Linear.V4:$cdot from linear-1.19.1.3, C

Percentage Accurate: 95.9% → 97.9%

Time: 2.5s

Alternatives: 12

Speedup: 1.1×

• 59.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  :pre TRUE
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((x * y) + (z * t)) + (a * b)) + (c * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = (((x * y) + (z * t)) + (a * b)) + (c * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((x * y) + (z * t)) + (a * b)) + (c * i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return (((x * y) + (z * t)) + (a * b)) + (c * i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) + Float64(a * b)) + Float64(c * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (((x * y) + (z * t)) + (a * b)) + (c * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]

ReFlow

f(x, y, z, t, a, b, c, i):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i: real): real =
	(((x * y) + (z * t)) + (a * b)) + (c * i)
END code

Initial Program: 95.9% accurate, 1.0× speedup

Math

\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  :pre TRUE
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((x * y) + (z * t)) + (a * b)) + (c * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = (((x * y) + (z * t)) + (a * b)) + (c * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((x * y) + (z * t)) + (a * b)) + (c * i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return (((x * y) + (z * t)) + (a * b)) + (c * i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) + Float64(a * b)) + Float64(c * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (((x * y) + (z * t)) + (a * b)) + (c * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]

ReFlow

f(x, y, z, t, a, b, c, i):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i: real): real =
	(((x * y) + (z * t)) + (a * b)) + (c * i)
END code

Alternative 1: 97.9% accurate, 1.1× speedup

Math

\[\mathsf{fma}\left(x, y, \mathsf{fma}\left(i, c, \mathsf{fma}\left(b, a, t \cdot z\right)\right)\right) \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  :pre TRUE
  (fma x y (fma i c (fma b a (* t z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return fma(x, y, fma(i, c, fma(b, a, (t * z))));
}

Julia

function code(x, y, z, t, a, b, c, i)
	return fma(x, y, fma(i, c, fma(b, a, Float64(t * z))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(x * y + N[(i * c + N[(b * a + N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

ReFlow

f(x, y, z, t, a, b, c, i):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i: real): real =
	(x * y) + ((i * c) + ((b * a) + (t * z)))
END code

Derivation

1. Initial program 95.9%

   \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

3. Applied rewrites 97.9%

   \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(i, c, \mathsf{fma}\left(b, a, t \cdot z\right)\right)\right) \]
4. Add Preprocessing

Alternative 2: 89.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+42}:\\ \;\;\;\;\mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+84}:\\ \;\;\;\;\mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, \mathsf{fma}\left(i, c, t \cdot z\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  :pre TRUE
  (if (<= (* x y) -2e+42)
  (fma a b (fma c i (* x y)))
  (if (<= (* x y) 5e+84)
    (fma a b (fma c i (* t z)))
    (fma x y (fma i c (* t z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -2e+42) {
		tmp = fma(a, b, fma(c, i, (x * y)));
	} else if ((x * y) <= 5e+84) {
		tmp = fma(a, b, fma(c, i, (t * z)));
	} else {
		tmp = fma(x, y, fma(i, c, (t * z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -2e+42)
		tmp = fma(a, b, fma(c, i, Float64(x * y)));
	elseif (Float64(x * y) <= 5e+84)
		tmp = fma(a, b, fma(c, i, Float64(t * z)));
	else
		tmp = fma(x, y, fma(i, c, Float64(t * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+42], N[(a * b + N[(c * i + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+84], N[(a * b + N[(c * i + N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * y + N[(i * c + N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

ReFlow

f(x, y, z, t, a, b, c, i):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i: real): real =
	LET tmp_1 = IF ((x * y) <= (5000000000000000073153476153374365154850214939323275296393053935848981821255741079552)) THEN ((a * b) + ((c * i) + (t * z))) ELSE ((x * y) + ((i * c) + (t * z))) ENDIF IN
	LET tmp = IF ((x * y) <= (-2000000000000000089771425356151833571098624)) THEN ((a * b) + ((c * i) + (x * y))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.0000000000000001e42

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in z around 0

      \[\leadsto a \cdot b + \left(c \cdot i + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 75.2%

      \[\leadsto \mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right) \]

   if -2.0000000000000001e42 < (*.f64 x y) < 5.0000000000000001e84

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in x around 0

      \[\leadsto a \cdot b + \left(c \cdot i + t \cdot z\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 75.4%

      \[\leadsto \mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, t \cdot z\right)\right) \]

   if 5.0000000000000001e84 < (*.f64 x y)

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 74.6%

      \[\leadsto \mathsf{fma}\left(c, i, \mathsf{fma}\left(t, z, x \cdot y\right)\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 74.6%

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

Alternative 3: 89.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.1382117749624694 \cdot 10^{+42}:\\ \;\;\;\;\mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 9.39991363007265 \cdot 10^{+97}:\\ \;\;\;\;\mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, i, \mathsf{fma}\left(t, z, x \cdot y\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  :pre TRUE
  (if (<= (* x y) -3.1382117749624694e+42)
  (fma a b (fma c i (* x y)))
  (if (<= (* x y) 9.39991363007265e+97)
    (fma a b (fma c i (* t z)))
    (fma c i (fma t z (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -3.1382117749624694e+42) {
		tmp = fma(a, b, fma(c, i, (x * y)));
	} else if ((x * y) <= 9.39991363007265e+97) {
		tmp = fma(a, b, fma(c, i, (t * z)));
	} else {
		tmp = fma(c, i, fma(t, z, (x * y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -3.1382117749624694e+42)
		tmp = fma(a, b, fma(c, i, Float64(x * y)));
	elseif (Float64(x * y) <= 9.39991363007265e+97)
		tmp = fma(a, b, fma(c, i, Float64(t * z)));
	else
		tmp = fma(c, i, fma(t, z, Float64(x * y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -3.1382117749624694e+42], N[(a * b + N[(c * i + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 9.39991363007265e+97], N[(a * b + N[(c * i + N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * i + N[(t * z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

ReFlow

f(x, y, z, t, a, b, c, i):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i: real): real =
	LET tmp_1 = IF ((x * y) <= (93999136300726496045263588239683999000219775412683399171711992468226925889669915361728257616510976)) THEN ((a * b) + ((c * i) + (t * z))) ELSE ((c * i) + ((t * z) + (x * y))) ENDIF IN
	LET tmp = IF ((x * y) <= (-3138211774962469442935189429245078050701312)) THEN ((a * b) + ((c * i) + (x * y))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.1382117749624694e42

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in z around 0

      \[\leadsto a \cdot b + \left(c \cdot i + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 75.2%

      \[\leadsto \mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right) \]

   if -3.1382117749624694e42 < (*.f64 x y) < 9.3999136300726496e97

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in x around 0

      \[\leadsto a \cdot b + \left(c \cdot i + t \cdot z\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 75.4%

      \[\leadsto \mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, t \cdot z\right)\right) \]

   if 9.3999136300726496e97 < (*.f64 x y)

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 74.6%

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

Alternative 4: 89.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right)\\ \mathbf{if}\;x \cdot y \leq -3.1382117749624694 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 6.334657605915576 \cdot 10^{+58}:\\ \;\;\;\;\mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma a b (fma c i (* x y)))))
  (if (<= (* x y) -3.1382117749624694e+42)
    t_1
    (if (<= (* x y) 6.334657605915576e+58)
      (fma a b (fma c i (* t z)))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(a, b, fma(c, i, (x * y)));
	double tmp;
	if ((x * y) <= -3.1382117749624694e+42) {
		tmp = t_1;
	} else if ((x * y) <= 6.334657605915576e+58) {
		tmp = fma(a, b, fma(c, i, (t * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(a, b, fma(c, i, Float64(x * y)))
	tmp = 0.0
	if (Float64(x * y) <= -3.1382117749624694e+42)
		tmp = t_1;
	elseif (Float64(x * y) <= 6.334657605915576e+58)
		tmp = fma(a, b, fma(c, i, Float64(t * z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a * b + N[(c * i + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -3.1382117749624694e+42], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 6.334657605915576e+58], N[(a * b + N[(c * i + N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t, a, b, c, i):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i: real): real =
	LET t_1 = ((a * b) + ((c * i) + (x * y))) IN
		LET tmp_1 = IF ((x * y) <= (63346576059155758991410536067508989763166509466962578374656)) THEN ((a * b) + ((c * i) + (t * z))) ELSE t_1 ENDIF IN
		LET tmp = IF ((x * y) <= (-3138211774962469442935189429245078050701312)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -3.1382117749624694e42 or 6.3346576059155759e58 < (*.f64 x y)

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in z around 0

      \[\leadsto a \cdot b + \left(c \cdot i + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 75.2%

      \[\leadsto \mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right) \]

   if -3.1382117749624694e42 < (*.f64 x y) < 6.3346576059155759e58

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in x around 0

      \[\leadsto a \cdot b + \left(c \cdot i + t \cdot z\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 75.4%

      \[\leadsto \mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, t \cdot z\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.4310301300448993 \cdot 10^{+92}:\\ \;\;\;\;\mathsf{fma}\left(a, b, x \cdot y\right)\\ \mathbf{elif}\;x \cdot y \leq 9.39991363007265 \cdot 10^{+97}:\\ \;\;\;\;\mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, i, x \cdot y\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  :pre TRUE
  (if (<= (* x y) -2.4310301300448993e+92)
  (fma a b (* x y))
  (if (<= (* x y) 9.39991363007265e+97)
    (fma a b (fma c i (* t z)))
    (fma c i (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -2.4310301300448993e+92) {
		tmp = fma(a, b, (x * y));
	} else if ((x * y) <= 9.39991363007265e+97) {
		tmp = fma(a, b, fma(c, i, (t * z)));
	} else {
		tmp = fma(c, i, (x * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -2.4310301300448993e+92)
		tmp = fma(a, b, Float64(x * y));
	elseif (Float64(x * y) <= 9.39991363007265e+97)
		tmp = fma(a, b, fma(c, i, Float64(t * z)));
	else
		tmp = fma(c, i, Float64(x * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -2.4310301300448993e+92], N[(a * b + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 9.39991363007265e+97], N[(a * b + N[(c * i + N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * i + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

ReFlow

f(x, y, z, t, a, b, c, i):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i: real): real =
	LET tmp_1 = IF ((x * y) <= (93999136300726496045263588239683999000219775412683399171711992468226925889669915361728257616510976)) THEN ((a * b) + ((c * i) + (t * z))) ELSE ((c * i) + (x * y)) ENDIF IN
	LET tmp = IF ((x * y) <= (-243103013004489926494550397719659858854683041112430769794729004330253462416167071178584752128)) THEN ((a * b) + (x * y)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.4310301300448993e92

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in z around 0

      \[\leadsto a \cdot b + \left(c \cdot i + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 75.2%

      \[\leadsto \mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right) \]

   5. Taylor expanded in c around 0

      \[\leadsto a \cdot b + x \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 52.2%

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

   if -2.4310301300448993e92 < (*.f64 x y) < 9.3999136300726496e97

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in x around 0

      \[\leadsto a \cdot b + \left(c \cdot i + t \cdot z\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 75.4%

      \[\leadsto \mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, t \cdot z\right)\right) \]

   if 9.3999136300726496e97 < (*.f64 x y)

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in z around 0

      \[\leadsto a \cdot b + \left(c \cdot i + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 75.2%

      \[\leadsto \mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right) \]

   5. Taylor expanded in c around 0

      \[\leadsto a \cdot b + x \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 52.2%

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

   8. Taylor expanded in x around 0

      \[\leadsto a \cdot b \]
   9. Step-by-step derivation

   10. Applied rewrites 28.0%

       \[\leadsto a \cdot b \]

   11. Taylor expanded in a around 0

       \[\leadsto c \cdot i + x \cdot y \]
   12. Step-by-step derivation

   13. Applied rewrites 51.1%

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

Alternative 6: 67.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(a, b, x \cdot y\right)\\ \mathbf{if}\;x \cdot y \leq -2.4310301300448993 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -1.0710483818950177 \cdot 10^{-139}:\\ \;\;\;\;\mathsf{fma}\left(a, b, c \cdot i\right)\\ \mathbf{elif}\;x \cdot y \leq 2.0945617706960675 \cdot 10^{+71}:\\ \;\;\;\;\mathsf{fma}\left(c, i, t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma a b (* x y))))
  (if (<= (* x y) -2.4310301300448993e+92)
    t_1
    (if (<= (* x y) -1.0710483818950177e-139)
      (fma a b (* c i))
      (if (<= (* x y) 2.0945617706960675e+71)
        (fma c i (* t z))
        t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(a, b, (x * y));
	double tmp;
	if ((x * y) <= -2.4310301300448993e+92) {
		tmp = t_1;
	} else if ((x * y) <= -1.0710483818950177e-139) {
		tmp = fma(a, b, (c * i));
	} else if ((x * y) <= 2.0945617706960675e+71) {
		tmp = fma(c, i, (t * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(a, b, Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -2.4310301300448993e+92)
		tmp = t_1;
	elseif (Float64(x * y) <= -1.0710483818950177e-139)
		tmp = fma(a, b, Float64(c * i));
	elseif (Float64(x * y) <= 2.0945617706960675e+71)
		tmp = fma(c, i, Float64(t * z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a * b + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.4310301300448993e+92], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1.0710483818950177e-139], N[(a * b + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.0945617706960675e+71], N[(c * i + N[(t * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

ReFlow

f(x, y, z, t, a, b, c, i):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i: real): real =
	LET t_1 = ((a * b) + (x * y)) IN
		LET tmp_2 = IF ((x * y) <= (209456177069606752178698508544923590488057895263761271119959979620040704)) THEN ((c * i) + (t * z)) ELSE t_1 ENDIF IN
		LET tmp_1 = IF ((x * y) <= (-107104838189501766554745995275851255731985160615416250000722709665921879326123707863483014578860596749555539699001121875121062033618750874554338613557799004664033572357213644088861858746389876811579280891752445574204462531453812729847870665888073826689752541393267131659263832828851840074128472893231792503326728285470215802339274372041721949955217496608383953571319580078125e-513)) THEN ((a * b) + (c * i)) ELSE tmp_2 ENDIF IN
		LET tmp = IF ((x * y) <= (-243103013004489926494550397719659858854683041112430769794729004330253462416167071178584752128)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.4310301300448993e92 or 2.0945617706960675e71 < (*.f64 x y)

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in z around 0

      \[\leadsto a \cdot b + \left(c \cdot i + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 75.2%

      \[\leadsto \mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right) \]

   5. Taylor expanded in c around 0

      \[\leadsto a \cdot b + x \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 52.2%

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

   if -2.4310301300448993e92 < (*.f64 x y) < -1.0710483818950177e-139

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in z around 0

      \[\leadsto a \cdot b + \left(c \cdot i + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 75.2%

      \[\leadsto \mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(a, b, c \cdot i\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 52.1%

      \[\leadsto \mathsf{fma}\left(a, b, c \cdot i\right) \]

   if -1.0710483818950177e-139 < (*.f64 x y) < 2.0945617706960675e71

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 74.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(c, i, t \cdot z\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 51.3%

      \[\leadsto \mathsf{fma}\left(c, i, t \cdot z\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 67.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.4310301300448993 \cdot 10^{+92}:\\ \;\;\;\;\mathsf{fma}\left(a, b, x \cdot y\right)\\ \mathbf{elif}\;x \cdot y \leq 9.39991363007265 \cdot 10^{+97}:\\ \;\;\;\;\mathsf{fma}\left(a, b, c \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, i, x \cdot y\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  :pre TRUE
  (if (<= (* x y) -2.4310301300448993e+92)
  (fma a b (* x y))
  (if (<= (* x y) 9.39991363007265e+97)
    (fma a b (* c i))
    (fma c i (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -2.4310301300448993e+92) {
		tmp = fma(a, b, (x * y));
	} else if ((x * y) <= 9.39991363007265e+97) {
		tmp = fma(a, b, (c * i));
	} else {
		tmp = fma(c, i, (x * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -2.4310301300448993e+92)
		tmp = fma(a, b, Float64(x * y));
	elseif (Float64(x * y) <= 9.39991363007265e+97)
		tmp = fma(a, b, Float64(c * i));
	else
		tmp = fma(c, i, Float64(x * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -2.4310301300448993e+92], N[(a * b + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 9.39991363007265e+97], N[(a * b + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(c * i + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

ReFlow

f(x, y, z, t, a, b, c, i):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i: real): real =
	LET tmp_1 = IF ((x * y) <= (93999136300726496045263588239683999000219775412683399171711992468226925889669915361728257616510976)) THEN ((a * b) + (c * i)) ELSE ((c * i) + (x * y)) ENDIF IN
	LET tmp = IF ((x * y) <= (-243103013004489926494550397719659858854683041112430769794729004330253462416167071178584752128)) THEN ((a * b) + (x * y)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.4310301300448993e92

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in z around 0

      \[\leadsto a \cdot b + \left(c \cdot i + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 75.2%

      \[\leadsto \mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right) \]

   5. Taylor expanded in c around 0

      \[\leadsto a \cdot b + x \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 52.2%

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

   if -2.4310301300448993e92 < (*.f64 x y) < 9.3999136300726496e97

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in z around 0

      \[\leadsto a \cdot b + \left(c \cdot i + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 75.2%

      \[\leadsto \mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(a, b, c \cdot i\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 52.1%

      \[\leadsto \mathsf{fma}\left(a, b, c \cdot i\right) \]

   if 9.3999136300726496e97 < (*.f64 x y)

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in z around 0

      \[\leadsto a \cdot b + \left(c \cdot i + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 75.2%

      \[\leadsto \mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right) \]

   5. Taylor expanded in c around 0

      \[\leadsto a \cdot b + x \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 52.2%

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

   8. Taylor expanded in x around 0

      \[\leadsto a \cdot b \]
   9. Step-by-step derivation

   10. Applied rewrites 28.0%

       \[\leadsto a \cdot b \]

   11. Taylor expanded in a around 0

       \[\leadsto c \cdot i + x \cdot y \]
   12. Step-by-step derivation

   13. Applied rewrites 51.1%

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

Alternative 8: 66.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(c, i, x \cdot y\right)\\ \mathbf{if}\;c \cdot i \leq -4 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 2 \cdot 10^{+37}:\\ \;\;\;\;\mathsf{fma}\left(a, b, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma c i (* x y))))
  (if (<= (* c i) -4e+125)
    t_1
    (if (<= (* c i) 2e+37) (fma a b (* x y)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(c, i, (x * y));
	double tmp;
	if ((c * i) <= -4e+125) {
		tmp = t_1;
	} else if ((c * i) <= 2e+37) {
		tmp = fma(a, b, (x * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(c, i, Float64(x * y))
	tmp = 0.0
	if (Float64(c * i) <= -4e+125)
		tmp = t_1;
	elseif (Float64(c * i) <= 2e+37)
		tmp = fma(a, b, Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * i + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -4e+125], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 2e+37], N[(a * b + N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t, a, b, c, i):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i: real): real =
	LET t_1 = ((c * i) + (x * y)) IN
		LET tmp_1 = IF ((c * i) <= (19999999999999999077525316404242284544)) THEN ((a * b) + (x * y)) ELSE t_1 ENDIF IN
		LET tmp = IF ((c * i) <= (-399999999999999969947104647597152817017868347933935384575690388890117679990317210641265397505127061500612023365462212913135616)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -3.9999999999999997e125 or 1.9999999999999999e37 < (*.f64 c i)

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in z around 0

      \[\leadsto a \cdot b + \left(c \cdot i + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 75.2%

      \[\leadsto \mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right) \]

   5. Taylor expanded in c around 0

      \[\leadsto a \cdot b + x \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 52.2%

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

   8. Taylor expanded in x around 0

      \[\leadsto a \cdot b \]
   9. Step-by-step derivation

   10. Applied rewrites 28.0%

       \[\leadsto a \cdot b \]

   11. Taylor expanded in a around 0

       \[\leadsto c \cdot i + x \cdot y \]
   12. Step-by-step derivation

   13. Applied rewrites 51.1%

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

   if -3.9999999999999997e125 < (*.f64 c i) < 1.9999999999999999e37

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in z around 0

      \[\leadsto a \cdot b + \left(c \cdot i + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 75.2%

      \[\leadsto \mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right) \]

   5. Taylor expanded in c around 0

      \[\leadsto a \cdot b + x \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 52.2%

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

Alternative 9: 63.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{+150}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{fma}\left(a, b, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot z\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  :pre TRUE
  (if (<= (* z t) -4e+150)
  (* t z)
  (if (<= (* z t) 2e+152) (fma a b (* x y)) (* t z))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z * t) <= -4e+150) {
		tmp = t * z;
	} else if ((z * t) <= 2e+152) {
		tmp = fma(a, b, (x * y));
	} else {
		tmp = t * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(z * t) <= -4e+150)
		tmp = Float64(t * z);
	elseif (Float64(z * t) <= 2e+152)
		tmp = fma(a, b, Float64(x * y));
	else
		tmp = Float64(t * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(z * t), $MachinePrecision], -4e+150], N[(t * z), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e+152], N[(a * b + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(t * z), $MachinePrecision]]]

ReFlow

f(x, y, z, t, a, b, c, i):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i: real): real =
	LET tmp_1 = IF ((z * t) <= (200000000000000009250216271808398948002452544790145376983777454402545107507559301846766839764406850263979324900979381181838795379032883593269504018219008)) THEN ((a * b) + (x * y)) ELSE (t * z) ENDIF IN
	LET tmp = IF ((z * t) <= (-3999999999999999923342384689749498362292480056121275172364659240616400448814714331905193074464884607850808241064704021762268129324833615792933494063104)) THEN (t * z) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -3.9999999999999999e150 or 2.0000000000000001e152 < (*.f64 z t)

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in z around 0

      \[\leadsto a \cdot b + \left(c \cdot i + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 75.2%

      \[\leadsto \mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right) \]

   5. Taylor expanded in c around 0

      \[\leadsto a \cdot b + x \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 52.2%

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

   8. Taylor expanded in x around 0

      \[\leadsto a \cdot b \]
   9. Step-by-step derivation

   10. Applied rewrites 28.0%

       \[\leadsto a \cdot b \]

   11. Taylor expanded in z around inf

       \[\leadsto t \cdot z \]
   12. Step-by-step derivation

   13. Applied rewrites 27.3%

       \[\leadsto t \cdot z \]

   if -3.9999999999999999e150 < (*.f64 z t) < 2.0000000000000001e152

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in z around 0

      \[\leadsto a \cdot b + \left(c \cdot i + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 75.2%

      \[\leadsto \mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right) \]

   5. Taylor expanded in c around 0

      \[\leadsto a \cdot b + x \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 52.2%

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

Alternative 10: 43.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.872718146010244 \cdot 10^{+82}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 2.2915198281696953 \cdot 10^{+27}:\\ \;\;\;\;t \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  :pre TRUE
  (if (<= (* a b) -1.872718146010244e+82)
  (* a b)
  (if (<= (* a b) 2.2915198281696953e+27) (* t z) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1.872718146010244e+82) {
		tmp = a * b;
	} else if ((a * b) <= 2.2915198281696953e+27) {
		tmp = t * z;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-1.872718146010244d+82)) then
        tmp = a * b
    else if ((a * b) <= 2.2915198281696953d+27) then
        tmp = t * z
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1.872718146010244e+82) {
		tmp = a * b;
	} else if ((a * b) <= 2.2915198281696953e+27) {
		tmp = t * z;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -1.872718146010244e+82:
		tmp = a * b
	elif (a * b) <= 2.2915198281696953e+27:
		tmp = t * z
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -1.872718146010244e+82)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 2.2915198281696953e+27)
		tmp = Float64(t * z);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -1.872718146010244e+82)
		tmp = a * b;
	elseif ((a * b) <= 2.2915198281696953e+27)
		tmp = t * z;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -1.872718146010244e+82], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.2915198281696953e+27], N[(t * z), $MachinePrecision], N[(a * b), $MachinePrecision]]]

ReFlow

f(x, y, z, t, a, b, c, i):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i: real): real =
	LET tmp_1 = IF ((a * b) <= (2291519828169695259242004480)) THEN (t * z) ELSE (a * b) ENDIF IN
	LET tmp = IF ((a * b) <= (-18727181460102439296841648963870213440793756189383544716934324050261809778630066176)) THEN (a * b) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.8727181460102439e82 or 2.2915198281696953e27 < (*.f64 a b)

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in z around 0

      \[\leadsto a \cdot b + \left(c \cdot i + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 75.2%

      \[\leadsto \mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right) \]

   5. Taylor expanded in c around 0

      \[\leadsto a \cdot b + x \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 52.2%

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

   8. Taylor expanded in x around 0

      \[\leadsto a \cdot b \]
   9. Step-by-step derivation

   10. Applied rewrites 28.0%

       \[\leadsto a \cdot b \]

   if -1.8727181460102439e82 < (*.f64 a b) < 2.2915198281696953e27

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in z around 0

      \[\leadsto a \cdot b + \left(c \cdot i + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 75.2%

      \[\leadsto \mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right) \]

   5. Taylor expanded in c around 0

      \[\leadsto a \cdot b + x \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 52.2%

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

   8. Taylor expanded in x around 0

      \[\leadsto a \cdot b \]
   9. Step-by-step derivation

   10. Applied rewrites 28.0%

       \[\leadsto a \cdot b \]

   11. Taylor expanded in z around inf

       \[\leadsto t \cdot z \]
   12. Step-by-step derivation

   13. Applied rewrites 27.3%

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

Alternative 11: 43.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;c \cdot i \leq -4.503682490157631 \cdot 10^{+125}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 3.8261387039131425 \cdot 10^{+38}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  :pre TRUE
  (if (<= (* c i) -4.503682490157631e+125)
  (* c i)
  (if (<= (* c i) 3.8261387039131425e+38) (* a b) (* c i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -4.503682490157631e+125) {
		tmp = c * i;
	} else if ((c * i) <= 3.8261387039131425e+38) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-4.503682490157631d+125)) then
        tmp = c * i
    else if ((c * i) <= 3.8261387039131425d+38) then
        tmp = a * b
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -4.503682490157631e+125) {
		tmp = c * i;
	} else if ((c * i) <= 3.8261387039131425e+38) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -4.503682490157631e+125:
		tmp = c * i
	elif (c * i) <= 3.8261387039131425e+38:
		tmp = a * b
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -4.503682490157631e+125)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 3.8261387039131425e+38)
		tmp = Float64(a * b);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -4.503682490157631e+125)
		tmp = c * i;
	elseif ((c * i) <= 3.8261387039131425e+38)
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -4.503682490157631e+125], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 3.8261387039131425e+38], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]

ReFlow

f(x, y, z, t, a, b, c, i):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i: real): real =
	LET tmp_1 = IF ((c * i) <= (382613870391314253124613801303561207808)) THEN (a * b) ELSE (c * i) ENDIF IN
	LET tmp = IF ((c * i) <= (-450368249015763130012492365230978570302056270030389531470603338831907784298328625971329005887457494838939231393676931761176576)) THEN (c * i) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -4.5036824901576313e125 or 3.8261387039131425e38 < (*.f64 c i)

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in z around 0

      \[\leadsto a \cdot b + \left(c \cdot i + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 75.2%

      \[\leadsto \mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right) \]

   5. Taylor expanded in c around 0

      \[\leadsto a \cdot b + x \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 52.2%

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

   8. Taylor expanded in x around 0

      \[\leadsto a \cdot b \]
   9. Step-by-step derivation

   10. Applied rewrites 28.0%

       \[\leadsto a \cdot b \]

   11. Taylor expanded in c around inf

       \[\leadsto c \cdot i \]
   12. Step-by-step derivation

   13. Applied rewrites 27.1%

       \[\leadsto c \cdot i \]

   if -4.5036824901576313e125 < (*.f64 c i) < 3.8261387039131425e38

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in z around 0

      \[\leadsto a \cdot b + \left(c \cdot i + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 75.2%

      \[\leadsto \mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right) \]

   5. Taylor expanded in c around 0

      \[\leadsto a \cdot b + x \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 52.2%

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

   8. Taylor expanded in x around 0

      \[\leadsto a \cdot b \]
   9. Step-by-step derivation

   10. Applied rewrites 28.0%

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

Alternative 12: 28.0% accurate, 5.2× speedup

Math

\[a \cdot b \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  :pre TRUE
  (* a b))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return a * b;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = a * b
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return a * b;
}

Python

def code(x, y, z, t, a, b, c, i):
	return a * b

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(a * b)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = a * b;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(a * b), $MachinePrecision]

ReFlow

f(x, y, z, t, a, b, c, i):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i: real): real =
	a * b
END code

Derivation

1. Initial program 95.9%

   \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

2. Taylor expanded in z around 0

   \[\leadsto a \cdot b + \left(c \cdot i + x \cdot y\right) \]
3. Step-by-step derivation

4. Applied rewrites 75.2%

   \[\leadsto \mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right) \]

5. Taylor expanded in c around 0

   \[\leadsto a \cdot b + x \cdot y \]
6. Step-by-step derivation

7. Applied rewrites 52.2%

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

8. Taylor expanded in x around 0

   \[\leadsto a \cdot b \]
9. Step-by-step derivation

10. Applied rewrites 28.0%

    \[\leadsto a \cdot b \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3, C"
  :precision binary64
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))