Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 1.4s

Alternatives: 7

Speedup: 1.1×

• 80.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x + (y * (z + 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 = x + (y * (z + x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x + (y * (z + 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 = x + (y * (z + x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.1× speedup

Math

\[\mathsf{fma}\left(y, z + x, x\right) \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (fma y (+ z x) x))

C

double code(double x, double y, double z) {
	return fma(y, (z + x), x);
}

Julia

function code(x, y, z)
	return fma(y, Float64(z + x), x)
end

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + y \cdot \left(z + x\right) \]
2. Step-by-step derivation

3. Applied rewrites 100.0%

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

Alternative 2: 98.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_0 := y \cdot \left(x + z\right)\\ \mathbf{if}\;y \leq -1.3910059451961023:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.0036597640836557375:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* y (+ x z))))
  (if (<= y -1.3910059451961023)
    t_0
    (if (<= y 0.0036597640836557375) (fma y z x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x + z);
	double tmp;
	if (y <= -1.3910059451961023) {
		tmp = t_0;
	} else if (y <= 0.0036597640836557375) {
		tmp = fma(y, z, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x + z))
	tmp = 0.0
	if (y <= -1.3910059451961023)
		tmp = t_0;
	elseif (y <= 0.0036597640836557375)
		tmp = fma(y, z, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3910059451961023], t$95$0, If[LessEqual[y, 0.0036597640836557375], N[(y * z + x), $MachinePrecision], t$95$0]]]

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 t_0 = (y * (x + z)) IN
		LET tmp_1 = IF (y <= (36597640836557375314253004461306773009710013866424560546875e-61)) THEN ((y * z) + x) ELSE t_0 ENDIF IN
		LET tmp = IF (y <= (-13910059451961023224697555633611045777797698974609375e-52)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -1.3910059451961023 or 0.0036597640836557375 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(1 + y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 62.1%

      \[\leadsto x \cdot \left(1 + y\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 62.1%

      \[\leadsto \mathsf{fma}\left(y, x, x\right) \]

   7. Taylor expanded in y around inf

      \[\leadsto y \cdot \left(x + z\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 64.3%

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

   if -1.3910059451961023 < y < 0.0036597640836557375

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0

      \[\leadsto x + y \cdot z \]
   3. Step-by-step derivation

   4. Applied rewrites 76.4%

      \[\leadsto x + y \cdot z \]
   5. Step-by-step derivation

   6. Applied rewrites 76.4%

      \[\leadsto \mathsf{fma}\left(y, z, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 85.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -4.420245809256181 \cdot 10^{-50}:\\ \;\;\;\;\mathsf{fma}\left(y, x, x\right)\\ \mathbf{elif}\;x \leq 456191841.59206736:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, x\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= x -4.420245809256181e-50)
  (fma y x x)
  (if (<= x 456191841.59206736) (fma y z x) (fma y x x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.420245809256181e-50) {
		tmp = fma(y, x, x);
	} else if (x <= 456191841.59206736) {
		tmp = fma(y, z, x);
	} else {
		tmp = fma(y, x, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.420245809256181e-50)
		tmp = fma(y, x, x);
	elseif (x <= 456191841.59206736)
		tmp = fma(y, z, x);
	else
		tmp = fma(y, x, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.420245809256181e-50], N[(y * x + x), $MachinePrecision], If[LessEqual[x, 456191841.59206736], N[(y * z + x), $MachinePrecision], N[(y * x + 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 <= (45619184159206736087799072265625e-23)) THEN ((y * z) + x) ELSE ((y * x) + x) ENDIF IN
	LET tmp = IF (x <= (-44202458092561807173146183805990310442416852708706562951185861630934021423055811815087956022190442979509568437286867776620587384972527189574975636787712574005126953125e-216)) THEN ((y * x) + x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < -4.4202458092561807e-50 or 456191841.59206736 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(1 + y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 62.1%

      \[\leadsto x \cdot \left(1 + y\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 62.1%

      \[\leadsto \mathsf{fma}\left(y, x, x\right) \]

   if -4.4202458092561807e-50 < x < 456191841.59206736

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0

      \[\leadsto x + y \cdot z \]
   3. Step-by-step derivation

   4. Applied rewrites 76.4%

      \[\leadsto x + y \cdot z \]
   5. Step-by-step derivation

   6. Applied rewrites 76.4%

      \[\leadsto \mathsf{fma}\left(y, z, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 74.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -1.2014353339475216 \cdot 10^{-53}:\\ \;\;\;\;\mathsf{fma}\left(y, x, x\right)\\ \mathbf{elif}\;x \leq 1.3907246641268288 \cdot 10^{-133}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, x\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= x -1.2014353339475216e-53)
  (fma y x x)
  (if (<= x 1.3907246641268288e-133) (* y z) (fma y x x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.2014353339475216e-53) {
		tmp = fma(y, x, x);
	} else if (x <= 1.3907246641268288e-133) {
		tmp = y * z;
	} else {
		tmp = fma(y, x, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.2014353339475216e-53)
		tmp = fma(y, x, x);
	elseif (x <= 1.3907246641268288e-133)
		tmp = Float64(y * z);
	else
		tmp = fma(y, x, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.2014353339475216e-53], N[(y * x + x), $MachinePrecision], If[LessEqual[x, 1.3907246641268288e-133], N[(y * z), $MachinePrecision], N[(y * x + 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 <= (13907246641268287719553288589367698732274009277678938853341083963550402305825730272558285284260707557226592286720658421468340914383077588215032524302117800378662076704866440675793204111827833749549383931163536547600078549247750976353053708772891633938598045310131695191357079148094045872458853184477607279647119117250357415993544663024295005016028881072998046875e-494)) THEN (y * z) ELSE ((y * x) + x) ENDIF IN
	LET tmp = IF (x <= (-1201435333947521567179383940228922831410793169252770766996959593329040310462231836384689301534482831918011668944531164721304996863097958037513990348088555037975311279296875e-224)) THEN ((y * x) + x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < -1.2014353339475216e-53 or 1.3907246641268288e-133 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(1 + y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 62.1%

      \[\leadsto x \cdot \left(1 + y\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 62.1%

      \[\leadsto \mathsf{fma}\left(y, x, x\right) \]

   if -1.2014353339475216e-53 < x < 1.3907246641268288e-133

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(1 + y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 62.1%

      \[\leadsto x \cdot \left(1 + y\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 62.1%

      \[\leadsto \mathsf{fma}\left(y, x, x\right) \]

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 41.4%

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

Alternative 5: 62.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -1.7369450345442874 \cdot 10^{+177}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1.6957869950355719 \cdot 10^{+109}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.9567418453105813 \cdot 10^{-16}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.3080107308185876 \cdot 10^{-32}:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= y -1.7369450345442874e+177)
  (* y z)
  (if (<= y -1.6957869950355719e+109)
    (* x y)
    (if (<= y -1.9567418453105813e-16)
      (* y z)
      (if (<= y 2.3080107308185876e-32) (* x 1.0) (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.7369450345442874e+177) {
		tmp = y * z;
	} else if (y <= -1.6957869950355719e+109) {
		tmp = x * y;
	} else if (y <= -1.9567418453105813e-16) {
		tmp = y * z;
	} else if (y <= 2.3080107308185876e-32) {
		tmp = x * 1.0;
	} else {
		tmp = y * z;
	}
	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 (y <= (-1.7369450345442874d+177)) then
        tmp = y * z
    else if (y <= (-1.6957869950355719d+109)) then
        tmp = x * y
    else if (y <= (-1.9567418453105813d-16)) then
        tmp = y * z
    else if (y <= 2.3080107308185876d-32) then
        tmp = x * 1.0d0
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.7369450345442874e+177) {
		tmp = y * z;
	} else if (y <= -1.6957869950355719e+109) {
		tmp = x * y;
	} else if (y <= -1.9567418453105813e-16) {
		tmp = y * z;
	} else if (y <= 2.3080107308185876e-32) {
		tmp = x * 1.0;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.7369450345442874e+177:
		tmp = y * z
	elif y <= -1.6957869950355719e+109:
		tmp = x * y
	elif y <= -1.9567418453105813e-16:
		tmp = y * z
	elif y <= 2.3080107308185876e-32:
		tmp = x * 1.0
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.7369450345442874e+177)
		tmp = Float64(y * z);
	elseif (y <= -1.6957869950355719e+109)
		tmp = Float64(x * y);
	elseif (y <= -1.9567418453105813e-16)
		tmp = Float64(y * z);
	elseif (y <= 2.3080107308185876e-32)
		tmp = Float64(x * 1.0);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.7369450345442874e+177)
		tmp = y * z;
	elseif (y <= -1.6957869950355719e+109)
		tmp = x * y;
	elseif (y <= -1.9567418453105813e-16)
		tmp = y * z;
	elseif (y <= 2.3080107308185876e-32)
		tmp = x * 1.0;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.7369450345442874e+177], N[(y * z), $MachinePrecision], If[LessEqual[y, -1.6957869950355719e+109], N[(x * y), $MachinePrecision], If[LessEqual[y, -1.9567418453105813e-16], N[(y * z), $MachinePrecision], If[LessEqual[y, 2.3080107308185876e-32], N[(x * 1.0), $MachinePrecision], N[(y * z), $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_3 = IF (y <= (2308010730818587590762110147375810142062287416606639275854782999805688643013554654814280253649627638878882862627506256103515625e-158)) THEN (x * (1)) ELSE (y * z) ENDIF IN
	LET tmp_2 = IF (y <= (-195674184531058127709734167246648549435989266850367818140199460685835219919681549072265625e-105)) THEN (y * z) ELSE tmp_3 ENDIF IN
	LET tmp_1 = IF (y <= (-16957869950355718931465531247763550139979082796806578673657974316572747102086548313566244811727926991247114240)) THEN (x * y) ELSE tmp_2 ENDIF IN
	LET tmp = IF (y <= (-1736945034544287412347033863073873456965503088732749302439491853026289663537555191881741523762841739547105102182173562149034075232772331190135807316162207859763136650384978739200)) THEN (y * z) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if y < -1.7369450345442874e177 or -1.6957869950355719e109 < y < -1.9567418453105813e-16 or 2.3080107308185876e-32 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(1 + y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 62.1%

      \[\leadsto x \cdot \left(1 + y\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 62.1%

      \[\leadsto \mathsf{fma}\left(y, x, x\right) \]

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 41.4%

      \[\leadsto y \cdot z \]

   if -1.7369450345442874e177 < y < -1.6957869950355719e109

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(1 + y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 62.1%

      \[\leadsto x \cdot \left(1 + y\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 62.1%

      \[\leadsto \mathsf{fma}\left(y, x, x\right) \]

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 27.2%

      \[\leadsto x \cdot y \]

   if -1.9567418453105813e-16 < y < 2.3080107308185876e-32

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(1 + y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 62.1%

      \[\leadsto x \cdot \left(1 + y\right) \]

   5. Taylor expanded in y around 0

      \[\leadsto x \cdot 1 \]
   6. Step-by-step derivation

   7. Applied rewrites 37.3%

      \[\leadsto x \cdot 1 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 61.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -1.3910059451961023:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 0.0036597640836557375:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= y -1.3910059451961023)
  (* x y)
  (if (<= y 0.0036597640836557375) (* x 1.0) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.3910059451961023) {
		tmp = x * y;
	} else if (y <= 0.0036597640836557375) {
		tmp = x * 1.0;
	} else {
		tmp = x * y;
	}
	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 (y <= (-1.3910059451961023d0)) then
        tmp = x * y
    else if (y <= 0.0036597640836557375d0) then
        tmp = x * 1.0d0
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.3910059451961023) {
		tmp = x * y;
	} else if (y <= 0.0036597640836557375) {
		tmp = x * 1.0;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.3910059451961023:
		tmp = x * y
	elif y <= 0.0036597640836557375:
		tmp = x * 1.0
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.3910059451961023)
		tmp = Float64(x * y);
	elseif (y <= 0.0036597640836557375)
		tmp = Float64(x * 1.0);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.3910059451961023)
		tmp = x * y;
	elseif (y <= 0.0036597640836557375)
		tmp = x * 1.0;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.3910059451961023], N[(x * y), $MachinePrecision], If[LessEqual[y, 0.0036597640836557375], N[(x * 1.0), $MachinePrecision], N[(x * y), $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 (y <= (36597640836557375314253004461306773009710013866424560546875e-61)) THEN (x * (1)) ELSE (x * y) ENDIF IN
	LET tmp = IF (y <= (-13910059451961023224697555633611045777797698974609375e-52)) THEN (x * y) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -1.3910059451961023 or 0.0036597640836557375 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(1 + y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 62.1%

      \[\leadsto x \cdot \left(1 + y\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 62.1%

      \[\leadsto \mathsf{fma}\left(y, x, x\right) \]

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 27.2%

      \[\leadsto x \cdot y \]

   if -1.3910059451961023 < y < 0.0036597640836557375

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(1 + y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 62.1%

      \[\leadsto x \cdot \left(1 + y\right) \]

   5. Taylor expanded in y around 0

      \[\leadsto x \cdot 1 \]
   6. Step-by-step derivation

   7. Applied rewrites 37.3%

      \[\leadsto x \cdot 1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 37.3% accurate, 2.3× speedup

Math

\[x \cdot 1 \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (* x 1.0))

C

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

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 = x * 1.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x * 1.0), $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 =
	x * (1)
END code

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around inf

   \[\leadsto x \cdot \left(1 + y\right) \]
3. Step-by-step derivation

4. Applied rewrites 62.1%

   \[\leadsto x \cdot \left(1 + y\right) \]

5. Taylor expanded in y around 0

   \[\leadsto x \cdot 1 \]
6. Step-by-step derivation

7. Applied rewrites 37.3%

   \[\leadsto x \cdot 1 \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))