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

Percentage Accurate: 95.6% → 97.5%

Time: 12.7s

Alternatives: 18

Speedup: 0.5×

• 41.9% 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: 95.6% 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: 97.5% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (+ (+ (* a b) (+ (* x y) (* z t))) (* c i)) INFINITY)
   (+ (fma z t (* a b)) (+ (* x y) (* c i)))
   (fma 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) + ((x * y) + (z * t))) + (c * i)) <= ((double) INFINITY)) {
		tmp = fma(z, t, (a * b)) + ((x * y) + (c * i));
	} else {
		tmp = fma(t, z, (a * b));
	}
	return tmp;
}

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(z * t + N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * z + N[(a * b), $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. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-def 100.0%

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

      5. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. fma-udef 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-def 100.0%

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

      5. associate-+l+ 100.0%

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

      6. fma-udef 100.0%

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

      7. associate-+r+ 100.0%

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

   5. Applied egg-rr 100.0%

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

   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. Taylor expanded in x around 0 31.3%

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

      1. +-commutative 31.3%

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

      2. *-commutative 31.3%

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

      3. fma-def 50.0%

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

   4. Applied egg-rr 50.0%

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

   5. Taylor expanded in c around 0 50.4%

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

      1. fma-def 56.6%

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

   7. Simplified 56.6%

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

   8. Taylor expanded in a around 0 50.4%

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

      1. +-commutative 50.4%

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

      2. fma-def 69.1%

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

   10. Simplified 69.1%

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

4. Final simplification 98.1%

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

Alternative 2: 97.8% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 93.7%

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

   1. +-commutative 93.7%

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

   2. fma-def 95.3%

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

   3. associate-+l+ 95.3%

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

   4. fma-def 96.9%

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

   5. fma-def 98.0%

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

3. Simplified 98.0%

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

4. Final simplification 98.0%

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

Alternative 3: 97.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   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. Taylor expanded in x around 0 31.3%

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

      1. +-commutative 31.3%

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

      2. *-commutative 31.3%

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

      3. fma-def 50.0%

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

   4. Applied egg-rr 50.0%

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

   5. Taylor expanded in c around 0 50.4%

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

      1. fma-def 56.6%

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

   7. Simplified 56.6%

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

4. Final simplification 97.3%

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

Alternative 4: 97.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   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. Step-by-step derivation

      1. +-commutative 0.0%

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

      2. fma-def 25.0%

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

      3. +-commutative 25.0%

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

      4. fma-def 31.3%

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

      5. fma-def 43.8%

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

   3. Simplified 43.8%

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

      1. fma-udef 37.5%

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

      2. fma-def 25.0%

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

      3. associate-+r+ 25.0%

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

   5. Applied egg-rr 25.0%

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

   6. Taylor expanded in a around inf 62.8%

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

4. Final simplification 97.7%

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

Alternative 5: 97.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   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. Taylor expanded in x around 0 31.3%

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

      1. +-commutative 31.3%

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

      2. *-commutative 31.3%

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

      3. fma-def 50.0%

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

   4. Applied egg-rr 50.0%

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

   5. Taylor expanded in c around 0 50.4%

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

      1. fma-def 56.6%

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

   7. Simplified 56.6%

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

   8. Taylor expanded in a around 0 50.4%

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

      1. +-commutative 50.4%

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

      2. fma-def 69.1%

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

   10. Simplified 69.1%

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

4. Final simplification 98.1%

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

Alternative 6: 64.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := a \cdot b + x \cdot y\\ \mathbf{if}\;c \cdot i \leq -2.8 \cdot 10^{+181}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq -7.2 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq -1.45 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq -1.6 \cdot 10^{-253}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq 4.9 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))) (t_2 (+ (* a b) (* x y))))
   (if (<= (* c i) -2.8e+181)
     (* c i)
     (if (<= (* c i) -2e+56)
       t_1
       (if (<= (* c i) -7.2e+14)
         t_2
         (if (<= (* c i) -1.45e-98)
           t_1
           (if (<= (* c i) -1.6e-253)
             t_2
             (if (<= (* c i) 4.9e+66) t_1 (+ (* a b) (* c i))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if ((c * i) <= -2.8e+181) {
		tmp = c * i;
	} else if ((c * i) <= -2e+56) {
		tmp = t_1;
	} else if ((c * i) <= -7.2e+14) {
		tmp = t_2;
	} else if ((c * i) <= -1.45e-98) {
		tmp = t_1;
	} else if ((c * i) <= -1.6e-253) {
		tmp = t_2;
	} else if ((c * i) <= 4.9e+66) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (c * i);
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    t_2 = (a * b) + (x * y)
    if ((c * i) <= (-2.8d+181)) then
        tmp = c * i
    else if ((c * i) <= (-2d+56)) then
        tmp = t_1
    else if ((c * i) <= (-7.2d+14)) then
        tmp = t_2
    else if ((c * i) <= (-1.45d-98)) then
        tmp = t_1
    else if ((c * i) <= (-1.6d-253)) then
        tmp = t_2
    else if ((c * i) <= 4.9d+66) then
        tmp = t_1
    else
        tmp = (a * b) + (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 t_1 = (a * b) + (z * t);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if ((c * i) <= -2.8e+181) {
		tmp = c * i;
	} else if ((c * i) <= -2e+56) {
		tmp = t_1;
	} else if ((c * i) <= -7.2e+14) {
		tmp = t_2;
	} else if ((c * i) <= -1.45e-98) {
		tmp = t_1;
	} else if ((c * i) <= -1.6e-253) {
		tmp = t_2;
	} else if ((c * i) <= 4.9e+66) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	t_2 = (a * b) + (x * y)
	tmp = 0
	if (c * i) <= -2.8e+181:
		tmp = c * i
	elif (c * i) <= -2e+56:
		tmp = t_1
	elif (c * i) <= -7.2e+14:
		tmp = t_2
	elif (c * i) <= -1.45e-98:
		tmp = t_1
	elif (c * i) <= -1.6e-253:
		tmp = t_2
	elif (c * i) <= 4.9e+66:
		tmp = t_1
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(x * y))
	tmp = 0.0
	if (Float64(c * i) <= -2.8e+181)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -2e+56)
		tmp = t_1;
	elseif (Float64(c * i) <= -7.2e+14)
		tmp = t_2;
	elseif (Float64(c * i) <= -1.45e-98)
		tmp = t_1;
	elseif (Float64(c * i) <= -1.6e-253)
		tmp = t_2;
	elseif (Float64(c * i) <= 4.9e+66)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * b) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	t_2 = (a * b) + (x * y);
	tmp = 0.0;
	if ((c * i) <= -2.8e+181)
		tmp = c * i;
	elseif ((c * i) <= -2e+56)
		tmp = t_1;
	elseif ((c * i) <= -7.2e+14)
		tmp = t_2;
	elseif ((c * i) <= -1.45e-98)
		tmp = t_1;
	elseif ((c * i) <= -1.6e-253)
		tmp = t_2;
	elseif ((c * i) <= 4.9e+66)
		tmp = t_1;
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -2.8e+181], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -2e+56], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -7.2e+14], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], -1.45e-98], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -1.6e-253], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 4.9e+66], t$95$1, N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -2.79999999999999984e181

   1. Initial program 85.7%

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

   2. Taylor expanded in c around inf 69.3%

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

   if -2.79999999999999984e181 < (*.f64 c i) < -2.00000000000000018e56 or -7.2e14 < (*.f64 c i) < -1.45e-98 or -1.5999999999999999e-253 < (*.f64 c i) < 4.89999999999999975e66

   1. Initial program 96.4%

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

   2. Taylor expanded in x around 0 75.7%

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

      1. +-commutative 75.7%

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

      2. *-commutative 75.7%

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

      3. fma-def 77.9%

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

   4. Applied egg-rr 77.9%

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

   5. Taylor expanded in c around 0 72.5%

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

   if -2.00000000000000018e56 < (*.f64 c i) < -7.2e14 or -1.45e-98 < (*.f64 c i) < -1.5999999999999999e-253

   1. Initial program 95.5%

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

   2. Taylor expanded in z around 0 84.6%

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

   3. Taylor expanded in c around 0 82.4%

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

   if 4.89999999999999975e66 < (*.f64 c i)

   1. Initial program 88.2%

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

   2. Taylor expanded in a around inf 77.3%

      \[\leadsto \color{blue}{a \cdot b} + c \cdot i \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.8 \cdot 10^{+181}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2 \cdot 10^{+56}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -7.2 \cdot 10^{+14}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -1.45 \cdot 10^{-98}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -1.6 \cdot 10^{-253}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 4.9 \cdot 10^{+66}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]

Alternative 7: 96.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((a * b) + ((x * y) + (z * t))) + (c * i);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((a * b) + ((x * y) + (z * t))) + (c * i)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = a * b
	return tmp

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((a * b) + ((x * y) + (z * t))) + (c * i);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

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

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

   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. Taylor expanded in x around 0 31.3%

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

      1. +-commutative 31.3%

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

      2. *-commutative 31.3%

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

      3. fma-def 50.0%

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

   4. Applied egg-rr 50.0%

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

   5. Taylor expanded in a around inf 50.8%

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

4. Final simplification 96.9%

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

Alternative 8: 42.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.08 \cdot 10^{+247}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.55 \cdot 10^{-53}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -9.2 \cdot 10^{-222}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 4.4 \cdot 10^{-282}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 2.45 \cdot 10^{-231}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 3.6 \cdot 10^{+71}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1.08e+247)
   (* c i)
   (if (<= (* c i) -2.55e-53)
     (* z t)
     (if (<= (* c i) -9.2e-222)
       (* a b)
       (if (<= (* c i) 4.4e-282)
         (* z t)
         (if (<= (* c i) 2.45e-231)
           (* a b)
           (if (<= (* c i) 3.6e+71) (* z t) (* 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) <= -1.08e+247) {
		tmp = c * i;
	} else if ((c * i) <= -2.55e-53) {
		tmp = z * t;
	} else if ((c * i) <= -9.2e-222) {
		tmp = a * b;
	} else if ((c * i) <= 4.4e-282) {
		tmp = z * t;
	} else if ((c * i) <= 2.45e-231) {
		tmp = a * b;
	} else if ((c * i) <= 3.6e+71) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	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 ((c * i) <= (-1.08d+247)) then
        tmp = c * i
    else if ((c * i) <= (-2.55d-53)) then
        tmp = z * t
    else if ((c * i) <= (-9.2d-222)) then
        tmp = a * b
    else if ((c * i) <= 4.4d-282) then
        tmp = z * t
    else if ((c * i) <= 2.45d-231) then
        tmp = a * b
    else if ((c * i) <= 3.6d+71) then
        tmp = z * t
    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) <= -1.08e+247) {
		tmp = c * i;
	} else if ((c * i) <= -2.55e-53) {
		tmp = z * t;
	} else if ((c * i) <= -9.2e-222) {
		tmp = a * b;
	} else if ((c * i) <= 4.4e-282) {
		tmp = z * t;
	} else if ((c * i) <= 2.45e-231) {
		tmp = a * b;
	} else if ((c * i) <= 3.6e+71) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1.08e+247:
		tmp = c * i
	elif (c * i) <= -2.55e-53:
		tmp = z * t
	elif (c * i) <= -9.2e-222:
		tmp = a * b
	elif (c * i) <= 4.4e-282:
		tmp = z * t
	elif (c * i) <= 2.45e-231:
		tmp = a * b
	elif (c * i) <= 3.6e+71:
		tmp = z * t
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -1.08e+247)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -2.55e-53)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= -9.2e-222)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 4.4e-282)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 2.45e-231)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 3.6e+71)
		tmp = Float64(z * t);
	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) <= -1.08e+247)
		tmp = c * i;
	elseif ((c * i) <= -2.55e-53)
		tmp = z * t;
	elseif ((c * i) <= -9.2e-222)
		tmp = a * b;
	elseif ((c * i) <= 4.4e-282)
		tmp = z * t;
	elseif ((c * i) <= 2.45e-231)
		tmp = a * b;
	elseif ((c * i) <= 3.6e+71)
		tmp = z * t;
	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], -1.08e+247], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -2.55e-53], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -9.2e-222], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4.4e-282], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.45e-231], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 3.6e+71], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.08e247 or 3.6e71 < (*.f64 c i)

   1. Initial program 87.5%

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

   2. Taylor expanded in c around inf 72.2%

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

   if -1.08e247 < (*.f64 c i) < -2.55000000000000022e-53 or -9.2000000000000005e-222 < (*.f64 c i) < 4.39999999999999962e-282 or 2.45000000000000002e-231 < (*.f64 c i) < 3.6e71

   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 70.4%

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

      1. +-commutative 70.4%

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

      2. *-commutative 70.4%

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

      3. fma-def 72.5%

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

   4. Applied egg-rr 72.5%

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

   5. Taylor expanded in z around inf 44.8%

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

   if -2.55000000000000022e-53 < (*.f64 c i) < -9.2000000000000005e-222 or 4.39999999999999962e-282 < (*.f64 c i) < 2.45000000000000002e-231

   1. Initial program 95.6%

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

   2. Taylor expanded in x around 0 69.7%

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

      1. +-commutative 69.7%

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

      2. *-commutative 69.7%

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

      3. fma-def 69.7%

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

   4. Applied egg-rr 69.7%

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

   5. Taylor expanded in a around inf 57.0%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.08 \cdot 10^{+247}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.55 \cdot 10^{-53}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -9.2 \cdot 10^{-222}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 4.4 \cdot 10^{-282}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 2.45 \cdot 10^{-231}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 3.6 \cdot 10^{+71}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 9: 83.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -2.1 \cdot 10^{+191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -1.6 \cdot 10^{+146}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -2.1 \cdot 10^{+81}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.55 \cdot 10^{+175}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* x y))))
   (if (<= (* x y) -2.1e+191)
     t_1
     (if (<= (* x y) -1.6e+146)
       (+ (* c i) (* z t))
       (if (<= (* x y) -2.1e+81)
         (+ (* x y) (* z t))
         (if (<= (* x y) 1.55e+175) (+ (* c i) (+ (* a b) (* z t))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (x * y);
	double tmp;
	if ((x * y) <= -2.1e+191) {
		tmp = t_1;
	} else if ((x * y) <= -1.6e+146) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= -2.1e+81) {
		tmp = (x * y) + (z * t);
	} else if ((x * y) <= 1.55e+175) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (x * y)
    if ((x * y) <= (-2.1d+191)) then
        tmp = t_1
    else if ((x * y) <= (-1.6d+146)) then
        tmp = (c * i) + (z * t)
    else if ((x * y) <= (-2.1d+81)) then
        tmp = (x * y) + (z * t)
    else if ((x * y) <= 1.55d+175) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = t_1
    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 t_1 = (a * b) + (x * y);
	double tmp;
	if ((x * y) <= -2.1e+191) {
		tmp = t_1;
	} else if ((x * y) <= -1.6e+146) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= -2.1e+81) {
		tmp = (x * y) + (z * t);
	} else if ((x * y) <= 1.55e+175) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (x * y)
	tmp = 0
	if (x * y) <= -2.1e+191:
		tmp = t_1
	elif (x * y) <= -1.6e+146:
		tmp = (c * i) + (z * t)
	elif (x * y) <= -2.1e+81:
		tmp = (x * y) + (z * t)
	elif (x * y) <= 1.55e+175:
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -2.1e+191)
		tmp = t_1;
	elseif (Float64(x * y) <= -1.6e+146)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(x * y) <= -2.1e+81)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	elseif (Float64(x * y) <= 1.55e+175)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (x * y);
	tmp = 0.0;
	if ((x * y) <= -2.1e+191)
		tmp = t_1;
	elseif ((x * y) <= -1.6e+146)
		tmp = (c * i) + (z * t);
	elseif ((x * y) <= -2.1e+81)
		tmp = (x * y) + (z * t);
	elseif ((x * y) <= 1.55e+175)
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.1e+191], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1.6e+146], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2.1e+81], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.55e+175], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -2.1000000000000001e191 or 1.54999999999999992e175 < (*.f64 x y)

   1. Initial program 83.8%

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

   2. Taylor expanded in z around 0 80.3%

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

   3. Taylor expanded in c around 0 78.9%

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

   if -2.1000000000000001e191 < (*.f64 x y) < -1.6e146

   1. Initial program 90.9%

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

   2. Taylor expanded in z around inf 77.6%

      \[\leadsto \color{blue}{t \cdot z} + c \cdot i \]

   if -1.6e146 < (*.f64 x y) < -2.0999999999999999e81

   1. Initial program 87.5%

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

   2. Taylor expanded in a around 0 87.5%

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

      1. *-commutative 87.5%

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

      2. fma-def 87.5%

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

   4. Applied egg-rr 87.5%

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

   5. Taylor expanded in c around 0 87.5%

      \[\leadsto \color{blue}{t \cdot z + x \cdot y} \]

   if -2.0999999999999999e81 < (*.f64 x y) < 1.54999999999999992e175

   1. Initial program 98.2%

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

   2. Taylor expanded in x around 0 89.2%

      \[\leadsto \color{blue}{\left(a \cdot b + t \cdot z\right)} + c \cdot i \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.1 \cdot 10^{+191}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.6 \cdot 10^{+146}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -2.1 \cdot 10^{+81}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.55 \cdot 10^{+175}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]

Alternative 10: 67.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -3.3 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq -2.7 \cdot 10^{-218}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 0:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.8 \cdot 10^{+71}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))))
   (if (<= (* c i) -3.3e+103)
     t_1
     (if (<= (* c i) -2.7e-218)
       (+ (* a b) (* x y))
       (if (<= (* c i) 0.0)
         (+ (* x y) (* z t))
         (if (<= (* c i) 1.8e+71) (+ (* a b) (* z t)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double tmp;
	if ((c * i) <= -3.3e+103) {
		tmp = t_1;
	} else if ((c * i) <= -2.7e-218) {
		tmp = (a * b) + (x * y);
	} else if ((c * i) <= 0.0) {
		tmp = (x * y) + (z * t);
	} else if ((c * i) <= 1.8e+71) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (c * i) + (z * t)
    if ((c * i) <= (-3.3d+103)) then
        tmp = t_1
    else if ((c * i) <= (-2.7d-218)) then
        tmp = (a * b) + (x * y)
    else if ((c * i) <= 0.0d0) then
        tmp = (x * y) + (z * t)
    else if ((c * i) <= 1.8d+71) then
        tmp = (a * b) + (z * t)
    else
        tmp = t_1
    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 t_1 = (c * i) + (z * t);
	double tmp;
	if ((c * i) <= -3.3e+103) {
		tmp = t_1;
	} else if ((c * i) <= -2.7e-218) {
		tmp = (a * b) + (x * y);
	} else if ((c * i) <= 0.0) {
		tmp = (x * y) + (z * t);
	} else if ((c * i) <= 1.8e+71) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	tmp = 0
	if (c * i) <= -3.3e+103:
		tmp = t_1
	elif (c * i) <= -2.7e-218:
		tmp = (a * b) + (x * y)
	elif (c * i) <= 0.0:
		tmp = (x * y) + (z * t)
	elif (c * i) <= 1.8e+71:
		tmp = (a * b) + (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -3.3e+103)
		tmp = t_1;
	elseif (Float64(c * i) <= -2.7e-218)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (Float64(c * i) <= 0.0)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	elseif (Float64(c * i) <= 1.8e+71)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -3.3e+103)
		tmp = t_1;
	elseif ((c * i) <= -2.7e-218)
		tmp = (a * b) + (x * y);
	elseif ((c * i) <= 0.0)
		tmp = (x * y) + (z * t);
	elseif ((c * i) <= 1.8e+71)
		tmp = (a * b) + (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -3.3e+103], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -2.7e-218], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 0.0], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.8e+71], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -3.30000000000000009e103 or 1.8e71 < (*.f64 c i)

   1. Initial program 88.9%

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

   2. Taylor expanded in z around inf 78.7%

      \[\leadsto \color{blue}{t \cdot z} + c \cdot i \]

   if -3.30000000000000009e103 < (*.f64 c i) < -2.7e-218

   1. Initial program 95.8%

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

   2. Taylor expanded in z around 0 74.9%

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

   3. Taylor expanded in c around 0 72.3%

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

   if -2.7e-218 < (*.f64 c i) < 0.0

   1. Initial program 94.8%

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

   2. Taylor expanded in a around 0 80.1%

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

      1. *-commutative 80.1%

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

      2. fma-def 80.1%

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

   4. Applied egg-rr 80.1%

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

   5. Taylor expanded in c around 0 80.1%

      \[\leadsto \color{blue}{t \cdot z + x \cdot y} \]

   if 0.0 < (*.f64 c i) < 1.8e71

   1. Initial program 96.8%

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

   2. Taylor expanded in x around 0 76.1%

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

      1. +-commutative 76.1%

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

      2. *-commutative 76.1%

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

      3. fma-def 77.7%

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

   4. Applied egg-rr 77.7%

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

   5. Taylor expanded in c around 0 74.0%

      \[\leadsto \color{blue}{a \cdot b + t \cdot z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.3 \cdot 10^{+103}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -2.7 \cdot 10^{-218}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 0:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.8 \cdot 10^{+71}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]

Alternative 11: 38.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+66}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+38}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+35}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-114}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-192}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-263}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-300}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-194}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-10}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2e+66)
   (* z t)
   (if (<= z -2.2e+38)
     (* c i)
     (if (<= z -1.25e+35)
       (* z t)
       (if (<= z -7.5e-114)
         (* x y)
         (if (<= z -2.6e-192)
           (* c i)
           (if (<= z -1.25e-263)
             (* x y)
             (if (<= z 3.6e-300)
               (* c i)
               (if (<= z 3e-194)
                 (* x y)
                 (if (<= z 3.9e-10) (* a b) (* z t)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2e+66) {
		tmp = z * t;
	} else if (z <= -2.2e+38) {
		tmp = c * i;
	} else if (z <= -1.25e+35) {
		tmp = z * t;
	} else if (z <= -7.5e-114) {
		tmp = x * y;
	} else if (z <= -2.6e-192) {
		tmp = c * i;
	} else if (z <= -1.25e-263) {
		tmp = x * y;
	} else if (z <= 3.6e-300) {
		tmp = c * i;
	} else if (z <= 3e-194) {
		tmp = x * y;
	} else if (z <= 3.9e-10) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	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 (z <= (-2d+66)) then
        tmp = z * t
    else if (z <= (-2.2d+38)) then
        tmp = c * i
    else if (z <= (-1.25d+35)) then
        tmp = z * t
    else if (z <= (-7.5d-114)) then
        tmp = x * y
    else if (z <= (-2.6d-192)) then
        tmp = c * i
    else if (z <= (-1.25d-263)) then
        tmp = x * y
    else if (z <= 3.6d-300) then
        tmp = c * i
    else if (z <= 3d-194) then
        tmp = x * y
    else if (z <= 3.9d-10) then
        tmp = a * b
    else
        tmp = z * t
    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 (z <= -2e+66) {
		tmp = z * t;
	} else if (z <= -2.2e+38) {
		tmp = c * i;
	} else if (z <= -1.25e+35) {
		tmp = z * t;
	} else if (z <= -7.5e-114) {
		tmp = x * y;
	} else if (z <= -2.6e-192) {
		tmp = c * i;
	} else if (z <= -1.25e-263) {
		tmp = x * y;
	} else if (z <= 3.6e-300) {
		tmp = c * i;
	} else if (z <= 3e-194) {
		tmp = x * y;
	} else if (z <= 3.9e-10) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2e+66:
		tmp = z * t
	elif z <= -2.2e+38:
		tmp = c * i
	elif z <= -1.25e+35:
		tmp = z * t
	elif z <= -7.5e-114:
		tmp = x * y
	elif z <= -2.6e-192:
		tmp = c * i
	elif z <= -1.25e-263:
		tmp = x * y
	elif z <= 3.6e-300:
		tmp = c * i
	elif z <= 3e-194:
		tmp = x * y
	elif z <= 3.9e-10:
		tmp = a * b
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2e+66)
		tmp = Float64(z * t);
	elseif (z <= -2.2e+38)
		tmp = Float64(c * i);
	elseif (z <= -1.25e+35)
		tmp = Float64(z * t);
	elseif (z <= -7.5e-114)
		tmp = Float64(x * y);
	elseif (z <= -2.6e-192)
		tmp = Float64(c * i);
	elseif (z <= -1.25e-263)
		tmp = Float64(x * y);
	elseif (z <= 3.6e-300)
		tmp = Float64(c * i);
	elseif (z <= 3e-194)
		tmp = Float64(x * y);
	elseif (z <= 3.9e-10)
		tmp = Float64(a * b);
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2e+66)
		tmp = z * t;
	elseif (z <= -2.2e+38)
		tmp = c * i;
	elseif (z <= -1.25e+35)
		tmp = z * t;
	elseif (z <= -7.5e-114)
		tmp = x * y;
	elseif (z <= -2.6e-192)
		tmp = c * i;
	elseif (z <= -1.25e-263)
		tmp = x * y;
	elseif (z <= 3.6e-300)
		tmp = c * i;
	elseif (z <= 3e-194)
		tmp = x * y;
	elseif (z <= 3.9e-10)
		tmp = a * b;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2e+66], N[(z * t), $MachinePrecision], If[LessEqual[z, -2.2e+38], N[(c * i), $MachinePrecision], If[LessEqual[z, -1.25e+35], N[(z * t), $MachinePrecision], If[LessEqual[z, -7.5e-114], N[(x * y), $MachinePrecision], If[LessEqual[z, -2.6e-192], N[(c * i), $MachinePrecision], If[LessEqual[z, -1.25e-263], N[(x * y), $MachinePrecision], If[LessEqual[z, 3.6e-300], N[(c * i), $MachinePrecision], If[LessEqual[z, 3e-194], N[(x * y), $MachinePrecision], If[LessEqual[z, 3.9e-10], N[(a * b), $MachinePrecision], N[(z * t), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.99999999999999989e66 or -2.20000000000000006e38 < z < -1.25000000000000005e35 or 3.9e-10 < z

   1. Initial program 89.1%

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

   2. Taylor expanded in x around 0 80.2%

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

      1. +-commutative 80.2%

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

      2. *-commutative 80.2%

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

      3. fma-def 82.5%

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

   4. Applied egg-rr 82.5%

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

   5. Taylor expanded in z around inf 56.5%

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

   if -1.99999999999999989e66 < z < -2.20000000000000006e38 or -7.5000000000000002e-114 < z < -2.6000000000000002e-192 or -1.25000000000000002e-263 < z < 3.60000000000000016e-300

   1. Initial program 96.6%

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

   2. Taylor expanded in c around inf 64.5%

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

   if -1.25000000000000005e35 < z < -7.5000000000000002e-114 or -2.6000000000000002e-192 < z < -1.25000000000000002e-263 or 3.60000000000000016e-300 < z < 3e-194

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 92.0%

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

   3. Taylor expanded in x around inf 44.0%

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

   if 3e-194 < z < 3.9e-10

   1. Initial program 97.0%

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

   2. Taylor expanded in x around 0 76.8%

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

      1. +-commutative 76.8%

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

      2. *-commutative 76.8%

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

      3. fma-def 76.8%

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

   4. Applied egg-rr 76.8%

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

   5. Taylor expanded in a around inf 52.2%

      \[\leadsto \color{blue}{a \cdot b} \]
3. Recombined 4 regimes into one program.

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+66}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+38}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+35}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-114}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-192}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-263}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-300}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-194}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-10}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]

Alternative 12: 66.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq -4 \cdot 10^{-254}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 5.6 \cdot 10^{+68}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))))
   (if (<= (* c i) -1e+103)
     t_1
     (if (<= (* c i) -4e-254)
       (+ (* a b) (* x y))
       (if (<= (* c i) 5.6e+68) (+ (* a b) (* z t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double tmp;
	if ((c * i) <= -1e+103) {
		tmp = t_1;
	} else if ((c * i) <= -4e-254) {
		tmp = (a * b) + (x * y);
	} else if ((c * i) <= 5.6e+68) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (c * i) + (z * t)
    if ((c * i) <= (-1d+103)) then
        tmp = t_1
    else if ((c * i) <= (-4d-254)) then
        tmp = (a * b) + (x * y)
    else if ((c * i) <= 5.6d+68) then
        tmp = (a * b) + (z * t)
    else
        tmp = t_1
    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 t_1 = (c * i) + (z * t);
	double tmp;
	if ((c * i) <= -1e+103) {
		tmp = t_1;
	} else if ((c * i) <= -4e-254) {
		tmp = (a * b) + (x * y);
	} else if ((c * i) <= 5.6e+68) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	tmp = 0
	if (c * i) <= -1e+103:
		tmp = t_1
	elif (c * i) <= -4e-254:
		tmp = (a * b) + (x * y)
	elif (c * i) <= 5.6e+68:
		tmp = (a * b) + (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -1e+103)
		tmp = t_1;
	elseif (Float64(c * i) <= -4e-254)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (Float64(c * i) <= 5.6e+68)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -1e+103)
		tmp = t_1;
	elseif ((c * i) <= -4e-254)
		tmp = (a * b) + (x * y);
	elseif ((c * i) <= 5.6e+68)
		tmp = (a * b) + (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -1e+103], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -4e-254], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5.6e+68], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1e103 or 5.6e68 < (*.f64 c i)

   1. Initial program 88.9%

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

   2. Taylor expanded in z around inf 78.7%

      \[\leadsto \color{blue}{t \cdot z} + c \cdot i \]

   if -1e103 < (*.f64 c i) < -3.9999999999999996e-254

   1. Initial program 96.2%

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

   2. Taylor expanded in z around 0 73.2%

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

   3. Taylor expanded in c around 0 70.8%

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

   if -3.9999999999999996e-254 < (*.f64 c i) < 5.6e68

   1. Initial program 95.8%

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

   2. Taylor expanded in x around 0 72.4%

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

      1. +-commutative 72.4%

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

      2. *-commutative 72.4%

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

      3. fma-def 75.5%

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

   4. Applied egg-rr 75.5%

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

   5. Taylor expanded in c around 0 71.0%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+103}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -4 \cdot 10^{-254}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 5.6 \cdot 10^{+68}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]

Alternative 13: 87.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.5 \cdot 10^{+77} \lor \neg \left(x \cdot y \leq 4.8 \cdot 10^{+175}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -6.5e+77) (not (<= (* x y) 4.8e+175)))
   (+ (* c i) (+ (* a b) (* x y)))
   (+ (* c i) (+ (* a b) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -6.5e+77) || !((x * y) <= 4.8e+175)) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	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 (((x * y) <= (-6.5d+77)) .or. (.not. ((x * y) <= 4.8d+175))) then
        tmp = (c * i) + ((a * b) + (x * y))
    else
        tmp = (c * i) + ((a * b) + (z * t))
    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 (((x * y) <= -6.5e+77) || !((x * y) <= 4.8e+175)) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -6.5e+77) or not ((x * y) <= 4.8e+175):
		tmp = (c * i) + ((a * b) + (x * y))
	else:
		tmp = (c * i) + ((a * b) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -6.5e+77) || !(Float64(x * y) <= 4.8e+175))
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -6.5e+77) || ~(((x * y) <= 4.8e+175)))
		tmp = (c * i) + ((a * b) + (x * y));
	else
		tmp = (c * i) + ((a * b) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -6.5e+77], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4.8e+175]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -6.5e77 or 4.8e175 < (*.f64 x y)

   1. Initial program 85.4%

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

   2. Taylor expanded in z around 0 77.8%

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

   if -6.5e77 < (*.f64 x y) < 4.8e175

   1. Initial program 98.2%

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

   2. Taylor expanded in x around 0 89.7%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.5 \cdot 10^{+77} \lor \neg \left(x \cdot y \leq 4.8 \cdot 10^{+175}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]

Alternative 14: 87.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.2 \cdot 10^{+29} \lor \neg \left(x \cdot y \leq 3200000000000\right):\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -6.2e+29) (not (<= (* x y) 3200000000000.0)))
   (+ (* c i) (+ (* x y) (* z t)))
   (+ (* c i) (+ (* a b) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -6.2e+29) || !((x * y) <= 3200000000000.0)) {
		tmp = (c * i) + ((x * y) + (z * t));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	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 (((x * y) <= (-6.2d+29)) .or. (.not. ((x * y) <= 3200000000000.0d0))) then
        tmp = (c * i) + ((x * y) + (z * t))
    else
        tmp = (c * i) + ((a * b) + (z * t))
    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 (((x * y) <= -6.2e+29) || !((x * y) <= 3200000000000.0)) {
		tmp = (c * i) + ((x * y) + (z * t));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -6.2e+29) or not ((x * y) <= 3200000000000.0):
		tmp = (c * i) + ((x * y) + (z * t))
	else:
		tmp = (c * i) + ((a * b) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -6.2e+29) || !(Float64(x * y) <= 3200000000000.0))
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -6.2e+29) || ~(((x * y) <= 3200000000000.0)))
		tmp = (c * i) + ((x * y) + (z * t));
	else
		tmp = (c * i) + ((a * b) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -6.2e+29], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3200000000000.0]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -6.1999999999999998e29 or 3.2e12 < (*.f64 x y)

   1. Initial program 89.4%

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

   2. Taylor expanded in a around 0 79.2%

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

   if -6.1999999999999998e29 < (*.f64 x y) < 3.2e12

   1. Initial program 98.4%

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

   2. Taylor expanded in x around 0 95.3%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.2 \cdot 10^{+29} \lor \neg \left(x \cdot y \leq 3200000000000\right):\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]

Alternative 15: 51.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{-77}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+24}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+218}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= t -2.4e-77)
     (* z t)
     (if (<= t 4.1e-10)
       t_1
       (if (<= t 6e+24) (* x y) (if (<= t 1.3e+218) t_1 (* z t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double tmp;
	if (t <= -2.4e-77) {
		tmp = z * t;
	} else if (t <= 4.1e-10) {
		tmp = t_1;
	} else if (t <= 6e+24) {
		tmp = x * y;
	} else if (t <= 1.3e+218) {
		tmp = t_1;
	} else {
		tmp = z * t;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (c * i)
    if (t <= (-2.4d-77)) then
        tmp = z * t
    else if (t <= 4.1d-10) then
        tmp = t_1
    else if (t <= 6d+24) then
        tmp = x * y
    else if (t <= 1.3d+218) then
        tmp = t_1
    else
        tmp = z * t
    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 t_1 = (a * b) + (c * i);
	double tmp;
	if (t <= -2.4e-77) {
		tmp = z * t;
	} else if (t <= 4.1e-10) {
		tmp = t_1;
	} else if (t <= 6e+24) {
		tmp = x * y;
	} else if (t <= 1.3e+218) {
		tmp = t_1;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	tmp = 0
	if t <= -2.4e-77:
		tmp = z * t
	elif t <= 4.1e-10:
		tmp = t_1
	elif t <= 6e+24:
		tmp = x * y
	elif t <= 1.3e+218:
		tmp = t_1
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (t <= -2.4e-77)
		tmp = Float64(z * t);
	elseif (t <= 4.1e-10)
		tmp = t_1;
	elseif (t <= 6e+24)
		tmp = Float64(x * y);
	elseif (t <= 1.3e+218)
		tmp = t_1;
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (c * i);
	tmp = 0.0;
	if (t <= -2.4e-77)
		tmp = z * t;
	elseif (t <= 4.1e-10)
		tmp = t_1;
	elseif (t <= 6e+24)
		tmp = x * y;
	elseif (t <= 1.3e+218)
		tmp = t_1;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.4e-77], N[(z * t), $MachinePrecision], If[LessEqual[t, 4.1e-10], t$95$1, If[LessEqual[t, 6e+24], N[(x * y), $MachinePrecision], If[LessEqual[t, 1.3e+218], t$95$1, N[(z * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.3999999999999999e-77 or 1.30000000000000001e218 < t

   1. Initial program 92.1%

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

   2. Taylor expanded in x around 0 80.3%

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

      1. +-commutative 80.3%

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

      2. *-commutative 80.3%

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

      3. fma-def 82.3%

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

   4. Applied egg-rr 82.3%

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

   5. Taylor expanded in z around inf 52.6%

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

   if -2.3999999999999999e-77 < t < 4.0999999999999998e-10 or 5.9999999999999999e24 < t < 1.30000000000000001e218

   1. Initial program 94.5%

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

   2. Taylor expanded in a around inf 56.1%

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

   if 4.0999999999999998e-10 < t < 5.9999999999999999e24

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 57.2%

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

   3. Taylor expanded in x around inf 46.5%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-77}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-10}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+24}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+218}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]

Alternative 16: 64.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4.8 \cdot 10^{+185}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 1.05 \cdot 10^{+67}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -4.8e+185)
   (* c i)
   (if (<= (* c i) 1.05e+67) (+ (* a b) (* 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) {
	double tmp;
	if ((c * i) <= -4.8e+185) {
		tmp = c * i;
	} else if ((c * i) <= 1.05e+67) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (a * b) + (c * i);
	}
	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 ((c * i) <= (-4.8d+185)) then
        tmp = c * i
    else if ((c * i) <= 1.05d+67) then
        tmp = (a * b) + (z * t)
    else
        tmp = (a * b) + (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) <= -4.8e+185) {
		tmp = c * i;
	} else if ((c * i) <= 1.05e+67) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -4.8e+185:
		tmp = c * i
	elif (c * i) <= 1.05e+67:
		tmp = (a * b) + (z * t)
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -4.8e+185)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 1.05e+67)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	else
		tmp = Float64(Float64(a * b) + 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) <= -4.8e+185)
		tmp = c * i;
	elseif ((c * i) <= 1.05e+67)
		tmp = (a * b) + (z * t);
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -4.8e+185], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.05e+67], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -4.79999999999999978e185

   1. Initial program 85.7%

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

   2. Taylor expanded in c around inf 69.3%

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

   if -4.79999999999999978e185 < (*.f64 c i) < 1.0500000000000001e67

   1. Initial program 96.2%

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

   2. Taylor expanded in x around 0 70.3%

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

      1. +-commutative 70.3%

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

      2. *-commutative 70.3%

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

      3. fma-def 72.0%

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

   4. Applied egg-rr 72.0%

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

   5. Taylor expanded in c around 0 67.4%

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

   if 1.0500000000000001e67 < (*.f64 c i)

   1. Initial program 88.2%

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

   2. Taylor expanded in a around inf 77.3%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4.8 \cdot 10^{+185}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 1.05 \cdot 10^{+67}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]

Alternative 17: 42.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.5 \cdot 10^{+103} \lor \neg \left(c \cdot i \leq 3.8 \cdot 10^{+67}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -2.5e+103) (not (<= (* c i) 3.8e+67))) (* c i) (* a b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -2.5e+103) || !((c * i) <= 3.8e+67)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	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 (((c * i) <= (-2.5d+103)) .or. (.not. ((c * i) <= 3.8d+67))) then
        tmp = c * i
    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 (((c * i) <= -2.5e+103) || !((c * i) <= 3.8e+67)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -2.5e+103) or not ((c * i) <= 3.8e+67):
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -2.5e+103) || !(Float64(c * i) <= 3.8e+67))
		tmp = Float64(c * i);
	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 (((c * i) <= -2.5e+103) || ~(((c * i) <= 3.8e+67)))
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -2.5e+103], N[Not[LessEqual[N[(c * i), $MachinePrecision], 3.8e+67]], $MachinePrecision]], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -2.5e103 or 3.8000000000000002e67 < (*.f64 c i)

   1. Initial program 88.9%

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

   2. Taylor expanded in c around inf 63.1%

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

   if -2.5e103 < (*.f64 c i) < 3.8000000000000002e67

   1. Initial program 96.0%

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

   2. Taylor expanded in x around 0 70.5%

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

      1. +-commutative 70.5%

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

      2. *-commutative 70.5%

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

      3. fma-def 72.2%

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

   4. Applied egg-rr 72.2%

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

   5. Taylor expanded in a around inf 37.0%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.5 \cdot 10^{+103} \lor \neg \left(c \cdot i \leq 3.8 \cdot 10^{+67}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 18: 27.3% accurate, 5.0× speedup

Math

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

FPCore

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

Derivation

1. Initial program 93.7%

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

2. Taylor expanded in x around 0 74.2%

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

   1. +-commutative 74.2%

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

   2. *-commutative 74.2%

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

   3. fma-def 75.3%

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

4. Applied egg-rr 75.3%

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

5. Taylor expanded in a around inf 28.7%

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

6. Final simplification 28.7%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023322 
(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)))