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

Percentage Accurate: 95.6% → 97.7%

Time: 3.7s

Alternatives: 13

Speedup: 1.3×

• 41.8% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.6%

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

   1. lift-+.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. lift-+.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. +-commutative N/A

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

   9. *-commutative N/A

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

   10. lower-fma.f64 N/A

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

   11. +-commutative N/A

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

   12. *-commutative N/A

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

   13. lower-fma.f64 N/A

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

   14. *-commutative N/A

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

   15. +-commutative N/A

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

   16. lower-fma.f64 N/A

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

   17. *-commutative N/A

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

   18. lower-*.f64 97.7

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

4. Applied rewrites 97.7%

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

Alternative 2: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, y, t \cdot z\right)\\ t_2 := x \cdot y + z \cdot t\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+267}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{+36}:\\ \;\;\;\;\mathsf{fma}\left(b, a, x \cdot y\right)\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+113}:\\ \;\;\;\;\mathsf{fma}\left(b, a, c \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma x y (* t z))) (t_2 (+ (* x y) (* z t))))
   (if (<= t_2 -1e+267)
     t_1
     (if (<= t_2 -1e+36)
       (fma b a (* x y))
       (if (<= t_2 4e+113) (fma b a (* 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 = fma(x, y, (t * z));
	double t_2 = (x * y) + (z * t);
	double tmp;
	if (t_2 <= -1e+267) {
		tmp = t_1;
	} else if (t_2 <= -1e+36) {
		tmp = fma(b, a, (x * y));
	} else if (t_2 <= 4e+113) {
		tmp = fma(b, a, (c * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(x, y, Float64(t * z))
	t_2 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (t_2 <= -1e+267)
		tmp = t_1;
	elseif (t_2 <= -1e+36)
		tmp = fma(b, a, Float64(x * y));
	elseif (t_2 <= 4e+113)
		tmp = fma(b, a, Float64(c * i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * y + N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+267], t$95$1, If[LessEqual[t$95$2, -1e+36], N[(b * a + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e+113], N[(b * a + N[(c * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (*.f64 x y) (*.f64 z t)) < -9.9999999999999997e266 or 4e113 < (+.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 91.0%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. +-commutative N/A

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

      16. lower-fma.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 95.4

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

   4. Applied rewrites 95.4%

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

   5. Taylor expanded in c around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. +-commutative N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. +-commutative N/A

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

      11. associate-+l+ N/A

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

      12. *-commutative N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower-*.f64 87.0

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

   7. Applied rewrites 87.0%

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

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(x, y, t \cdot z\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 79.3

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

   10. Applied rewrites 79.3%

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

   if -9.9999999999999997e266 < (+.f64 (*.f64 x y) (*.f64 z t)) < -1.00000000000000004e36

   1. Initial program 98.9%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 76.2

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

   5. Applied rewrites 76.2%

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

   6. Taylor expanded in x around inf

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

      1. lower-*.f64 53.6

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

   8. Applied rewrites 53.6%

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

   if -1.00000000000000004e36 < (+.f64 (*.f64 x y) (*.f64 z t)) < 4e113

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 89.7

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

   5. Applied rewrites 89.7%

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

   6. Taylor expanded in x around 0

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

      1. lift-*.f64 79.7

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

   8. Applied rewrites 79.7%

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

Alternative 3: 63.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, a, t \cdot z\right)\\ t_2 := \mathsf{fma}\left(b, a, c \cdot i\right)\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+154}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-215}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+106}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma b a (* t z))) (t_2 (fma b a (* c i))))
   (if (<= (* x y) -2e+154)
     (* y x)
     (if (<= (* x y) -1e+17)
       t_1
       (if (<= (* x y) 2e-215)
         t_2
         (if (<= (* x y) 1e-39) t_1 (if (<= (* x y) 4e+106) t_2 (* y x))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(b, a, (t * z));
	double t_2 = fma(b, a, (c * i));
	double tmp;
	if ((x * y) <= -2e+154) {
		tmp = y * x;
	} else if ((x * y) <= -1e+17) {
		tmp = t_1;
	} else if ((x * y) <= 2e-215) {
		tmp = t_2;
	} else if ((x * y) <= 1e-39) {
		tmp = t_1;
	} else if ((x * y) <= 4e+106) {
		tmp = t_2;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(b, a, Float64(t * z))
	t_2 = fma(b, a, Float64(c * i))
	tmp = 0.0
	if (Float64(x * y) <= -2e+154)
		tmp = Float64(y * x);
	elseif (Float64(x * y) <= -1e+17)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-215)
		tmp = t_2;
	elseif (Float64(x * y) <= 1e-39)
		tmp = t_1;
	elseif (Float64(x * y) <= 4e+106)
		tmp = t_2;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * a + N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * a + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+154], N[(y * x), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1e+17], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-215], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 1e-39], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4e+106], t$95$2, N[(y * x), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.00000000000000007e154 or 4.00000000000000036e106 < (*.f64 x y)

   1. Initial program 91.1%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 65.9

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

   5. Applied rewrites 65.9%

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

   if -2.00000000000000007e154 < (*.f64 x y) < -1e17 or 2.00000000000000008e-215 < (*.f64 x y) < 9.99999999999999929e-40

   1. Initial program 98.0%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. +-commutative N/A

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

      16. lower-fma.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 99.1

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

   4. Applied rewrites 99.1%

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

   5. Taylor expanded in c around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. +-commutative N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. +-commutative N/A

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

      11. associate-+l+ N/A

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

      12. *-commutative N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower-*.f64 71.1

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

   7. Applied rewrites 71.1%

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

   8. Taylor expanded in x around 0

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

      1. *-commutative N/A

         \[\leadsto b \cdot a + t \cdot z \]

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 58.5

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

   10. Applied rewrites 58.5%

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

   if -1e17 < (*.f64 x y) < 2.00000000000000008e-215 or 9.99999999999999929e-40 < (*.f64 x y) < 4.00000000000000036e106

   1. Initial program 97.6%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 70.5

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

   5. Applied rewrites 70.5%

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

   6. Taylor expanded in x around 0

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

      1. lift-*.f64 64.2

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

   8. Applied rewrites 64.2%

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

Alternative 4: 67.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, y, t \cdot z\right)\\ t_2 := \mathsf{fma}\left(b, a, c \cdot i\right)\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{-123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-21}:\\ \;\;\;\;\mathsf{fma}\left(i, c, x \cdot y\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma x y (* t z))) (t_2 (fma b a (* c i))))
   (if (<= (* a b) -5e+65)
     t_2
     (if (<= (* a b) -2e-123)
       t_1
       (if (<= (* a b) 2e-21)
         (fma i c (* x y))
         (if (<= (* a b) 1e+103) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(x, y, (t * z));
	double t_2 = fma(b, a, (c * i));
	double tmp;
	if ((a * b) <= -5e+65) {
		tmp = t_2;
	} else if ((a * b) <= -2e-123) {
		tmp = t_1;
	} else if ((a * b) <= 2e-21) {
		tmp = fma(i, c, (x * y));
	} else if ((a * b) <= 1e+103) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(x, y, Float64(t * z))
	t_2 = fma(b, a, Float64(c * i))
	tmp = 0.0
	if (Float64(a * b) <= -5e+65)
		tmp = t_2;
	elseif (Float64(a * b) <= -2e-123)
		tmp = t_1;
	elseif (Float64(a * b) <= 2e-21)
		tmp = fma(i, c, Float64(x * y));
	elseif (Float64(a * b) <= 1e+103)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * y + N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * a + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+65], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -2e-123], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 2e-21], N[(i * c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+103], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.99999999999999973e65 or 1e103 < (*.f64 a b)

   1. Initial program 91.9%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 85.7

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

   5. Applied rewrites 85.7%

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

   6. Taylor expanded in x around 0

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

      1. lift-*.f64 73.4

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

   8. Applied rewrites 73.4%

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

   if -4.99999999999999973e65 < (*.f64 a b) < -2.0000000000000001e-123 or 1.99999999999999982e-21 < (*.f64 a b) < 1e103

   1. Initial program 97.6%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. +-commutative N/A

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

      16. lower-fma.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 98.8

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

   4. Applied rewrites 98.8%

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

   5. Taylor expanded in c around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. +-commutative N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. +-commutative N/A

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

      11. associate-+l+ N/A

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

      12. *-commutative N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower-*.f64 71.3

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

   7. Applied rewrites 71.3%

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

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(x, y, t \cdot z\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 57.4

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

   10. Applied rewrites 57.4%

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

   if -2.0000000000000001e-123 < (*.f64 a b) < 1.99999999999999982e-21

   1. Initial program 97.8%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. +-commutative N/A

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

      16. lower-fma.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 98.6

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

   4. Applied rewrites 98.6%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. +-commutative N/A

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

      6. lower-*.f64 66.8

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

   7. Applied rewrites 66.8%

      \[\leadsto \mathsf{fma}\left(i, c, \color{blue}{x \cdot y}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 42.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+35}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{-123}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-21}:\\ \;\;\;\;i \cdot c\\ \mathbf{elif}\;a \cdot b \leq 10^{+103}:\\ \;\;\;\;t \cdot z\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -5e+35)
   (* b a)
   (if (<= (* a b) -2e-123)
     (* t z)
     (if (<= (* a b) 2e-21)
       (* i c)
       (if (<= (* a b) 1e+103) (* t z) (* b a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -5e+35) {
		tmp = b * a;
	} else if ((a * b) <= -2e-123) {
		tmp = t * z;
	} else if ((a * b) <= 2e-21) {
		tmp = i * c;
	} else if ((a * b) <= 1e+103) {
		tmp = t * z;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    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+35)) then
        tmp = b * a
    else if ((a * b) <= (-2d-123)) then
        tmp = t * z
    else if ((a * b) <= 2d-21) then
        tmp = i * c
    else if ((a * b) <= 1d+103) then
        tmp = t * z
    else
        tmp = b * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -5e+35) {
		tmp = b * a;
	} else if ((a * b) <= -2e-123) {
		tmp = t * z;
	} else if ((a * b) <= 2e-21) {
		tmp = i * c;
	} else if ((a * b) <= 1e+103) {
		tmp = t * z;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -5e+35:
		tmp = b * a
	elif (a * b) <= -2e-123:
		tmp = t * z
	elif (a * b) <= 2e-21:
		tmp = i * c
	elif (a * b) <= 1e+103:
		tmp = t * z
	else:
		tmp = b * a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -5e+35)
		tmp = Float64(b * a);
	elseif (Float64(a * b) <= -2e-123)
		tmp = Float64(t * z);
	elseif (Float64(a * b) <= 2e-21)
		tmp = Float64(i * c);
	elseif (Float64(a * b) <= 1e+103)
		tmp = Float64(t * z);
	else
		tmp = Float64(b * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -5e+35)
		tmp = b * a;
	elseif ((a * b) <= -2e-123)
		tmp = t * z;
	elseif ((a * b) <= 2e-21)
		tmp = i * c;
	elseif ((a * b) <= 1e+103)
		tmp = t * z;
	else
		tmp = b * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -5e+35], N[(b * a), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -2e-123], N[(t * z), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e-21], N[(i * c), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+103], N[(t * z), $MachinePrecision], N[(b * a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.00000000000000021e35 or 1e103 < (*.f64 a b)

   1. Initial program 92.1%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 58.3

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

   5. Applied rewrites 58.3%

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

   if -5.00000000000000021e35 < (*.f64 a b) < -2.0000000000000001e-123 or 1.99999999999999982e-21 < (*.f64 a b) < 1e103

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 29.7

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

   5. Applied rewrites 29.7%

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

   if -2.0000000000000001e-123 < (*.f64 a b) < 1.99999999999999982e-21

   1. Initial program 97.8%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 34.5

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

   5. Applied rewrites 34.5%

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

Alternative 6: 89.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, a, \mathsf{fma}\left(i, c, y \cdot x\right)\right)\\ \mathbf{if}\;c \cdot i \leq -5000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 10^{+42}:\\ \;\;\;\;\mathsf{fma}\left(x, y, \mathsf{fma}\left(z, t, a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma b a (fma i c (* y x)))))
   (if (<= (* c i) -5000000.0)
     t_1
     (if (<= (* c i) 1e+42) (fma x y (fma z t (* a b))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(b, a, fma(i, c, (y * x)));
	double tmp;
	if ((c * i) <= -5000000.0) {
		tmp = t_1;
	} else if ((c * i) <= 1e+42) {
		tmp = fma(x, y, fma(z, t, (a * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(b, a, fma(i, c, Float64(y * x)))
	tmp = 0.0
	if (Float64(c * i) <= -5000000.0)
		tmp = t_1;
	elseif (Float64(c * i) <= 1e+42)
		tmp = fma(x, y, fma(z, t, Float64(a * b)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * a + N[(i * c + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -5000000.0], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 1e+42], N[(x * y + N[(z * t + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -5e6 or 1.00000000000000004e42 < (*.f64 c i)

   1. Initial program 92.9%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 83.4

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

   5. Applied rewrites 83.4%

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

   if -5e6 < (*.f64 c i) < 1.00000000000000004e42

   1. Initial program 97.8%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. +-commutative N/A

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

      16. lower-fma.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 99.0

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

   4. Applied rewrites 99.0%

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

   5. Taylor expanded in c around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. +-commutative N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. +-commutative N/A

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

      11. associate-+l+ N/A

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

      12. *-commutative N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower-*.f64 94.7

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

   7. Applied rewrites 94.7%

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

Alternative 7: 88.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, a, \mathsf{fma}\left(t, z, y \cdot x\right)\right)\\ \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-15}:\\ \;\;\;\;\mathsf{fma}\left(b, a, \mathsf{fma}\left(i, c, y \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma b a (fma t z (* y x)))))
   (if (<= (* z t) -2e+14)
     t_1
     (if (<= (* z t) 2e-15) (fma b a (fma i c (* y x))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(b, a, fma(t, z, (y * x)));
	double tmp;
	if ((z * t) <= -2e+14) {
		tmp = t_1;
	} else if ((z * t) <= 2e-15) {
		tmp = fma(b, a, fma(i, c, (y * x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(b, a, fma(t, z, Float64(y * x)))
	tmp = 0.0
	if (Float64(z * t) <= -2e+14)
		tmp = t_1;
	elseif (Float64(z * t) <= 2e-15)
		tmp = fma(b, a, fma(i, c, Float64(y * x)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * a + N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -2e+14], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 2e-15], N[(b * a + N[(i * c + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -2e14 or 2.0000000000000002e-15 < (*.f64 z t)

   1. Initial program 93.8%

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

   3. Taylor expanded in c around 0

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 81.4

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

   5. Applied rewrites 81.4%

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

   if -2e14 < (*.f64 z t) < 2.0000000000000002e-15

   1. Initial program 97.3%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 95.6

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

   5. Applied rewrites 95.6%

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

Alternative 8: 86.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, a, t \cdot z\right)\\ \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+267}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 10^{+173}:\\ \;\;\;\;\mathsf{fma}\left(b, a, \mathsf{fma}\left(i, c, y \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma b a (* t z))))
   (if (<= (* z t) -1e+267)
     t_1
     (if (<= (* z t) 1e+173) (fma b a (fma i c (* y x))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(b, a, (t * z));
	double tmp;
	if ((z * t) <= -1e+267) {
		tmp = t_1;
	} else if ((z * t) <= 1e+173) {
		tmp = fma(b, a, fma(i, c, (y * x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(b, a, Float64(t * z))
	tmp = 0.0
	if (Float64(z * t) <= -1e+267)
		tmp = t_1;
	elseif (Float64(z * t) <= 1e+173)
		tmp = fma(b, a, fma(i, c, Float64(y * x)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * a + N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -1e+267], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 1e+173], N[(b * a + N[(i * c + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -9.9999999999999997e266 or 1e173 < (*.f64 z t)

   1. Initial program 88.7%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. +-commutative N/A

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

      16. lower-fma.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 94.1

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

   4. Applied rewrites 94.1%

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

   5. Taylor expanded in c around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. +-commutative N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. +-commutative N/A

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

      11. associate-+l+ N/A

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

      12. *-commutative N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower-*.f64 88.1

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

   7. Applied rewrites 88.1%

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

   8. Taylor expanded in x around 0

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

      1. *-commutative N/A

         \[\leadsto b \cdot a + t \cdot z \]

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 83.5

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

   10. Applied rewrites 83.5%

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

   if -9.9999999999999997e266 < (*.f64 z t) < 1e173

   1. Initial program 97.4%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 86.8

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

   5. Applied rewrites 86.8%

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

Alternative 9: 43.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+35}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-121}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;a \cdot b \leq 10^{+103}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -5e+35)
   (* b a)
   (if (<= (* a b) -1e-121) (* t z) (if (<= (* a b) 1e+103) (* y x) (* b a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -5e+35) {
		tmp = b * a;
	} else if ((a * b) <= -1e-121) {
		tmp = t * z;
	} else if ((a * b) <= 1e+103) {
		tmp = y * x;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    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+35)) then
        tmp = b * a
    else if ((a * b) <= (-1d-121)) then
        tmp = t * z
    else if ((a * b) <= 1d+103) then
        tmp = y * x
    else
        tmp = b * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -5e+35) {
		tmp = b * a;
	} else if ((a * b) <= -1e-121) {
		tmp = t * z;
	} else if ((a * b) <= 1e+103) {
		tmp = y * x;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -5e+35:
		tmp = b * a
	elif (a * b) <= -1e-121:
		tmp = t * z
	elif (a * b) <= 1e+103:
		tmp = y * x
	else:
		tmp = b * a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -5e+35)
		tmp = Float64(b * a);
	elseif (Float64(a * b) <= -1e-121)
		tmp = Float64(t * z);
	elseif (Float64(a * b) <= 1e+103)
		tmp = Float64(y * x);
	else
		tmp = Float64(b * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -5e+35)
		tmp = b * a;
	elseif ((a * b) <= -1e-121)
		tmp = t * z;
	elseif ((a * b) <= 1e+103)
		tmp = y * x;
	else
		tmp = b * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -5e+35], N[(b * a), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1e-121], N[(t * z), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+103], N[(y * x), $MachinePrecision], N[(b * a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.00000000000000021e35 or 1e103 < (*.f64 a b)

   1. Initial program 92.1%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 58.3

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

   5. Applied rewrites 58.3%

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

   if -5.00000000000000021e35 < (*.f64 a b) < -9.9999999999999998e-122

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 31.6

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

   5. Applied rewrites 31.6%

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

   if -9.9999999999999998e-122 < (*.f64 a b) < 1e103

   1. Initial program 97.7%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 34.3

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

   5. Applied rewrites 34.3%

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

Alternative 10: 67.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, a, c \cdot i\right)\\ \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 2 \cdot 10^{+198}:\\ \;\;\;\;\mathsf{fma}\left(b, a, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma b a (* c i))))
   (if (<= (* c i) -1e+68)
     t_1
     (if (<= (* c i) 2e+198) (fma b a (* x y)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(b, a, (c * i));
	double tmp;
	if ((c * i) <= -1e+68) {
		tmp = t_1;
	} else if ((c * i) <= 2e+198) {
		tmp = fma(b, a, (x * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(b, a, Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -1e+68)
		tmp = t_1;
	elseif (Float64(c * i) <= 2e+198)
		tmp = fma(b, a, Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * a + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -1e+68], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 2e+198], N[(b * a + N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -9.99999999999999953e67 or 2.00000000000000004e198 < (*.f64 c i)

   1. Initial program 90.8%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 86.9

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

   5. Applied rewrites 86.9%

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

   6. Taylor expanded in x around 0

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

      1. lift-*.f64 76.8

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

   8. Applied rewrites 76.8%

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

   if -9.99999999999999953e67 < (*.f64 c i) < 2.00000000000000004e198

   1. Initial program 97.7%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 71.0

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

   5. Applied rewrites 71.0%

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

   6. Taylor expanded in x around inf

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

      1. lower-*.f64 62.7

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

   8. Applied rewrites 62.7%

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

Alternative 11: 62.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+154}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(b, a, t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -2e+154)
   (* y x)
   (if (<= (* x y) 4e+106) (fma b a (* t z)) (* y x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -2e+154) {
		tmp = y * x;
	} else if ((x * y) <= 4e+106) {
		tmp = fma(b, a, (t * z));
	} else {
		tmp = y * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -2e+154)
		tmp = Float64(y * x);
	elseif (Float64(x * y) <= 4e+106)
		tmp = fma(b, a, Float64(t * z));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+154], N[(y * x), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+106], N[(b * a + N[(t * z), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.00000000000000007e154 or 4.00000000000000036e106 < (*.f64 x y)

   1. Initial program 91.1%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 65.9

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

   5. Applied rewrites 65.9%

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

   if -2.00000000000000007e154 < (*.f64 x y) < 4.00000000000000036e106

   1. Initial program 97.7%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. +-commutative N/A

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

      16. lower-fma.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 98.8

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

   4. Applied rewrites 98.8%

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

   5. Taylor expanded in c around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. +-commutative N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. +-commutative N/A

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

      11. associate-+l+ N/A

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

      12. *-commutative N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower-*.f64 69.0

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

   7. Applied rewrites 69.0%

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

   8. Taylor expanded in x around 0

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

      1. *-commutative N/A

         \[\leadsto b \cdot a + t \cdot z \]

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 60.8

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

   10. Applied rewrites 60.8%

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

Alternative 12: 43.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2 \cdot 10^{+90}:\\ \;\;\;\;i \cdot c\\ \mathbf{elif}\;c \cdot i \leq 10^{+36}:\\ \;\;\;\;b \cdot a\\ \mathbf{else}:\\ \;\;\;\;i \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -2e+90) (* i c) (if (<= (* c i) 1e+36) (* b a) (* i c))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -2e+90) {
		tmp = i * c;
	} else if ((c * i) <= 1e+36) {
		tmp = b * a;
	} else {
		tmp = i * c;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    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) <= (-2d+90)) then
        tmp = i * c
    else if ((c * i) <= 1d+36) then
        tmp = b * a
    else
        tmp = i * c
    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) <= -2e+90) {
		tmp = i * c;
	} else if ((c * i) <= 1e+36) {
		tmp = b * a;
	} else {
		tmp = i * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -2e+90:
		tmp = i * c
	elif (c * i) <= 1e+36:
		tmp = b * a
	else:
		tmp = i * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -2e+90)
		tmp = Float64(i * c);
	elseif (Float64(c * i) <= 1e+36)
		tmp = Float64(b * a);
	else
		tmp = Float64(i * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -2e+90)
		tmp = i * c;
	elseif ((c * i) <= 1e+36)
		tmp = b * a;
	else
		tmp = i * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -2e+90], N[(i * c), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1e+36], N[(b * a), $MachinePrecision], N[(i * c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -1.99999999999999993e90 or 1.00000000000000004e36 < (*.f64 c i)

   1. Initial program 92.3%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 57.8

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

   5. Applied rewrites 57.8%

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

   if -1.99999999999999993e90 < (*.f64 c i) < 1.00000000000000004e36

   1. Initial program 97.7%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 33.6

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

   5. Applied rewrites 33.6%

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

Alternative 13: 27.6% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.6%

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

3. Taylor expanded in a around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 27.6

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

5. Applied rewrites 27.6%

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

Reproduce

herbie shell --seed 2025089 
(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)))