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

Percentage Accurate: 96.1% → 98.7%

Time: 8.5s

Alternatives: 12

Speedup: 0.5×

• 40.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \end{array} \]

FPCore

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

Initial Program: 96.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \end{array} \]

FPCore

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

Alternative 1: 98.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot c + \left(b \cdot a + \left(t \cdot z + y \cdot x\right)\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{b}, z, \mathsf{fma}\left(\frac{y}{b}, x, a\right)\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* i c) (+ (* b a) (+ (* t z) (* y x))))))
   (if (<= t_1 INFINITY) t_1 (* (fma (/ t b) z (fma (/ y b) x a)) b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (i * c) + ((b * a) + ((t * z) + (y * x)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma((t / b), z, fma((y / b), x, a)) * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(i * c) + Float64(Float64(b * a) + Float64(Float64(t * z) + Float64(y * x))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(fma(Float64(t / b), z, fma(Float64(y / b), x, a)) * b);
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i)) < +inf.0

   1. Initial program 100.0%

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

   if +inf.0 < (+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i))

   1. Initial program 0.0%

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

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{a \cdot b + \left(t \cdot z + x \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{b \cdot a} + \left(t \cdot z + x \cdot y\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, a, t \cdot z + x \cdot y\right)} \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, a, \color{blue}{x \cdot y + t \cdot z}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, a, \color{blue}{y \cdot x} + t \cdot z\right) \]

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 56.3

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

   5. Applied rewrites 56.3%

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

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(a + \left(\frac{t \cdot z}{b} + \frac{x \cdot y}{b}\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 68.8%

      \[\leadsto \mathsf{fma}\left(\frac{t}{b}, z, \mathsf{fma}\left(\frac{y}{b}, x, a\right)\right) \cdot \color{blue}{b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot c + \left(b \cdot a + \left(t \cdot z + y \cdot x\right)\right) \leq \infty:\\ \;\;\;\;i \cdot c + \left(b \cdot a + \left(t \cdot z + y \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{b}, z, \mathsf{fma}\left(\frac{y}{b}, x, a\right)\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, x, t \cdot z\right)\\ t_2 := t \cdot z + y \cdot x\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-24}:\\ \;\;\;\;\mathsf{fma}\left(b, a, y \cdot x\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+150}:\\ \;\;\;\;\mathsf{fma}\left(i, c, b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma y x (* t z))) (t_2 (+ (* t z) (* y x))))
   (if (<= t_2 -5e+109)
     t_1
     (if (<= t_2 -2e-24)
       (fma b a (* y x))
       (if (<= t_2 2e+150) (fma i c (* b a)) 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(y, x, (t * z));
	double t_2 = (t * z) + (y * x);
	double tmp;
	if (t_2 <= -5e+109) {
		tmp = t_1;
	} else if (t_2 <= -2e-24) {
		tmp = fma(b, a, (y * x));
	} else if (t_2 <= 2e+150) {
		tmp = fma(i, c, (b * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(y, x, Float64(t * z))
	t_2 = Float64(Float64(t * z) + Float64(y * x))
	tmp = 0.0
	if (t_2 <= -5e+109)
		tmp = t_1;
	elseif (t_2 <= -2e-24)
		tmp = fma(b, a, Float64(y * x));
	elseif (t_2 <= 2e+150)
		tmp = fma(i, c, Float64(b * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(y * x + N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+109], t$95$1, If[LessEqual[t$95$2, -2e-24], N[(b * a + N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+150], N[(i * c + N[(b * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (*.f64 x y) (*.f64 z t)) < -5.0000000000000001e109 or 1.99999999999999996e150 < (+.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 88.7%

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

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{a \cdot b + \left(t \cdot z + x \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{b \cdot a} + \left(t \cdot z + x \cdot y\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, a, t \cdot z + x \cdot y\right)} \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, a, \color{blue}{x \cdot y + t \cdot z}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, a, \color{blue}{y \cdot x} + t \cdot z\right) \]

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 90.6

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

   5. Applied rewrites 90.6%

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

   6. Taylor expanded in b around 0

      \[\leadsto t \cdot z + \color{blue}{x \cdot y} \]
   7. Step-by-step derivation

   8. Applied rewrites 81.7%

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

   if -5.0000000000000001e109 < (+.f64 (*.f64 x y) (*.f64 z t)) < -1.99999999999999985e-24

   1. Initial program 100.0%

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

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{a \cdot b + \left(t \cdot z + x \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{b \cdot a} + \left(t \cdot z + x \cdot y\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, a, t \cdot z + x \cdot y\right)} \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, a, \color{blue}{x \cdot y + t \cdot z}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, a, \color{blue}{y \cdot x} + t \cdot z\right) \]

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 88.0

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

   5. Applied rewrites 88.0%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(b, a, x \cdot y\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 70.6%

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

   if -1.99999999999999985e-24 < (+.f64 (*.f64 x y) (*.f64 z t)) < 1.99999999999999996e150

   1. Initial program 98.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{a \cdot b} + c \cdot i \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{b \cdot a} + c \cdot i \]

      2. lower-*.f64 81.4

         \[\leadsto \color{blue}{b \cdot a} + c \cdot i \]

   5. Applied rewrites 81.4%

      \[\leadsto \color{blue}{b \cdot a} + c \cdot i \]
   6. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{b \cdot a + c \cdot i} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{c \cdot i + b \cdot a} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot i} + b \cdot a \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{i \cdot c} + b \cdot a \]

      5. lower-fma.f64 82.4

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

   7. Applied rewrites 82.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, c, b \cdot a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot z + y \cdot x \leq -5 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t \cdot z\right)\\ \mathbf{elif}\;t \cdot z + y \cdot x \leq -2 \cdot 10^{-24}:\\ \;\;\;\;\mathsf{fma}\left(b, a, y \cdot x\right)\\ \mathbf{elif}\;t \cdot z + y \cdot x \leq 2 \cdot 10^{+150}:\\ \;\;\;\;\mathsf{fma}\left(i, c, b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot c + \left(b \cdot a + \left(t \cdot z + y \cdot x\right)\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, a, \mathsf{fma}\left(y, x, t \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* i c) (+ (* b a) (+ (* t z) (* y x))))))
   (if (<= t_1 INFINITY) t_1 (fma b a (fma y x (* t z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (i * c) + ((b * a) + ((t * z) + (y * x)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(b, a, fma(y, x, (t * z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(i * c) + Float64(Float64(b * a) + Float64(Float64(t * z) + Float64(y * x))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = fma(b, a, fma(y, x, Float64(t * z)));
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i)) < +inf.0

   1. Initial program 100.0%

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

   if +inf.0 < (+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i))

   1. Initial program 0.0%

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

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{a \cdot b + \left(t \cdot z + x \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{b \cdot a} + \left(t \cdot z + x \cdot y\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, a, t \cdot z + x \cdot y\right)} \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, a, \color{blue}{x \cdot y + t \cdot z}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, a, \color{blue}{y \cdot x} + t \cdot z\right) \]

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 56.3

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

   5. Applied rewrites 56.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, a, \mathsf{fma}\left(y, x, z \cdot t\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot c + \left(b \cdot a + \left(t \cdot z + y \cdot x\right)\right) \leq \infty:\\ \;\;\;\;i \cdot c + \left(b \cdot a + \left(t \cdot z + y \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, a, \mathsf{fma}\left(y, x, t \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, a, \mathsf{fma}\left(y, x, t \cdot z\right)\right)\\ \mathbf{if}\;y \cdot x \leq -2 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \cdot x \leq 2 \cdot 10^{+150}:\\ \;\;\;\;\mathsf{fma}\left(b, a, \mathsf{fma}\left(i, c, t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma b a (fma y x (* t z)))))
   (if (<= (* y x) -2e-24)
     t_1
     (if (<= (* y x) 2e+150) (fma b a (fma i c (* 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(b, a, fma(y, x, (t * z)));
	double tmp;
	if ((y * x) <= -2e-24) {
		tmp = t_1;
	} else if ((y * x) <= 2e+150) {
		tmp = fma(b, a, fma(i, c, (t * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(b, a, fma(y, x, Float64(t * z)))
	tmp = 0.0
	if (Float64(y * x) <= -2e-24)
		tmp = t_1;
	elseif (Float64(y * x) <= 2e+150)
		tmp = fma(b, a, fma(i, c, 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[(b * a + N[(y * x + N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * x), $MachinePrecision], -2e-24], t$95$1, If[LessEqual[N[(y * x), $MachinePrecision], 2e+150], N[(b * a + N[(i * c + N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.99999999999999985e-24 or 1.99999999999999996e150 < (*.f64 x y)

   1. Initial program 90.6%

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

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{a \cdot b + \left(t \cdot z + x \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{b \cdot a} + \left(t \cdot z + x \cdot y\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, a, t \cdot z + x \cdot y\right)} \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, a, \color{blue}{x \cdot y + t \cdot z}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, a, \color{blue}{y \cdot x} + t \cdot z\right) \]

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 89.9

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

   5. Applied rewrites 89.9%

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

   if -1.99999999999999985e-24 < (*.f64 x y) < 1.99999999999999996e150

   1. Initial program 95.6%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{a \cdot b + \left(c \cdot i + t \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{b \cdot a} + \left(c \cdot i + t \cdot z\right) \]

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 94.4

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

   5. Applied rewrites 94.4%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -2 \cdot 10^{-24}:\\ \;\;\;\;\mathsf{fma}\left(b, a, \mathsf{fma}\left(y, x, t \cdot z\right)\right)\\ \mathbf{elif}\;y \cdot x \leq 2 \cdot 10^{+150}:\\ \;\;\;\;\mathsf{fma}\left(b, a, \mathsf{fma}\left(i, c, t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, a, \mathsf{fma}\left(y, x, t \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq -5 \cdot 10^{+174}:\\ \;\;\;\;\mathsf{fma}\left(b, a, y \cdot x\right)\\ \mathbf{elif}\;y \cdot x \leq 3 \cdot 10^{+220}:\\ \;\;\;\;\mathsf{fma}\left(b, a, \mathsf{fma}\left(i, c, t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* y x) -5e+174)
   (fma b a (* y x))
   (if (<= (* y x) 3e+220) (fma b a (fma i c (* t z))) (fma y x (* t z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y * x) <= -5e+174) {
		tmp = fma(b, a, (y * x));
	} else if ((y * x) <= 3e+220) {
		tmp = fma(b, a, fma(i, c, (t * z)));
	} else {
		tmp = fma(y, x, (t * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(y * x) <= -5e+174)
		tmp = fma(b, a, Float64(y * x));
	elseif (Float64(y * x) <= 3e+220)
		tmp = fma(b, a, fma(i, c, Float64(t * z)));
	else
		tmp = fma(y, x, Float64(t * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(y * x), $MachinePrecision], -5e+174], N[(b * a + N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * x), $MachinePrecision], 3e+220], N[(b * a + N[(i * c + N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * x + N[(t * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.9999999999999997e174

   1. Initial program 81.5%

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

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{a \cdot b + \left(t \cdot z + x \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{b \cdot a} + \left(t \cdot z + x \cdot y\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, a, t \cdot z + x \cdot y\right)} \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, a, \color{blue}{x \cdot y + t \cdot z}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, a, \color{blue}{y \cdot x} + t \cdot z\right) \]

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 85.5

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

   5. Applied rewrites 85.5%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(b, a, x \cdot y\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 78.5%

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

   if -4.9999999999999997e174 < (*.f64 x y) < 3.00000000000000024e220

   1. Initial program 95.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{a \cdot b + \left(c \cdot i + t \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{b \cdot a} + \left(c \cdot i + t \cdot z\right) \]

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 88.3

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

   5. Applied rewrites 88.3%

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

   if 3.00000000000000024e220 < (*.f64 x y)

   1. Initial program 90.0%

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

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{a \cdot b + \left(t \cdot z + x \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{b \cdot a} + \left(t \cdot z + x \cdot y\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, a, t \cdot z + x \cdot y\right)} \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, a, \color{blue}{x \cdot y + t \cdot z}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, a, \color{blue}{y \cdot x} + t \cdot z\right) \]

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in b around 0

      \[\leadsto t \cdot z + \color{blue}{x \cdot y} \]
   7. Step-by-step derivation

   8. Applied rewrites 100.0%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{x}, z \cdot t\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -5 \cdot 10^{+174}:\\ \;\;\;\;\mathsf{fma}\left(b, a, y \cdot x\right)\\ \mathbf{elif}\;y \cdot x \leq 3 \cdot 10^{+220}:\\ \;\;\;\;\mathsf{fma}\left(b, a, \mathsf{fma}\left(i, c, t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 43.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \cdot z \leq -2.2 \cdot 10^{+39}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;t \cdot z \leq 2.85 \cdot 10^{-294}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;t \cdot z \leq 6.8 \cdot 10^{+91}:\\ \;\;\;\;b \cdot a\\ \mathbf{else}:\\ \;\;\;\;t \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* t z) -2.2e+39)
   (* t z)
   (if (<= (* t z) 2.85e-294)
     (* y x)
     (if (<= (* t z) 6.8e+91) (* b a) (* t z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((t * z) <= -2.2e+39) {
		tmp = t * z;
	} else if ((t * z) <= 2.85e-294) {
		tmp = y * x;
	} else if ((t * z) <= 6.8e+91) {
		tmp = b * a;
	} else {
		tmp = t * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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 ((t * z) <= (-2.2d+39)) then
        tmp = t * z
    else if ((t * z) <= 2.85d-294) then
        tmp = y * x
    else if ((t * z) <= 6.8d+91) then
        tmp = b * a
    else
        tmp = t * z
    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 ((t * z) <= -2.2e+39) {
		tmp = t * z;
	} else if ((t * z) <= 2.85e-294) {
		tmp = y * x;
	} else if ((t * z) <= 6.8e+91) {
		tmp = b * a;
	} else {
		tmp = t * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (t * z) <= -2.2e+39:
		tmp = t * z
	elif (t * z) <= 2.85e-294:
		tmp = y * x
	elif (t * z) <= 6.8e+91:
		tmp = b * a
	else:
		tmp = t * z
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(t * z) <= -2.2e+39)
		tmp = Float64(t * z);
	elseif (Float64(t * z) <= 2.85e-294)
		tmp = Float64(y * x);
	elseif (Float64(t * z) <= 6.8e+91)
		tmp = Float64(b * a);
	else
		tmp = Float64(t * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((t * z) <= -2.2e+39)
		tmp = t * z;
	elseif ((t * z) <= 2.85e-294)
		tmp = y * x;
	elseif ((t * z) <= 6.8e+91)
		tmp = b * a;
	else
		tmp = t * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(t * z), $MachinePrecision], -2.2e+39], N[(t * z), $MachinePrecision], If[LessEqual[N[(t * z), $MachinePrecision], 2.85e-294], N[(y * x), $MachinePrecision], If[LessEqual[N[(t * z), $MachinePrecision], 6.8e+91], N[(b * a), $MachinePrecision], N[(t * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -2.2000000000000001e39 or 6.8000000000000002e91 < (*.f64 z t)

   1. Initial program 88.6%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot z} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot t} \]

      2. lower-*.f64 67.1

         \[\leadsto \color{blue}{z \cdot t} \]

   5. Applied rewrites 67.1%

      \[\leadsto \color{blue}{z \cdot t} \]

   if -2.2000000000000001e39 < (*.f64 z t) < 2.85000000000000016e-294

   1. Initial program 95.1%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot y} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{y \cdot x} \]

      2. lower-*.f64 43.1

         \[\leadsto \color{blue}{y \cdot x} \]

   5. Applied rewrites 43.1%

      \[\leadsto \color{blue}{y \cdot x} \]

   if 2.85000000000000016e-294 < (*.f64 z t) < 6.8000000000000002e91

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{a \cdot b} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{b \cdot a} \]

      2. lower-*.f64 48.6

         \[\leadsto \color{blue}{b \cdot a} \]

   5. Applied rewrites 48.6%

      \[\leadsto \color{blue}{b \cdot a} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot z \leq -2.2 \cdot 10^{+39}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;t \cdot z \leq 2.85 \cdot 10^{-294}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;t \cdot z \leq 6.8 \cdot 10^{+91}:\\ \;\;\;\;b \cdot a\\ \mathbf{else}:\\ \;\;\;\;t \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 42.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+72}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;b \cdot a \leq 10^{-244}:\\ \;\;\;\;i \cdot c\\ \mathbf{elif}\;b \cdot a \leq 10^{+156}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* b a) -1e+72)
   (* b a)
   (if (<= (* b a) 1e-244) (* i c) (if (<= (* b a) 1e+156) (* y x) (* b a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b * a) <= -1e+72) {
		tmp = b * a;
	} else if ((b * a) <= 1e-244) {
		tmp = i * c;
	} else if ((b * a) <= 1e+156) {
		tmp = y * x;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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 ((b * a) <= (-1d+72)) then
        tmp = b * a
    else if ((b * a) <= 1d-244) then
        tmp = i * c
    else if ((b * a) <= 1d+156) then
        tmp = y * x
    else
        tmp = b * a
    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 ((b * a) <= -1e+72) {
		tmp = b * a;
	} else if ((b * a) <= 1e-244) {
		tmp = i * c;
	} else if ((b * a) <= 1e+156) {
		tmp = y * x;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b * a) <= -1e+72:
		tmp = b * a
	elif (b * a) <= 1e-244:
		tmp = i * c
	elif (b * a) <= 1e+156:
		tmp = y * x
	else:
		tmp = b * a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(b * a) <= -1e+72)
		tmp = Float64(b * a);
	elseif (Float64(b * a) <= 1e-244)
		tmp = Float64(i * c);
	elseif (Float64(b * a) <= 1e+156)
		tmp = Float64(y * x);
	else
		tmp = Float64(b * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((b * a) <= -1e+72)
		tmp = b * a;
	elseif ((b * a) <= 1e-244)
		tmp = i * c;
	elseif ((b * a) <= 1e+156)
		tmp = y * x;
	else
		tmp = b * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(b * a), $MachinePrecision], -1e+72], N[(b * a), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 1e-244], N[(i * c), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 1e+156], N[(y * x), $MachinePrecision], N[(b * a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -9.99999999999999944e71 or 9.9999999999999998e155 < (*.f64 a b)

   1. Initial program 91.5%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{a \cdot b} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{b \cdot a} \]

      2. lower-*.f64 62.9

         \[\leadsto \color{blue}{b \cdot a} \]

   5. Applied rewrites 62.9%

      \[\leadsto \color{blue}{b \cdot a} \]

   if -9.99999999999999944e71 < (*.f64 a b) < 9.9999999999999993e-245

   1. Initial program 94.2%

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

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot i} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{i \cdot c} \]

      2. lower-*.f64 35.3

         \[\leadsto \color{blue}{i \cdot c} \]

   5. Applied rewrites 35.3%

      \[\leadsto \color{blue}{i \cdot c} \]

   if 9.9999999999999993e-245 < (*.f64 a b) < 9.9999999999999998e155

   1. Initial program 96.6%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot y} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{y \cdot x} \]

      2. lower-*.f64 35.6

         \[\leadsto \color{blue}{y \cdot x} \]

   5. Applied rewrites 35.6%

      \[\leadsto \color{blue}{y \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+72}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;b \cdot a \leq 10^{-244}:\\ \;\;\;\;i \cdot c\\ \mathbf{elif}\;b \cdot a \leq 10^{+156}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -2 \cdot 10^{+91}:\\ \;\;\;\;\mathsf{fma}\left(b, a, t \cdot z\right)\\ \mathbf{elif}\;b \cdot a \leq 10^{+164}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, a, y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* b a) -2e+91)
   (fma b a (* t z))
   (if (<= (* b a) 1e+164) (fma y x (* t z)) (fma b a (* y x)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b * a) <= -2e+91) {
		tmp = fma(b, a, (t * z));
	} else if ((b * a) <= 1e+164) {
		tmp = fma(y, x, (t * z));
	} else {
		tmp = fma(b, a, (y * x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(b * a) <= -2e+91)
		tmp = fma(b, a, Float64(t * z));
	elseif (Float64(b * a) <= 1e+164)
		tmp = fma(y, x, Float64(t * z));
	else
		tmp = fma(b, a, Float64(y * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(b * a), $MachinePrecision], -2e+91], N[(b * a + N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 1e+164], N[(y * x + N[(t * z), $MachinePrecision]), $MachinePrecision], N[(b * a + N[(y * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.00000000000000016e91

   1. Initial program 91.8%

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

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{a \cdot b + \left(t \cdot z + x \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{b \cdot a} + \left(t \cdot z + x \cdot y\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, a, t \cdot z + x \cdot y\right)} \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, a, \color{blue}{x \cdot y + t \cdot z}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, a, \color{blue}{y \cdot x} + t \cdot z\right) \]

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 85.6

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

   5. Applied rewrites 85.6%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(b, a, t \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 79.4%

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

   if -2.00000000000000016e91 < (*.f64 a b) < 1e164

   1. Initial program 95.3%

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

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{a \cdot b + \left(t \cdot z + x \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{b \cdot a} + \left(t \cdot z + x \cdot y\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, a, t \cdot z + x \cdot y\right)} \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, a, \color{blue}{x \cdot y + t \cdot z}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, a, \color{blue}{y \cdot x} + t \cdot z\right) \]

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 74.4

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

   5. Applied rewrites 74.4%

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

   6. Taylor expanded in b around 0

      \[\leadsto t \cdot z + \color{blue}{x \cdot y} \]
   7. Step-by-step derivation

   8. Applied rewrites 69.4%

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

   if 1e164 < (*.f64 a b)

   1. Initial program 88.9%

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

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{a \cdot b + \left(t \cdot z + x \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{b \cdot a} + \left(t \cdot z + x \cdot y\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, a, t \cdot z + x \cdot y\right)} \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, a, \color{blue}{x \cdot y + t \cdot z}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, a, \color{blue}{y \cdot x} + t \cdot z\right) \]

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 86.8

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

   5. Applied rewrites 86.8%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(b, a, x \cdot y\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 81.4%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -2 \cdot 10^{+91}:\\ \;\;\;\;\mathsf{fma}\left(b, a, t \cdot z\right)\\ \mathbf{elif}\;b \cdot a \leq 10^{+164}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, a, y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, a, y \cdot x\right)\\ \mathbf{if}\;b \cdot a \leq -2 \cdot 10^{+214}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot a \leq 10^{+164}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma b a (* y x))))
   (if (<= (* b a) -2e+214)
     t_1
     (if (<= (* b a) 1e+164) (fma y x (* 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(b, a, (y * x));
	double tmp;
	if ((b * a) <= -2e+214) {
		tmp = t_1;
	} else if ((b * a) <= 1e+164) {
		tmp = fma(y, x, (t * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(b, a, Float64(y * x))
	tmp = 0.0
	if (Float64(b * a) <= -2e+214)
		tmp = t_1;
	elseif (Float64(b * a) <= 1e+164)
		tmp = fma(y, x, 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[(b * a + N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -2e+214], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 1e+164], N[(y * x + N[(t * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.9999999999999999e214 or 1e164 < (*.f64 a b)

   1. Initial program 87.3%

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

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{a \cdot b + \left(t \cdot z + x \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{b \cdot a} + \left(t \cdot z + x \cdot y\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, a, t \cdot z + x \cdot y\right)} \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, a, \color{blue}{x \cdot y + t \cdot z}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, a, \color{blue}{y \cdot x} + t \cdot z\right) \]

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 85.8

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

   5. Applied rewrites 85.8%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(b, a, x \cdot y\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 84.3%

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

   if -1.9999999999999999e214 < (*.f64 a b) < 1e164

   1. Initial program 95.8%

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

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{a \cdot b + \left(t \cdot z + x \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{b \cdot a} + \left(t \cdot z + x \cdot y\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, a, t \cdot z + x \cdot y\right)} \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, a, \color{blue}{x \cdot y + t \cdot z}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, a, \color{blue}{y \cdot x} + t \cdot z\right) \]

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 75.8

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

   5. Applied rewrites 75.8%

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

   6. Taylor expanded in b around 0

      \[\leadsto t \cdot z + \color{blue}{x \cdot y} \]
   7. Step-by-step derivation

   8. Applied rewrites 67.3%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{x}, z \cdot t\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -2 \cdot 10^{+214}:\\ \;\;\;\;\mathsf{fma}\left(b, a, y \cdot x\right)\\ \mathbf{elif}\;b \cdot a \leq 10^{+164}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, a, y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -2 \cdot 10^{+214}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;b \cdot a \leq 10^{+164}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* b a) -2e+214)
   (* b a)
   (if (<= (* b a) 1e+164) (fma y x (* t z)) (* b a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b * a) <= -2e+214) {
		tmp = b * a;
	} else if ((b * a) <= 1e+164) {
		tmp = fma(y, x, (t * z));
	} else {
		tmp = b * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(b * a) <= -2e+214)
		tmp = Float64(b * a);
	elseif (Float64(b * a) <= 1e+164)
		tmp = fma(y, x, Float64(t * z));
	else
		tmp = Float64(b * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(b * a), $MachinePrecision], -2e+214], N[(b * a), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 1e+164], N[(y * x + N[(t * z), $MachinePrecision]), $MachinePrecision], N[(b * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.9999999999999999e214 or 1e164 < (*.f64 a b)

   1. Initial program 87.3%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{a \cdot b} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{b \cdot a} \]

      2. lower-*.f64 78.1

         \[\leadsto \color{blue}{b \cdot a} \]

   5. Applied rewrites 78.1%

      \[\leadsto \color{blue}{b \cdot a} \]

   if -1.9999999999999999e214 < (*.f64 a b) < 1e164

   1. Initial program 95.8%

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

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{a \cdot b + \left(t \cdot z + x \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{b \cdot a} + \left(t \cdot z + x \cdot y\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, a, t \cdot z + x \cdot y\right)} \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, a, \color{blue}{x \cdot y + t \cdot z}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, a, \color{blue}{y \cdot x} + t \cdot z\right) \]

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 75.8

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

   5. Applied rewrites 75.8%

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

   6. Taylor expanded in b around 0

      \[\leadsto t \cdot z + \color{blue}{x \cdot y} \]
   7. Step-by-step derivation

   8. Applied rewrites 67.3%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{x}, z \cdot t\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -2 \cdot 10^{+214}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;b \cdot a \leq 10^{+164}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 43.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+72}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;b \cdot a \leq 10^{+86}:\\ \;\;\;\;i \cdot c\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* b a) -1e+72) (* b a) (if (<= (* b a) 1e+86) (* i c) (* b a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b * a) <= -1e+72) {
		tmp = b * a;
	} else if ((b * a) <= 1e+86) {
		tmp = i * c;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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 ((b * a) <= (-1d+72)) then
        tmp = b * a
    else if ((b * a) <= 1d+86) then
        tmp = i * c
    else
        tmp = b * a
    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 ((b * a) <= -1e+72) {
		tmp = b * a;
	} else if ((b * a) <= 1e+86) {
		tmp = i * c;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b * a) <= -1e+72:
		tmp = b * a
	elif (b * a) <= 1e+86:
		tmp = i * c
	else:
		tmp = b * a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(b * a) <= -1e+72)
		tmp = Float64(b * a);
	elseif (Float64(b * a) <= 1e+86)
		tmp = Float64(i * c);
	else
		tmp = Float64(b * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((b * a) <= -1e+72)
		tmp = b * a;
	elseif ((b * a) <= 1e+86)
		tmp = i * c;
	else
		tmp = b * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(b * a), $MachinePrecision], -1e+72], N[(b * a), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 1e+86], N[(i * c), $MachinePrecision], N[(b * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -9.99999999999999944e71 or 1e86 < (*.f64 a b)

   1. Initial program 92.2%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{a \cdot b} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{b \cdot a} \]

      2. lower-*.f64 59.6

         \[\leadsto \color{blue}{b \cdot a} \]

   5. Applied rewrites 59.6%

      \[\leadsto \color{blue}{b \cdot a} \]

   if -9.99999999999999944e71 < (*.f64 a b) < 1e86

   1. Initial program 94.8%

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

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot i} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{i \cdot c} \]

      2. lower-*.f64 31.0

         \[\leadsto \color{blue}{i \cdot c} \]

   5. Applied rewrites 31.0%

      \[\leadsto \color{blue}{i \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+72}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;b \cdot a \leq 10^{+86}:\\ \;\;\;\;i \cdot c\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 27.9% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ b \cdot a \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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 = b * a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.7%

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

3. Taylor expanded in b around inf

   \[\leadsto \color{blue}{a \cdot b} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{b \cdot a} \]

   2. lower-*.f64 27.5

      \[\leadsto \color{blue}{b \cdot a} \]

5. Applied rewrites 27.5%

   \[\leadsto \color{blue}{b \cdot a} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024243 
(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)))