Linear.V3:$cdot from linear-1.19.1.3, B

Percentage Accurate: 97.5% → 98.6%

Time: 4.3s

Alternatives: 6

Speedup: 1.2×

• 33.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(b, a, \mathsf{fma}\left(t, z, y \cdot x\right)\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

   \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 97.3

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

   6. lift-+.f64 N/A

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

   7. +-commutative N/A

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

   8. lift-*.f64 N/A

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

   9. *-commutative N/A

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

   10. lower-fma.f64 98.0

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

   11. lift-*.f64 N/A

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

   12. *-commutative N/A

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

   13. lower-*.f64 98.0

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

4. Applied rewrites 98.0%

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

Alternative 2: 85.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.5 \cdot 10^{+94} \lor \neg \left(x \cdot y \leq 10^{+37}\right):\\ \;\;\;\;\mathsf{fma}\left(y, x, b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, a, t \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -1.5e+94) (not (<= (* x y) 1e+37)))
   (fma y x (* b a))
   (fma b a (* t z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * y) <= -1.5e+94) || !((x * y) <= 1e+37)) {
		tmp = fma(y, x, (b * a));
	} else {
		tmp = fma(b, a, (t * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(x * y) <= -1.5e+94) || !(Float64(x * y) <= 1e+37))
		tmp = fma(y, x, Float64(b * a));
	else
		tmp = fma(b, a, Float64(t * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.5e+94], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1e+37]], $MachinePrecision]], N[(y * x + N[(b * a), $MachinePrecision]), $MachinePrecision], N[(b * a + N[(t * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.5e94 or 9.99999999999999954e36 < (*.f64 x y)

   1. Initial program 91.7%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{x \cdot y + a \cdot b} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{y \cdot x} + a \cdot b \]

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 85.9

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

   5. Applied rewrites 85.9%

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

   if -1.5e94 < (*.f64 x y) < 9.99999999999999954e36

   1. Initial program 99.4%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 100.0

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 100.0

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 90.4

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

   7. Applied rewrites 90.4%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.5 \cdot 10^{+94} \lor \neg \left(x \cdot y \leq 10^{+37}\right):\\ \;\;\;\;\mathsf{fma}\left(y, x, b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, a, t \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-19} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{+22}\right):\\ \;\;\;\;\mathsf{fma}\left(t, z, b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, b \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* z t) -5e-19) (not (<= (* z t) 5e+22)))
   (fma t z (* b a))
   (fma y x (* b a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((z * t) <= -5e-19) || !((z * t) <= 5e+22)) {
		tmp = fma(t, z, (b * a));
	} else {
		tmp = fma(y, x, (b * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(z * t) <= -5e-19) || !(Float64(z * t) <= 5e+22))
		tmp = fma(t, z, Float64(b * a));
	else
		tmp = fma(y, x, Float64(b * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -5e-19], N[Not[LessEqual[N[(z * t), $MachinePrecision], 5e+22]], $MachinePrecision]], N[(t * z + N[(b * a), $MachinePrecision]), $MachinePrecision], N[(y * x + N[(b * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -5.0000000000000004e-19 or 4.9999999999999996e22 < (*.f64 z t)

   1. Initial program 95.4%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{t \cdot z + a \cdot b} \]

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 85.0

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

   5. Applied rewrites 85.0%

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

   if -5.0000000000000004e-19 < (*.f64 z t) < 4.9999999999999996e22

   1. Initial program 97.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{x \cdot y + a \cdot b} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{y \cdot x} + a \cdot b \]

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 92.0

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

   5. Applied rewrites 92.0%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-19} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{+22}\right):\\ \;\;\;\;\mathsf{fma}\left(t, z, b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, b \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-19} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{+22}\right):\\ \;\;\;\;\mathsf{fma}\left(t, z, b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, a, y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* z t) -5e-19) (not (<= (* z t) 5e+22)))
   (fma t z (* b a))
   (fma b a (* y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((z * t) <= -5e-19) || !((z * t) <= 5e+22)) {
		tmp = fma(t, z, (b * a));
	} else {
		tmp = fma(b, a, (y * x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(z * t) <= -5e-19) || !(Float64(z * t) <= 5e+22))
		tmp = fma(t, z, Float64(b * a));
	else
		tmp = fma(b, a, Float64(y * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -5e-19], N[Not[LessEqual[N[(z * t), $MachinePrecision], 5e+22]], $MachinePrecision]], N[(t * z + N[(b * a), $MachinePrecision]), $MachinePrecision], N[(b * a + N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -5.0000000000000004e-19 or 4.9999999999999996e22 < (*.f64 z t)

   1. Initial program 95.4%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{t \cdot z + a \cdot b} \]

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 85.0

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

   5. Applied rewrites 85.0%

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

   if -5.0000000000000004e-19 < (*.f64 z t) < 4.9999999999999996e22

   1. Initial program 97.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{x \cdot y + a \cdot b} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{y \cdot x} + a \cdot b \]

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 92.0

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

   5. Applied rewrites 92.0%

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

   7. Applied rewrites 91.2%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-19} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{+22}\right):\\ \;\;\;\;\mathsf{fma}\left(t, z, b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, a, y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(b, a, y \cdot x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

3. Taylor expanded in z around 0

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

   1. +-commutative N/A

      \[\leadsto \color{blue}{x \cdot y + a \cdot b} \]

   2. *-commutative N/A

      \[\leadsto \color{blue}{y \cdot x} + a \cdot b \]

   3. lower-fma.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 64.8

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

5. Applied rewrites 64.8%

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

7. Applied rewrites 64.0%

   \[\leadsto \mathsf{fma}\left(b, \color{blue}{a}, y \cdot x\right) \]
8. Add Preprocessing

Alternative 6: 36.8% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

3. Taylor expanded in z around 0

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

   1. +-commutative N/A

      \[\leadsto \color{blue}{x \cdot y + a \cdot b} \]

   2. *-commutative N/A

      \[\leadsto \color{blue}{y \cdot x} + a \cdot b \]

   3. lower-fma.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 64.8

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

5. Applied rewrites 64.8%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 35.2%

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

Reproduce

herbie shell --seed 2024339 
(FPCore (x y z t a b)
  :name "Linear.V3:$cdot from linear-1.19.1.3, B"
  :precision binary64
  (+ (+ (* x y) (* z t)) (* a b)))