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

Percentage Accurate: 95.6% → 98.0%

Time: 6.5s

Alternatives: 12

Speedup: 0.5×

• Unsound rule application detected in e-graph. Results may not be sound.

• 42.1% 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: 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 96.9%

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

   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 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 98.0%

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

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 2: 42.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.12 \cdot 10^{+93}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -8.5 \cdot 10^{-206}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 1.15 \cdot 10^{-155}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 4.8 \cdot 10^{-91}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 390000000000:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 8.6 \cdot 10^{+102}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 8.5 \cdot 10^{+180}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -1.12e+93)
   (* a b)
   (if (<= (* a b) -8.5e-206)
     (* c i)
     (if (<= (* a b) 1.15e-155)
       (* z t)
       (if (<= (* a b) 4.8e-91)
         (* c i)
         (if (<= (* a b) 390000000000.0)
           (* z t)
           (if (<= (* a b) 8.6e+102)
             (* c i)
             (if (<= (* a b) 8.5e+180) (* z t) (* a b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1.12e+93) {
		tmp = a * b;
	} else if ((a * b) <= -8.5e-206) {
		tmp = c * i;
	} else if ((a * b) <= 1.15e-155) {
		tmp = z * t;
	} else if ((a * b) <= 4.8e-91) {
		tmp = c * i;
	} else if ((a * b) <= 390000000000.0) {
		tmp = z * t;
	} else if ((a * b) <= 8.6e+102) {
		tmp = c * i;
	} else if ((a * b) <= 8.5e+180) {
		tmp = z * t;
	} 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 ((a * b) <= (-1.12d+93)) then
        tmp = a * b
    else if ((a * b) <= (-8.5d-206)) then
        tmp = c * i
    else if ((a * b) <= 1.15d-155) then
        tmp = z * t
    else if ((a * b) <= 4.8d-91) then
        tmp = c * i
    else if ((a * b) <= 390000000000.0d0) then
        tmp = z * t
    else if ((a * b) <= 8.6d+102) then
        tmp = c * i
    else if ((a * b) <= 8.5d+180) then
        tmp = z * t
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1.12e+93) {
		tmp = a * b;
	} else if ((a * b) <= -8.5e-206) {
		tmp = c * i;
	} else if ((a * b) <= 1.15e-155) {
		tmp = z * t;
	} else if ((a * b) <= 4.8e-91) {
		tmp = c * i;
	} else if ((a * b) <= 390000000000.0) {
		tmp = z * t;
	} else if ((a * b) <= 8.6e+102) {
		tmp = c * i;
	} else if ((a * b) <= 8.5e+180) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -1.12e+93:
		tmp = a * b
	elif (a * b) <= -8.5e-206:
		tmp = c * i
	elif (a * b) <= 1.15e-155:
		tmp = z * t
	elif (a * b) <= 4.8e-91:
		tmp = c * i
	elif (a * b) <= 390000000000.0:
		tmp = z * t
	elif (a * b) <= 8.6e+102:
		tmp = c * i
	elif (a * b) <= 8.5e+180:
		tmp = z * t
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -1.12e+93)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -8.5e-206)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 1.15e-155)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 4.8e-91)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 390000000000.0)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 8.6e+102)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 8.5e+180)
		tmp = Float64(z * t);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -1.12e+93)
		tmp = a * b;
	elseif ((a * b) <= -8.5e-206)
		tmp = c * i;
	elseif ((a * b) <= 1.15e-155)
		tmp = z * t;
	elseif ((a * b) <= 4.8e-91)
		tmp = c * i;
	elseif ((a * b) <= 390000000000.0)
		tmp = z * t;
	elseif ((a * b) <= 8.6e+102)
		tmp = c * i;
	elseif ((a * b) <= 8.5e+180)
		tmp = z * t;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -1.12e+93], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -8.5e-206], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.15e-155], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 4.8e-91], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 390000000000.0], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 8.6e+102], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 8.5e+180], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.12e93 or 8.50000000000000077e180 < (*.f64 a b)

   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 a around inf 72.3%

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

   if -1.12e93 < (*.f64 a b) < -8.5000000000000005e-206 or 1.15000000000000003e-155 < (*.f64 a b) < 4.80000000000000022e-91 or 3.9e11 < (*.f64 a b) < 8.6000000000000002e102

   1. Initial program 96.1%

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

   2. Taylor expanded in c around inf 46.5%

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

   if -8.5000000000000005e-206 < (*.f64 a b) < 1.15000000000000003e-155 or 4.80000000000000022e-91 < (*.f64 a b) < 3.9e11 or 8.6000000000000002e102 < (*.f64 a b) < 8.50000000000000077e180

   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 inf 47.2%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.12 \cdot 10^{+93}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -8.5 \cdot 10^{-206}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 1.15 \cdot 10^{-155}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 4.8 \cdot 10^{-91}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 390000000000:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 8.6 \cdot 10^{+102}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 8.5 \cdot 10^{+180}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 3: 97.2% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (+ (* a b) (+ (* z t) (* x y))) (* c i))))
   (if (<= t_1 INFINITY) t_1 (+ (* 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) + ((z * t) + (x * y))) + (c * i);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (z * t);
	}
	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) + ((z * t) + (x * y))) + (c * i);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((a * b) + ((z * t) + (x * y))) + (c * i)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (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(z * t) + Float64(x * y))) + Float64(c * i))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * b) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((a * b) + ((z * t) + (x * y))) + (c * i);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (a * b) + (z * t);
	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[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(a * b), $MachinePrecision] + 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 33.3%

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

   3. Taylor expanded in c around 0 50.1%

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

4. Final simplification 97.6%

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

Alternative 4: 72.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + \left(a \cdot b + z \cdot t\right)\\ t_2 := c \cdot i + x \cdot y\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{+260}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{+105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (+ (* a b) (* z t)))) (t_2 (+ (* c i) (* x y))))
   (if (<= x -1.55e+260)
     t_2
     (if (<= x -1.3e+198)
       t_1
       (if (<= x -1.02e+105)
         t_2
         (if (<= x 2.45e-71) t_1 (+ (* a b) (* x y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + ((a * b) + (z * t));
	double t_2 = (c * i) + (x * y);
	double tmp;
	if (x <= -1.55e+260) {
		tmp = t_2;
	} else if (x <= -1.3e+198) {
		tmp = t_1;
	} else if (x <= -1.02e+105) {
		tmp = t_2;
	} else if (x <= 2.45e-71) {
		tmp = t_1;
	} else {
		tmp = (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (c * i) + ((a * b) + (z * t))
    t_2 = (c * i) + (x * y)
    if (x <= (-1.55d+260)) then
        tmp = t_2
    else if (x <= (-1.3d+198)) then
        tmp = t_1
    else if (x <= (-1.02d+105)) then
        tmp = t_2
    else if (x <= 2.45d-71) then
        tmp = t_1
    else
        tmp = (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 t_1 = (c * i) + ((a * b) + (z * t));
	double t_2 = (c * i) + (x * y);
	double tmp;
	if (x <= -1.55e+260) {
		tmp = t_2;
	} else if (x <= -1.3e+198) {
		tmp = t_1;
	} else if (x <= -1.02e+105) {
		tmp = t_2;
	} else if (x <= 2.45e-71) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + ((a * b) + (z * t))
	t_2 = (c * i) + (x * y)
	tmp = 0
	if x <= -1.55e+260:
		tmp = t_2
	elif x <= -1.3e+198:
		tmp = t_1
	elif x <= -1.02e+105:
		tmp = t_2
	elif x <= 2.45e-71:
		tmp = t_1
	else:
		tmp = (a * b) + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)))
	t_2 = Float64(Float64(c * i) + Float64(x * y))
	tmp = 0.0
	if (x <= -1.55e+260)
		tmp = t_2;
	elseif (x <= -1.3e+198)
		tmp = t_1;
	elseif (x <= -1.02e+105)
		tmp = t_2;
	elseif (x <= 2.45e-71)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * b) + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + ((a * b) + (z * t));
	t_2 = (c * i) + (x * y);
	tmp = 0.0;
	if (x <= -1.55e+260)
		tmp = t_2;
	elseif (x <= -1.3e+198)
		tmp = t_1;
	elseif (x <= -1.02e+105)
		tmp = t_2;
	elseif (x <= 2.45e-71)
		tmp = t_1;
	else
		tmp = (a * b) + (x * y);
	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[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.55e+260], t$95$2, If[LessEqual[x, -1.3e+198], t$95$1, If[LessEqual[x, -1.02e+105], t$95$2, If[LessEqual[x, 2.45e-71], t$95$1, N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.5499999999999999e260 or -1.2999999999999999e198 < x < -1.02e105

   1. Initial program 86.6%

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

   2. Taylor expanded in z around 0 89.9%

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

   3. Taylor expanded in a around 0 86.8%

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

   if -1.5499999999999999e260 < x < -1.2999999999999999e198 or -1.02e105 < x < 2.4499999999999999e-71

   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 88.8%

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

   if 2.4499999999999999e-71 < x

   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 z around 0 74.6%

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

   3. Taylor expanded in c around 0 58.0%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+260}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+198}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{+105}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{-71}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]

Alternative 5: 82.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+103} \lor \neg \left(x \leq 5 \cdot 10^{-78}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -8.2e+103) (not (<= x 5e-78)))
   (+ (* 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 <= -8.2e+103) || !(x <= 5e-78)) {
		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 <= (-8.2d+103)) .or. (.not. (x <= 5d-78))) 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 <= -8.2e+103) || !(x <= 5e-78)) {
		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 <= -8.2e+103) or not (x <= 5e-78):
		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 ((x <= -8.2e+103) || !(x <= 5e-78))
		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 <= -8.2e+103) || ~((x <= 5e-78)))
		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[x, -8.2e+103], N[Not[LessEqual[x, 5e-78]], $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 x < -8.2000000000000003e103 or 4.9999999999999996e-78 < x

   1. Initial program 93.0%

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

   2. Taylor expanded in z around 0 77.2%

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

   if -8.2000000000000003e103 < x < 4.9999999999999996e-78

   1. Initial program 97.2%

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

   2. Taylor expanded in x around 0 89.6%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+103} \lor \neg \left(x \leq 5 \cdot 10^{-78}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]

Alternative 6: 62.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.65 \cdot 10^{+138}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 2.9 \cdot 10^{+109}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -2.65e+138)
   (* c i)
   (if (<= (* c i) 2.9e+109) (+ (* a b) (* 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) <= -2.65e+138) {
		tmp = c * i;
	} else if ((c * i) <= 2.9e+109) {
		tmp = (a * b) + (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) <= (-2.65d+138)) then
        tmp = c * i
    else if ((c * i) <= 2.9d+109) then
        tmp = (a * b) + (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) <= -2.65e+138) {
		tmp = c * i;
	} else if ((c * i) <= 2.9e+109) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -2.65e+138:
		tmp = c * i
	elif (c * i) <= 2.9e+109:
		tmp = (a * b) + (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) <= -2.65e+138)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 2.9e+109)
		tmp = Float64(Float64(a * b) + 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) <= -2.65e+138)
		tmp = c * i;
	elseif ((c * i) <= 2.9e+109)
		tmp = (a * b) + (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], -2.65e+138], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.9e+109], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(c * i), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -2.64999999999999992e138 or 2.9e109 < (*.f64 c i)

   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 c around inf 67.2%

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

   if -2.64999999999999992e138 < (*.f64 c i) < 2.9e109

   1. Initial program 97.2%

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

   2. Taylor expanded in x around 0 76.2%

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

   3. Taylor expanded in c around 0 68.7%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.65 \cdot 10^{+138}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 2.9 \cdot 10^{+109}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 7: 37.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+73}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-52}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;z \leq -1.24 \cdot 10^{-306}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-273}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-6}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -9.2e+73)
   (* z t)
   (if (<= z -7e-52)
     (* a b)
     (if (<= z -1.24e-306)
       (* x y)
       (if (<= z 4.8e-273) (* a b) (if (<= z 4.5e-6) (* 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 (z <= -9.2e+73) {
		tmp = z * t;
	} else if (z <= -7e-52) {
		tmp = a * b;
	} else if (z <= -1.24e-306) {
		tmp = x * y;
	} else if (z <= 4.8e-273) {
		tmp = a * b;
	} else if (z <= 4.5e-6) {
		tmp = 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 (z <= (-9.2d+73)) then
        tmp = z * t
    else if (z <= (-7d-52)) then
        tmp = a * b
    else if (z <= (-1.24d-306)) then
        tmp = x * y
    else if (z <= 4.8d-273) then
        tmp = a * b
    else if (z <= 4.5d-6) then
        tmp = 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 (z <= -9.2e+73) {
		tmp = z * t;
	} else if (z <= -7e-52) {
		tmp = a * b;
	} else if (z <= -1.24e-306) {
		tmp = x * y;
	} else if (z <= 4.8e-273) {
		tmp = a * b;
	} else if (z <= 4.5e-6) {
		tmp = c * i;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -9.2e+73:
		tmp = z * t
	elif z <= -7e-52:
		tmp = a * b
	elif z <= -1.24e-306:
		tmp = x * y
	elif z <= 4.8e-273:
		tmp = a * b
	elif z <= 4.5e-6:
		tmp = c * i
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -9.2e+73)
		tmp = Float64(z * t);
	elseif (z <= -7e-52)
		tmp = Float64(a * b);
	elseif (z <= -1.24e-306)
		tmp = Float64(x * y);
	elseif (z <= 4.8e-273)
		tmp = Float64(a * b);
	elseif (z <= 4.5e-6)
		tmp = 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 (z <= -9.2e+73)
		tmp = z * t;
	elseif (z <= -7e-52)
		tmp = a * b;
	elseif (z <= -1.24e-306)
		tmp = x * y;
	elseif (z <= 4.8e-273)
		tmp = a * b;
	elseif (z <= 4.5e-6)
		tmp = c * i;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -9.2e+73], N[(z * t), $MachinePrecision], If[LessEqual[z, -7e-52], N[(a * b), $MachinePrecision], If[LessEqual[z, -1.24e-306], N[(x * y), $MachinePrecision], If[LessEqual[z, 4.8e-273], N[(a * b), $MachinePrecision], If[LessEqual[z, 4.5e-6], N[(c * i), $MachinePrecision], N[(z * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.199999999999999e73 or 4.50000000000000011e-6 < z

   1. Initial program 93.8%

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

   2. Taylor expanded in z around inf 53.8%

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

   if -9.199999999999999e73 < z < -7.0000000000000001e-52 or -1.2399999999999999e-306 < z < 4.79999999999999963e-273

   1. Initial program 97.1%

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

   2. Taylor expanded in a around inf 42.2%

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

   if -7.0000000000000001e-52 < z < -1.2399999999999999e-306

   1. Initial program 94.6%

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

   2. Taylor expanded in x around inf 39.6%

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

   if 4.79999999999999963e-273 < z < 4.50000000000000011e-6

   1. Initial program 98.1%

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

   2. Taylor expanded in c around inf 42.0%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+73}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-52}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;z \leq -1.24 \cdot 10^{-306}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-273}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-6}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]

Alternative 8: 54.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-272}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-35}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))))
   (if (<= z -8.2e+18)
     t_1
     (if (<= z 2.1e-272)
       (+ (* a b) (* x y))
       (if (<= z 3.7e-35) (* c i) 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) + (z * t);
	double tmp;
	if (z <= -8.2e+18) {
		tmp = t_1;
	} else if (z <= 2.1e-272) {
		tmp = (a * b) + (x * y);
	} else if (z <= 3.7e-35) {
		tmp = c * i;
	} 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) + (z * t)
    if (z <= (-8.2d+18)) then
        tmp = t_1
    else if (z <= 2.1d-272) then
        tmp = (a * b) + (x * y)
    else if (z <= 3.7d-35) then
        tmp = c * i
    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) + (z * t);
	double tmp;
	if (z <= -8.2e+18) {
		tmp = t_1;
	} else if (z <= 2.1e-272) {
		tmp = (a * b) + (x * y);
	} else if (z <= 3.7e-35) {
		tmp = c * i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	tmp = 0
	if z <= -8.2e+18:
		tmp = t_1
	elif z <= 2.1e-272:
		tmp = (a * b) + (x * y)
	elif z <= 3.7e-35:
		tmp = c * i
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (z <= -8.2e+18)
		tmp = t_1;
	elseif (z <= 2.1e-272)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (z <= 3.7e-35)
		tmp = Float64(c * i);
	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) + (z * t);
	tmp = 0.0;
	if (z <= -8.2e+18)
		tmp = t_1;
	elseif (z <= 2.1e-272)
		tmp = (a * b) + (x * y);
	elseif (z <= 3.7e-35)
		tmp = c * i;
	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[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.2e+18], t$95$1, If[LessEqual[z, 2.1e-272], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e-35], N[(c * i), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.2e18 or 3.6999999999999999e-35 < z

   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 x around 0 87.7%

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

   3. Taylor expanded in c around 0 68.7%

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

   if -8.2e18 < z < 2.09999999999999987e-272

   1. Initial program 95.0%

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

   2. Taylor expanded in z around 0 83.4%

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

   3. Taylor expanded in c around 0 65.7%

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

   if 2.09999999999999987e-272 < z < 3.6999999999999999e-35

   1. Initial program 98.0%

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

   2. Taylor expanded in c around inf 40.4%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+18}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-272}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-35}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 9: 60.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-275}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))))
   (if (<= z -7.5e+15)
     t_1
     (if (<= z 5.1e-275)
       (+ (* a b) (* x y))
       (if (<= z 0.65) (+ (* a b) (* c i)) 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) + (z * t);
	double tmp;
	if (z <= -7.5e+15) {
		tmp = t_1;
	} else if (z <= 5.1e-275) {
		tmp = (a * b) + (x * y);
	} else if (z <= 0.65) {
		tmp = (a * b) + (c * i);
	} 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) + (z * t)
    if (z <= (-7.5d+15)) then
        tmp = t_1
    else if (z <= 5.1d-275) then
        tmp = (a * b) + (x * y)
    else if (z <= 0.65d0) then
        tmp = (a * b) + (c * i)
    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) + (z * t);
	double tmp;
	if (z <= -7.5e+15) {
		tmp = t_1;
	} else if (z <= 5.1e-275) {
		tmp = (a * b) + (x * y);
	} else if (z <= 0.65) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	tmp = 0
	if z <= -7.5e+15:
		tmp = t_1
	elif z <= 5.1e-275:
		tmp = (a * b) + (x * y)
	elif z <= 0.65:
		tmp = (a * b) + (c * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (z <= -7.5e+15)
		tmp = t_1;
	elseif (z <= 5.1e-275)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (z <= 0.65)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	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) + (z * t);
	tmp = 0.0;
	if (z <= -7.5e+15)
		tmp = t_1;
	elseif (z <= 5.1e-275)
		tmp = (a * b) + (x * y);
	elseif (z <= 0.65)
		tmp = (a * b) + (c * i);
	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[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e+15], t$95$1, If[LessEqual[z, 5.1e-275], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.65], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5e15 or 0.650000000000000022 < z

   1. Initial program 94.3%

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

   2. Taylor expanded in x around 0 87.3%

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

   3. Taylor expanded in c around 0 69.3%

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

   if -7.5e15 < z < 5.09999999999999984e-275

   1. Initial program 95.0%

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

   2. Taylor expanded in z around 0 83.4%

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

   3. Taylor expanded in c around 0 65.7%

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

   if 5.09999999999999984e-275 < z < 0.650000000000000022

   1. Initial program 98.1%

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

   2. Taylor expanded in x around 0 74.1%

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

   3. Taylor expanded in t around 0 67.0%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+15}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-275}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 10: 42.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.6 \cdot 10^{+21}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 1.95 \cdot 10^{+56}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -3.6e+21) (* c i) (if (<= (* c i) 1.95e+56) (* 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) <= -3.6e+21) {
		tmp = c * i;
	} else if ((c * i) <= 1.95e+56) {
		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) <= (-3.6d+21)) then
        tmp = c * i
    else if ((c * i) <= 1.95d+56) 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) <= -3.6e+21) {
		tmp = c * i;
	} else if ((c * i) <= 1.95e+56) {
		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) <= -3.6e+21:
		tmp = c * i
	elif (c * i) <= 1.95e+56:
		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) <= -3.6e+21)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 1.95e+56)
		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) <= -3.6e+21)
		tmp = c * i;
	elseif ((c * i) <= 1.95e+56)
		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], -3.6e+21], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.95e+56], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -3.6e21 or 1.94999999999999997e56 < (*.f64 c i)

   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 c around inf 52.8%

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

   if -3.6e21 < (*.f64 c i) < 1.94999999999999997e56

   1. Initial program 97.1%

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

   2. Taylor expanded in a around inf 39.0%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.6 \cdot 10^{+21}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 1.95 \cdot 10^{+56}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 11: 56.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+15}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-270}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -4.6e+15)
   (+ (* a b) (* z t))
   (if (<= z 1.9e-270) (+ (* a b) (* x y)) (+ (* 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 (z <= -4.6e+15) {
		tmp = (a * b) + (z * t);
	} else if (z <= 1.9e-270) {
		tmp = (a * b) + (x * y);
	} 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 (z <= (-4.6d+15)) then
        tmp = (a * b) + (z * t)
    else if (z <= 1.9d-270) then
        tmp = (a * b) + (x * y)
    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 (z <= -4.6e+15) {
		tmp = (a * b) + (z * t);
	} else if (z <= 1.9e-270) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -4.6e+15:
		tmp = (a * b) + (z * t)
	elif z <= 1.9e-270:
		tmp = (a * b) + (x * y)
	else:
		tmp = (c * i) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -4.6e+15)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (z <= 1.9e-270)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	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 (z <= -4.6e+15)
		tmp = (a * b) + (z * t);
	elseif (z <= 1.9e-270)
		tmp = (a * b) + (x * y);
	else
		tmp = (c * i) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -4.6e+15], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-270], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6e15

   1. Initial program 92.2%

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

   2. Taylor expanded in x around 0 84.6%

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

   3. Taylor expanded in c around 0 72.8%

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

   if -4.6e15 < z < 1.90000000000000021e-270

   1. Initial program 95.0%

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

   2. Taylor expanded in z around 0 83.4%

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

   3. Taylor expanded in c around 0 65.7%

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

   if 1.90000000000000021e-270 < z

   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 82.8%

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

   3. Taylor expanded in a around 0 64.1%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+15}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-270}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]

Alternative 12: 26.8% 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. Taylor expanded in a around inf 27.3%

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

3. Final simplification 27.3%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023174 
(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)))