):
	return (1.0 / 2.0) * (x + (y * math.sqrt(z)))

Julia

function code(x, y, z)
	return Float64(Float64(1.0 / 2.0) * Float64(x + Float64(y * sqrt(z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (1.0 / 2.0) * (x + (y * sqrt(z)));
end

Wolfram

code[x_, y_, z_] := N[(N[(1.0 / 2.0), $MachinePrecision] * N[(x + N[(y * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

ReFlow

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

Alternative 1: 99.8% accurate, 1.3× speedup

Math

\[0.5 \cdot \left(x + y \cdot \sqrt{z}\right) \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return 0.5 * (x + (y * math.sqrt(z)))

Julia

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

MATLAB

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

Wolfram

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

ReFlow

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

Derivation

1. Initial program 99.8%

   \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]

2. Evaluated real constant 99.8%

   \[\leadsto 0.5 \cdot \left(x + y \cdot \sqrt{z}\right) \]
3. Add Preprocessing

Alternative 2: 99.8% accurate, 1.4× speedup

Math

\[0.5 \cdot \mathsf{fma}\left(\sqrt{z}, y, x\right) \]

FPCore

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

C

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

Julia

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

Wolfram

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

ReFlow

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

Derivation

1. Initial program 99.8%

   \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]
2. Step-by-step derivation

3. Applied rewrites 99.8%

   \[\leadsto 0.5 \cdot \mathsf{fma}\left(\sqrt{z}, y, x\right) \]
4. Add Preprocessing

Alternative 3: 74.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -17135672566.239237:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;x \leq 5.62844316176412 \cdot 10^{-46}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \sqrt{z}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= x -17135672566.239237)
  (* 0.5 x)
  (if (<= x 5.62844316176412e-46) (* 0.5 (* y (sqrt z))) (* 0.5 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -17135672566.239237) {
		tmp = 0.5 * x;
	} else if (x <= 5.62844316176412e-46) {
		tmp = 0.5 * (y * sqrt(z));
	} else {
		tmp = 0.5 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-17135672566.239237d0)) then
        tmp = 0.5d0 * x
    else if (x <= 5.62844316176412d-46) then
        tmp = 0.5d0 * (y * sqrt(z))
    else
        tmp = 0.5d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -17135672566.239237) {
		tmp = 0.5 * x;
	} else if (x <= 5.62844316176412e-46) {
		tmp = 0.5 * (y * Math.sqrt(z));
	} else {
		tmp = 0.5 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -17135672566.239237:
		tmp = 0.5 * x
	elif x <= 5.62844316176412e-46:
		tmp = 0.5 * (y * math.sqrt(z))
	else:
		tmp = 0.5 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -17135672566.239237)
		tmp = Float64(0.5 * x);
	elseif (x <= 5.62844316176412e-46)
		tmp = Float64(0.5 * Float64(y * sqrt(z)));
	else
		tmp = Float64(0.5 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -17135672566.239237)
		tmp = 0.5 * x;
	elseif (x <= 5.62844316176412e-46)
		tmp = 0.5 * (y * sqrt(z));
	else
		tmp = 0.5 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -17135672566.239237], N[(0.5 * x), $MachinePrecision], If[LessEqual[x, 5.62844316176412e-46], N[(0.5 * N[(y * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * x), $MachinePrecision]]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET tmp_1 = IF (x <= (5628443161764119920644829953410590951875344298681555851493315816868097534915156825371220837143217692897771044975596156645369916304844082333147525787353515625e-202)) THEN ((5e-1) * (y * (sqrt(z)))) ELSE ((5e-1) * x) ENDIF IN
	LET tmp = IF (x <= (-171356725662392368316650390625e-19)) THEN ((5e-1) * x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < -17135672566.239237 or 5.6284431617641199e-46 < x

   1. Initial program 99.8%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 51.3%

      \[\leadsto 0.5 \cdot x \]

   if -17135672566.239237 < x < 5.6284431617641199e-46

   1. Initial program 99.8%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{2} \cdot \left(y \cdot \sqrt{z}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 50.0%

      \[\leadsto 0.5 \cdot \left(y \cdot \sqrt{z}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 51.3% accurate, 3.8× speedup

Math

\[0.5 \cdot x \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

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

Derivation

1. Initial program 99.8%

   \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]

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 z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))