Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E

Percentage Accurate: 99.6% → 99.8%

Time: 1.6s

Alternatives: 12

Speedup: 1.1×

• 79.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (+ x (* (* (- y x) 6.0) z)))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * 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 = x + (((y - x) * 6.0d0) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * z), $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 - x) * (6)) * z)
END code

Initial Program: 99.6% accurate, 1.0× speedup

Math

\[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (+ x (* (* (- y x) 6.0) z)))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * 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 = x + (((y - x) * 6.0d0) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * z), $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 - x) * (6)) * z)
END code

Alternative 1: 99.6% accurate, 1.1× speedup

Math

\[\mathsf{fma}\left(-6, \left(x - y\right) \cdot z, x\right) \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (fma -6.0 (* (- x y) z) x))

C

double code(double x, double y, double z) {
	return fma(-6.0, ((x - y) * z), x);
}

Julia

function code(x, y, z)
	return fma(-6.0, Float64(Float64(x - y) * z), x)
end

Wolfram

code[x_, y_, z_] := N[(-6.0 * N[(N[(x - y), $MachinePrecision] * z), $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 =
	((-6) * ((x - y) * z)) + x
END code

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Step-by-step derivation

3. Applied rewrites 99.8%

   \[\leadsto \mathsf{fma}\left(-6, \left(x - y\right) \cdot z, x\right) \]
4. Add Preprocessing

Alternative 2: 98.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := z \cdot \left(6 \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -28165673201.033638:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 7.845250112058621 \cdot 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(z, y \cdot 6, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* z (* 6.0 (- y x)))))
  (if (<= z -28165673201.033638)
    t_0
    (if (<= z 7.845250112058621e-9) (fma z (* y 6.0) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * (6.0 * (y - x));
	double tmp;
	if (z <= -28165673201.033638) {
		tmp = t_0;
	} else if (z <= 7.845250112058621e-9) {
		tmp = fma(z, (y * 6.0), x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(6.0 * Float64(y - x)))
	tmp = 0.0
	if (z <= -28165673201.033638)
		tmp = t_0;
	elseif (z <= 7.845250112058621e-9)
		tmp = fma(z, Float64(y * 6.0), x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(6.0 * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -28165673201.033638], t$95$0, If[LessEqual[z, 7.845250112058621e-9], N[(z * N[(y * 6.0), $MachinePrecision] + 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 = (z * ((6) * (y - x))) IN
		LET tmp_1 = IF (z <= (78452501120586211901078397558915999976392185999429784715175628662109375e-79)) THEN ((z * (y * (6))) + x) ELSE t_0 ENDIF IN
		LET tmp = IF (z <= (-2816567320103363800048828125e-17)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -28165673201.033638 or 7.8452501120586212e-9 < z

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around inf

      \[\leadsto z \cdot \left(6 \cdot \left(y - x\right) + \frac{x}{z}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 87.9%

      \[\leadsto z \cdot \mathsf{fma}\left(6, y - x, \frac{x}{z}\right) \]

   5. Taylor expanded in z around inf

      \[\leadsto z \cdot \left(6 \cdot \left(y - x\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 64.9%

      \[\leadsto z \cdot \left(6 \cdot \left(y - x\right)\right) \]

   if -28165673201.033638 < z < 7.8452501120586212e-9

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in x around 0

      \[\leadsto x + \left(y \cdot 6\right) \cdot z \]
   3. Step-by-step derivation

   4. Applied rewrites 75.5%

      \[\leadsto x + \left(y \cdot 6\right) \cdot z \]
   5. Step-by-step derivation

   6. Applied rewrites 75.5%

      \[\leadsto \mathsf{fma}\left(z, y \cdot 6, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 85.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -1.9574573609995736 \cdot 10^{+91}:\\ \;\;\;\;\mathsf{fma}\left(z, -6 \cdot x, x\right)\\ \mathbf{elif}\;x \leq 0.0005660629841236394:\\ \;\;\;\;\mathsf{fma}\left(z, y \cdot 6, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-6, z, 1\right) \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= x -1.9574573609995736e+91)
  (fma z (* -6.0 x) x)
  (if (<= x 0.0005660629841236394)
    (fma z (* y 6.0) x)
    (* (fma -6.0 z 1.0) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.9574573609995736e+91) {
		tmp = fma(z, (-6.0 * x), x);
	} else if (x <= 0.0005660629841236394) {
		tmp = fma(z, (y * 6.0), x);
	} else {
		tmp = fma(-6.0, z, 1.0) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.9574573609995736e+91)
		tmp = fma(z, Float64(-6.0 * x), x);
	elseif (x <= 0.0005660629841236394)
		tmp = fma(z, Float64(y * 6.0), x);
	else
		tmp = Float64(fma(-6.0, z, 1.0) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.9574573609995736e+91], N[(z * N[(-6.0 * x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[x, 0.0005660629841236394], N[(z * N[(y * 6.0), $MachinePrecision] + x), $MachinePrecision], N[(N[(-6.0 * z + 1.0), $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 =
	LET tmp_1 = IF (x <= (566062984123639448448550570702764161978848278522491455078125e-63)) THEN ((z * (y * (6))) + x) ELSE ((((-6) * z) + (1)) * x) ENDIF IN
	LET tmp = IF (x <= (-19574573609995735600635967846953792076791839711159263895675501474379448978998529820238807040)) THEN ((z * ((-6) * x)) + x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if x < -1.9574573609995736e91

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in x around inf

      \[\leadsto x + \left(-6 \cdot x\right) \cdot z \]
   3. Step-by-step derivation

   4. Applied rewrites 62.2%

      \[\leadsto x + \left(-6 \cdot x\right) \cdot z \]
   5. Step-by-step derivation

   6. Applied rewrites 62.2%

      \[\leadsto \mathsf{fma}\left(z, -6 \cdot x, x\right) \]

   if -1.9574573609995736e91 < x < 5.6606298412363945e-4

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in x around 0

      \[\leadsto x + \left(y \cdot 6\right) \cdot z \]
   3. Step-by-step derivation

   4. Applied rewrites 75.5%

      \[\leadsto x + \left(y \cdot 6\right) \cdot z \]
   5. Step-by-step derivation

   6. Applied rewrites 75.5%

      \[\leadsto \mathsf{fma}\left(z, y \cdot 6, x\right) \]

   if 5.6606298412363945e-4 < x

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(1 + -6 \cdot z\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 62.4%

      \[\leadsto x \cdot \left(1 + -6 \cdot z\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 62.4%

      \[\leadsto \mathsf{fma}\left(-6, z, 1\right) \cdot x \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 85.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -1.9574573609995736 \cdot 10^{+91}:\\ \;\;\;\;\mathsf{fma}\left(z, -6 \cdot x, x\right)\\ \mathbf{elif}\;x \leq 0.0005660629841236394:\\ \;\;\;\;\mathsf{fma}\left(6, y \cdot z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-6, z, 1\right) \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= x -1.9574573609995736e+91)
  (fma z (* -6.0 x) x)
  (if (<= x 0.0005660629841236394)
    (fma 6.0 (* y z) x)
    (* (fma -6.0 z 1.0) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.9574573609995736e+91) {
		tmp = fma(z, (-6.0 * x), x);
	} else if (x <= 0.0005660629841236394) {
		tmp = fma(6.0, (y * z), x);
	} else {
		tmp = fma(-6.0, z, 1.0) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.9574573609995736e+91)
		tmp = fma(z, Float64(-6.0 * x), x);
	elseif (x <= 0.0005660629841236394)
		tmp = fma(6.0, Float64(y * z), x);
	else
		tmp = Float64(fma(-6.0, z, 1.0) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.9574573609995736e+91], N[(z * N[(-6.0 * x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[x, 0.0005660629841236394], N[(6.0 * N[(y * z), $MachinePrecision] + x), $MachinePrecision], N[(N[(-6.0 * z + 1.0), $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 =
	LET tmp_1 = IF (x <= (566062984123639448448550570702764161978848278522491455078125e-63)) THEN (((6) * (y * z)) + x) ELSE ((((-6) * z) + (1)) * x) ENDIF IN
	LET tmp = IF (x <= (-19574573609995735600635967846953792076791839711159263895675501474379448978998529820238807040)) THEN ((z * ((-6) * x)) + x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if x < -1.9574573609995736e91

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in x around inf

      \[\leadsto x + \left(-6 \cdot x\right) \cdot z \]
   3. Step-by-step derivation

   4. Applied rewrites 62.2%

      \[\leadsto x + \left(-6 \cdot x\right) \cdot z \]
   5. Step-by-step derivation

   6. Applied rewrites 62.2%

      \[\leadsto \mathsf{fma}\left(z, -6 \cdot x, x\right) \]

   if -1.9574573609995736e91 < x < 5.6606298412363945e-4

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in x around 0

      \[\leadsto x + \left(y \cdot 6\right) \cdot z \]
   3. Step-by-step derivation

   4. Applied rewrites 75.5%

      \[\leadsto x + \left(y \cdot 6\right) \cdot z \]
   5. Step-by-step derivation

   6. Applied rewrites 75.6%

      \[\leadsto \mathsf{fma}\left(6, y \cdot z, x\right) \]

   if 5.6606298412363945e-4 < x

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(1 + -6 \cdot z\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 62.4%

      \[\leadsto x \cdot \left(1 + -6 \cdot z\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 62.4%

      \[\leadsto \mathsf{fma}\left(-6, z, 1\right) \cdot x \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 85.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -1.9574573609995736 \cdot 10^{+91}:\\ \;\;\;\;\mathsf{fma}\left(-6, z \cdot x, x\right)\\ \mathbf{elif}\;x \leq 0.0005660629841236394:\\ \;\;\;\;\mathsf{fma}\left(6, y \cdot z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-6, z, 1\right) \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= x -1.9574573609995736e+91)
  (fma -6.0 (* z x) x)
  (if (<= x 0.0005660629841236394)
    (fma 6.0 (* y z) x)
    (* (fma -6.0 z 1.0) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.9574573609995736e+91) {
		tmp = fma(-6.0, (z * x), x);
	} else if (x <= 0.0005660629841236394) {
		tmp = fma(6.0, (y * z), x);
	} else {
		tmp = fma(-6.0, z, 1.0) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.9574573609995736e+91)
		tmp = fma(-6.0, Float64(z * x), x);
	elseif (x <= 0.0005660629841236394)
		tmp = fma(6.0, Float64(y * z), x);
	else
		tmp = Float64(fma(-6.0, z, 1.0) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.9574573609995736e+91], N[(-6.0 * N[(z * x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[x, 0.0005660629841236394], N[(6.0 * N[(y * z), $MachinePrecision] + x), $MachinePrecision], N[(N[(-6.0 * z + 1.0), $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 =
	LET tmp_1 = IF (x <= (566062984123639448448550570702764161978848278522491455078125e-63)) THEN (((6) * (y * z)) + x) ELSE ((((-6) * z) + (1)) * x) ENDIF IN
	LET tmp = IF (x <= (-19574573609995735600635967846953792076791839711159263895675501474379448978998529820238807040)) THEN (((-6) * (z * x)) + x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if x < -1.9574573609995736e91

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(1 + -6 \cdot z\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 62.4%

      \[\leadsto x \cdot \left(1 + -6 \cdot z\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 62.4%

      \[\leadsto \mathsf{fma}\left(-6, z \cdot x, x\right) \]

   if -1.9574573609995736e91 < x < 5.6606298412363945e-4

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in x around 0

      \[\leadsto x + \left(y \cdot 6\right) \cdot z \]
   3. Step-by-step derivation

   4. Applied rewrites 75.5%

      \[\leadsto x + \left(y \cdot 6\right) \cdot z \]
   5. Step-by-step derivation

   6. Applied rewrites 75.6%

      \[\leadsto \mathsf{fma}\left(6, y \cdot z, x\right) \]

   if 5.6606298412363945e-4 < x

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(1 + -6 \cdot z\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 62.4%

      \[\leadsto x \cdot \left(1 + -6 \cdot z\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 62.4%

      \[\leadsto \mathsf{fma}\left(-6, z, 1\right) \cdot x \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := z \cdot \left(6 \cdot y\right)\\ \mathbf{if}\;y \leq -2.034826382675621 \cdot 10^{+177}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.727325893764305 \cdot 10^{+120}:\\ \;\;\;\;\mathsf{fma}\left(-6, z, 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* z (* 6.0 y))))
  (if (<= y -2.034826382675621e+177)
    t_0
    (if (<= y 2.727325893764305e+120) (* (fma -6.0 z 1.0) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * (6.0 * y);
	double tmp;
	if (y <= -2.034826382675621e+177) {
		tmp = t_0;
	} else if (y <= 2.727325893764305e+120) {
		tmp = fma(-6.0, z, 1.0) * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(6.0 * y))
	tmp = 0.0
	if (y <= -2.034826382675621e+177)
		tmp = t_0;
	elseif (y <= 2.727325893764305e+120)
		tmp = Float64(fma(-6.0, z, 1.0) * x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(6.0 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.034826382675621e+177], t$95$0, If[LessEqual[y, 2.727325893764305e+120], N[(N[(-6.0 * z + 1.0), $MachinePrecision] * 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 = (z * ((6) * y)) IN
		LET tmp_1 = IF (y <= (2727325893764304952337864284099369734672726102996935792482044238117505441831551720658621706644790338763370656773728894976)) THEN ((((-6) * z) + (1)) * x) ELSE t_0 ENDIF IN
		LET tmp = IF (y <= (-2034826382675620969538188077698691635021966652104782161099435007919111885452274644684976849485284282903270108001271516845889509387433253108116847946518093992975655544772733435904)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -2.034826382675621e177 or 2.727325893764305e120 < y

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around inf

      \[\leadsto z \cdot \left(6 \cdot \left(y - x\right) + \frac{x}{z}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 87.9%

      \[\leadsto z \cdot \mathsf{fma}\left(6, y - x, \frac{x}{z}\right) \]

   5. Taylor expanded in z around inf

      \[\leadsto z \cdot \left(6 \cdot \left(y - x\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 64.9%

      \[\leadsto z \cdot \left(6 \cdot \left(y - x\right)\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto z \cdot \left(6 \cdot y\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 41.3%

       \[\leadsto z \cdot \left(6 \cdot y\right) \]

   if -2.034826382675621e177 < y < 2.727325893764305e120

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(1 + -6 \cdot z\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 62.4%

      \[\leadsto x \cdot \left(1 + -6 \cdot z\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 62.4%

      \[\leadsto \mathsf{fma}\left(-6, z, 1\right) \cdot x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := z \cdot \left(6 \cdot y\right)\\ \mathbf{if}\;y \leq -2.034826382675621 \cdot 10^{+177}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.727325893764305 \cdot 10^{+120}:\\ \;\;\;\;\mathsf{fma}\left(-6, z \cdot x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* z (* 6.0 y))))
  (if (<= y -2.034826382675621e+177)
    t_0
    (if (<= y 2.727325893764305e+120) (fma -6.0 (* z x) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * (6.0 * y);
	double tmp;
	if (y <= -2.034826382675621e+177) {
		tmp = t_0;
	} else if (y <= 2.727325893764305e+120) {
		tmp = fma(-6.0, (z * x), x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(6.0 * y))
	tmp = 0.0
	if (y <= -2.034826382675621e+177)
		tmp = t_0;
	elseif (y <= 2.727325893764305e+120)
		tmp = fma(-6.0, Float64(z * x), x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(6.0 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.034826382675621e+177], t$95$0, If[LessEqual[y, 2.727325893764305e+120], N[(-6.0 * N[(z * x), $MachinePrecision] + 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 = (z * ((6) * y)) IN
		LET tmp_1 = IF (y <= (2727325893764304952337864284099369734672726102996935792482044238117505441831551720658621706644790338763370656773728894976)) THEN (((-6) * (z * x)) + x) ELSE t_0 ENDIF IN
		LET tmp = IF (y <= (-2034826382675620969538188077698691635021966652104782161099435007919111885452274644684976849485284282903270108001271516845889509387433253108116847946518093992975655544772733435904)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -2.034826382675621e177 or 2.727325893764305e120 < y

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around inf

      \[\leadsto z \cdot \left(6 \cdot \left(y - x\right) + \frac{x}{z}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 87.9%

      \[\leadsto z \cdot \mathsf{fma}\left(6, y - x, \frac{x}{z}\right) \]

   5. Taylor expanded in z around inf

      \[\leadsto z \cdot \left(6 \cdot \left(y - x\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 64.9%

      \[\leadsto z \cdot \left(6 \cdot \left(y - x\right)\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto z \cdot \left(6 \cdot y\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 41.3%

       \[\leadsto z \cdot \left(6 \cdot y\right) \]

   if -2.034826382675621e177 < y < 2.727325893764305e120

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(1 + -6 \cdot z\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 62.4%

      \[\leadsto x \cdot \left(1 + -6 \cdot z\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 62.4%

      \[\leadsto \mathsf{fma}\left(-6, z \cdot x, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 60.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -8.278241671405412 \cdot 10^{+113}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.5998878487717716 \cdot 10^{-87}:\\ \;\;\;\;z \cdot \left(6 \cdot y\right)\\ \mathbf{elif}\;z \leq 1.4132947115915006 \cdot 10^{-40}:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= z -8.278241671405412e+113)
  (* -6.0 (* x z))
  (if (<= z -1.5998878487717716e-87)
    (* z (* 6.0 y))
    (if (<= z 1.4132947115915006e-40) (* x 1.0) (* 6.0 (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.278241671405412e+113) {
		tmp = -6.0 * (x * z);
	} else if (z <= -1.5998878487717716e-87) {
		tmp = z * (6.0 * y);
	} else if (z <= 1.4132947115915006e-40) {
		tmp = x * 1.0;
	} else {
		tmp = 6.0 * (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 (z <= (-8.278241671405412d+113)) then
        tmp = (-6.0d0) * (x * z)
    else if (z <= (-1.5998878487717716d-87)) then
        tmp = z * (6.0d0 * y)
    else if (z <= 1.4132947115915006d-40) then
        tmp = x * 1.0d0
    else
        tmp = 6.0d0 * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.278241671405412e+113) {
		tmp = -6.0 * (x * z);
	} else if (z <= -1.5998878487717716e-87) {
		tmp = z * (6.0 * y);
	} else if (z <= 1.4132947115915006e-40) {
		tmp = x * 1.0;
	} else {
		tmp = 6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -8.278241671405412e+113:
		tmp = -6.0 * (x * z)
	elif z <= -1.5998878487717716e-87:
		tmp = z * (6.0 * y)
	elif z <= 1.4132947115915006e-40:
		tmp = x * 1.0
	else:
		tmp = 6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8.278241671405412e+113)
		tmp = Float64(-6.0 * Float64(x * z));
	elseif (z <= -1.5998878487717716e-87)
		tmp = Float64(z * Float64(6.0 * y));
	elseif (z <= 1.4132947115915006e-40)
		tmp = Float64(x * 1.0);
	else
		tmp = Float64(6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -8.278241671405412e+113)
		tmp = -6.0 * (x * z);
	elseif (z <= -1.5998878487717716e-87)
		tmp = z * (6.0 * y);
	elseif (z <= 1.4132947115915006e-40)
		tmp = x * 1.0;
	else
		tmp = 6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8.278241671405412e+113], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.5998878487717716e-87], N[(z * N[(6.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4132947115915006e-40], N[(x * 1.0), $MachinePrecision], N[(6.0 * N[(y * z), $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 =
	LET tmp_2 = IF (z <= (14132947115915006468182910235642061199906833362565967651395812855413318177857125598375794078304482317867511731446228395725484006106853485107421875e-185)) THEN (x * (1)) ELSE ((6) * (y * z)) ENDIF IN
	LET tmp_1 = IF (z <= (-159988784877177164685523371169830722870522374072384409119026858684832480050318864005140114871679013601761552483193181404403016128515199488354968070059220853336754264519220820635743157089849151568897638446024723319315030689580225953250192105770111083984375e-341)) THEN (z * ((6) * y)) ELSE tmp_2 ENDIF IN
	LET tmp = IF (z <= (-827824167140541243899520753986607661237673954454153700601859801186490414593025111553349927768106486631838959796224)) THEN ((-6) * (x * z)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if z < -8.2782416714054124e113

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(1 + -6 \cdot z\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 62.4%

      \[\leadsto x \cdot \left(1 + -6 \cdot z\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 62.4%

      \[\leadsto \mathsf{fma}\left(-6, z, 1\right) \cdot x \]

   7. Taylor expanded in z around inf

      \[\leadsto -6 \cdot \left(x \cdot z\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 28.2%

      \[\leadsto -6 \cdot \left(x \cdot z\right) \]

   if -8.2782416714054124e113 < z < -1.5998878487717716e-87

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around inf

      \[\leadsto z \cdot \left(6 \cdot \left(y - x\right) + \frac{x}{z}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 87.9%

      \[\leadsto z \cdot \mathsf{fma}\left(6, y - x, \frac{x}{z}\right) \]

   5. Taylor expanded in z around inf

      \[\leadsto z \cdot \left(6 \cdot \left(y - x\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 64.9%

      \[\leadsto z \cdot \left(6 \cdot \left(y - x\right)\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto z \cdot \left(6 \cdot y\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 41.3%

       \[\leadsto z \cdot \left(6 \cdot y\right) \]

   if -1.5998878487717716e-87 < z < 1.4132947115915006e-40

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(1 + -6 \cdot z\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 62.4%

      \[\leadsto x \cdot \left(1 + -6 \cdot z\right) \]

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 36.5%

      \[\leadsto x \cdot 1 \]

   if 1.4132947115915006e-40 < z

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(1 + -6 \cdot z\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 62.4%

      \[\leadsto x \cdot \left(1 + -6 \cdot z\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 62.4%

      \[\leadsto \mathsf{fma}\left(-6, z, 1\right) \cdot x \]

   7. Taylor expanded in x around 0

      \[\leadsto 6 \cdot \left(y \cdot z\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 41.3%

      \[\leadsto 6 \cdot \left(y \cdot z\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 9: 60.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := z \cdot \left(6 \cdot y\right)\\ \mathbf{if}\;z \leq -8.278241671405412 \cdot 10^{+113}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.5998878487717716 \cdot 10^{-87}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.4132947115915006 \cdot 10^{-40}:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* z (* 6.0 y))))
  (if (<= z -8.278241671405412e+113)
    (* -6.0 (* x z))
    (if (<= z -1.5998878487717716e-87)
      t_0
      (if (<= z 1.4132947115915006e-40) (* x 1.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * (6.0 * y);
	double tmp;
	if (z <= -8.278241671405412e+113) {
		tmp = -6.0 * (x * z);
	} else if (z <= -1.5998878487717716e-87) {
		tmp = t_0;
	} else if (z <= 1.4132947115915006e-40) {
		tmp = x * 1.0;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = z * (6.0d0 * y)
    if (z <= (-8.278241671405412d+113)) then
        tmp = (-6.0d0) * (x * z)
    else if (z <= (-1.5998878487717716d-87)) then
        tmp = t_0
    else if (z <= 1.4132947115915006d-40) then
        tmp = x * 1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (6.0 * y);
	double tmp;
	if (z <= -8.278241671405412e+113) {
		tmp = -6.0 * (x * z);
	} else if (z <= -1.5998878487717716e-87) {
		tmp = t_0;
	} else if (z <= 1.4132947115915006e-40) {
		tmp = x * 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (6.0 * y)
	tmp = 0
	if z <= -8.278241671405412e+113:
		tmp = -6.0 * (x * z)
	elif z <= -1.5998878487717716e-87:
		tmp = t_0
	elif z <= 1.4132947115915006e-40:
		tmp = x * 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(6.0 * y))
	tmp = 0.0
	if (z <= -8.278241671405412e+113)
		tmp = Float64(-6.0 * Float64(x * z));
	elseif (z <= -1.5998878487717716e-87)
		tmp = t_0;
	elseif (z <= 1.4132947115915006e-40)
		tmp = Float64(x * 1.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (6.0 * y);
	tmp = 0.0;
	if (z <= -8.278241671405412e+113)
		tmp = -6.0 * (x * z);
	elseif (z <= -1.5998878487717716e-87)
		tmp = t_0;
	elseif (z <= 1.4132947115915006e-40)
		tmp = x * 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(6.0 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.278241671405412e+113], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.5998878487717716e-87], t$95$0, If[LessEqual[z, 1.4132947115915006e-40], N[(x * 1.0), $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 = (z * ((6) * y)) IN
		LET tmp_2 = IF (z <= (14132947115915006468182910235642061199906833362565967651395812855413318177857125598375794078304482317867511731446228395725484006106853485107421875e-185)) THEN (x * (1)) ELSE t_0 ENDIF IN
		LET tmp_1 = IF (z <= (-159988784877177164685523371169830722870522374072384409119026858684832480050318864005140114871679013601761552483193181404403016128515199488354968070059220853336754264519220820635743157089849151568897638446024723319315030689580225953250192105770111083984375e-341)) THEN t_0 ELSE tmp_2 ENDIF IN
		LET tmp = IF (z <= (-827824167140541243899520753986607661237673954454153700601859801186490414593025111553349927768106486631838959796224)) THEN ((-6) * (x * z)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if z < -8.2782416714054124e113

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(1 + -6 \cdot z\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 62.4%

      \[\leadsto x \cdot \left(1 + -6 \cdot z\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 62.4%

      \[\leadsto \mathsf{fma}\left(-6, z, 1\right) \cdot x \]

   7. Taylor expanded in z around inf

      \[\leadsto -6 \cdot \left(x \cdot z\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 28.2%

      \[\leadsto -6 \cdot \left(x \cdot z\right) \]

   if -8.2782416714054124e113 < z < -1.5998878487717716e-87 or 1.4132947115915006e-40 < z

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around inf

      \[\leadsto z \cdot \left(6 \cdot \left(y - x\right) + \frac{x}{z}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 87.9%

      \[\leadsto z \cdot \mathsf{fma}\left(6, y - x, \frac{x}{z}\right) \]

   5. Taylor expanded in z around inf

      \[\leadsto z \cdot \left(6 \cdot \left(y - x\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 64.9%

      \[\leadsto z \cdot \left(6 \cdot \left(y - x\right)\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto z \cdot \left(6 \cdot y\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 41.3%

       \[\leadsto z \cdot \left(6 \cdot y\right) \]

   if -1.5998878487717716e-87 < z < 1.4132947115915006e-40

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(1 + -6 \cdot z\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 62.4%

      \[\leadsto x \cdot \left(1 + -6 \cdot z\right) \]

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 36.5%

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

Alternative 10: 60.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_0 := z \cdot \left(6 \cdot y\right)\\ \mathbf{if}\;z \leq -1.5998878487717716 \cdot 10^{-87}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.4132947115915006 \cdot 10^{-40}:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* z (* 6.0 y))))
  (if (<= z -1.5998878487717716e-87)
    t_0
    (if (<= z 1.4132947115915006e-40) (* x 1.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * (6.0 * y);
	double tmp;
	if (z <= -1.5998878487717716e-87) {
		tmp = t_0;
	} else if (z <= 1.4132947115915006e-40) {
		tmp = x * 1.0;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = z * (6.0d0 * y)
    if (z <= (-1.5998878487717716d-87)) then
        tmp = t_0
    else if (z <= 1.4132947115915006d-40) then
        tmp = x * 1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (6.0 * y);
	double tmp;
	if (z <= -1.5998878487717716e-87) {
		tmp = t_0;
	} else if (z <= 1.4132947115915006e-40) {
		tmp = x * 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (6.0 * y)
	tmp = 0
	if z <= -1.5998878487717716e-87:
		tmp = t_0
	elif z <= 1.4132947115915006e-40:
		tmp = x * 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(6.0 * y))
	tmp = 0.0
	if (z <= -1.5998878487717716e-87)
		tmp = t_0;
	elseif (z <= 1.4132947115915006e-40)
		tmp = Float64(x * 1.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (6.0 * y);
	tmp = 0.0;
	if (z <= -1.5998878487717716e-87)
		tmp = t_0;
	elseif (z <= 1.4132947115915006e-40)
		tmp = x * 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(6.0 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5998878487717716e-87], t$95$0, If[LessEqual[z, 1.4132947115915006e-40], N[(x * 1.0), $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 = (z * ((6) * y)) IN
		LET tmp_1 = IF (z <= (14132947115915006468182910235642061199906833362565967651395812855413318177857125598375794078304482317867511731446228395725484006106853485107421875e-185)) THEN (x * (1)) ELSE t_0 ENDIF IN
		LET tmp = IF (z <= (-159988784877177164685523371169830722870522374072384409119026858684832480050318864005140114871679013601761552483193181404403016128515199488354968070059220853336754264519220820635743157089849151568897638446024723319315030689580225953250192105770111083984375e-341)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -1.5998878487717716e-87 or 1.4132947115915006e-40 < z

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around inf

      \[\leadsto z \cdot \left(6 \cdot \left(y - x\right) + \frac{x}{z}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 87.9%

      \[\leadsto z \cdot \mathsf{fma}\left(6, y - x, \frac{x}{z}\right) \]

   5. Taylor expanded in z around inf

      \[\leadsto z \cdot \left(6 \cdot \left(y - x\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 64.9%

      \[\leadsto z \cdot \left(6 \cdot \left(y - x\right)\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto z \cdot \left(6 \cdot y\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 41.3%

       \[\leadsto z \cdot \left(6 \cdot y\right) \]

   if -1.5998878487717716e-87 < z < 1.4132947115915006e-40

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(1 + -6 \cdot z\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 62.4%

      \[\leadsto x \cdot \left(1 + -6 \cdot z\right) \]

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 36.5%

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

Alternative 11: 36.5% accurate, 3.0× 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 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

2. Taylor expanded in x around inf

   \[\leadsto x \cdot \left(1 + -6 \cdot z\right) \]
3. Step-by-step derivation

4. Applied rewrites 62.4%

   \[\leadsto x \cdot \left(1 + -6 \cdot z\right) \]

5. Taylor expanded in z around 0

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

7. Applied rewrites 36.5%

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

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64
  (+ x (* (* (- y x) 6.0) z)))