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

Percentage Accurate: 96.1% → 98.0%

Time: 8.4s

Alternatives: 16

Speedup: 0.5×

• 41.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% 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 95.3%

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

   1. +-commutative 95.3%

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

   2. fma-def 96.1%

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

   3. associate-+l+ 96.1%

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

   4. fma-def 97.6%

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

   5. fma-def 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 2: 97.7% accurate, 0.1× speedup

Math

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

FPCore

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

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, ((a * b) + (z * t))));
}

Julia

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

Wolfram

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

Derivation

1. Initial program 95.3%

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

   1. +-commutative 95.3%

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

   2. fma-def 96.1%

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

   3. associate-+l+ 96.1%

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

   4. fma-def 97.6%

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

   5. fma-def 98.4%

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

3. Simplified 98.4%

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

   1. fma-udef 97.6%

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

5. Applied egg-rr 97.6%

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

6. Final simplification 97.6%

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

Alternative 3: 97.3% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (+ (+ (* a b) (+ (* x y) (* z t))) (* c i)) INFINITY)
   (+ (fma x y (* z t)) (+ (* a b) (* 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 ((((a * b) + ((x * y) + (z * t))) + (c * i)) <= ((double) INFINITY)) {
		tmp = fma(x, y, (z * t)) + ((a * b) + (c * i));
	} else {
		tmp = 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(x, y, Float64(z * t)) + Float64(Float64(a * b) + Float64(c * i)));
	else
		tmp = 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[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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%

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

      1. associate-+l+ 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

   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. 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 16.7%

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

      3. associate-+l+ 16.7%

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

      4. fma-def 50.0%

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

      5. fma-def 66.7%

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

   3. Simplified 66.7%

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

      1. fma-udef 50.0%

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

   5. Applied egg-rr 50.0%

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

   6. Taylor expanded in a around inf 50.1%

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

4. Final simplification 97.6%

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

Alternative 4: 97.8% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 98.3%

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

      1. +-commutative 98.3%

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

      2. fma-def 99.2%

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

      3. associate-+l+ 99.2%

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

      4. fma-def 99.2%

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

      5. fma-def 99.2%

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

   3. Simplified 99.2%

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

      1. fma-udef 99.2%

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

      2. fma-udef 99.2%

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

      3. associate-+l+ 99.2%

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

      4. +-commutative 99.2%

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

      5. associate-+r+ 99.2%

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

   5. Applied egg-rr 99.2%

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

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

   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 37.5%

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

   3. Taylor expanded in t around 0 50.1%

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

      1. fma-def 62.6%

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

   5. Simplified 62.6%

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

4. Final simplification 98.0%

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

Alternative 5: 42.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.7 \cdot 10^{+18}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -8.6 \cdot 10^{-45}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -1 \cdot 10^{-314}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.15 \cdot 10^{-129}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 3.3 \cdot 10^{-82}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 9.5 \cdot 10^{+101}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 4.8 \cdot 10^{+234}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1.7e+18)
   (* c i)
   (if (<= (* c i) -8.6e-45)
     (* x y)
     (if (<= (* c i) -1e-314)
       (* z t)
       (if (<= (* c i) 1.15e-129)
         (* a b)
         (if (<= (* c i) 3.3e-82)
           (* z t)
           (if (<= (* c i) 9.5e+101)
             (* a b)
             (if (<= (* c i) 4.8e+234) (* 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) <= -1.7e+18) {
		tmp = c * i;
	} else if ((c * i) <= -8.6e-45) {
		tmp = x * y;
	} else if ((c * i) <= -1e-314) {
		tmp = z * t;
	} else if ((c * i) <= 1.15e-129) {
		tmp = a * b;
	} else if ((c * i) <= 3.3e-82) {
		tmp = z * t;
	} else if ((c * i) <= 9.5e+101) {
		tmp = a * b;
	} else if ((c * i) <= 4.8e+234) {
		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) <= (-1.7d+18)) then
        tmp = c * i
    else if ((c * i) <= (-8.6d-45)) then
        tmp = x * y
    else if ((c * i) <= (-1d-314)) then
        tmp = z * t
    else if ((c * i) <= 1.15d-129) then
        tmp = a * b
    else if ((c * i) <= 3.3d-82) then
        tmp = z * t
    else if ((c * i) <= 9.5d+101) then
        tmp = a * b
    else if ((c * i) <= 4.8d+234) 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) <= -1.7e+18) {
		tmp = c * i;
	} else if ((c * i) <= -8.6e-45) {
		tmp = x * y;
	} else if ((c * i) <= -1e-314) {
		tmp = z * t;
	} else if ((c * i) <= 1.15e-129) {
		tmp = a * b;
	} else if ((c * i) <= 3.3e-82) {
		tmp = z * t;
	} else if ((c * i) <= 9.5e+101) {
		tmp = a * b;
	} else if ((c * i) <= 4.8e+234) {
		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) <= -1.7e+18:
		tmp = c * i
	elif (c * i) <= -8.6e-45:
		tmp = x * y
	elif (c * i) <= -1e-314:
		tmp = z * t
	elif (c * i) <= 1.15e-129:
		tmp = a * b
	elif (c * i) <= 3.3e-82:
		tmp = z * t
	elif (c * i) <= 9.5e+101:
		tmp = a * b
	elif (c * i) <= 4.8e+234:
		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) <= -1.7e+18)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -8.6e-45)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= -1e-314)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 1.15e-129)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 3.3e-82)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 9.5e+101)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 4.8e+234)
		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) <= -1.7e+18)
		tmp = c * i;
	elseif ((c * i) <= -8.6e-45)
		tmp = x * y;
	elseif ((c * i) <= -1e-314)
		tmp = z * t;
	elseif ((c * i) <= 1.15e-129)
		tmp = a * b;
	elseif ((c * i) <= 3.3e-82)
		tmp = z * t;
	elseif ((c * i) <= 9.5e+101)
		tmp = a * b;
	elseif ((c * i) <= 4.8e+234)
		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], -1.7e+18], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -8.6e-45], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1e-314], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.15e-129], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 3.3e-82], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 9.5e+101], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4.8e+234], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -1.7e18 or 4.80000000000000023e234 < (*.f64 c i)

   1. Initial program 91.8%

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

   2. Taylor expanded in c around inf 66.0%

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

   if -1.7e18 < (*.f64 c i) < -8.5999999999999998e-45

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-def 99.9%

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

      3. associate-+l+ 99.9%

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

      4. fma-def 100.0%

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

      5. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around inf 47.2%

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

   if -8.5999999999999998e-45 < (*.f64 c i) < -9.9999999996e-315 or 1.15e-129 < (*.f64 c i) < 3.30000000000000022e-82 or 9.49999999999999947e101 < (*.f64 c i) < 4.80000000000000023e234

   1. Initial program 96.9%

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

      1. +-commutative 96.9%

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

      2. fma-def 96.9%

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

      3. associate-+l+ 96.9%

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

      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 96.9%

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

   3. Simplified 96.9%

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

      1. fma-udef 96.9%

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

   5. Applied egg-rr 96.9%

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

   6. Taylor expanded in z around inf 56.8%

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

   if -9.9999999996e-315 < (*.f64 c i) < 1.15e-129 or 3.30000000000000022e-82 < (*.f64 c i) < 9.49999999999999947e101

   1. Initial program 96.6%

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

      1. +-commutative 96.6%

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

      2. fma-def 96.6%

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

      3. associate-+l+ 96.6%

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

      4. fma-def 97.7%

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

      5. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 97.7%

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

   5. Applied egg-rr 97.7%

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

   6. Taylor expanded in a around inf 49.6%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.7 \cdot 10^{+18}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -8.6 \cdot 10^{-45}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -1 \cdot 10^{-314}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.15 \cdot 10^{-129}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 3.3 \cdot 10^{-82}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 9.5 \cdot 10^{+101}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 4.8 \cdot 10^{+234}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 6: 65.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + x \cdot y\\ t_2 := a \cdot b + c \cdot i\\ t_3 := c \cdot i + z \cdot t\\ \mathbf{if}\;a \cdot b \leq -1.38 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq -2.8 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq -40000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq 7 \cdot 10^{-118}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \cdot b \leq 4.2 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 5.7 \cdot 10^{+76}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* x y)))
        (t_2 (+ (* a b) (* c i)))
        (t_3 (+ (* c i) (* z t))))
   (if (<= (* a b) -1.38e+104)
     t_2
     (if (<= (* a b) -2.8e+38)
       t_1
       (if (<= (* a b) -40000000000.0)
         t_2
         (if (<= (* a b) 7e-118)
           t_3
           (if (<= (* a b) 4.2e-66)
             t_1
             (if (<= (* a b) 5.7e+76) t_3 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (x * y);
	double t_2 = (a * b) + (c * i);
	double t_3 = (c * i) + (z * t);
	double tmp;
	if ((a * b) <= -1.38e+104) {
		tmp = t_2;
	} else if ((a * b) <= -2.8e+38) {
		tmp = t_1;
	} else if ((a * b) <= -40000000000.0) {
		tmp = t_2;
	} else if ((a * b) <= 7e-118) {
		tmp = t_3;
	} else if ((a * b) <= 4.2e-66) {
		tmp = t_1;
	} else if ((a * b) <= 5.7e+76) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (c * i) + (x * y)
    t_2 = (a * b) + (c * i)
    t_3 = (c * i) + (z * t)
    if ((a * b) <= (-1.38d+104)) then
        tmp = t_2
    else if ((a * b) <= (-2.8d+38)) then
        tmp = t_1
    else if ((a * b) <= (-40000000000.0d0)) then
        tmp = t_2
    else if ((a * b) <= 7d-118) then
        tmp = t_3
    else if ((a * b) <= 4.2d-66) then
        tmp = t_1
    else if ((a * b) <= 5.7d+76) then
        tmp = t_3
    else
        tmp = t_2
    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) + (x * y);
	double t_2 = (a * b) + (c * i);
	double t_3 = (c * i) + (z * t);
	double tmp;
	if ((a * b) <= -1.38e+104) {
		tmp = t_2;
	} else if ((a * b) <= -2.8e+38) {
		tmp = t_1;
	} else if ((a * b) <= -40000000000.0) {
		tmp = t_2;
	} else if ((a * b) <= 7e-118) {
		tmp = t_3;
	} else if ((a * b) <= 4.2e-66) {
		tmp = t_1;
	} else if ((a * b) <= 5.7e+76) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (x * y)
	t_2 = (a * b) + (c * i)
	t_3 = (c * i) + (z * t)
	tmp = 0
	if (a * b) <= -1.38e+104:
		tmp = t_2
	elif (a * b) <= -2.8e+38:
		tmp = t_1
	elif (a * b) <= -40000000000.0:
		tmp = t_2
	elif (a * b) <= 7e-118:
		tmp = t_3
	elif (a * b) <= 4.2e-66:
		tmp = t_1
	elif (a * b) <= 5.7e+76:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(x * y))
	t_2 = Float64(Float64(a * b) + Float64(c * i))
	t_3 = Float64(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -1.38e+104)
		tmp = t_2;
	elseif (Float64(a * b) <= -2.8e+38)
		tmp = t_1;
	elseif (Float64(a * b) <= -40000000000.0)
		tmp = t_2;
	elseif (Float64(a * b) <= 7e-118)
		tmp = t_3;
	elseif (Float64(a * b) <= 4.2e-66)
		tmp = t_1;
	elseif (Float64(a * b) <= 5.7e+76)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (x * y);
	t_2 = (a * b) + (c * i);
	t_3 = (c * i) + (z * t);
	tmp = 0.0;
	if ((a * b) <= -1.38e+104)
		tmp = t_2;
	elseif ((a * b) <= -2.8e+38)
		tmp = t_1;
	elseif ((a * b) <= -40000000000.0)
		tmp = t_2;
	elseif ((a * b) <= 7e-118)
		tmp = t_3;
	elseif ((a * b) <= 4.2e-66)
		tmp = t_1;
	elseif ((a * b) <= 5.7e+76)
		tmp = t_3;
	else
		tmp = t_2;
	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[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1.38e+104], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -2.8e+38], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -40000000000.0], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 7e-118], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], 4.2e-66], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 5.7e+76], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.38e104 or -2.8e38 < (*.f64 a b) < -4e10 or 5.70000000000000004e76 < (*.f64 a b)

   1. Initial program 89.2%

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

   2. Taylor expanded in a around inf 79.8%

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

   if -1.38e104 < (*.f64 a b) < -2.8e38 or 7e-118 < (*.f64 a b) < 4.2000000000000001e-66

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 74.1%

      \[\leadsto \color{blue}{y \cdot x} + c \cdot i \]

   if -4e10 < (*.f64 a b) < 7e-118 or 4.2000000000000001e-66 < (*.f64 a b) < 5.70000000000000004e76

   1. Initial program 99.1%

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

   2. Taylor expanded in z around inf 74.7%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.38 \cdot 10^{+104}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -2.8 \cdot 10^{+38}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -40000000000:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 7 \cdot 10^{-118}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 4.2 \cdot 10^{-66}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 5.7 \cdot 10^{+76}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]

Alternative 7: 65.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ t_2 := x \cdot y + z \cdot t\\ t_3 := a \cdot b + c \cdot i\\ \mathbf{if}\;a \cdot b \leq -1.15 \cdot 10^{+104}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{+39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq -60000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \cdot b \leq 6.4 \cdot 10^{-131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 2.4 \cdot 10^{-73}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq 3.7 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t)))
        (t_2 (+ (* x y) (* z t)))
        (t_3 (+ (* a b) (* c i))))
   (if (<= (* a b) -1.15e+104)
     t_3
     (if (<= (* a b) -1e+39)
       t_2
       (if (<= (* a b) -60000000000.0)
         t_3
         (if (<= (* a b) 6.4e-131)
           t_1
           (if (<= (* a b) 2.4e-73)
             t_2
             (if (<= (* a b) 3.7e+79) t_1 t_3))))))))

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 t_2 = (x * y) + (z * t);
	double t_3 = (a * b) + (c * i);
	double tmp;
	if ((a * b) <= -1.15e+104) {
		tmp = t_3;
	} else if ((a * b) <= -1e+39) {
		tmp = t_2;
	} else if ((a * b) <= -60000000000.0) {
		tmp = t_3;
	} else if ((a * b) <= 6.4e-131) {
		tmp = t_1;
	} else if ((a * b) <= 2.4e-73) {
		tmp = t_2;
	} else if ((a * b) <= 3.7e+79) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (c * i) + (z * t)
    t_2 = (x * y) + (z * t)
    t_3 = (a * b) + (c * i)
    if ((a * b) <= (-1.15d+104)) then
        tmp = t_3
    else if ((a * b) <= (-1d+39)) then
        tmp = t_2
    else if ((a * b) <= (-60000000000.0d0)) then
        tmp = t_3
    else if ((a * b) <= 6.4d-131) then
        tmp = t_1
    else if ((a * b) <= 2.4d-73) then
        tmp = t_2
    else if ((a * b) <= 3.7d+79) then
        tmp = t_1
    else
        tmp = t_3
    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 t_2 = (x * y) + (z * t);
	double t_3 = (a * b) + (c * i);
	double tmp;
	if ((a * b) <= -1.15e+104) {
		tmp = t_3;
	} else if ((a * b) <= -1e+39) {
		tmp = t_2;
	} else if ((a * b) <= -60000000000.0) {
		tmp = t_3;
	} else if ((a * b) <= 6.4e-131) {
		tmp = t_1;
	} else if ((a * b) <= 2.4e-73) {
		tmp = t_2;
	} else if ((a * b) <= 3.7e+79) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	t_2 = (x * y) + (z * t)
	t_3 = (a * b) + (c * i)
	tmp = 0
	if (a * b) <= -1.15e+104:
		tmp = t_3
	elif (a * b) <= -1e+39:
		tmp = t_2
	elif (a * b) <= -60000000000.0:
		tmp = t_3
	elif (a * b) <= 6.4e-131:
		tmp = t_1
	elif (a * b) <= 2.4e-73:
		tmp = t_2
	elif (a * b) <= 3.7e+79:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	t_2 = Float64(Float64(x * y) + Float64(z * t))
	t_3 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(a * b) <= -1.15e+104)
		tmp = t_3;
	elseif (Float64(a * b) <= -1e+39)
		tmp = t_2;
	elseif (Float64(a * b) <= -60000000000.0)
		tmp = t_3;
	elseif (Float64(a * b) <= 6.4e-131)
		tmp = t_1;
	elseif (Float64(a * b) <= 2.4e-73)
		tmp = t_2;
	elseif (Float64(a * b) <= 3.7e+79)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (z * t);
	t_2 = (x * y) + (z * t);
	t_3 = (a * b) + (c * i);
	tmp = 0.0;
	if ((a * b) <= -1.15e+104)
		tmp = t_3;
	elseif ((a * b) <= -1e+39)
		tmp = t_2;
	elseif ((a * b) <= -60000000000.0)
		tmp = t_3;
	elseif ((a * b) <= 6.4e-131)
		tmp = t_1;
	elseif ((a * b) <= 2.4e-73)
		tmp = t_2;
	elseif ((a * b) <= 3.7e+79)
		tmp = t_1;
	else
		tmp = t_3;
	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]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1.15e+104], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], -1e+39], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -60000000000.0], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], 6.4e-131], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 2.4e-73], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 3.7e+79], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.14999999999999992e104 or -9.9999999999999994e38 < (*.f64 a b) < -6e10 or 3.70000000000000009e79 < (*.f64 a b)

   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 inf 79.4%

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

   if -1.14999999999999992e104 < (*.f64 a b) < -9.9999999999999994e38 or 6.3999999999999999e-131 < (*.f64 a b) < 2.40000000000000006e-73

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. fma-def 100.0%

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

      4. fma-def 100.0%

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

      5. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 96.5%

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

   5. Taylor expanded in c around 0 78.5%

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

   if -6e10 < (*.f64 a b) < 6.3999999999999999e-131 or 2.40000000000000006e-73 < (*.f64 a b) < 3.70000000000000009e79

   1. Initial program 99.1%

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

   2. Taylor expanded in z around inf 74.3%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.15 \cdot 10^{+104}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{+39}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -60000000000:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 6.4 \cdot 10^{-131}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.4 \cdot 10^{-73}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 3.7 \cdot 10^{+79}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]

Alternative 8: 97.3% 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. 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 16.7%

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

      3. associate-+l+ 16.7%

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

      4. fma-def 50.0%

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

      5. fma-def 66.7%

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

   3. Simplified 66.7%

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

      1. fma-udef 50.0%

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

   5. Applied egg-rr 50.0%

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

   6. Taylor expanded in a around inf 50.1%

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

4. Final simplification 97.6%

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

Alternative 9: 41.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.05 \cdot 10^{-28}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1 \cdot 10^{-314}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 4 \cdot 10^{-127}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 1.25 \cdot 10^{-73}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.4 \cdot 10^{+102}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 7.2 \cdot 10^{+235}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1.05e-28)
   (* c i)
   (if (<= (* c i) -1e-314)
     (* z t)
     (if (<= (* c i) 4e-127)
       (* a b)
       (if (<= (* c i) 1.25e-73)
         (* z t)
         (if (<= (* c i) 1.4e+102)
           (* a b)
           (if (<= (* c i) 7.2e+235) (* 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) <= -1.05e-28) {
		tmp = c * i;
	} else if ((c * i) <= -1e-314) {
		tmp = z * t;
	} else if ((c * i) <= 4e-127) {
		tmp = a * b;
	} else if ((c * i) <= 1.25e-73) {
		tmp = z * t;
	} else if ((c * i) <= 1.4e+102) {
		tmp = a * b;
	} else if ((c * i) <= 7.2e+235) {
		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) <= (-1.05d-28)) then
        tmp = c * i
    else if ((c * i) <= (-1d-314)) then
        tmp = z * t
    else if ((c * i) <= 4d-127) then
        tmp = a * b
    else if ((c * i) <= 1.25d-73) then
        tmp = z * t
    else if ((c * i) <= 1.4d+102) then
        tmp = a * b
    else if ((c * i) <= 7.2d+235) 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) <= -1.05e-28) {
		tmp = c * i;
	} else if ((c * i) <= -1e-314) {
		tmp = z * t;
	} else if ((c * i) <= 4e-127) {
		tmp = a * b;
	} else if ((c * i) <= 1.25e-73) {
		tmp = z * t;
	} else if ((c * i) <= 1.4e+102) {
		tmp = a * b;
	} else if ((c * i) <= 7.2e+235) {
		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) <= -1.05e-28:
		tmp = c * i
	elif (c * i) <= -1e-314:
		tmp = z * t
	elif (c * i) <= 4e-127:
		tmp = a * b
	elif (c * i) <= 1.25e-73:
		tmp = z * t
	elif (c * i) <= 1.4e+102:
		tmp = a * b
	elif (c * i) <= 7.2e+235:
		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) <= -1.05e-28)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -1e-314)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 4e-127)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 1.25e-73)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 1.4e+102)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 7.2e+235)
		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) <= -1.05e-28)
		tmp = c * i;
	elseif ((c * i) <= -1e-314)
		tmp = z * t;
	elseif ((c * i) <= 4e-127)
		tmp = a * b;
	elseif ((c * i) <= 1.25e-73)
		tmp = z * t;
	elseif ((c * i) <= 1.4e+102)
		tmp = a * b;
	elseif ((c * i) <= 7.2e+235)
		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], -1.05e-28], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1e-314], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4e-127], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.25e-73], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.4e+102], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 7.2e+235], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.05000000000000003e-28 or 7.19999999999999971e235 < (*.f64 c i)

   1. Initial program 92.8%

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

   2. Taylor expanded in c around inf 60.3%

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

   if -1.05000000000000003e-28 < (*.f64 c i) < -9.9999999996e-315 or 4.0000000000000001e-127 < (*.f64 c i) < 1.25e-73 or 1.40000000000000009e102 < (*.f64 c i) < 7.19999999999999971e235

   1. Initial program 97.1%

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

      1. +-commutative 97.1%

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

      2. fma-def 97.1%

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

      3. associate-+l+ 97.1%

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

      4. fma-def 97.1%

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

      5. fma-def 97.1%

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

   3. Simplified 97.1%

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

      1. fma-udef 97.1%

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

   5. Applied egg-rr 97.1%

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

   6. Taylor expanded in z around inf 55.0%

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

   if -9.9999999996e-315 < (*.f64 c i) < 4.0000000000000001e-127 or 1.25e-73 < (*.f64 c i) < 1.40000000000000009e102

   1. Initial program 96.6%

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

      1. +-commutative 96.6%

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

      2. fma-def 96.6%

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

      3. associate-+l+ 96.6%

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

      4. fma-def 97.7%

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

      5. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 97.7%

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

   5. Applied egg-rr 97.7%

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

   6. Taylor expanded in a around inf 49.6%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.05 \cdot 10^{-28}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1 \cdot 10^{-314}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 4 \cdot 10^{-127}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 1.25 \cdot 10^{-73}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.4 \cdot 10^{+102}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 7.2 \cdot 10^{+235}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 10: 87.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+21}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{elif}\;a \cdot b \leq 2.9 \cdot 10^{+16}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -5e+21)
   (+ (* c i) (+ (* a b) (* x y)))
   (if (<= (* a b) 2.9e+16)
     (+ (* 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 ((a * b) <= -5e+21) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else if ((a * b) <= 2.9e+16) {
		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 ((a * b) <= (-5d+21)) then
        tmp = (c * i) + ((a * b) + (x * y))
    else if ((a * b) <= 2.9d+16) 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 ((a * b) <= -5e+21) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else if ((a * b) <= 2.9e+16) {
		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 (a * b) <= -5e+21:
		tmp = (c * i) + ((a * b) + (x * y))
	elif (a * b) <= 2.9e+16:
		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(a * b) <= -5e+21)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)));
	elseif (Float64(a * b) <= 2.9e+16)
		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 ((a * b) <= -5e+21)
		tmp = (c * i) + ((a * b) + (x * y));
	elseif ((a * b) <= 2.9e+16)
		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[LessEqual[N[(a * b), $MachinePrecision], -5e+21], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.9e+16], 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 3 regimes

2. if (*.f64 a b) < -5e21

   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 z around 0 89.6%

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

   if -5e21 < (*.f64 a b) < 2.9e16

   1. Initial program 99.2%

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

   2. Taylor expanded in a around 0 94.4%

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

   if 2.9e16 < (*.f64 a b)

   1. Initial program 86.1%

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

   2. Taylor expanded in x around 0 83.3%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+21}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{elif}\;a \cdot b \leq 2.9 \cdot 10^{+16}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]

Alternative 11: 66.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -57000000000 \lor \neg \left(a \cdot b \leq 7.5 \cdot 10^{+76}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -57000000000.0) (not (<= (* a b) 7.5e+76)))
   (+ (* a b) (* c i))
   (+ (* c i) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((a * b) <= -57000000000.0) || !((a * b) <= 7.5e+76)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (c * i) + (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 (((a * b) <= (-57000000000.0d0)) .or. (.not. ((a * b) <= 7.5d+76))) then
        tmp = (a * b) + (c * i)
    else
        tmp = (c * i) + (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 (((a * b) <= -57000000000.0) || !((a * b) <= 7.5e+76)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((a * b) <= -57000000000.0) or not ((a * b) <= 7.5e+76):
		tmp = (a * b) + (c * i)
	else:
		tmp = (c * i) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(a * b) <= -57000000000.0) || !(Float64(a * b) <= 7.5e+76))
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = Float64(Float64(c * i) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((a * b) <= -57000000000.0) || ~(((a * b) <= 7.5e+76)))
		tmp = (a * b) + (c * i);
	else
		tmp = (c * i) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -57000000000.0], N[Not[LessEqual[N[(a * b), $MachinePrecision], 7.5e+76]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -5.7e10 or 7.4999999999999995e76 < (*.f64 a b)

   1. Initial program 90.4%

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

   2. Taylor expanded in a around inf 74.6%

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

   if -5.7e10 < (*.f64 a b) < 7.4999999999999995e76

   1. Initial program 99.2%

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

   2. Taylor expanded in z around inf 71.5%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -57000000000 \lor \neg \left(a \cdot b \leq 7.5 \cdot 10^{+76}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]

Alternative 12: 82.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-63} \lor \neg \left(t \leq 1.95 \cdot 10^{+121}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= t -1.15e-63) (not (<= t 1.95e+121)))
   (+ (* c i) (+ (* a b) (* z t)))
   (+ (* c i) (+ (* a b) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((t <= -1.15e-63) || !(t <= 1.95e+121)) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((a * b) + (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((t <= (-1.15d-63)) .or. (.not. (t <= 1.95d+121))) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (c * i) + ((a * b) + (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((t <= -1.15e-63) || !(t <= 1.95e+121)) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((a * b) + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (t <= -1.15e-63) or not (t <= 1.95e+121):
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (c * i) + ((a * b) + (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((t <= -1.15e-63) || !(t <= 1.95e+121))
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((t <= -1.15e-63) || ~((t <= 1.95e+121)))
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (c * i) + ((a * b) + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[t, -1.15e-63], N[Not[LessEqual[t, 1.95e+121]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.15e-63 or 1.94999999999999992e121 < t

   1. Initial program 93.3%

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

   2. Taylor expanded in x around 0 85.0%

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

   if -1.15e-63 < t < 1.94999999999999992e121

   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 z around 0 89.7%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-63} \lor \neg \left(t \leq 1.95 \cdot 10^{+121}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \end{array} \]

Alternative 13: 77.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+205}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+62}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -4.1e+205)
   (+ (* c i) (* x y))
   (if (<= x 1.15e+62) (+ (* c i) (+ (* a b) (* z t))) (+ (* x y) (* 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 <= -4.1e+205) {
		tmp = (c * i) + (x * y);
	} else if (x <= 1.15e+62) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (x * y) + (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 <= (-4.1d+205)) then
        tmp = (c * i) + (x * y)
    else if (x <= 1.15d+62) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (x * y) + (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 <= -4.1e+205) {
		tmp = (c * i) + (x * y);
	} else if (x <= 1.15e+62) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (x * y) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -4.1e+205:
		tmp = (c * i) + (x * y)
	elif x <= 1.15e+62:
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (x * y) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -4.1e+205)
		tmp = Float64(Float64(c * i) + Float64(x * y));
	elseif (x <= 1.15e+62)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(x * y) + 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 <= -4.1e+205)
		tmp = (c * i) + (x * y);
	elseif (x <= 1.15e+62)
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (x * y) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -4.1e+205], N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e+62], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.1000000000000003e205

   1. Initial program 95.7%

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

   2. Taylor expanded in x around inf 70.2%

      \[\leadsto \color{blue}{y \cdot x} + c \cdot i \]

   if -4.1000000000000003e205 < x < 1.14999999999999992e62

   1. Initial program 96.7%

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

   2. Taylor expanded in x around 0 86.7%

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

   if 1.14999999999999992e62 < x

   1. Initial program 89.6%

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

      1. associate-+l+ 89.6%

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

      2. associate-+l+ 89.6%

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

      3. fma-def 95.8%

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

      4. fma-def 97.9%

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

      5. fma-def 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in a around 0 75.4%

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

   5. Taylor expanded in c around 0 61.0%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+205}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+62}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \]

Alternative 14: 43.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4 \cdot 10^{+20}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 2.1 \cdot 10^{+115}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -4e+20) (* c i) (if (<= (* c i) 2.1e+115) (* 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) <= -4e+20) {
		tmp = c * i;
	} else if ((c * i) <= 2.1e+115) {
		tmp = a * b;
	} 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) <= (-4d+20)) then
        tmp = c * i
    else if ((c * i) <= 2.1d+115) then
        tmp = a * b
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -4e+20) {
		tmp = c * i;
	} else if ((c * i) <= 2.1e+115) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -4e+20:
		tmp = c * i
	elif (c * i) <= 2.1e+115:
		tmp = a * b
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -4e+20)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 2.1e+115)
		tmp = Float64(a * b);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -4e+20)
		tmp = c * i;
	elseif ((c * i) <= 2.1e+115)
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -4e+20], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.1e+115], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -4e20 or 2.10000000000000003e115 < (*.f64 c i)

   1. Initial program 93.1%

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

   2. Taylor expanded in c around inf 58.4%

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

   if -4e20 < (*.f64 c i) < 2.10000000000000003e115

   1. Initial program 96.7%

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

      1. +-commutative 96.7%

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

      2. fma-def 96.7%

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

      3. associate-+l+ 96.7%

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

      4. fma-def 97.4%

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

      5. fma-def 98.7%

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

   3. Simplified 98.7%

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

      1. fma-udef 97.4%

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

   5. Applied egg-rr 97.4%

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

   6. Taylor expanded in a around inf 41.6%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4 \cdot 10^{+20}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 2.1 \cdot 10^{+115}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 15: 55.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+69}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+133}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= t -1.05e+69) (* z t) (if (<= t 9e+133) (+ (* a b) (* c i)) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (t <= -1.05e+69) {
		tmp = z * t;
	} else if (t <= 9e+133) {
		tmp = (a * b) + (c * i);
	} 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 (t <= (-1.05d+69)) then
        tmp = z * t
    else if (t <= 9d+133) then
        tmp = (a * b) + (c * i)
    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 (t <= -1.05e+69) {
		tmp = z * t;
	} else if (t <= 9e+133) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if t <= -1.05e+69:
		tmp = z * t
	elif t <= 9e+133:
		tmp = (a * b) + (c * i)
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (t <= -1.05e+69)
		tmp = Float64(z * t);
	elseif (t <= 9e+133)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	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 (t <= -1.05e+69)
		tmp = z * t;
	elseif (t <= 9e+133)
		tmp = (a * b) + (c * i);
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[t, -1.05e+69], N[(z * t), $MachinePrecision], If[LessEqual[t, 9e+133], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(z * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05000000000000008e69 or 8.9999999999999997e133 < t

   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 94.7%

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

      3. associate-+l+ 94.7%

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

      4. fma-def 96.8%

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

      5. fma-def 98.9%

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

   3. Simplified 98.9%

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

      1. fma-udef 96.8%

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

   5. Applied egg-rr 96.8%

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

   6. Taylor expanded in z around inf 59.8%

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

   if -1.05000000000000008e69 < t < 8.9999999999999997e133

   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 a around inf 63.9%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+69}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+133}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]

Alternative 16: 27.4% 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 95.3%

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

   1. +-commutative 95.3%

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

   2. fma-def 96.1%

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

   3. associate-+l+ 96.1%

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

   4. fma-def 97.6%

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

   5. fma-def 98.4%

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

3. Simplified 98.4%

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

   1. fma-udef 97.6%

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

5. Applied egg-rr 97.6%

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

6. Taylor expanded in a around inf 30.6%

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

7. Final simplification 30.6%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023185 
(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)))