Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 74.0% → 82.3%

Time: 8.2s

Alternatives: 21

Speedup: 0.5×

• 58.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 74.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.3%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

   4. Applied rewrites 91.3%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 26.0

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

   4. Applied rewrites 26.0%

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

   5. Taylor expanded in a around 0

      \[\leadsto \left(a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) - \color{blue}{b \cdot \left(c \cdot z\right)} \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(x \cdot \left(y \cdot z\right) - \color{blue}{b \cdot \left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot a + \left(x \cdot \left(y \cdot z\right) - \color{blue}{b} \cdot \left(c \cdot z\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right), a, x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \left(t \cdot x\right) - \left(-1 \cdot b\right) \cdot i, a, x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \left(t \cdot x\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot i, a, x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right) \]

      6. fp-cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \left(t \cdot x\right) + b \cdot i, a, x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(\left(-1 \cdot t\right) \cdot x + b \cdot i, a, x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right) \]

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 N/A

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

   7. Applied rewrites 43.9%

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

Alternative 2: 70.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot y - a \cdot t\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{+131}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot a - c \cdot z, b, \left(-i\right) \cdot \left(j \cdot y\right)\right)\\ \mathbf{elif}\;b \leq -1.88 \cdot 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-t, x, i \cdot b\right), a, \left(z \cdot y\right) \cdot x - \left(c \cdot b\right) \cdot z\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, x, \left(c \cdot t - i \cdot y\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, x, \left(-\left(c \cdot z - i \cdot a\right)\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* z y) (* a t))))
   (if (<= b -7.2e+131)
     (fma (- (* i a) (* c z)) b (* (- i) (* j y)))
     (if (<= b -1.88e-34)
       (fma (fma (- t) x (* i b)) a (- (* (* z y) x) (* (* c b) z)))
       (if (<= b 4.5e+72)
         (fma t_1 x (* (- (* c t) (* i y)) j))
         (fma t_1 x (* (- (- (* c z) (* i a))) b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * y) - (a * t);
	double tmp;
	if (b <= -7.2e+131) {
		tmp = fma(((i * a) - (c * z)), b, (-i * (j * y)));
	} else if (b <= -1.88e-34) {
		tmp = fma(fma(-t, x, (i * b)), a, (((z * y) * x) - ((c * b) * z)));
	} else if (b <= 4.5e+72) {
		tmp = fma(t_1, x, (((c * t) - (i * y)) * j));
	} else {
		tmp = fma(t_1, x, (-((c * z) - (i * a)) * b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * y) - Float64(a * t))
	tmp = 0.0
	if (b <= -7.2e+131)
		tmp = fma(Float64(Float64(i * a) - Float64(c * z)), b, Float64(Float64(-i) * Float64(j * y)));
	elseif (b <= -1.88e-34)
		tmp = fma(fma(Float64(-t), x, Float64(i * b)), a, Float64(Float64(Float64(z * y) * x) - Float64(Float64(c * b) * z)));
	elseif (b <= 4.5e+72)
		tmp = fma(t_1, x, Float64(Float64(Float64(c * t) - Float64(i * y)) * j));
	else
		tmp = fma(t_1, x, Float64(Float64(-Float64(Float64(c * z) - Float64(i * a))) * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.2e+131], N[(N[(N[(i * a), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision] * b + N[((-i) * N[(j * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.88e-34], N[(N[((-t) * x + N[(i * b), $MachinePrecision]), $MachinePrecision] * a + N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] - N[(N[(c * b), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.5e+72], N[(t$95$1 * x + N[(N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * x + N[((-N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]) * b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.20000000000000063e131

   1. Initial program 72.4%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

   4. Applied rewrites 77.8%

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

   5. Taylor expanded in i around inf

      \[\leadsto \mathsf{fma}\left(i \cdot a - c \cdot z, b, -1 \cdot \left(i \cdot \left(j \cdot y\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(i \cdot a - c \cdot z, b, \left(-1 \cdot i\right) \cdot \left(j \cdot y\right)\right) \]

      2. mul-1-neg N/A

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

      3. lift-neg.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 72.2

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

   7. Applied rewrites 72.2%

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

   if -7.20000000000000063e131 < b < -1.88e-34

   1. Initial program 74.4%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 61.6

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

   4. Applied rewrites 61.6%

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

   5. Taylor expanded in a around 0

      \[\leadsto \left(a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) - \color{blue}{b \cdot \left(c \cdot z\right)} \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(x \cdot \left(y \cdot z\right) - \color{blue}{b \cdot \left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot a + \left(x \cdot \left(y \cdot z\right) - \color{blue}{b} \cdot \left(c \cdot z\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right), a, x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \left(t \cdot x\right) - \left(-1 \cdot b\right) \cdot i, a, x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \left(t \cdot x\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot i, a, x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right) \]

      6. fp-cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \left(t \cdot x\right) + b \cdot i, a, x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(\left(-1 \cdot t\right) \cdot x + b \cdot i, a, x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right) \]

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 N/A

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

   7. Applied rewrites 60.7%

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

   if -1.88e-34 < b < 4.4999999999999998e72

   1. Initial program 73.9%

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

   2. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 70.7

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

   4. Applied rewrites 70.7%

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

   if 4.4999999999999998e72 < b

   1. Initial program 75.2%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 69.5

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

   4. Applied rewrites 69.5%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift--.f64 N/A

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

      10. fp-cancel-sub-sign-inv N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lower--.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. lift-*.f64 N/A

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

   6. Applied rewrites 71.7%

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

Alternative 3: 69.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot y - a \cdot t\\ t_2 := \mathsf{fma}\left(t\_1, x, \left(-\left(c \cdot z - i \cdot a\right)\right) \cdot b\right)\\ \mathbf{if}\;b \leq -6.2 \cdot 10^{-32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, x, \left(c \cdot t - i \cdot y\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* z y) (* a t)))
        (t_2 (fma t_1 x (* (- (- (* c z) (* i a))) b))))
   (if (<= b -6.2e-32)
     t_2
     (if (<= b 4.5e+72) (fma t_1 x (* (- (* c t) (* i y)) j)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * y) - (a * t);
	double t_2 = fma(t_1, x, (-((c * z) - (i * a)) * b));
	double tmp;
	if (b <= -6.2e-32) {
		tmp = t_2;
	} else if (b <= 4.5e+72) {
		tmp = fma(t_1, x, (((c * t) - (i * y)) * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * y) - Float64(a * t))
	t_2 = fma(t_1, x, Float64(Float64(-Float64(Float64(c * z) - Float64(i * a))) * b))
	tmp = 0.0
	if (b <= -6.2e-32)
		tmp = t_2;
	elseif (b <= 4.5e+72)
		tmp = fma(t_1, x, Float64(Float64(Float64(c * t) - Float64(i * y)) * j));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * x + N[((-N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]) * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.2e-32], t$95$2, If[LessEqual[b, 4.5e+72], N[(t$95$1 * x + N[(N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.20000000000000021e-32 or 4.4999999999999998e72 < b

   1. Initial program 74.2%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 67.8

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

   4. Applied rewrites 67.8%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift--.f64 N/A

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

      10. fp-cancel-sub-sign-inv N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lower--.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. lift-*.f64 N/A

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

   6. Applied rewrites 69.8%

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

   if -6.20000000000000021e-32 < b < 4.4999999999999998e72

   1. Initial program 73.8%

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

   2. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 70.7

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

   4. Applied rewrites 70.7%

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

Alternative 4: 69.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot y - a \cdot t\\ \mathbf{if}\;b \leq -3 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot a - c \cdot z, b, \left(-i\right) \cdot \left(j \cdot y\right)\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, x, \left(c \cdot t - i \cdot y\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* z y) (* a t))))
   (if (<= b -3e+21)
     (fma (- (* i a) (* c z)) b (* (- i) (* j y)))
     (if (<= b 5.6e+72)
       (fma t_1 x (* (- (* c t) (* i y)) j))
       (- (* t_1 x) (* (- (* c z) (* i a)) b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * y) - (a * t);
	double tmp;
	if (b <= -3e+21) {
		tmp = fma(((i * a) - (c * z)), b, (-i * (j * y)));
	} else if (b <= 5.6e+72) {
		tmp = fma(t_1, x, (((c * t) - (i * y)) * j));
	} else {
		tmp = (t_1 * x) - (((c * z) - (i * a)) * b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * y) - Float64(a * t))
	tmp = 0.0
	if (b <= -3e+21)
		tmp = fma(Float64(Float64(i * a) - Float64(c * z)), b, Float64(Float64(-i) * Float64(j * y)));
	elseif (b <= 5.6e+72)
		tmp = fma(t_1, x, Float64(Float64(Float64(c * t) - Float64(i * y)) * j));
	else
		tmp = Float64(Float64(t_1 * x) - Float64(Float64(Float64(c * z) - Float64(i * a)) * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3e+21], N[(N[(N[(i * a), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision] * b + N[((-i) * N[(j * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.6e+72], N[(t$95$1 * x + N[(N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 * x), $MachinePrecision] - N[(N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3e21

   1. Initial program 72.6%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

   4. Applied rewrites 77.4%

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

   5. Taylor expanded in i around inf

      \[\leadsto \mathsf{fma}\left(i \cdot a - c \cdot z, b, -1 \cdot \left(i \cdot \left(j \cdot y\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(i \cdot a - c \cdot z, b, \left(-1 \cdot i\right) \cdot \left(j \cdot y\right)\right) \]

      2. mul-1-neg N/A

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

      3. lift-neg.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 68.0

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

   7. Applied rewrites 68.0%

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

   if -3e21 < b < 5.5999999999999998e72

   1. Initial program 74.1%

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

   2. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 70.0

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

   4. Applied rewrites 70.0%

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

   if 5.5999999999999998e72 < b

   1. Initial program 75.2%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 69.5

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

   4. Applied rewrites 69.5%

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

Alternative 5: 69.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot a - c \cdot z\\ \mathbf{if}\;b \leq -3 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, \left(-i\right) \cdot \left(j \cdot y\right)\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot y - a \cdot t, x, \left(c \cdot t - i \cdot y\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, \left(-a\right) \cdot \left(t \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* i a) (* c z))))
   (if (<= b -3e+21)
     (fma t_1 b (* (- i) (* j y)))
     (if (<= b 3.4e+74)
       (fma (- (* z y) (* a t)) x (* (- (* c t) (* i y)) j))
       (fma t_1 b (* (- a) (* t x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * a) - (c * z);
	double tmp;
	if (b <= -3e+21) {
		tmp = fma(t_1, b, (-i * (j * y)));
	} else if (b <= 3.4e+74) {
		tmp = fma(((z * y) - (a * t)), x, (((c * t) - (i * y)) * j));
	} else {
		tmp = fma(t_1, b, (-a * (t * x)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * a) - Float64(c * z))
	tmp = 0.0
	if (b <= -3e+21)
		tmp = fma(t_1, b, Float64(Float64(-i) * Float64(j * y)));
	elseif (b <= 3.4e+74)
		tmp = fma(Float64(Float64(z * y) - Float64(a * t)), x, Float64(Float64(Float64(c * t) - Float64(i * y)) * j));
	else
		tmp = fma(t_1, b, Float64(Float64(-a) * Float64(t * x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * a), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3e+21], N[(t$95$1 * b + N[((-i) * N[(j * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.4e+74], N[(N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision] * x + N[(N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * b + N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3e21

   1. Initial program 72.6%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

   4. Applied rewrites 77.4%

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

   5. Taylor expanded in i around inf

      \[\leadsto \mathsf{fma}\left(i \cdot a - c \cdot z, b, -1 \cdot \left(i \cdot \left(j \cdot y\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(i \cdot a - c \cdot z, b, \left(-1 \cdot i\right) \cdot \left(j \cdot y\right)\right) \]

      2. mul-1-neg N/A

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

      3. lift-neg.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 68.0

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

   7. Applied rewrites 68.0%

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

   if -3e21 < b < 3.3999999999999999e74

   1. Initial program 74.1%

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

   2. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 69.9

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

   4. Applied rewrites 69.9%

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

   if 3.3999999999999999e74 < b

   1. Initial program 75.2%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

   4. Applied rewrites 80.4%

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

   5. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma}\left(i \cdot a - c \cdot z, b, -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(i \cdot a - c \cdot z, b, \left(-1 \cdot a\right) \cdot \left(t \cdot x\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot a - c \cdot z, b, \left(-1 \cdot a\right) \cdot \left(t \cdot x\right)\right) \]

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-*.f64 71.5

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

   7. Applied rewrites 71.5%

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

Alternative 6: 60.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot a - c \cdot z\\ t_2 := \mathsf{fma}\left(t\_1, b, \left(-a\right) \cdot \left(t \cdot x\right)\right)\\ \mathbf{if}\;b \leq -1.55 \cdot 10^{+62}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, \left(-i\right) \cdot \left(j \cdot y\right)\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-46}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-272}:\\ \;\;\;\;\left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z\right) \cdot b\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+97}:\\ \;\;\;\;\left(-\left(c \cdot b\right) \cdot z\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* i a) (* c z))) (t_2 (fma t_1 b (* (- a) (* t x)))))
   (if (<= b -1.55e+62)
     (fma t_1 b (* (- i) (* j y)))
     (if (<= b -3e-46)
       t_2
       (if (<= b 3.7e-272)
         (- (* (- (* z y) (* a t)) x) (* (* c z) b))
         (if (<= b 6.6e+97)
           (+ (- (* (* c b) z)) (* j (- (* c t) (* i y))))
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * a) - (c * z);
	double t_2 = fma(t_1, b, (-a * (t * x)));
	double tmp;
	if (b <= -1.55e+62) {
		tmp = fma(t_1, b, (-i * (j * y)));
	} else if (b <= -3e-46) {
		tmp = t_2;
	} else if (b <= 3.7e-272) {
		tmp = (((z * y) - (a * t)) * x) - ((c * z) * b);
	} else if (b <= 6.6e+97) {
		tmp = -((c * b) * z) + (j * ((c * t) - (i * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * a) - Float64(c * z))
	t_2 = fma(t_1, b, Float64(Float64(-a) * Float64(t * x)))
	tmp = 0.0
	if (b <= -1.55e+62)
		tmp = fma(t_1, b, Float64(Float64(-i) * Float64(j * y)));
	elseif (b <= -3e-46)
		tmp = t_2;
	elseif (b <= 3.7e-272)
		tmp = Float64(Float64(Float64(Float64(z * y) - Float64(a * t)) * x) - Float64(Float64(c * z) * b));
	elseif (b <= 6.6e+97)
		tmp = Float64(Float64(-Float64(Float64(c * b) * z)) + Float64(j * Float64(Float64(c * t) - Float64(i * y))));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * a), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * b + N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.55e+62], N[(t$95$1 * b + N[((-i) * N[(j * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3e-46], t$95$2, If[LessEqual[b, 3.7e-272], N[(N[(N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] - N[(N[(c * z), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.6e+97], N[((-N[(N[(c * b), $MachinePrecision] * z), $MachinePrecision]) + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.55000000000000007e62

   1. Initial program 72.1%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

   4. Applied rewrites 77.3%

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

   5. Taylor expanded in i around inf

      \[\leadsto \mathsf{fma}\left(i \cdot a - c \cdot z, b, -1 \cdot \left(i \cdot \left(j \cdot y\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(i \cdot a - c \cdot z, b, \left(-1 \cdot i\right) \cdot \left(j \cdot y\right)\right) \]

      2. mul-1-neg N/A

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

      3. lift-neg.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 69.9

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

   7. Applied rewrites 69.9%

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

   if -1.55000000000000007e62 < b < -2.99999999999999987e-46 or 6.6000000000000003e97 < b

   1. Initial program 75.2%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

   4. Applied rewrites 79.1%

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

   5. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma}\left(i \cdot a - c \cdot z, b, -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(i \cdot a - c \cdot z, b, \left(-1 \cdot a\right) \cdot \left(t \cdot x\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot a - c \cdot z, b, \left(-1 \cdot a\right) \cdot \left(t \cdot x\right)\right) \]

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-*.f64 65.4

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

   7. Applied rewrites 65.4%

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

   if -2.99999999999999987e-46 < b < 3.6999999999999997e-272

   1. Initial program 72.6%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 48.5

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

   4. Applied rewrites 48.5%

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

   5. Taylor expanded in z around inf

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

      1. lift-*.f64 45.5

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

   7. Applied rewrites 45.5%

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

   if 3.6999999999999997e-272 < b < 6.6000000000000003e97

   1. Initial program 75.3%

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

   2. Taylor expanded in c around inf

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto \left(-b \cdot \left(c \cdot z\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. associate-*r* N/A

         \[\leadsto \left(-\left(b \cdot c\right) \cdot z\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \left(-\left(b \cdot c\right) \cdot z\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. *-commutative N/A

         \[\leadsto \left(-\left(c \cdot b\right) \cdot z\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. lower-*.f64 51.9

         \[\leadsto \left(-\left(c \cdot b\right) \cdot z\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Applied rewrites 51.9%

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

Alternative 7: 59.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot a - c \cdot z\\ t_2 := \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+28}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-84}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, \left(z \cdot y\right) \cdot x\right)\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, \left(-i\right) \cdot \left(j \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* i a) (* c z))) (t_2 (* (fma (- a) x (* j c)) t)))
   (if (<= t -3.7e+28)
     t_2
     (if (<= t 4.5e-84)
       (fma t_1 b (* (* z y) x))
       (if (<= t 3.3e+38) (fma t_1 b (* (- i) (* j y))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * a) - (c * z);
	double t_2 = fma(-a, x, (j * c)) * t;
	double tmp;
	if (t <= -3.7e+28) {
		tmp = t_2;
	} else if (t <= 4.5e-84) {
		tmp = fma(t_1, b, ((z * y) * x));
	} else if (t <= 3.3e+38) {
		tmp = fma(t_1, b, (-i * (j * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * a) - Float64(c * z))
	t_2 = Float64(fma(Float64(-a), x, Float64(j * c)) * t)
	tmp = 0.0
	if (t <= -3.7e+28)
		tmp = t_2;
	elseif (t <= 4.5e-84)
		tmp = fma(t_1, b, Float64(Float64(z * y) * x));
	elseif (t <= 3.3e+38)
		tmp = fma(t_1, b, Float64(Float64(-i) * Float64(j * y)));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * a), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -3.7e+28], t$95$2, If[LessEqual[t, 4.5e-84], N[(t$95$1 * b + N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e+38], N[(t$95$1 * b + N[((-i) * N[(j * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.6999999999999999e28 or 3.2999999999999999e38 < t

   1. Initial program 65.1%

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

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot \color{blue}{t} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot \color{blue}{t} \]

      3. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot a\right) \cdot x + c \cdot j\right) \cdot t \]

      4. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(a\right)\right) \cdot x + c \cdot j\right) \cdot t \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(a\right), x, c \cdot j\right) \cdot t \]

      6. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-a, x, c \cdot j\right) \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t \]

      8. lower-*.f64 61.3

         \[\leadsto \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t \]

   4. Applied rewrites 61.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]

   if -3.6999999999999999e28 < t < 4.50000000000000016e-84

   1. Initial program 81.3%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

   4. Applied rewrites 83.6%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 60.4

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

   7. Applied rewrites 60.4%

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

   if 4.50000000000000016e-84 < t < 3.2999999999999999e38

   1. Initial program 77.1%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

   4. Applied rewrites 79.7%

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

   5. Taylor expanded in i around inf

      \[\leadsto \mathsf{fma}\left(i \cdot a - c \cdot z, b, -1 \cdot \left(i \cdot \left(j \cdot y\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(i \cdot a - c \cdot z, b, \left(-1 \cdot i\right) \cdot \left(j \cdot y\right)\right) \]

      2. mul-1-neg N/A

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

      3. lift-neg.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 52.4

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

   7. Applied rewrites 52.4%

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

Alternative 8: 57.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot a - c \cdot z, b, \left(z \cdot y\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- a) x (* j c)) t)))
   (if (<= t -3.7e+28)
     t_1
     (if (<= t 3.3e+38) (fma (- (* i a) (* c z)) b (* (* z y) x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-a, x, (j * c)) * t;
	double tmp;
	if (t <= -3.7e+28) {
		tmp = t_1;
	} else if (t <= 3.3e+38) {
		tmp = fma(((i * a) - (c * z)), b, ((z * y) * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-a), x, Float64(j * c)) * t)
	tmp = 0.0
	if (t <= -3.7e+28)
		tmp = t_1;
	elseif (t <= 3.3e+38)
		tmp = fma(Float64(Float64(i * a) - Float64(c * z)), b, Float64(Float64(z * y) * x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -3.7e+28], t$95$1, If[LessEqual[t, 3.3e+38], N[(N[(N[(i * a), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision] * b + N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.6999999999999999e28 or 3.2999999999999999e38 < t

   1. Initial program 65.1%

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

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot \color{blue}{t} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot \color{blue}{t} \]

      3. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot a\right) \cdot x + c \cdot j\right) \cdot t \]

      4. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(a\right)\right) \cdot x + c \cdot j\right) \cdot t \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(a\right), x, c \cdot j\right) \cdot t \]

      6. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-a, x, c \cdot j\right) \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t \]

      8. lower-*.f64 61.3

         \[\leadsto \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t \]

   4. Applied rewrites 61.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]

   if -3.6999999999999999e28 < t < 3.2999999999999999e38

   1. Initial program 80.6%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

   4. Applied rewrites 83.0%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 58.7

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

   7. Applied rewrites 58.7%

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

Alternative 9: 53.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot a - c \cdot z\\ \mathbf{if}\;b \leq -2.05 \cdot 10^{+21}:\\ \;\;\;\;t\_1 \cdot b\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-272}:\\ \;\;\;\;\left(z \cdot y - a \cdot t\right) \cdot x\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+74}:\\ \;\;\;\;\left(\left(-t\right) \cdot \mathsf{fma}\left(i, \frac{y}{t}, -c\right)\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, \left(j \cdot t\right) \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* i a) (* c z))))
   (if (<= b -2.05e+21)
     (* t_1 b)
     (if (<= b 3.7e-272)
       (* (- (* z y) (* a t)) x)
       (if (<= b 2.5e+74)
         (* (* (- t) (fma i (/ y t) (- c))) j)
         (fma t_1 b (* (* j t) c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * a) - (c * z);
	double tmp;
	if (b <= -2.05e+21) {
		tmp = t_1 * b;
	} else if (b <= 3.7e-272) {
		tmp = ((z * y) - (a * t)) * x;
	} else if (b <= 2.5e+74) {
		tmp = (-t * fma(i, (y / t), -c)) * j;
	} else {
		tmp = fma(t_1, b, ((j * t) * c));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * a) - Float64(c * z))
	tmp = 0.0
	if (b <= -2.05e+21)
		tmp = Float64(t_1 * b);
	elseif (b <= 3.7e-272)
		tmp = Float64(Float64(Float64(z * y) - Float64(a * t)) * x);
	elseif (b <= 2.5e+74)
		tmp = Float64(Float64(Float64(-t) * fma(i, Float64(y / t), Float64(-c))) * j);
	else
		tmp = fma(t_1, b, Float64(Float64(j * t) * c));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * a), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.05e+21], N[(t$95$1 * b), $MachinePrecision], If[LessEqual[b, 3.7e-272], N[(N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[b, 2.5e+74], N[(N[((-t) * N[(i * N[(y / t), $MachinePrecision] + (-c)), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], N[(t$95$1 * b + N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.05e21

   1. Initial program 72.6%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot b \]

      4. *-commutative N/A

         \[\leadsto \left(i \cdot a - c \cdot z\right) \cdot b \]

      5. lift-*.f64 N/A

         \[\leadsto \left(i \cdot a - c \cdot z\right) \cdot b \]

      6. lift-*.f64 60.9

         \[\leadsto \left(i \cdot a - c \cdot z\right) \cdot b \]

   4. Applied rewrites 60.9%

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

   if -2.05e21 < b < 3.6999999999999997e-272

   1. Initial program 73.3%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 43.8

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

   4. Applied rewrites 43.8%

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

   if 3.6999999999999997e-272 < b < 2.49999999999999982e74

   1. Initial program 74.9%

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

   2. Taylor expanded in j around inf

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

      1. *-commutative N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      3. lift--.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

      4. lift-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

      5. lift-*.f64 44.2

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

   4. Applied rewrites 44.2%

      \[\leadsto \color{blue}{\left(c \cdot t - i \cdot y\right) \cdot j} \]

   5. Taylor expanded in t around -inf

      \[\leadsto \left(-1 \cdot \left(t \cdot \left(-1 \cdot c + \frac{i \cdot y}{t}\right)\right)\right) \cdot j \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot t\right) \cdot \left(-1 \cdot c + \frac{i \cdot y}{t}\right)\right) \cdot j \]

      2. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(t\right)\right) \cdot \left(-1 \cdot c + \frac{i \cdot y}{t}\right)\right) \cdot j \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(t\right)\right) \cdot \left(-1 \cdot c + \frac{i \cdot y}{t}\right)\right) \cdot j \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(\left(-t\right) \cdot \left(-1 \cdot c + \frac{i \cdot y}{t}\right)\right) \cdot j \]

      5. +-commutative N/A

         \[\leadsto \left(\left(-t\right) \cdot \left(\frac{i \cdot y}{t} + -1 \cdot c\right)\right) \cdot j \]

      6. associate-/l* N/A

         \[\leadsto \left(\left(-t\right) \cdot \left(i \cdot \frac{y}{t} + -1 \cdot c\right)\right) \cdot j \]

      7. lower-fma.f64 N/A

         \[\leadsto \left(\left(-t\right) \cdot \mathsf{fma}\left(i, \frac{y}{t}, -1 \cdot c\right)\right) \cdot j \]

      8. lower-/.f64 N/A

         \[\leadsto \left(\left(-t\right) \cdot \mathsf{fma}\left(i, \frac{y}{t}, -1 \cdot c\right)\right) \cdot j \]

      9. mul-1-neg N/A

         \[\leadsto \left(\left(-t\right) \cdot \mathsf{fma}\left(i, \frac{y}{t}, \mathsf{neg}\left(c\right)\right)\right) \cdot j \]

      10. lower-neg.f64 43.8

          \[\leadsto \left(\left(-t\right) \cdot \mathsf{fma}\left(i, \frac{y}{t}, -c\right)\right) \cdot j \]

   7. Applied rewrites 43.8%

      \[\leadsto \left(\left(-t\right) \cdot \mathsf{fma}\left(i, \frac{y}{t}, -c\right)\right) \cdot j \]

   if 2.49999999999999982e74 < b

   1. Initial program 75.2%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

   4. Applied rewrites 80.4%

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

   5. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 71.7

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

   7. Applied rewrites 71.7%

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

Alternative 10: 53.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(i \cdot a - c \cdot z\right) \cdot b\\ \mathbf{if}\;b \leq -2.05 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-272}:\\ \;\;\;\;\left(z \cdot y - a \cdot t\right) \cdot x\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+74}:\\ \;\;\;\;\left(\left(-t\right) \cdot \mathsf{fma}\left(i, \frac{y}{t}, -c\right)\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- (* i a) (* c z)) b)))
   (if (<= b -2.05e+21)
     t_1
     (if (<= b 3.7e-272)
       (* (- (* z y) (* a t)) x)
       (if (<= b 2.5e+74) (* (* (- t) (fma i (/ y t) (- c))) j) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((i * a) - (c * z)) * b;
	double tmp;
	if (b <= -2.05e+21) {
		tmp = t_1;
	} else if (b <= 3.7e-272) {
		tmp = ((z * y) - (a * t)) * x;
	} else if (b <= 2.5e+74) {
		tmp = (-t * fma(i, (y / t), -c)) * j;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(i * a) - Float64(c * z)) * b)
	tmp = 0.0
	if (b <= -2.05e+21)
		tmp = t_1;
	elseif (b <= 3.7e-272)
		tmp = Float64(Float64(Float64(z * y) - Float64(a * t)) * x);
	elseif (b <= 2.5e+74)
		tmp = Float64(Float64(Float64(-t) * fma(i, Float64(y / t), Float64(-c))) * j);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(i * a), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.05e+21], t$95$1, If[LessEqual[b, 3.7e-272], N[(N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[b, 2.5e+74], N[(N[((-t) * N[(i * N[(y / t), $MachinePrecision] + (-c)), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.05e21 or 2.49999999999999982e74 < b

   1. Initial program 73.8%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot b \]

      4. *-commutative N/A

         \[\leadsto \left(i \cdot a - c \cdot z\right) \cdot b \]

      5. lift-*.f64 N/A

         \[\leadsto \left(i \cdot a - c \cdot z\right) \cdot b \]

      6. lift-*.f64 63.5

         \[\leadsto \left(i \cdot a - c \cdot z\right) \cdot b \]

   4. Applied rewrites 63.5%

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

   if -2.05e21 < b < 3.6999999999999997e-272

   1. Initial program 73.3%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 43.8

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

   4. Applied rewrites 43.8%

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

   if 3.6999999999999997e-272 < b < 2.49999999999999982e74

   1. Initial program 74.9%

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

   2. Taylor expanded in j around inf

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

      1. *-commutative N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      3. lift--.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

      4. lift-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

      5. lift-*.f64 44.2

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

   4. Applied rewrites 44.2%

      \[\leadsto \color{blue}{\left(c \cdot t - i \cdot y\right) \cdot j} \]

   5. Taylor expanded in t around -inf

      \[\leadsto \left(-1 \cdot \left(t \cdot \left(-1 \cdot c + \frac{i \cdot y}{t}\right)\right)\right) \cdot j \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot t\right) \cdot \left(-1 \cdot c + \frac{i \cdot y}{t}\right)\right) \cdot j \]

      2. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(t\right)\right) \cdot \left(-1 \cdot c + \frac{i \cdot y}{t}\right)\right) \cdot j \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(t\right)\right) \cdot \left(-1 \cdot c + \frac{i \cdot y}{t}\right)\right) \cdot j \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(\left(-t\right) \cdot \left(-1 \cdot c + \frac{i \cdot y}{t}\right)\right) \cdot j \]

      5. +-commutative N/A

         \[\leadsto \left(\left(-t\right) \cdot \left(\frac{i \cdot y}{t} + -1 \cdot c\right)\right) \cdot j \]

      6. associate-/l* N/A

         \[\leadsto \left(\left(-t\right) \cdot \left(i \cdot \frac{y}{t} + -1 \cdot c\right)\right) \cdot j \]

      7. lower-fma.f64 N/A

         \[\leadsto \left(\left(-t\right) \cdot \mathsf{fma}\left(i, \frac{y}{t}, -1 \cdot c\right)\right) \cdot j \]

      8. lower-/.f64 N/A

         \[\leadsto \left(\left(-t\right) \cdot \mathsf{fma}\left(i, \frac{y}{t}, -1 \cdot c\right)\right) \cdot j \]

      9. mul-1-neg N/A

         \[\leadsto \left(\left(-t\right) \cdot \mathsf{fma}\left(i, \frac{y}{t}, \mathsf{neg}\left(c\right)\right)\right) \cdot j \]

      10. lower-neg.f64 43.8

          \[\leadsto \left(\left(-t\right) \cdot \mathsf{fma}\left(i, \frac{y}{t}, -c\right)\right) \cdot j \]

   7. Applied rewrites 43.8%

      \[\leadsto \left(\left(-t\right) \cdot \mathsf{fma}\left(i, \frac{y}{t}, -c\right)\right) \cdot j \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 52.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(i \cdot a - c \cdot z\right) \cdot b\\ \mathbf{if}\;b \leq -2.05 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-272}:\\ \;\;\;\;\left(z \cdot y - a \cdot t\right) \cdot x\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+72}:\\ \;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- (* i a) (* c z)) b)))
   (if (<= b -2.05e+21)
     t_1
     (if (<= b 3.7e-272)
       (* (- (* z y) (* a t)) x)
       (if (<= b 4.5e+72) (* (- (* c t) (* i y)) j) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((i * a) - (c * z)) * b;
	double tmp;
	if (b <= -2.05e+21) {
		tmp = t_1;
	} else if (b <= 3.7e-272) {
		tmp = ((z * y) - (a * t)) * x;
	} else if (b <= 4.5e+72) {
		tmp = ((c * t) - (i * y)) * j;
	} else {
		tmp = t_1;
	}
	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, j)
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), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((i * a) - (c * z)) * b
    if (b <= (-2.05d+21)) then
        tmp = t_1
    else if (b <= 3.7d-272) then
        tmp = ((z * y) - (a * t)) * x
    else if (b <= 4.5d+72) then
        tmp = ((c * t) - (i * y)) * j
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((i * a) - (c * z)) * b;
	double tmp;
	if (b <= -2.05e+21) {
		tmp = t_1;
	} else if (b <= 3.7e-272) {
		tmp = ((z * y) - (a * t)) * x;
	} else if (b <= 4.5e+72) {
		tmp = ((c * t) - (i * y)) * j;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((i * a) - (c * z)) * b
	tmp = 0
	if b <= -2.05e+21:
		tmp = t_1
	elif b <= 3.7e-272:
		tmp = ((z * y) - (a * t)) * x
	elif b <= 4.5e+72:
		tmp = ((c * t) - (i * y)) * j
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(i * a) - Float64(c * z)) * b)
	tmp = 0.0
	if (b <= -2.05e+21)
		tmp = t_1;
	elseif (b <= 3.7e-272)
		tmp = Float64(Float64(Float64(z * y) - Float64(a * t)) * x);
	elseif (b <= 4.5e+72)
		tmp = Float64(Float64(Float64(c * t) - Float64(i * y)) * j);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((i * a) - (c * z)) * b;
	tmp = 0.0;
	if (b <= -2.05e+21)
		tmp = t_1;
	elseif (b <= 3.7e-272)
		tmp = ((z * y) - (a * t)) * x;
	elseif (b <= 4.5e+72)
		tmp = ((c * t) - (i * y)) * j;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(i * a), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.05e+21], t$95$1, If[LessEqual[b, 3.7e-272], N[(N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[b, 4.5e+72], N[(N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.05e21 or 4.4999999999999998e72 < b

   1. Initial program 73.8%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot b \]

      4. *-commutative N/A

         \[\leadsto \left(i \cdot a - c \cdot z\right) \cdot b \]

      5. lift-*.f64 N/A

         \[\leadsto \left(i \cdot a - c \cdot z\right) \cdot b \]

      6. lift-*.f64 63.4

         \[\leadsto \left(i \cdot a - c \cdot z\right) \cdot b \]

   4. Applied rewrites 63.4%

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

   if -2.05e21 < b < 3.6999999999999997e-272

   1. Initial program 73.3%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 43.8

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

   4. Applied rewrites 43.8%

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

   if 3.6999999999999997e-272 < b < 4.4999999999999998e72

   1. Initial program 74.9%

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

   2. Taylor expanded in j around inf

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

      1. *-commutative N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      3. lift--.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

      4. lift-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

      5. lift-*.f64 44.2

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

   4. Applied rewrites 44.2%

      \[\leadsto \color{blue}{\left(c \cdot t - i \cdot y\right) \cdot j} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 52.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(i \cdot a - c \cdot z\right) \cdot b\\ \mathbf{if}\;b \leq -2.9 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+72}:\\ \;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- (* i a) (* c z)) b)))
   (if (<= b -2.9e+19) t_1 (if (<= b 4.5e+72) (* (- (* c t) (* i y)) j) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((i * a) - (c * z)) * b;
	double tmp;
	if (b <= -2.9e+19) {
		tmp = t_1;
	} else if (b <= 4.5e+72) {
		tmp = ((c * t) - (i * y)) * j;
	} else {
		tmp = t_1;
	}
	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, j)
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), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((i * a) - (c * z)) * b
    if (b <= (-2.9d+19)) then
        tmp = t_1
    else if (b <= 4.5d+72) then
        tmp = ((c * t) - (i * y)) * j
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((i * a) - (c * z)) * b;
	double tmp;
	if (b <= -2.9e+19) {
		tmp = t_1;
	} else if (b <= 4.5e+72) {
		tmp = ((c * t) - (i * y)) * j;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((i * a) - (c * z)) * b
	tmp = 0
	if b <= -2.9e+19:
		tmp = t_1
	elif b <= 4.5e+72:
		tmp = ((c * t) - (i * y)) * j
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(i * a) - Float64(c * z)) * b)
	tmp = 0.0
	if (b <= -2.9e+19)
		tmp = t_1;
	elseif (b <= 4.5e+72)
		tmp = Float64(Float64(Float64(c * t) - Float64(i * y)) * j);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((i * a) - (c * z)) * b;
	tmp = 0.0;
	if (b <= -2.9e+19)
		tmp = t_1;
	elseif (b <= 4.5e+72)
		tmp = ((c * t) - (i * y)) * j;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(i * a), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.9e+19], t$95$1, If[LessEqual[b, 4.5e+72], N[(N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.9e19 or 4.4999999999999998e72 < b

   1. Initial program 73.7%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot b \]

      4. *-commutative N/A

         \[\leadsto \left(i \cdot a - c \cdot z\right) \cdot b \]

      5. lift-*.f64 N/A

         \[\leadsto \left(i \cdot a - c \cdot z\right) \cdot b \]

      6. lift-*.f64 63.3

         \[\leadsto \left(i \cdot a - c \cdot z\right) \cdot b \]

   4. Applied rewrites 63.3%

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

   if -2.9e19 < b < 4.4999999999999998e72

   1. Initial program 74.1%

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

   2. Taylor expanded in j around inf

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

      1. *-commutative N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      3. lift--.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

      4. lift-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

      5. lift-*.f64 45.1

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

   4. Applied rewrites 45.1%

      \[\leadsto \color{blue}{\left(c \cdot t - i \cdot y\right) \cdot j} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 41.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-b\right) \cdot \left(c \cdot z\right)\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+17}:\\ \;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- b) (* c z))))
   (if (<= z -1.15e+65)
     t_1
     (if (<= z 2.9e+17) (* (- (* c t) (* i y)) j) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -b * (c * z);
	double tmp;
	if (z <= -1.15e+65) {
		tmp = t_1;
	} else if (z <= 2.9e+17) {
		tmp = ((c * t) - (i * y)) * j;
	} else {
		tmp = t_1;
	}
	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, j)
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), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -b * (c * z)
    if (z <= (-1.15d+65)) then
        tmp = t_1
    else if (z <= 2.9d+17) then
        tmp = ((c * t) - (i * y)) * j
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -b * (c * z);
	double tmp;
	if (z <= -1.15e+65) {
		tmp = t_1;
	} else if (z <= 2.9e+17) {
		tmp = ((c * t) - (i * y)) * j;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = -b * (c * z)
	tmp = 0
	if z <= -1.15e+65:
		tmp = t_1
	elif z <= 2.9e+17:
		tmp = ((c * t) - (i * y)) * j
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(-b) * Float64(c * z))
	tmp = 0.0
	if (z <= -1.15e+65)
		tmp = t_1;
	elseif (z <= 2.9e+17)
		tmp = Float64(Float64(Float64(c * t) - Float64(i * y)) * j);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = -b * (c * z);
	tmp = 0.0;
	if (z <= -1.15e+65)
		tmp = t_1;
	elseif (z <= 2.9e+17)
		tmp = ((c * t) - (i * y)) * j;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-b) * N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e+65], t$95$1, If[LessEqual[z, 2.9e+17], N[(N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e65 or 2.9e17 < z

   1. Initial program 65.9%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 64.2

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

   4. Applied rewrites 64.2%

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

   5. Taylor expanded in c around inf

      \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(c \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot b\right) \cdot \left(c \cdot \color{blue}{z}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot \color{blue}{z}\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(-b\right) \cdot \left(c \cdot z\right) \]

      5. lift-*.f64 37.1

         \[\leadsto \left(-b\right) \cdot \left(c \cdot z\right) \]

   7. Applied rewrites 37.1%

      \[\leadsto \left(-b\right) \cdot \color{blue}{\left(c \cdot z\right)} \]

   if -1.15e65 < z < 2.9e17

   1. Initial program 80.2%

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

   2. Taylor expanded in j around inf

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

      1. *-commutative N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      3. lift--.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

      4. lift-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

      5. lift-*.f64 45.2

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

   4. Applied rewrites 45.2%

      \[\leadsto \color{blue}{\left(c \cdot t - i \cdot y\right) \cdot j} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 31.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-b\right) \cdot \left(c \cdot z\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-61}:\\ \;\;\;\;\left(c \cdot t\right) \cdot j\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-157}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+36}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- b) (* c z))))
   (if (<= z -1e+65)
     t_1
     (if (<= z -6e-61)
       (* (* c t) j)
       (if (<= z 3.4e-157)
         (* (- a) (* t x))
         (if (<= z 4.6e+36) (* (* i b) a) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -b * (c * z);
	double tmp;
	if (z <= -1e+65) {
		tmp = t_1;
	} else if (z <= -6e-61) {
		tmp = (c * t) * j;
	} else if (z <= 3.4e-157) {
		tmp = -a * (t * x);
	} else if (z <= 4.6e+36) {
		tmp = (i * b) * a;
	} else {
		tmp = t_1;
	}
	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, j)
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), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -b * (c * z)
    if (z <= (-1d+65)) then
        tmp = t_1
    else if (z <= (-6d-61)) then
        tmp = (c * t) * j
    else if (z <= 3.4d-157) then
        tmp = -a * (t * x)
    else if (z <= 4.6d+36) then
        tmp = (i * b) * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -b * (c * z);
	double tmp;
	if (z <= -1e+65) {
		tmp = t_1;
	} else if (z <= -6e-61) {
		tmp = (c * t) * j;
	} else if (z <= 3.4e-157) {
		tmp = -a * (t * x);
	} else if (z <= 4.6e+36) {
		tmp = (i * b) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = -b * (c * z)
	tmp = 0
	if z <= -1e+65:
		tmp = t_1
	elif z <= -6e-61:
		tmp = (c * t) * j
	elif z <= 3.4e-157:
		tmp = -a * (t * x)
	elif z <= 4.6e+36:
		tmp = (i * b) * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(-b) * Float64(c * z))
	tmp = 0.0
	if (z <= -1e+65)
		tmp = t_1;
	elseif (z <= -6e-61)
		tmp = Float64(Float64(c * t) * j);
	elseif (z <= 3.4e-157)
		tmp = Float64(Float64(-a) * Float64(t * x));
	elseif (z <= 4.6e+36)
		tmp = Float64(Float64(i * b) * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = -b * (c * z);
	tmp = 0.0;
	if (z <= -1e+65)
		tmp = t_1;
	elseif (z <= -6e-61)
		tmp = (c * t) * j;
	elseif (z <= 3.4e-157)
		tmp = -a * (t * x);
	elseif (z <= 4.6e+36)
		tmp = (i * b) * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-b) * N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e+65], t$95$1, If[LessEqual[z, -6e-61], N[(N[(c * t), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[z, 3.4e-157], N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+36], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.9999999999999999e64 or 4.59999999999999993e36 < z

   1. Initial program 65.6%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 64.2

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

   4. Applied rewrites 64.2%

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

   5. Taylor expanded in c around inf

      \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(c \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot b\right) \cdot \left(c \cdot \color{blue}{z}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot \color{blue}{z}\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(-b\right) \cdot \left(c \cdot z\right) \]

      5. lift-*.f64 37.8

         \[\leadsto \left(-b\right) \cdot \left(c \cdot z\right) \]

   7. Applied rewrites 37.8%

      \[\leadsto \left(-b\right) \cdot \color{blue}{\left(c \cdot z\right)} \]

   if -9.9999999999999999e64 < z < -6.00000000000000024e-61

   1. Initial program 77.7%

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

   2. Taylor expanded in j around inf

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

      1. *-commutative N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      3. lift--.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

      4. lift-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

      5. lift-*.f64 40.6

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

   4. Applied rewrites 40.6%

      \[\leadsto \color{blue}{\left(c \cdot t - i \cdot y\right) \cdot j} \]

   5. Taylor expanded in y around 0

      \[\leadsto \left(c \cdot t\right) \cdot j \]
   6. Step-by-step derivation

      1. lift-*.f64 21.6

         \[\leadsto \left(c \cdot t\right) \cdot j \]

   7. Applied rewrites 21.6%

      \[\leadsto \left(c \cdot t\right) \cdot j \]

   if -6.00000000000000024e-61 < z < 3.39999999999999977e-157

   1. Initial program 81.0%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 52.6

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

   4. Applied rewrites 52.6%

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

   5. Taylor expanded in t around inf

      \[\leadsto -1 \cdot \color{blue}{\left(a \cdot \left(t \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \left(t \cdot \color{blue}{x}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \left(t \cdot \color{blue}{x}\right) \]

      3. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t \cdot x\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(-a\right) \cdot \left(t \cdot x\right) \]

      5. lower-*.f64 26.2

         \[\leadsto \left(-a\right) \cdot \left(t \cdot x\right) \]

   7. Applied rewrites 26.2%

      \[\leadsto \left(-a\right) \cdot \color{blue}{\left(t \cdot x\right)} \]

   if 3.39999999999999977e-157 < z < 4.59999999999999993e36

   1. Initial program 79.3%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 57.4

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

   4. Applied rewrites 57.4%

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

   5. Taylor expanded in i around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b \cdot i\right) \cdot a \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b \cdot i\right) \cdot a \]

      3. *-commutative N/A

         \[\leadsto \left(i \cdot b\right) \cdot a \]

      4. lower-*.f64 25.1

         \[\leadsto \left(i \cdot b\right) \cdot a \]

   7. Applied rewrites 25.1%

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

Alternative 15: 30.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-83}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;t \leq 3200000000:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+175}:\\ \;\;\;\;\left(c \cdot t\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- a) (* t x))))
   (if (<= t -1.05e+42)
     t_1
     (if (<= t 1.55e-83)
       (* (* z y) x)
       (if (<= t 3200000000.0)
         (* (* i b) a)
         (if (<= t 2.5e+175) (* (* c t) j) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -a * (t * x);
	double tmp;
	if (t <= -1.05e+42) {
		tmp = t_1;
	} else if (t <= 1.55e-83) {
		tmp = (z * y) * x;
	} else if (t <= 3200000000.0) {
		tmp = (i * b) * a;
	} else if (t <= 2.5e+175) {
		tmp = (c * t) * j;
	} else {
		tmp = t_1;
	}
	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, j)
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), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -a * (t * x)
    if (t <= (-1.05d+42)) then
        tmp = t_1
    else if (t <= 1.55d-83) then
        tmp = (z * y) * x
    else if (t <= 3200000000.0d0) then
        tmp = (i * b) * a
    else if (t <= 2.5d+175) then
        tmp = (c * t) * j
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -a * (t * x);
	double tmp;
	if (t <= -1.05e+42) {
		tmp = t_1;
	} else if (t <= 1.55e-83) {
		tmp = (z * y) * x;
	} else if (t <= 3200000000.0) {
		tmp = (i * b) * a;
	} else if (t <= 2.5e+175) {
		tmp = (c * t) * j;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = -a * (t * x)
	tmp = 0
	if t <= -1.05e+42:
		tmp = t_1
	elif t <= 1.55e-83:
		tmp = (z * y) * x
	elif t <= 3200000000.0:
		tmp = (i * b) * a
	elif t <= 2.5e+175:
		tmp = (c * t) * j
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(-a) * Float64(t * x))
	tmp = 0.0
	if (t <= -1.05e+42)
		tmp = t_1;
	elseif (t <= 1.55e-83)
		tmp = Float64(Float64(z * y) * x);
	elseif (t <= 3200000000.0)
		tmp = Float64(Float64(i * b) * a);
	elseif (t <= 2.5e+175)
		tmp = Float64(Float64(c * t) * j);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = -a * (t * x);
	tmp = 0.0;
	if (t <= -1.05e+42)
		tmp = t_1;
	elseif (t <= 1.55e-83)
		tmp = (z * y) * x;
	elseif (t <= 3200000000.0)
		tmp = (i * b) * a;
	elseif (t <= 2.5e+175)
		tmp = (c * t) * j;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e+42], t$95$1, If[LessEqual[t, 1.55e-83], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, 3200000000.0], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t, 2.5e+175], N[(N[(c * t), $MachinePrecision] * j), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.04999999999999998e42 or 2.5e175 < t

   1. Initial program 63.2%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 53.4

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

   4. Applied rewrites 53.4%

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

   5. Taylor expanded in t around inf

      \[\leadsto -1 \cdot \color{blue}{\left(a \cdot \left(t \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \left(t \cdot \color{blue}{x}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \left(t \cdot \color{blue}{x}\right) \]

      3. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t \cdot x\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(-a\right) \cdot \left(t \cdot x\right) \]

      5. lower-*.f64 38.4

         \[\leadsto \left(-a\right) \cdot \left(t \cdot x\right) \]

   7. Applied rewrites 38.4%

      \[\leadsto \left(-a\right) \cdot \color{blue}{\left(t \cdot x\right)} \]

   if -1.04999999999999998e42 < t < 1.54999999999999996e-83

   1. Initial program 81.2%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 31.5

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

   4. Applied rewrites 31.5%

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

   5. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot z\right) \cdot x \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(z \cdot y\right) \cdot x \]

      2. lift-*.f64 25.3

         \[\leadsto \left(z \cdot y\right) \cdot x \]

   7. Applied rewrites 25.3%

      \[\leadsto \left(z \cdot y\right) \cdot x \]

   if 1.54999999999999996e-83 < t < 3.2e9

   1. Initial program 75.7%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 58.9

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

   4. Applied rewrites 58.9%

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

   5. Taylor expanded in i around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b \cdot i\right) \cdot a \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b \cdot i\right) \cdot a \]

      3. *-commutative N/A

         \[\leadsto \left(i \cdot b\right) \cdot a \]

      4. lower-*.f64 24.8

         \[\leadsto \left(i \cdot b\right) \cdot a \]

   7. Applied rewrites 24.8%

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

   if 3.2e9 < t < 2.5e175

   1. Initial program 71.8%

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

   2. Taylor expanded in j around inf

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

      1. *-commutative N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      3. lift--.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

      4. lift-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

      5. lift-*.f64 43.7

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

   4. Applied rewrites 43.7%

      \[\leadsto \color{blue}{\left(c \cdot t - i \cdot y\right) \cdot j} \]

   5. Taylor expanded in y around 0

      \[\leadsto \left(c \cdot t\right) \cdot j \]
   6. Step-by-step derivation

      1. lift-*.f64 28.4

         \[\leadsto \left(c \cdot t\right) \cdot j \]

   7. Applied rewrites 28.4%

      \[\leadsto \left(c \cdot t\right) \cdot j \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 16: 30.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot t\right) \cdot j\\ \mathbf{if}\;t \leq -4 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-83}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;t \leq 3200000000:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* c t) j)))
   (if (<= t -4e+56)
     t_1
     (if (<= t 1.55e-83)
       (* (* z y) x)
       (if (<= t 3200000000.0) (* (* i b) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (c * t) * j;
	double tmp;
	if (t <= -4e+56) {
		tmp = t_1;
	} else if (t <= 1.55e-83) {
		tmp = (z * y) * x;
	} else if (t <= 3200000000.0) {
		tmp = (i * b) * a;
	} else {
		tmp = t_1;
	}
	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, j)
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), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (c * t) * j
    if (t <= (-4d+56)) then
        tmp = t_1
    else if (t <= 1.55d-83) then
        tmp = (z * y) * x
    else if (t <= 3200000000.0d0) then
        tmp = (i * b) * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (c * t) * j;
	double tmp;
	if (t <= -4e+56) {
		tmp = t_1;
	} else if (t <= 1.55e-83) {
		tmp = (z * y) * x;
	} else if (t <= 3200000000.0) {
		tmp = (i * b) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (c * t) * j
	tmp = 0
	if t <= -4e+56:
		tmp = t_1
	elif t <= 1.55e-83:
		tmp = (z * y) * x
	elif t <= 3200000000.0:
		tmp = (i * b) * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(c * t) * j)
	tmp = 0.0
	if (t <= -4e+56)
		tmp = t_1;
	elseif (t <= 1.55e-83)
		tmp = Float64(Float64(z * y) * x);
	elseif (t <= 3200000000.0)
		tmp = Float64(Float64(i * b) * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (c * t) * j;
	tmp = 0.0;
	if (t <= -4e+56)
		tmp = t_1;
	elseif (t <= 1.55e-83)
		tmp = (z * y) * x;
	elseif (t <= 3200000000.0)
		tmp = (i * b) * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(c * t), $MachinePrecision] * j), $MachinePrecision]}, If[LessEqual[t, -4e+56], t$95$1, If[LessEqual[t, 1.55e-83], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, 3200000000.0], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.00000000000000037e56 or 3.2e9 < t

   1. Initial program 65.5%

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

   2. Taylor expanded in j around inf

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

      1. *-commutative N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      3. lift--.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

      4. lift-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

      5. lift-*.f64 45.9

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

   4. Applied rewrites 45.9%

      \[\leadsto \color{blue}{\left(c \cdot t - i \cdot y\right) \cdot j} \]

   5. Taylor expanded in y around 0

      \[\leadsto \left(c \cdot t\right) \cdot j \]
   6. Step-by-step derivation

      1. lift-*.f64 35.5

         \[\leadsto \left(c \cdot t\right) \cdot j \]

   7. Applied rewrites 35.5%

      \[\leadsto \left(c \cdot t\right) \cdot j \]

   if -4.00000000000000037e56 < t < 1.54999999999999996e-83

   1. Initial program 81.0%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 31.5

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

   4. Applied rewrites 31.5%

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

   5. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot z\right) \cdot x \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(z \cdot y\right) \cdot x \]

      2. lift-*.f64 25.2

         \[\leadsto \left(z \cdot y\right) \cdot x \]

   7. Applied rewrites 25.2%

      \[\leadsto \left(z \cdot y\right) \cdot x \]

   if 1.54999999999999996e-83 < t < 3.2e9

   1. Initial program 75.7%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 58.9

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

   4. Applied rewrites 58.9%

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

   5. Taylor expanded in i around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b \cdot i\right) \cdot a \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b \cdot i\right) \cdot a \]

      3. *-commutative N/A

         \[\leadsto \left(i \cdot b\right) \cdot a \]

      4. lower-*.f64 24.8

         \[\leadsto \left(i \cdot b\right) \cdot a \]

   7. Applied rewrites 24.8%

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

Alternative 17: 30.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{-27}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-180}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \mathbf{elif}\;b \leq 1.36 \cdot 10^{+66}:\\ \;\;\;\;\left(c \cdot t\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -5.2e-27)
   (* (* i b) a)
   (if (<= b 7.5e-180)
     (* (* x z) y)
     (if (<= b 1.36e+66) (* (* c t) j) (* (* b a) i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -5.2e-27) {
		tmp = (i * b) * a;
	} else if (b <= 7.5e-180) {
		tmp = (x * z) * y;
	} else if (b <= 1.36e+66) {
		tmp = (c * t) * j;
	} else {
		tmp = (b * a) * i;
	}
	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, j)
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), intent (in) :: j
    real(8) :: tmp
    if (b <= (-5.2d-27)) then
        tmp = (i * b) * a
    else if (b <= 7.5d-180) then
        tmp = (x * z) * y
    else if (b <= 1.36d+66) then
        tmp = (c * t) * j
    else
        tmp = (b * a) * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -5.2e-27) {
		tmp = (i * b) * a;
	} else if (b <= 7.5e-180) {
		tmp = (x * z) * y;
	} else if (b <= 1.36e+66) {
		tmp = (c * t) * j;
	} else {
		tmp = (b * a) * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -5.2e-27:
		tmp = (i * b) * a
	elif b <= 7.5e-180:
		tmp = (x * z) * y
	elif b <= 1.36e+66:
		tmp = (c * t) * j
	else:
		tmp = (b * a) * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -5.2e-27)
		tmp = Float64(Float64(i * b) * a);
	elseif (b <= 7.5e-180)
		tmp = Float64(Float64(x * z) * y);
	elseif (b <= 1.36e+66)
		tmp = Float64(Float64(c * t) * j);
	else
		tmp = Float64(Float64(b * a) * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -5.2e-27)
		tmp = (i * b) * a;
	elseif (b <= 7.5e-180)
		tmp = (x * z) * y;
	elseif (b <= 1.36e+66)
		tmp = (c * t) * j;
	else
		tmp = (b * a) * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -5.2e-27], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[b, 7.5e-180], N[(N[(x * z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[b, 1.36e+66], N[(N[(c * t), $MachinePrecision] * j), $MachinePrecision], N[(N[(b * a), $MachinePrecision] * i), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.20000000000000034e-27

   1. Initial program 73.6%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 66.7

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

   4. Applied rewrites 66.7%

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

   5. Taylor expanded in i around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b \cdot i\right) \cdot a \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b \cdot i\right) \cdot a \]

      3. *-commutative N/A

         \[\leadsto \left(i \cdot b\right) \cdot a \]

      4. lower-*.f64 34.6

         \[\leadsto \left(i \cdot b\right) \cdot a \]

   7. Applied rewrites 34.6%

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

   if -5.20000000000000034e-27 < b < 7.50000000000000015e-180

   1. Initial program 71.9%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right) \cdot \color{blue}{y} \]

      3. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot i\right) \cdot j + x \cdot z\right) \cdot y \]

      4. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(i\right)\right) \cdot j + x \cdot z\right) \cdot y \]

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 46.8

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

   4. Applied rewrites 46.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot z\right) \cdot y \]
   6. Step-by-step derivation

      1. lower-*.f64 25.1

         \[\leadsto \left(x \cdot z\right) \cdot y \]

   7. Applied rewrites 25.1%

      \[\leadsto \left(x \cdot z\right) \cdot y \]

   if 7.50000000000000015e-180 < b < 1.36e66

   1. Initial program 76.8%

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

   2. Taylor expanded in j around inf

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

      1. *-commutative N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      3. lift--.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

      4. lift-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

      5. lift-*.f64 43.2

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{\left(c \cdot t - i \cdot y\right) \cdot j} \]

   5. Taylor expanded in y around 0

      \[\leadsto \left(c \cdot t\right) \cdot j \]
   6. Step-by-step derivation

      1. lift-*.f64 24.3

         \[\leadsto \left(c \cdot t\right) \cdot j \]

   7. Applied rewrites 24.3%

      \[\leadsto \left(c \cdot t\right) \cdot j \]

   if 1.36e66 < b

   1. Initial program 75.1%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

   4. Applied rewrites 80.3%

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

   5. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot \color{blue}{i} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot \color{blue}{i} \]

      3. associate-*r* N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - \left(-1 \cdot a\right) \cdot b\right) \cdot i \]

      4. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot b\right) \cdot i \]

      5. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) + a \cdot b\right) \cdot i \]

      6. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot j\right) \cdot y + a \cdot b\right) \cdot i \]

      7. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(j\right)\right) \cdot y + a \cdot b\right) \cdot i \]

      8. lower-fma.f64 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 49.7

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

   7. Applied rewrites 49.7%

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

   8. Taylor expanded in y around 0

      \[\leadsto \left(a \cdot b\right) \cdot i \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b \cdot a\right) \cdot i \]

      2. lift-*.f64 39.4

         \[\leadsto \left(b \cdot a\right) \cdot i \]

   10. Applied rewrites 39.4%

       \[\leadsto \left(b \cdot a\right) \cdot i \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 18: 30.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{-27}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-180}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+65}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -5.2e-27)
   (* (* i b) a)
   (if (<= b 7.5e-180)
     (* (* x z) y)
     (if (<= b 3.3e+65) (* (* j t) c) (* (* b a) i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -5.2e-27) {
		tmp = (i * b) * a;
	} else if (b <= 7.5e-180) {
		tmp = (x * z) * y;
	} else if (b <= 3.3e+65) {
		tmp = (j * t) * c;
	} else {
		tmp = (b * a) * i;
	}
	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, j)
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), intent (in) :: j
    real(8) :: tmp
    if (b <= (-5.2d-27)) then
        tmp = (i * b) * a
    else if (b <= 7.5d-180) then
        tmp = (x * z) * y
    else if (b <= 3.3d+65) then
        tmp = (j * t) * c
    else
        tmp = (b * a) * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -5.2e-27) {
		tmp = (i * b) * a;
	} else if (b <= 7.5e-180) {
		tmp = (x * z) * y;
	} else if (b <= 3.3e+65) {
		tmp = (j * t) * c;
	} else {
		tmp = (b * a) * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -5.2e-27:
		tmp = (i * b) * a
	elif b <= 7.5e-180:
		tmp = (x * z) * y
	elif b <= 3.3e+65:
		tmp = (j * t) * c
	else:
		tmp = (b * a) * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -5.2e-27)
		tmp = Float64(Float64(i * b) * a);
	elseif (b <= 7.5e-180)
		tmp = Float64(Float64(x * z) * y);
	elseif (b <= 3.3e+65)
		tmp = Float64(Float64(j * t) * c);
	else
		tmp = Float64(Float64(b * a) * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -5.2e-27)
		tmp = (i * b) * a;
	elseif (b <= 7.5e-180)
		tmp = (x * z) * y;
	elseif (b <= 3.3e+65)
		tmp = (j * t) * c;
	else
		tmp = (b * a) * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -5.2e-27], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[b, 7.5e-180], N[(N[(x * z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[b, 3.3e+65], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], N[(N[(b * a), $MachinePrecision] * i), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.20000000000000034e-27

   1. Initial program 73.6%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 66.7

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

   4. Applied rewrites 66.7%

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

   5. Taylor expanded in i around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b \cdot i\right) \cdot a \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b \cdot i\right) \cdot a \]

      3. *-commutative N/A

         \[\leadsto \left(i \cdot b\right) \cdot a \]

      4. lower-*.f64 34.6

         \[\leadsto \left(i \cdot b\right) \cdot a \]

   7. Applied rewrites 34.6%

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

   if -5.20000000000000034e-27 < b < 7.50000000000000015e-180

   1. Initial program 71.9%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right) \cdot \color{blue}{y} \]

      3. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot i\right) \cdot j + x \cdot z\right) \cdot y \]

      4. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(i\right)\right) \cdot j + x \cdot z\right) \cdot y \]

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 46.8

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

   4. Applied rewrites 46.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot z\right) \cdot y \]
   6. Step-by-step derivation

      1. lower-*.f64 25.1

         \[\leadsto \left(x \cdot z\right) \cdot y \]

   7. Applied rewrites 25.1%

      \[\leadsto \left(x \cdot z\right) \cdot y \]

   if 7.50000000000000015e-180 < b < 3.30000000000000023e65

   1. Initial program 76.8%

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

   2. Taylor expanded in j around inf

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

      1. *-commutative N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      3. lift--.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

      4. lift-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

      5. lift-*.f64 43.2

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{\left(c \cdot t - i \cdot y\right) \cdot j} \]

   5. Taylor expanded in y around 0

      \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(j \cdot t\right) \cdot c \]

      2. lower-*.f64 N/A

         \[\leadsto \left(j \cdot t\right) \cdot c \]

      3. lower-*.f64 24.7

         \[\leadsto \left(j \cdot t\right) \cdot c \]

   7. Applied rewrites 24.7%

      \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{c} \]

   if 3.30000000000000023e65 < b

   1. Initial program 75.1%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

   4. Applied rewrites 80.4%

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

   5. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot \color{blue}{i} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot \color{blue}{i} \]

      3. associate-*r* N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - \left(-1 \cdot a\right) \cdot b\right) \cdot i \]

      4. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot b\right) \cdot i \]

      5. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) + a \cdot b\right) \cdot i \]

      6. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot j\right) \cdot y + a \cdot b\right) \cdot i \]

      7. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(j\right)\right) \cdot y + a \cdot b\right) \cdot i \]

      8. lower-fma.f64 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 49.8

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

   7. Applied rewrites 49.8%

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

   8. Taylor expanded in y around 0

      \[\leadsto \left(a \cdot b\right) \cdot i \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b \cdot a\right) \cdot i \]

      2. lift-*.f64 39.4

         \[\leadsto \left(b \cdot a\right) \cdot i \]

   10. Applied rewrites 39.4%

       \[\leadsto \left(b \cdot a\right) \cdot i \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 19: 29.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot z\right) \cdot y\\ \mathbf{if}\;z \leq -1.06 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-60}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+81}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* x z) y)))
   (if (<= z -1.06e+61)
     t_1
     (if (<= z -3.3e-60)
       (* (* j t) c)
       (if (<= z 1.35e+81) (* (* i b) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * z) * y;
	double tmp;
	if (z <= -1.06e+61) {
		tmp = t_1;
	} else if (z <= -3.3e-60) {
		tmp = (j * t) * c;
	} else if (z <= 1.35e+81) {
		tmp = (i * b) * a;
	} else {
		tmp = t_1;
	}
	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, j)
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), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * z) * y
    if (z <= (-1.06d+61)) then
        tmp = t_1
    else if (z <= (-3.3d-60)) then
        tmp = (j * t) * c
    else if (z <= 1.35d+81) then
        tmp = (i * b) * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * z) * y;
	double tmp;
	if (z <= -1.06e+61) {
		tmp = t_1;
	} else if (z <= -3.3e-60) {
		tmp = (j * t) * c;
	} else if (z <= 1.35e+81) {
		tmp = (i * b) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * z) * y
	tmp = 0
	if z <= -1.06e+61:
		tmp = t_1
	elif z <= -3.3e-60:
		tmp = (j * t) * c
	elif z <= 1.35e+81:
		tmp = (i * b) * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * z) * y)
	tmp = 0.0
	if (z <= -1.06e+61)
		tmp = t_1;
	elseif (z <= -3.3e-60)
		tmp = Float64(Float64(j * t) * c);
	elseif (z <= 1.35e+81)
		tmp = Float64(Float64(i * b) * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * z) * y;
	tmp = 0.0;
	if (z <= -1.06e+61)
		tmp = t_1;
	elseif (z <= -3.3e-60)
		tmp = (j * t) * c;
	elseif (z <= 1.35e+81)
		tmp = (i * b) * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[z, -1.06e+61], t$95$1, If[LessEqual[z, -3.3e-60], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[z, 1.35e+81], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0599999999999999e61 or 1.35e81 < z

   1. Initial program 64.4%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right) \cdot \color{blue}{y} \]

      3. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot i\right) \cdot j + x \cdot z\right) \cdot y \]

      4. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(i\right)\right) \cdot j + x \cdot z\right) \cdot y \]

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 47.7

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

   4. Applied rewrites 47.7%

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

   5. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot z\right) \cdot y \]
   6. Step-by-step derivation

      1. lower-*.f64 37.5

         \[\leadsto \left(x \cdot z\right) \cdot y \]

   7. Applied rewrites 37.5%

      \[\leadsto \left(x \cdot z\right) \cdot y \]

   if -1.0599999999999999e61 < z < -3.2999999999999998e-60

   1. Initial program 77.9%

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

   2. Taylor expanded in j around inf

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

      1. *-commutative N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      3. lift--.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

      4. lift-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

      5. lift-*.f64 40.5

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

   4. Applied rewrites 40.5%

      \[\leadsto \color{blue}{\left(c \cdot t - i \cdot y\right) \cdot j} \]

   5. Taylor expanded in y around 0

      \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(j \cdot t\right) \cdot c \]

      2. lower-*.f64 N/A

         \[\leadsto \left(j \cdot t\right) \cdot c \]

      3. lower-*.f64 21.9

         \[\leadsto \left(j \cdot t\right) \cdot c \]

   7. Applied rewrites 21.9%

      \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{c} \]

   if -3.2999999999999998e-60 < z < 1.35e81

   1. Initial program 80.4%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 54.9

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

   4. Applied rewrites 54.9%

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

   5. Taylor expanded in i around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b \cdot i\right) \cdot a \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b \cdot i\right) \cdot a \]

      3. *-commutative N/A

         \[\leadsto \left(i \cdot b\right) \cdot a \]

      4. lower-*.f64 26.3

         \[\leadsto \left(i \cdot b\right) \cdot a \]

   7. Applied rewrites 26.3%

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

Alternative 20: 29.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(i \cdot b\right) \cdot a\\ \mathbf{if}\;b \leq -3 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+65}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* i b) a)))
   (if (<= b -3e-28) t_1 (if (<= b 3.3e+65) (* (* j t) c) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * b) * a;
	double tmp;
	if (b <= -3e-28) {
		tmp = t_1;
	} else if (b <= 3.3e+65) {
		tmp = (j * t) * c;
	} else {
		tmp = t_1;
	}
	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, j)
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), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (i * b) * a
    if (b <= (-3d-28)) then
        tmp = t_1
    else if (b <= 3.3d+65) then
        tmp = (j * t) * c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * b) * a;
	double tmp;
	if (b <= -3e-28) {
		tmp = t_1;
	} else if (b <= 3.3e+65) {
		tmp = (j * t) * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (i * b) * a
	tmp = 0
	if b <= -3e-28:
		tmp = t_1
	elif b <= 3.3e+65:
		tmp = (j * t) * c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * b) * a)
	tmp = 0.0
	if (b <= -3e-28)
		tmp = t_1;
	elseif (b <= 3.3e+65)
		tmp = Float64(Float64(j * t) * c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (i * b) * a;
	tmp = 0.0;
	if (b <= -3e-28)
		tmp = t_1;
	elseif (b <= 3.3e+65)
		tmp = (j * t) * c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[b, -3e-28], t$95$1, If[LessEqual[b, 3.3e+65], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -3.00000000000000003e-28 or 3.30000000000000023e65 < b

   1. Initial program 74.2%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b \]

      14. lift-*.f64 N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b \]

      15. lift-*.f64 67.7

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b \]

   4. Applied rewrites 67.7%

      \[\leadsto \color{blue}{\left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in i around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b \cdot i\right) \cdot a \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b \cdot i\right) \cdot a \]

      3. *-commutative N/A

         \[\leadsto \left(i \cdot b\right) \cdot a \]

      4. lower-*.f64 37.0

         \[\leadsto \left(i \cdot b\right) \cdot a \]

   7. Applied rewrites 37.0%

      \[\leadsto \left(i \cdot b\right) \cdot \color{blue}{a} \]

   if -3.00000000000000003e-28 < b < 3.30000000000000023e65

   1. Initial program 73.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      3. lift--.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

      4. lift-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

      5. lift-*.f64 45.7

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

   4. Applied rewrites 45.7%

      \[\leadsto \color{blue}{\left(c \cdot t - i \cdot y\right) \cdot j} \]

   5. Taylor expanded in y around 0

      \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(j \cdot t\right) \cdot c \]

      2. lower-*.f64 N/A

         \[\leadsto \left(j \cdot t\right) \cdot c \]

      3. lower-*.f64 25.6

         \[\leadsto \left(j \cdot t\right) \cdot c \]

   7. Applied rewrites 25.6%

      \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{c} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 21.7% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \left(j \cdot t\right) \cdot c \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* (* j t) c))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return (j * t) * c;
}

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, j)
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), intent (in) :: j
    code = (j * t) * c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return (j * t) * c;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return (j * t) * c

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(j * t) * c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = (j * t) * c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision]

Derivation

1. Initial program 74.0%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

2. Taylor expanded in j around inf

   \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
3. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

   2. lower-*.f64 N/A

      \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

   3. lift--.f64 N/A

      \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

   4. lift-*.f64 N/A

      \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

   5. lift-*.f64 39.9

      \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot j \]

4. Applied rewrites 39.9%

   \[\leadsto \color{blue}{\left(c \cdot t - i \cdot y\right) \cdot j} \]

5. Taylor expanded in y around 0

   \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
6. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \left(j \cdot t\right) \cdot c \]

   2. lower-*.f64 N/A

      \[\leadsto \left(j \cdot t\right) \cdot c \]

   3. lower-*.f64 21.7

      \[\leadsto \left(j \cdot t\right) \cdot c \]

7. Applied rewrites 21.7%

   \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{c} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025120 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64
  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))