Data.Colour.Matrix:determinant from colour-2.3.3, A

Percentage Accurate: 73.4% → 82.3%

Time: 7.1s

Alternatives: 23

Speedup: 0.5×

• 58.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

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) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i, 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) - (t * i)))) + (j * ((c * a) - (y * i)))
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) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

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

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(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
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[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 73.4% accurate, 1.0× speedup

Math

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

FPCore

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

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) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i, 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) - (t * i)))) + (j * ((c * a) - (y * i)))
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) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

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

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(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
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[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 82.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := 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[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(i * t), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision] * b + N[(N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] * j + N[(N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-t) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * a), $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 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 91.5%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   4. Applied rewrites 91.5%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 44.6

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

   4. Applied rewrites 44.6%

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

Alternative 2: 69.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot y - a \cdot t\\ \mathbf{if}\;j \leq -4 \cdot 10^{+105}:\\ \;\;\;\;\left(y \cdot x - c \cdot b\right) \cdot z + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;j \leq -9 \cdot 10^{-255}:\\ \;\;\;\;t\_1 \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{+77}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, x, i \cdot b\right), t, \left(z \cdot y\right) \cdot x - \left(c \cdot b\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, x, \left(c \cdot a - i \cdot y\right) \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* z y) (* a t))))
   (if (<= j -4e+105)
     (+ (* (- (* y x) (* c b)) z) (* j (- (* c a) (* y i))))
     (if (<= j -9e-255)
       (- (* t_1 x) (* (- (* c z) (* i t)) b))
       (if (<= j 1.35e+77)
         (fma (fma (- a) x (* i b)) t (- (* (* z y) x) (* (* c b) z)))
         (fma t_1 x (* (- (* c a) (* i y)) j)))))))

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 (j <= -4e+105) {
		tmp = (((y * x) - (c * b)) * z) + (j * ((c * a) - (y * i)));
	} else if (j <= -9e-255) {
		tmp = (t_1 * x) - (((c * z) - (i * t)) * b);
	} else if (j <= 1.35e+77) {
		tmp = fma(fma(-a, x, (i * b)), t, (((z * y) * x) - ((c * b) * z)));
	} else {
		tmp = fma(t_1, x, (((c * a) - (i * y)) * j));
	}
	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 (j <= -4e+105)
		tmp = Float64(Float64(Float64(Float64(y * x) - Float64(c * b)) * z) + Float64(j * Float64(Float64(c * a) - Float64(y * i))));
	elseif (j <= -9e-255)
		tmp = Float64(Float64(t_1 * x) - Float64(Float64(Float64(c * z) - Float64(i * t)) * b));
	elseif (j <= 1.35e+77)
		tmp = fma(fma(Float64(-a), x, Float64(i * b)), t, Float64(Float64(Float64(z * y) * x) - Float64(Float64(c * b) * z)));
	else
		tmp = fma(t_1, x, Float64(Float64(Float64(c * a) - Float64(i * y)) * j));
	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[j, -4e+105], N[(N[(N[(N[(y * x), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -9e-255], N[(N[(t$95$1 * x), $MachinePrecision] - N[(N[(N[(c * z), $MachinePrecision] - N[(i * t), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.35e+77], N[(N[((-a) * x + N[(i * b), $MachinePrecision]), $MachinePrecision] * t + N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] - N[(N[(c * b), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * x + N[(N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.9999999999999998e105

   1. Initial program 71.5%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 70.9

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

   4. Applied rewrites 70.9%

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

   if -3.9999999999999998e105 < j < -8.99999999999999959e-255

   1. Initial program 74.9%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. lower-*.f64 65.7

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

   4. Applied rewrites 65.7%

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

   if -8.99999999999999959e-255 < j < 1.3499999999999999e77

   1. Initial program 72.9%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. lower-*.f64 68.5

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

   4. Applied rewrites 68.5%

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

   5. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-*r* N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lower--.f64 N/A

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

   7. Applied rewrites 67.9%

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

   if 1.3499999999999999e77 < j

   1. Initial program 73.8%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   4. Applied rewrites 78.8%

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

   5. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 71.8

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

   7. Applied rewrites 71.8%

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

Alternative 3: 69.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot y - a \cdot t\\ \mathbf{if}\;j \leq -4 \cdot 10^{+105}:\\ \;\;\;\;\left(y \cdot x - c \cdot b\right) \cdot z + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;j \leq 4.6 \cdot 10^{-74}:\\ \;\;\;\;t\_1 \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, x, \left(c \cdot a - i \cdot y\right) \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* z y) (* a t))))
   (if (<= j -4e+105)
     (+ (* (- (* y x) (* c b)) z) (* j (- (* c a) (* y i))))
     (if (<= j 4.6e-74)
       (- (* t_1 x) (* (- (* c z) (* i t)) b))
       (fma t_1 x (* (- (* c a) (* i y)) j))))))

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 (j <= -4e+105) {
		tmp = (((y * x) - (c * b)) * z) + (j * ((c * a) - (y * i)));
	} else if (j <= 4.6e-74) {
		tmp = (t_1 * x) - (((c * z) - (i * t)) * b);
	} else {
		tmp = fma(t_1, x, (((c * a) - (i * y)) * j));
	}
	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 (j <= -4e+105)
		tmp = Float64(Float64(Float64(Float64(y * x) - Float64(c * b)) * z) + Float64(j * Float64(Float64(c * a) - Float64(y * i))));
	elseif (j <= 4.6e-74)
		tmp = Float64(Float64(t_1 * x) - Float64(Float64(Float64(c * z) - Float64(i * t)) * b));
	else
		tmp = fma(t_1, x, Float64(Float64(Float64(c * a) - Float64(i * y)) * j));
	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[j, -4e+105], N[(N[(N[(N[(y * x), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.6e-74], N[(N[(t$95$1 * x), $MachinePrecision] - N[(N[(N[(c * z), $MachinePrecision] - N[(i * t), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * x + N[(N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if j < -3.9999999999999998e105

   1. Initial program 71.5%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 70.9

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

   4. Applied rewrites 70.9%

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

   if -3.9999999999999998e105 < j < 4.59999999999999961e-74

   1. Initial program 73.4%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. lower-*.f64 69.5

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

   4. Applied rewrites 69.5%

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

   if 4.59999999999999961e-74 < j

   1. Initial program 74.5%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   4. Applied rewrites 78.4%

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

   5. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 68.6

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

   7. Applied rewrites 68.6%

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

Alternative 4: 69.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot y - a \cdot t\\ \mathbf{if}\;j \leq -7.5 \cdot 10^{+105}:\\ \;\;\;\;\left(-\left(c \cdot b\right) \cdot z\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;j \leq 4.6 \cdot 10^{-74}:\\ \;\;\;\;t\_1 \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, x, \left(c \cdot a - i \cdot y\right) \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* z y) (* a t))))
   (if (<= j -7.5e+105)
     (+ (- (* (* c b) z)) (* j (- (* c a) (* y i))))
     (if (<= j 4.6e-74)
       (- (* t_1 x) (* (- (* c z) (* i t)) b))
       (fma t_1 x (* (- (* c a) (* i y)) j))))))

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 (j <= -7.5e+105) {
		tmp = -((c * b) * z) + (j * ((c * a) - (y * i)));
	} else if (j <= 4.6e-74) {
		tmp = (t_1 * x) - (((c * z) - (i * t)) * b);
	} else {
		tmp = fma(t_1, x, (((c * a) - (i * y)) * j));
	}
	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 (j <= -7.5e+105)
		tmp = Float64(Float64(-Float64(Float64(c * b) * z)) + Float64(j * Float64(Float64(c * a) - Float64(y * i))));
	elseif (j <= 4.6e-74)
		tmp = Float64(Float64(t_1 * x) - Float64(Float64(Float64(c * z) - Float64(i * t)) * b));
	else
		tmp = fma(t_1, x, Float64(Float64(Float64(c * a) - Float64(i * y)) * j));
	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[j, -7.5e+105], N[((-N[(N[(c * b), $MachinePrecision] * z), $MachinePrecision]) + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.6e-74], N[(N[(t$95$1 * x), $MachinePrecision] - N[(N[(N[(c * z), $MachinePrecision] - N[(i * t), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * x + N[(N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if j < -7.5000000000000002e105

   1. Initial program 71.4%

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

   2. Taylor expanded in c around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 67.8

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

   4. Applied rewrites 67.8%

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

   if -7.5000000000000002e105 < j < 4.59999999999999961e-74

   1. Initial program 73.5%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. lower-*.f64 69.4

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

   4. Applied rewrites 69.4%

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

   if 4.59999999999999961e-74 < j

   1. Initial program 74.5%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   4. Applied rewrites 78.4%

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

   5. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 68.6

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

   7. Applied rewrites 68.6%

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

Alternative 5: 68.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot t - c \cdot z\\ \mathbf{if}\;b \leq -4 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, \left(j \cdot c\right) \cdot a\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot y - a \cdot t, x, \left(c \cdot a - i \cdot y\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, \left(z \cdot y\right) \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* i t) (* c z))))
   (if (<= b -4e+41)
     (fma t_1 b (* (* j c) a))
     (if (<= b 3.2e+72)
       (fma (- (* z y) (* a t)) x (* (- (* c a) (* i y)) j))
       (fma t_1 b (* (* z y) 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 * t) - (c * z);
	double tmp;
	if (b <= -4e+41) {
		tmp = fma(t_1, b, ((j * c) * a));
	} else if (b <= 3.2e+72) {
		tmp = fma(((z * y) - (a * t)), x, (((c * a) - (i * y)) * j));
	} else {
		tmp = fma(t_1, b, ((z * y) * x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * t) - Float64(c * z))
	tmp = 0.0
	if (b <= -4e+41)
		tmp = fma(t_1, b, Float64(Float64(j * c) * a));
	elseif (b <= 3.2e+72)
		tmp = fma(Float64(Float64(z * y) - Float64(a * t)), x, Float64(Float64(Float64(c * a) - Float64(i * y)) * j));
	else
		tmp = fma(t_1, b, Float64(Float64(z * y) * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * t), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4e+41], N[(t$95$1 * b + N[(N[(j * c), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e+72], N[(N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision] * x + N[(N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * b + N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.00000000000000002e41

   1. Initial program 71.1%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   4. Applied rewrites 76.4%

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

   5. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 66.2

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

   7. Applied rewrites 66.2%

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

   if -4.00000000000000002e41 < b < 3.2000000000000001e72

   1. Initial program 74.0%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   4. Applied rewrites 75.2%

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

   5. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 70.4

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

   7. Applied rewrites 70.4%

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

   if 3.2000000000000001e72 < b

   1. Initial program 74.3%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   4. Applied rewrites 79.3%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 68.2

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

   7. Applied rewrites 68.2%

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

Alternative 6: 68.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot t - c \cdot z\\ \mathbf{if}\;b \leq -4 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, \left(j \cdot c\right) \cdot a\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(c \cdot a - i \cdot y, j, \left(z \cdot y - a \cdot t\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, \left(z \cdot y\right) \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* i t) (* c z))))
   (if (<= b -4e+41)
     (fma t_1 b (* (* j c) a))
     (if (<= b 3.2e+72)
       (fma (- (* c a) (* i y)) j (* (- (* z y) (* a t)) x))
       (fma t_1 b (* (* z y) 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 * t) - (c * z);
	double tmp;
	if (b <= -4e+41) {
		tmp = fma(t_1, b, ((j * c) * a));
	} else if (b <= 3.2e+72) {
		tmp = fma(((c * a) - (i * y)), j, (((z * y) - (a * t)) * x));
	} else {
		tmp = fma(t_1, b, ((z * y) * x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * t) - Float64(c * z))
	tmp = 0.0
	if (b <= -4e+41)
		tmp = fma(t_1, b, Float64(Float64(j * c) * a));
	elseif (b <= 3.2e+72)
		tmp = fma(Float64(Float64(c * a) - Float64(i * y)), j, Float64(Float64(Float64(z * y) - Float64(a * t)) * x));
	else
		tmp = fma(t_1, b, Float64(Float64(z * y) * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * t), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4e+41], N[(t$95$1 * b + N[(N[(j * c), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e+72], N[(N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] * j + N[(N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * b + N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.00000000000000002e41

   1. Initial program 71.1%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   4. Applied rewrites 76.4%

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

   5. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 66.2

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

   7. Applied rewrites 66.2%

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

   if -4.00000000000000002e41 < b < 3.2000000000000001e72

   1. Initial program 74.0%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 70.3

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

   4. Applied rewrites 70.3%

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

   if 3.2000000000000001e72 < b

   1. Initial program 74.3%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   4. Applied rewrites 79.3%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 68.2

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

   7. Applied rewrites 68.2%

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

Alternative 7: 59.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot t - c \cdot z\\ t_2 := \mathsf{fma}\left(-t, x, j \cdot c\right) \cdot a\\ \mathbf{if}\;a \leq -2.75 \cdot 10^{+191}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-60}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, \left(-a\right) \cdot \left(t \cdot x\right)\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+51}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, \left(z \cdot y\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* i t) (* c z))) (t_2 (* (fma (- t) x (* j c)) a)))
   (if (<= a -2.75e+191)
     t_2
     (if (<= a -1.35e-60)
       (fma t_1 b (* (- a) (* t x)))
       (if (<= a 1.05e+51) (fma t_1 b (* (* z y) x)) 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 * t) - (c * z);
	double t_2 = fma(-t, x, (j * c)) * a;
	double tmp;
	if (a <= -2.75e+191) {
		tmp = t_2;
	} else if (a <= -1.35e-60) {
		tmp = fma(t_1, b, (-a * (t * x)));
	} else if (a <= 1.05e+51) {
		tmp = fma(t_1, b, ((z * y) * x));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * t) - Float64(c * z))
	t_2 = Float64(fma(Float64(-t), x, Float64(j * c)) * a)
	tmp = 0.0
	if (a <= -2.75e+191)
		tmp = t_2;
	elseif (a <= -1.35e-60)
		tmp = fma(t_1, b, Float64(Float64(-a) * Float64(t * x)));
	elseif (a <= 1.05e+51)
		tmp = fma(t_1, b, Float64(Float64(z * y) * x));
	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 * t), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-t) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -2.75e+191], t$95$2, If[LessEqual[a, -1.35e-60], N[(t$95$1 * b + N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e+51], N[(t$95$1 * b + N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.7500000000000001e191 or 1.0500000000000001e51 < a

   1. Initial program 62.7%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 66.2

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

   4. Applied rewrites 66.2%

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

   if -2.7500000000000001e191 < a < -1.35e-60

   1. Initial program 72.8%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   4. Applied rewrites 75.8%

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

   5. Taylor expanded in t around inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-*.f64 51.1

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

   7. Applied rewrites 51.1%

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

   if -1.35e-60 < a < 1.0500000000000001e51

   1. Initial program 80.3%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   4. Applied rewrites 82.0%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 59.5

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

   7. Applied rewrites 59.5%

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

Alternative 8: 58.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-t, x, j \cdot c\right) \cdot a\\ \mathbf{if}\;a \leq -7 \cdot 10^{+175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+51}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot t - c \cdot z, b, \left(z \cdot y\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- t) x (* j c)) a)))
   (if (<= a -7e+175)
     t_1
     (if (<= a 1.05e+51) (fma (- (* i t) (* 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(-t, x, (j * c)) * a;
	double tmp;
	if (a <= -7e+175) {
		tmp = t_1;
	} else if (a <= 1.05e+51) {
		tmp = fma(((i * t) - (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(-t), x, Float64(j * c)) * a)
	tmp = 0.0
	if (a <= -7e+175)
		tmp = t_1;
	elseif (a <= 1.05e+51)
		tmp = fma(Float64(Float64(i * t) - 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[((-t) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -7e+175], t$95$1, If[LessEqual[a, 1.05e+51], N[(N[(N[(i * t), $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 a < -7.0000000000000006e175 or 1.0500000000000001e51 < a

   1. Initial program 62.6%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 66.2

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

   4. Applied rewrites 66.2%

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

   if -7.0000000000000006e175 < a < 1.0500000000000001e51

   1. Initial program 78.5%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   4. Applied rewrites 80.5%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 55.4

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

   7. Applied rewrites 55.4%

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

Alternative 9: 53.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-t, x, j \cdot c\right) \cdot a\\ \mathbf{if}\;a \leq -8.8 \cdot 10^{+175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-156}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot t - c \cdot z, b, \left(j \cdot c\right) \cdot a\right)\\ \mathbf{elif}\;a \leq 6200000000000:\\ \;\;\;\;\left(y \cdot x - c \cdot b\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- t) x (* j c)) a)))
   (if (<= a -8.8e+175)
     t_1
     (if (<= a -3.3e-156)
       (fma (- (* i t) (* c z)) b (* (* j c) a))
       (if (<= a 6200000000000.0) (* (- (* y x) (* c b)) z) 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(-t, x, (j * c)) * a;
	double tmp;
	if (a <= -8.8e+175) {
		tmp = t_1;
	} else if (a <= -3.3e-156) {
		tmp = fma(((i * t) - (c * z)), b, ((j * c) * a));
	} else if (a <= 6200000000000.0) {
		tmp = ((y * x) - (c * b)) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-t), x, Float64(j * c)) * a)
	tmp = 0.0
	if (a <= -8.8e+175)
		tmp = t_1;
	elseif (a <= -3.3e-156)
		tmp = fma(Float64(Float64(i * t) - Float64(c * z)), b, Float64(Float64(j * c) * a));
	elseif (a <= 6200000000000.0)
		tmp = Float64(Float64(Float64(y * x) - Float64(c * b)) * z);
	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[((-t) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -8.8e+175], t$95$1, If[LessEqual[a, -3.3e-156], N[(N[(N[(i * t), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision] * b + N[(N[(j * c), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6200000000000.0], N[(N[(N[(y * x), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.7999999999999997e175 or 6.2e12 < a

   1. Initial program 64.2%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 63.7

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

   4. Applied rewrites 63.7%

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

   if -8.7999999999999997e175 < a < -3.2999999999999999e-156

   1. Initial program 75.5%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   4. Applied rewrites 77.9%

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

   5. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 49.9

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

   7. Applied rewrites 49.9%

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

   if -3.2999999999999999e-156 < a < 6.2e12

   1. Initial program 80.5%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 46.4

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

   4. Applied rewrites 46.4%

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

Alternative 10: 53.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-t, x, j \cdot c\right) \cdot a\\ \mathbf{if}\;a \leq -7 \cdot 10^{+175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-156}:\\ \;\;\;\;\left(i \cdot t - c \cdot z\right) \cdot b\\ \mathbf{elif}\;a \leq 6200000000000:\\ \;\;\;\;\left(y \cdot x - c \cdot b\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- t) x (* j c)) a)))
   (if (<= a -7e+175)
     t_1
     (if (<= a -3.4e-156)
       (* (- (* i t) (* c z)) b)
       (if (<= a 6200000000000.0) (* (- (* y x) (* c b)) z) 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(-t, x, (j * c)) * a;
	double tmp;
	if (a <= -7e+175) {
		tmp = t_1;
	} else if (a <= -3.4e-156) {
		tmp = ((i * t) - (c * z)) * b;
	} else if (a <= 6200000000000.0) {
		tmp = ((y * x) - (c * b)) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-t), x, Float64(j * c)) * a)
	tmp = 0.0
	if (a <= -7e+175)
		tmp = t_1;
	elseif (a <= -3.4e-156)
		tmp = Float64(Float64(Float64(i * t) - Float64(c * z)) * b);
	elseif (a <= 6200000000000.0)
		tmp = Float64(Float64(Float64(y * x) - Float64(c * b)) * z);
	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[((-t) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -7e+175], t$95$1, If[LessEqual[a, -3.4e-156], N[(N[(N[(i * t), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[a, 6200000000000.0], N[(N[(N[(y * x), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.0000000000000006e175 or 6.2e12 < a

   1. Initial program 64.1%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 63.7

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

   4. Applied rewrites 63.7%

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

   if -7.0000000000000006e175 < a < -3.3999999999999999e-156

   1. Initial program 75.5%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 38.5

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

   4. Applied rewrites 38.5%

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

   if -3.3999999999999999e-156 < a < 6.2e12

   1. Initial program 80.5%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 46.4

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

   4. Applied rewrites 46.4%

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

Alternative 11: 52.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot a - i \cdot y\right) \cdot j\\ t_2 := \left(i \cdot t - c \cdot z\right) \cdot b\\ \mathbf{if}\;b \leq -9.2 \cdot 10^{+48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{-156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-275}:\\ \;\;\;\;\left(z \cdot y - a \cdot t\right) \cdot x\\ \mathbf{elif}\;b \leq 0.14:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- (* c a) (* i y)) j)) (t_2 (* (- (* i t) (* c z)) b)))
   (if (<= b -9.2e+48)
     t_2
     (if (<= b -8.8e-156)
       t_1
       (if (<= b 3.8e-275)
         (* (- (* z y) (* a t)) x)
         (if (<= b 0.14) t_1 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 = ((c * a) - (i * y)) * j;
	double t_2 = ((i * t) - (c * z)) * b;
	double tmp;
	if (b <= -9.2e+48) {
		tmp = t_2;
	} else if (b <= -8.8e-156) {
		tmp = t_1;
	} else if (b <= 3.8e-275) {
		tmp = ((z * y) - (a * t)) * x;
	} else if (b <= 0.14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = ((c * a) - (i * y)) * j
    t_2 = ((i * t) - (c * z)) * b
    if (b <= (-9.2d+48)) then
        tmp = t_2
    else if (b <= (-8.8d-156)) then
        tmp = t_1
    else if (b <= 3.8d-275) then
        tmp = ((z * y) - (a * t)) * x
    else if (b <= 0.14d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((c * a) - (i * y)) * j;
	double t_2 = ((i * t) - (c * z)) * b;
	double tmp;
	if (b <= -9.2e+48) {
		tmp = t_2;
	} else if (b <= -8.8e-156) {
		tmp = t_1;
	} else if (b <= 3.8e-275) {
		tmp = ((z * y) - (a * t)) * x;
	} else if (b <= 0.14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((c * a) - (i * y)) * j
	t_2 = ((i * t) - (c * z)) * b
	tmp = 0
	if b <= -9.2e+48:
		tmp = t_2
	elif b <= -8.8e-156:
		tmp = t_1
	elif b <= 3.8e-275:
		tmp = ((z * y) - (a * t)) * x
	elif b <= 0.14:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(c * a) - Float64(i * y)) * j)
	t_2 = Float64(Float64(Float64(i * t) - Float64(c * z)) * b)
	tmp = 0.0
	if (b <= -9.2e+48)
		tmp = t_2;
	elseif (b <= -8.8e-156)
		tmp = t_1;
	elseif (b <= 3.8e-275)
		tmp = Float64(Float64(Float64(z * y) - Float64(a * t)) * x);
	elseif (b <= 0.14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((c * a) - (i * y)) * j;
	t_2 = ((i * t) - (c * z)) * b;
	tmp = 0.0;
	if (b <= -9.2e+48)
		tmp = t_2;
	elseif (b <= -8.8e-156)
		tmp = t_1;
	elseif (b <= 3.8e-275)
		tmp = ((z * y) - (a * t)) * x;
	elseif (b <= 0.14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(i * t), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -9.2e+48], t$95$2, If[LessEqual[b, -8.8e-156], t$95$1, If[LessEqual[b, 3.8e-275], N[(N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[b, 0.14], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.2000000000000001e48 or 0.14000000000000001 < b

   1. Initial program 72.9%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 61.2

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

   4. Applied rewrites 61.2%

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

   if -9.2000000000000001e48 < b < -8.7999999999999996e-156 or 3.79999999999999972e-275 < b < 0.14000000000000001

   1. Initial program 75.0%

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

   2. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 45.5

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

   4. Applied rewrites 45.5%

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

   if -8.7999999999999996e-156 < b < 3.79999999999999972e-275

   1. Initial program 71.0%

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

   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

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 46.2

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

   4. Applied rewrites 46.2%

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

Alternative 12: 52.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot a - i \cdot y\right) \cdot j\\ \mathbf{if}\;j \leq -8.2 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.04 \cdot 10^{-265}:\\ \;\;\;\;\left(i \cdot t - c \cdot z\right) \cdot b\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{-50}:\\ \;\;\;\;\left(y \cdot x - c \cdot b\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- (* c a) (* i y)) j)))
   (if (<= j -8.2e+105)
     t_1
     (if (<= j 1.04e-265)
       (* (- (* i t) (* c z)) b)
       (if (<= j 1.15e-50) (* (- (* y x) (* c b)) z) 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 * a) - (i * y)) * j;
	double tmp;
	if (j <= -8.2e+105) {
		tmp = t_1;
	} else if (j <= 1.04e-265) {
		tmp = ((i * t) - (c * z)) * b;
	} else if (j <= 1.15e-50) {
		tmp = ((y * x) - (c * b)) * z;
	} 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 * a) - (i * y)) * j
    if (j <= (-8.2d+105)) then
        tmp = t_1
    else if (j <= 1.04d-265) then
        tmp = ((i * t) - (c * z)) * b
    else if (j <= 1.15d-50) then
        tmp = ((y * x) - (c * b)) * z
    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 * a) - (i * y)) * j;
	double tmp;
	if (j <= -8.2e+105) {
		tmp = t_1;
	} else if (j <= 1.04e-265) {
		tmp = ((i * t) - (c * z)) * b;
	} else if (j <= 1.15e-50) {
		tmp = ((y * x) - (c * b)) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((c * a) - (i * y)) * j
	tmp = 0
	if j <= -8.2e+105:
		tmp = t_1
	elif j <= 1.04e-265:
		tmp = ((i * t) - (c * z)) * b
	elif j <= 1.15e-50:
		tmp = ((y * x) - (c * b)) * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(c * a) - Float64(i * y)) * j)
	tmp = 0.0
	if (j <= -8.2e+105)
		tmp = t_1;
	elseif (j <= 1.04e-265)
		tmp = Float64(Float64(Float64(i * t) - Float64(c * z)) * b);
	elseif (j <= 1.15e-50)
		tmp = Float64(Float64(Float64(y * x) - Float64(c * b)) * z);
	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 * a) - (i * y)) * j;
	tmp = 0.0;
	if (j <= -8.2e+105)
		tmp = t_1;
	elseif (j <= 1.04e-265)
		tmp = ((i * t) - (c * z)) * b;
	elseif (j <= 1.15e-50)
		tmp = ((y * x) - (c * b)) * z;
	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[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]}, If[LessEqual[j, -8.2e+105], t$95$1, If[LessEqual[j, 1.04e-265], N[(N[(N[(i * t), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[j, 1.15e-50], N[(N[(N[(y * x), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -8.2000000000000005e105 or 1.1500000000000001e-50 < j

   1. Initial program 73.2%

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

   2. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 60.6

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

   4. Applied rewrites 60.6%

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

   if -8.2000000000000005e105 < j < 1.04e-265

   1. Initial program 73.8%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 45.2

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

   4. Applied rewrites 45.2%

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

   if 1.04e-265 < j < 1.1500000000000001e-50

   1. Initial program 73.0%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 46.1

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

   4. Applied rewrites 46.1%

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

Alternative 13: 50.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(i \cdot t - c \cdot z\right) \cdot b\\ \mathbf{if}\;b \leq -9.2 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 0.14:\\ \;\;\;\;\left(c \cdot a - i \cdot y\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- (* i t) (* c z)) b)))
   (if (<= b -9.2e+48) t_1 (if (<= b 0.14) (* (- (* c a) (* 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 * t) - (c * z)) * b;
	double tmp;
	if (b <= -9.2e+48) {
		tmp = t_1;
	} else if (b <= 0.14) {
		tmp = ((c * a) - (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 * t) - (c * z)) * b
    if (b <= (-9.2d+48)) then
        tmp = t_1
    else if (b <= 0.14d0) then
        tmp = ((c * a) - (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 * t) - (c * z)) * b;
	double tmp;
	if (b <= -9.2e+48) {
		tmp = t_1;
	} else if (b <= 0.14) {
		tmp = ((c * a) - (i * y)) * j;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((i * t) - (c * z)) * b
	tmp = 0
	if b <= -9.2e+48:
		tmp = t_1
	elif b <= 0.14:
		tmp = ((c * a) - (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 * t) - Float64(c * z)) * b)
	tmp = 0.0
	if (b <= -9.2e+48)
		tmp = t_1;
	elseif (b <= 0.14)
		tmp = Float64(Float64(Float64(c * a) - 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 * t) - (c * z)) * b;
	tmp = 0.0;
	if (b <= -9.2e+48)
		tmp = t_1;
	elseif (b <= 0.14)
		tmp = ((c * a) - (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 * t), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -9.2e+48], t$95$1, If[LessEqual[b, 0.14], N[(N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -9.2000000000000001e48 or 0.14000000000000001 < b

   1. Initial program 72.9%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 61.2

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

   4. Applied rewrites 61.2%

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

   if -9.2000000000000001e48 < b < 0.14000000000000001

   1. Initial program 73.8%

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

   2. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 46.3

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

   4. Applied rewrites 46.3%

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

Alternative 14: 42.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-b\right) \cdot \left(c \cdot z\right)\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+171}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+16}:\\ \;\;\;\;\left(c \cdot a - i \cdot y\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- b) (* c z))))
   (if (<= z -1.3e+171)
     t_1
     (if (<= z 1.55e+16) (* (- (* c a) (* 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 <= -1.3e+171) {
		tmp = t_1;
	} else if (z <= 1.55e+16) {
		tmp = ((c * a) - (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 <= (-1.3d+171)) then
        tmp = t_1
    else if (z <= 1.55d+16) then
        tmp = ((c * a) - (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 <= -1.3e+171) {
		tmp = t_1;
	} else if (z <= 1.55e+16) {
		tmp = ((c * a) - (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 <= -1.3e+171:
		tmp = t_1
	elif z <= 1.55e+16:
		tmp = ((c * a) - (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 <= -1.3e+171)
		tmp = t_1;
	elseif (z <= 1.55e+16)
		tmp = Float64(Float64(Float64(c * a) - 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 <= -1.3e+171)
		tmp = t_1;
	elseif (z <= 1.55e+16)
		tmp = ((c * a) - (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, -1.3e+171], t$95$1, If[LessEqual[z, 1.55e+16], N[(N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e171 or 1.55e16 < z

   1. Initial program 63.6%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. lower-*.f64 63.1

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

   4. Applied rewrites 63.1%

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

   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 39.1

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

   7. Applied rewrites 39.1%

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

   if -1.3e171 < z < 1.55e16

   1. Initial program 78.6%

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

   2. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 43.9

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

   4. Applied rewrites 43.9%

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

Alternative 15: 30.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(-i\right) \cdot y\right) \cdot j\\ t_2 := \left(-b\right) \cdot \left(c \cdot z\right)\\ \mathbf{if}\;z \leq -7.4 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-192}:\\ \;\;\;\;\left(-t\right) \cdot \left(a \cdot x\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+37}:\\ \;\;\;\;\left(\left(-a\right) \cdot t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* (- i) y) j)) (t_2 (* (- b) (* c z))))
   (if (<= z -7.4e+31)
     t_2
     (if (<= z -7e-106)
       t_1
       (if (<= z 9.6e-192)
         (* (- t) (* a x))
         (if (<= z 6e-11) t_1 (if (<= z 1.2e+37) (* (* (- a) t) x) 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 * y) * j;
	double t_2 = -b * (c * z);
	double tmp;
	if (z <= -7.4e+31) {
		tmp = t_2;
	} else if (z <= -7e-106) {
		tmp = t_1;
	} else if (z <= 9.6e-192) {
		tmp = -t * (a * x);
	} else if (z <= 6e-11) {
		tmp = t_1;
	} else if (z <= 1.2e+37) {
		tmp = (-a * t) * x;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (-i * y) * j
    t_2 = -b * (c * z)
    if (z <= (-7.4d+31)) then
        tmp = t_2
    else if (z <= (-7d-106)) then
        tmp = t_1
    else if (z <= 9.6d-192) then
        tmp = -t * (a * x)
    else if (z <= 6d-11) then
        tmp = t_1
    else if (z <= 1.2d+37) then
        tmp = (-a * t) * x
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (-i * y) * j;
	double t_2 = -b * (c * z);
	double tmp;
	if (z <= -7.4e+31) {
		tmp = t_2;
	} else if (z <= -7e-106) {
		tmp = t_1;
	} else if (z <= 9.6e-192) {
		tmp = -t * (a * x);
	} else if (z <= 6e-11) {
		tmp = t_1;
	} else if (z <= 1.2e+37) {
		tmp = (-a * t) * x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (-i * y) * j
	t_2 = -b * (c * z)
	tmp = 0
	if z <= -7.4e+31:
		tmp = t_2
	elif z <= -7e-106:
		tmp = t_1
	elif z <= 9.6e-192:
		tmp = -t * (a * x)
	elif z <= 6e-11:
		tmp = t_1
	elif z <= 1.2e+37:
		tmp = (-a * t) * x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(-i) * y) * j)
	t_2 = Float64(Float64(-b) * Float64(c * z))
	tmp = 0.0
	if (z <= -7.4e+31)
		tmp = t_2;
	elseif (z <= -7e-106)
		tmp = t_1;
	elseif (z <= 9.6e-192)
		tmp = Float64(Float64(-t) * Float64(a * x));
	elseif (z <= 6e-11)
		tmp = t_1;
	elseif (z <= 1.2e+37)
		tmp = Float64(Float64(Float64(-a) * t) * x);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (-i * y) * j;
	t_2 = -b * (c * z);
	tmp = 0.0;
	if (z <= -7.4e+31)
		tmp = t_2;
	elseif (z <= -7e-106)
		tmp = t_1;
	elseif (z <= 9.6e-192)
		tmp = -t * (a * x);
	elseif (z <= 6e-11)
		tmp = t_1;
	elseif (z <= 1.2e+37)
		tmp = (-a * t) * x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-i) * y), $MachinePrecision] * j), $MachinePrecision]}, Block[{t$95$2 = N[((-b) * N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.4e+31], t$95$2, If[LessEqual[z, -7e-106], t$95$1, If[LessEqual[z, 9.6e-192], N[((-t) * N[(a * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-11], t$95$1, If[LessEqual[z, 1.2e+37], N[(N[((-a) * t), $MachinePrecision] * x), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.3999999999999996e31 or 1.2e37 < z

   1. Initial program 64.6%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. lower-*.f64 63.2

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

   4. Applied rewrites 63.2%

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

   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 37.5

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

   7. Applied rewrites 37.5%

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

   if -7.3999999999999996e31 < z < -7e-106 or 9.5999999999999997e-192 < z < 6e-11

   1. Initial program 80.8%

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

   2. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 43.9

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

   4. Applied rewrites 43.9%

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

   5. Taylor expanded in y around inf

      \[\leadsto \left(-1 \cdot \left(i \cdot y\right)\right) \cdot j \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot i\right) \cdot y\right) \cdot j \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(-1 \cdot i\right) \cdot y\right) \cdot j \]

      3. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(i\right)\right) \cdot y\right) \cdot j \]

      4. lower-neg.f64 24.8

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

   7. Applied rewrites 24.8%

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

   if -7e-106 < z < 9.5999999999999997e-192

   1. Initial program 80.8%

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

   2. Taylor expanded in t around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 47.7

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

   4. Applied rewrites 47.7%

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

   5. Taylor expanded in x around inf

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

      1. lift-*.f64 26.4

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

   7. Applied rewrites 26.4%

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

   if 6e-11 < z < 1.2e37

   1. Initial program 80.8%

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

   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

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 34.1

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

   4. Applied rewrites 34.1%

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

   5. Taylor expanded in y around 0

      \[\leadsto \left(-1 \cdot \left(a \cdot t\right)\right) \cdot x \]
   6. Step-by-step derivation

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 24.3

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

   7. Applied rewrites 24.3%

      \[\leadsto \left(\left(-a\right) \cdot t\right) \cdot x \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 16: 30.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(-i\right) \cdot y\right) \cdot j\\ t_2 := \left(-b\right) \cdot \left(c \cdot z\right)\\ \mathbf{if}\;z \leq -7.4 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-192}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+37}:\\ \;\;\;\;\left(\left(-a\right) \cdot t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* (- i) y) j)) (t_2 (* (- b) (* c z))))
   (if (<= z -7.4e+31)
     t_2
     (if (<= z -7e-106)
       t_1
       (if (<= z 9.6e-192)
         (* (- a) (* t x))
         (if (<= z 6e-11) t_1 (if (<= z 1.2e+37) (* (* (- a) t) x) 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 * y) * j;
	double t_2 = -b * (c * z);
	double tmp;
	if (z <= -7.4e+31) {
		tmp = t_2;
	} else if (z <= -7e-106) {
		tmp = t_1;
	} else if (z <= 9.6e-192) {
		tmp = -a * (t * x);
	} else if (z <= 6e-11) {
		tmp = t_1;
	} else if (z <= 1.2e+37) {
		tmp = (-a * t) * x;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (-i * y) * j
    t_2 = -b * (c * z)
    if (z <= (-7.4d+31)) then
        tmp = t_2
    else if (z <= (-7d-106)) then
        tmp = t_1
    else if (z <= 9.6d-192) then
        tmp = -a * (t * x)
    else if (z <= 6d-11) then
        tmp = t_1
    else if (z <= 1.2d+37) then
        tmp = (-a * t) * x
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (-i * y) * j;
	double t_2 = -b * (c * z);
	double tmp;
	if (z <= -7.4e+31) {
		tmp = t_2;
	} else if (z <= -7e-106) {
		tmp = t_1;
	} else if (z <= 9.6e-192) {
		tmp = -a * (t * x);
	} else if (z <= 6e-11) {
		tmp = t_1;
	} else if (z <= 1.2e+37) {
		tmp = (-a * t) * x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (-i * y) * j
	t_2 = -b * (c * z)
	tmp = 0
	if z <= -7.4e+31:
		tmp = t_2
	elif z <= -7e-106:
		tmp = t_1
	elif z <= 9.6e-192:
		tmp = -a * (t * x)
	elif z <= 6e-11:
		tmp = t_1
	elif z <= 1.2e+37:
		tmp = (-a * t) * x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(-i) * y) * j)
	t_2 = Float64(Float64(-b) * Float64(c * z))
	tmp = 0.0
	if (z <= -7.4e+31)
		tmp = t_2;
	elseif (z <= -7e-106)
		tmp = t_1;
	elseif (z <= 9.6e-192)
		tmp = Float64(Float64(-a) * Float64(t * x));
	elseif (z <= 6e-11)
		tmp = t_1;
	elseif (z <= 1.2e+37)
		tmp = Float64(Float64(Float64(-a) * t) * x);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (-i * y) * j;
	t_2 = -b * (c * z);
	tmp = 0.0;
	if (z <= -7.4e+31)
		tmp = t_2;
	elseif (z <= -7e-106)
		tmp = t_1;
	elseif (z <= 9.6e-192)
		tmp = -a * (t * x);
	elseif (z <= 6e-11)
		tmp = t_1;
	elseif (z <= 1.2e+37)
		tmp = (-a * t) * x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-i) * y), $MachinePrecision] * j), $MachinePrecision]}, Block[{t$95$2 = N[((-b) * N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.4e+31], t$95$2, If[LessEqual[z, -7e-106], t$95$1, If[LessEqual[z, 9.6e-192], N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-11], t$95$1, If[LessEqual[z, 1.2e+37], N[(N[((-a) * t), $MachinePrecision] * x), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.3999999999999996e31 or 1.2e37 < z

   1. Initial program 64.6%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. lower-*.f64 63.2

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

   4. Applied rewrites 63.2%

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

   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 37.5

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

   7. Applied rewrites 37.5%

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

   if -7.3999999999999996e31 < z < -7e-106 or 9.5999999999999997e-192 < z < 6e-11

   1. Initial program 80.8%

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

   2. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 43.9

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

   4. Applied rewrites 43.9%

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

   5. Taylor expanded in y around inf

      \[\leadsto \left(-1 \cdot \left(i \cdot y\right)\right) \cdot j \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot i\right) \cdot y\right) \cdot j \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(-1 \cdot i\right) \cdot y\right) \cdot j \]

      3. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(i\right)\right) \cdot y\right) \cdot j \]

      4. lower-neg.f64 24.8

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

   7. Applied rewrites 24.8%

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

   if -7e-106 < z < 9.5999999999999997e-192

   1. Initial program 80.8%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. lower-*.f64 50.8

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

   4. Applied rewrites 50.8%

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

   5. Taylor expanded in a 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. mul-1-neg N/A

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

      3. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t \cdot \color{blue}{x}\right) \]

      4. lower-neg.f64 N/A

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

      5. lower-*.f64 26.4

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

   7. Applied rewrites 26.4%

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

   if 6e-11 < z < 1.2e37

   1. Initial program 80.8%

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

   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

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 34.1

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

   4. Applied rewrites 34.1%

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

   5. Taylor expanded in y around 0

      \[\leadsto \left(-1 \cdot \left(a \cdot t\right)\right) \cdot x \]
   6. Step-by-step derivation

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 24.3

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

   7. Applied rewrites 24.3%

      \[\leadsto \left(\left(-a\right) \cdot t\right) \cdot x \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 17: 30.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(-i\right) \cdot y\right) \cdot j\\ t_2 := \left(-b\right) \cdot \left(c \cdot z\right)\\ t_3 := \left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{if}\;z \leq -7.4 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-192}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+38}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* (- i) y) j))
        (t_2 (* (- b) (* c z)))
        (t_3 (* (- a) (* t x))))
   (if (<= z -7.4e+31)
     t_2
     (if (<= z -7e-106)
       t_1
       (if (<= z 9.6e-192)
         t_3
         (if (<= z 6e-11) t_1 (if (<= z 3.5e+38) t_3 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 * y) * j;
	double t_2 = -b * (c * z);
	double t_3 = -a * (t * x);
	double tmp;
	if (z <= -7.4e+31) {
		tmp = t_2;
	} else if (z <= -7e-106) {
		tmp = t_1;
	} else if (z <= 9.6e-192) {
		tmp = t_3;
	} else if (z <= 6e-11) {
		tmp = t_1;
	} else if (z <= 3.5e+38) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (-i * y) * j
    t_2 = -b * (c * z)
    t_3 = -a * (t * x)
    if (z <= (-7.4d+31)) then
        tmp = t_2
    else if (z <= (-7d-106)) then
        tmp = t_1
    else if (z <= 9.6d-192) then
        tmp = t_3
    else if (z <= 6d-11) then
        tmp = t_1
    else if (z <= 3.5d+38) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (-i * y) * j;
	double t_2 = -b * (c * z);
	double t_3 = -a * (t * x);
	double tmp;
	if (z <= -7.4e+31) {
		tmp = t_2;
	} else if (z <= -7e-106) {
		tmp = t_1;
	} else if (z <= 9.6e-192) {
		tmp = t_3;
	} else if (z <= 6e-11) {
		tmp = t_1;
	} else if (z <= 3.5e+38) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (-i * y) * j
	t_2 = -b * (c * z)
	t_3 = -a * (t * x)
	tmp = 0
	if z <= -7.4e+31:
		tmp = t_2
	elif z <= -7e-106:
		tmp = t_1
	elif z <= 9.6e-192:
		tmp = t_3
	elif z <= 6e-11:
		tmp = t_1
	elif z <= 3.5e+38:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(-i) * y) * j)
	t_2 = Float64(Float64(-b) * Float64(c * z))
	t_3 = Float64(Float64(-a) * Float64(t * x))
	tmp = 0.0
	if (z <= -7.4e+31)
		tmp = t_2;
	elseif (z <= -7e-106)
		tmp = t_1;
	elseif (z <= 9.6e-192)
		tmp = t_3;
	elseif (z <= 6e-11)
		tmp = t_1;
	elseif (z <= 3.5e+38)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (-i * y) * j;
	t_2 = -b * (c * z);
	t_3 = -a * (t * x);
	tmp = 0.0;
	if (z <= -7.4e+31)
		tmp = t_2;
	elseif (z <= -7e-106)
		tmp = t_1;
	elseif (z <= 9.6e-192)
		tmp = t_3;
	elseif (z <= 6e-11)
		tmp = t_1;
	elseif (z <= 3.5e+38)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-i) * y), $MachinePrecision] * j), $MachinePrecision]}, Block[{t$95$2 = N[((-b) * N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.4e+31], t$95$2, If[LessEqual[z, -7e-106], t$95$1, If[LessEqual[z, 9.6e-192], t$95$3, If[LessEqual[z, 6e-11], t$95$1, If[LessEqual[z, 3.5e+38], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.3999999999999996e31 or 3.50000000000000002e38 < z

   1. Initial program 64.5%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. lower-*.f64 63.2

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

   4. Applied rewrites 63.2%

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

   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 37.5

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

   7. Applied rewrites 37.5%

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

   if -7.3999999999999996e31 < z < -7e-106 or 9.5999999999999997e-192 < z < 6e-11

   1. Initial program 80.8%

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

   2. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 43.9

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

   4. Applied rewrites 43.9%

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

   5. Taylor expanded in y around inf

      \[\leadsto \left(-1 \cdot \left(i \cdot y\right)\right) \cdot j \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot i\right) \cdot y\right) \cdot j \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(-1 \cdot i\right) \cdot y\right) \cdot j \]

      3. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(i\right)\right) \cdot y\right) \cdot j \]

      4. lower-neg.f64 24.8

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

   7. Applied rewrites 24.8%

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

   if -7e-106 < z < 9.5999999999999997e-192 or 6e-11 < z < 3.50000000000000002e38

   1. Initial program 80.2%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. lower-*.f64 52.6

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

   4. Applied rewrites 52.6%

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

   5. Taylor expanded in a 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. mul-1-neg N/A

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

      3. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t \cdot \color{blue}{x}\right) \]

      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%

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

Alternative 18: 30.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-b\right) \cdot \left(c \cdot z\right)\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-69}:\\ \;\;\;\;\left(b \cdot t\right) \cdot i\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+38}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- b) (* c z))))
   (if (<= z -7.5e+52)
     t_1
     (if (<= z -8.2e-69)
       (* (* b t) i)
       (if (<= z 3.5e+38) (* (- a) (* t 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 = -b * (c * z);
	double tmp;
	if (z <= -7.5e+52) {
		tmp = t_1;
	} else if (z <= -8.2e-69) {
		tmp = (b * t) * i;
	} else if (z <= 3.5e+38) {
		tmp = -a * (t * x);
	} 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 <= (-7.5d+52)) then
        tmp = t_1
    else if (z <= (-8.2d-69)) then
        tmp = (b * t) * i
    else if (z <= 3.5d+38) then
        tmp = -a * (t * x)
    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 <= -7.5e+52) {
		tmp = t_1;
	} else if (z <= -8.2e-69) {
		tmp = (b * t) * i;
	} else if (z <= 3.5e+38) {
		tmp = -a * (t * x);
	} 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 <= -7.5e+52:
		tmp = t_1
	elif z <= -8.2e-69:
		tmp = (b * t) * i
	elif z <= 3.5e+38:
		tmp = -a * (t * x)
	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 <= -7.5e+52)
		tmp = t_1;
	elseif (z <= -8.2e-69)
		tmp = Float64(Float64(b * t) * i);
	elseif (z <= 3.5e+38)
		tmp = Float64(Float64(-a) * Float64(t * x));
	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 <= -7.5e+52)
		tmp = t_1;
	elseif (z <= -8.2e-69)
		tmp = (b * t) * i;
	elseif (z <= 3.5e+38)
		tmp = -a * (t * x);
	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, -7.5e+52], t$95$1, If[LessEqual[z, -8.2e-69], N[(N[(b * t), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[z, 3.5e+38], N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.49999999999999995e52 or 3.50000000000000002e38 < z

   1. Initial program 64.3%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - t \cdot i\right) \cdot b \]

      14. *-commutative N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b \]

      15. lift-*.f64 N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b \]

      16. lower-*.f64 63.3

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b \]

   4. Applied rewrites 63.3%

      \[\leadsto \color{blue}{\left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b} \]

   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 38.1

         \[\leadsto \left(-b\right) \cdot \left(c \cdot z\right) \]

   7. Applied rewrites 38.1%

      \[\leadsto \left(-b\right) \cdot \color{blue}{\left(c \cdot z\right)} \]

   if -7.49999999999999995e52 < z < -8.1999999999999998e-69

   1. Initial program 78.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around 0

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right) + \left(j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(i \cdot t - c \cdot z\right) \cdot b + \left(\color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, \color{blue}{b}, j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, \left(a \cdot c - i \cdot y\right) \cdot j + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, \left(c \cdot a - i \cdot y\right) \cdot j + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, \left(c \cdot a - y \cdot i\right) \cdot j + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      9. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, \mathsf{fma}\left(c \cdot a - y \cdot i, j, x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) \]

   4. Applied rewrites 81.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i \cdot t - c \cdot z, b, \mathsf{fma}\left(c \cdot a - i \cdot y, j, \left(z \cdot y - a \cdot t\right) \cdot x\right)\right)} \]

   5. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) \cdot \color{blue}{i} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) \cdot \color{blue}{i} \]

      3. associate-*r* N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - \left(-1 \cdot b\right) \cdot t\right) \cdot i \]

      4. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot t\right) \cdot i \]

      5. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right) \cdot i \]

      6. +-commutative N/A

         \[\leadsto \left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right) \cdot i \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, t, -1 \cdot \left(j \cdot y\right)\right) \cdot i \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(b, t, \mathsf{neg}\left(j \cdot y\right)\right) \cdot i \]

      9. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, t, -j \cdot y\right) \cdot i \]

      10. lower-*.f64 37.9

          \[\leadsto \mathsf{fma}\left(b, t, -j \cdot y\right) \cdot i \]

   7. Applied rewrites 37.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t, -j \cdot y\right) \cdot i} \]

   8. Taylor expanded in y around 0

      \[\leadsto \left(b \cdot t\right) \cdot i \]
   9. Step-by-step derivation

      1. lower-*.f64 19.6

         \[\leadsto \left(b \cdot t\right) \cdot i \]

   10. Applied rewrites 19.6%

       \[\leadsto \left(b \cdot t\right) \cdot i \]

   if -8.1999999999999998e-69 < z < 3.50000000000000002e38

   1. Initial program 80.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in j around 0

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) - \color{blue}{b \cdot \left(c \cdot z - i \cdot t\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x - \color{blue}{b} \cdot \left(c \cdot z - i \cdot t\right) \]

      3. *-commutative N/A

         \[\leadsto \left(y \cdot z - t \cdot a\right) \cdot x - b \cdot \left(c \cdot z - i \cdot t\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \left(y \cdot z - t \cdot a\right) \cdot x - \color{blue}{b} \cdot \left(c \cdot z - i \cdot t\right) \]

      5. lift--.f64 N/A

         \[\leadsto \left(y \cdot z - t \cdot a\right) \cdot x - b \cdot \left(c \cdot z - i \cdot t\right) \]

      6. *-commutative N/A

         \[\leadsto \left(z \cdot y - t \cdot a\right) \cdot x - b \cdot \left(c \cdot z - i \cdot t\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \left(z \cdot y - t \cdot a\right) \cdot x - b \cdot \left(c \cdot z - i \cdot t\right) \]

      8. *-commutative N/A

         \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - b \cdot \left(c \cdot z - i \cdot t\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - b \cdot \left(c \cdot z - i \cdot t\right) \]

      10. *-commutative N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot \color{blue}{b} \]

      11. *-commutative N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - t \cdot i\right) \cdot b \]

      12. lower-*.f64 N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - t \cdot i\right) \cdot \color{blue}{b} \]

      13. lift--.f64 N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - t \cdot i\right) \cdot b \]

      14. *-commutative N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b \]

      15. lift-*.f64 N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b \]

      16. lower-*.f64 53.8

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b \]

   4. Applied rewrites 53.8%

      \[\leadsto \color{blue}{\left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b} \]

   5. Taylor expanded in a 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. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t \cdot x\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t \cdot \color{blue}{x}\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(-a\right) \cdot \left(t \cdot x\right) \]

      5. lower-*.f64 25.5

         \[\leadsto \left(-a\right) \cdot \left(t \cdot x\right) \]

   7. Applied rewrites 25.5%

      \[\leadsto \left(-a\right) \cdot \color{blue}{\left(t \cdot x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 30.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{if}\;a \leq -8.5:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-156}:\\ \;\;\;\;\left(b \cdot t\right) \cdot i\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+21}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- a) (* t x))))
   (if (<= a -8.5)
     t_1
     (if (<= a -3.3e-156)
       (* (* b t) i)
       (if (<= a 1.9e+21) (* (* 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 = -a * (t * x);
	double tmp;
	if (a <= -8.5) {
		tmp = t_1;
	} else if (a <= -3.3e-156) {
		tmp = (b * t) * i;
	} else if (a <= 1.9e+21) {
		tmp = (z * y) * x;
	} 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 (a <= (-8.5d0)) then
        tmp = t_1
    else if (a <= (-3.3d-156)) then
        tmp = (b * t) * i
    else if (a <= 1.9d+21) then
        tmp = (z * y) * x
    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 (a <= -8.5) {
		tmp = t_1;
	} else if (a <= -3.3e-156) {
		tmp = (b * t) * i;
	} else if (a <= 1.9e+21) {
		tmp = (z * y) * x;
	} 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 a <= -8.5:
		tmp = t_1
	elif a <= -3.3e-156:
		tmp = (b * t) * i
	elif a <= 1.9e+21:
		tmp = (z * y) * x
	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 (a <= -8.5)
		tmp = t_1;
	elseif (a <= -3.3e-156)
		tmp = Float64(Float64(b * t) * i);
	elseif (a <= 1.9e+21)
		tmp = Float64(Float64(z * y) * x);
	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 (a <= -8.5)
		tmp = t_1;
	elseif (a <= -3.3e-156)
		tmp = (b * t) * i;
	elseif (a <= 1.9e+21)
		tmp = (z * y) * x;
	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[a, -8.5], t$95$1, If[LessEqual[a, -3.3e-156], N[(N[(b * t), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[a, 1.9e+21], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.5 or 1.9e21 < a

   1. Initial program 66.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in j around 0

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) - \color{blue}{b \cdot \left(c \cdot z - i \cdot t\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x - \color{blue}{b} \cdot \left(c \cdot z - i \cdot t\right) \]

      3. *-commutative N/A

         \[\leadsto \left(y \cdot z - t \cdot a\right) \cdot x - b \cdot \left(c \cdot z - i \cdot t\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \left(y \cdot z - t \cdot a\right) \cdot x - \color{blue}{b} \cdot \left(c \cdot z - i \cdot t\right) \]

      5. lift--.f64 N/A

         \[\leadsto \left(y \cdot z - t \cdot a\right) \cdot x - b \cdot \left(c \cdot z - i \cdot t\right) \]

      6. *-commutative N/A

         \[\leadsto \left(z \cdot y - t \cdot a\right) \cdot x - b \cdot \left(c \cdot z - i \cdot t\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \left(z \cdot y - t \cdot a\right) \cdot x - b \cdot \left(c \cdot z - i \cdot t\right) \]

      8. *-commutative N/A

         \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - b \cdot \left(c \cdot z - i \cdot t\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - b \cdot \left(c \cdot z - i \cdot t\right) \]

      10. *-commutative N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot \color{blue}{b} \]

      11. *-commutative N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - t \cdot i\right) \cdot b \]

      12. lower-*.f64 N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - t \cdot i\right) \cdot \color{blue}{b} \]

      13. lift--.f64 N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - t \cdot i\right) \cdot b \]

      14. *-commutative N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b \]

      15. lift-*.f64 N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b \]

      16. lower-*.f64 52.8

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b \]

   4. Applied rewrites 52.8%

      \[\leadsto \color{blue}{\left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b} \]

   5. Taylor expanded in a 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. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t \cdot x\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t \cdot \color{blue}{x}\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(-a\right) \cdot \left(t \cdot x\right) \]

      5. lower-*.f64 32.8

         \[\leadsto \left(-a\right) \cdot \left(t \cdot x\right) \]

   7. Applied rewrites 32.8%

      \[\leadsto \left(-a\right) \cdot \color{blue}{\left(t \cdot x\right)} \]

   if -8.5 < a < -3.2999999999999999e-156

   1. Initial program 79.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around 0

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right) + \left(j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(i \cdot t - c \cdot z\right) \cdot b + \left(\color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, \color{blue}{b}, j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, \left(a \cdot c - i \cdot y\right) \cdot j + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, \left(c \cdot a - i \cdot y\right) \cdot j + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, \left(c \cdot a - y \cdot i\right) \cdot j + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      9. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, \mathsf{fma}\left(c \cdot a - y \cdot i, j, x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) \]

   4. Applied rewrites 81.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i \cdot t - c \cdot z, b, \mathsf{fma}\left(c \cdot a - i \cdot y, j, \left(z \cdot y - a \cdot t\right) \cdot x\right)\right)} \]

   5. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) \cdot \color{blue}{i} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) \cdot \color{blue}{i} \]

      3. associate-*r* N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - \left(-1 \cdot b\right) \cdot t\right) \cdot i \]

      4. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot t\right) \cdot i \]

      5. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right) \cdot i \]

      6. +-commutative N/A

         \[\leadsto \left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right) \cdot i \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, t, -1 \cdot \left(j \cdot y\right)\right) \cdot i \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(b, t, \mathsf{neg}\left(j \cdot y\right)\right) \cdot i \]

      9. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, t, -j \cdot y\right) \cdot i \]

      10. lower-*.f64 44.1

          \[\leadsto \mathsf{fma}\left(b, t, -j \cdot y\right) \cdot i \]

   7. Applied rewrites 44.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t, -j \cdot y\right) \cdot i} \]

   8. Taylor expanded in y around 0

      \[\leadsto \left(b \cdot t\right) \cdot i \]
   9. Step-by-step derivation

      1. lower-*.f64 23.6

         \[\leadsto \left(b \cdot t\right) \cdot i \]

   10. Applied rewrites 23.6%

       \[\leadsto \left(b \cdot t\right) \cdot i \]

   if -3.2999999999999999e-156 < a < 1.9e21

   1. Initial program 80.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   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

         \[\leadsto \left(z \cdot y - t \cdot a\right) \cdot x \]

      6. lower-*.f64 N/A

         \[\leadsto \left(z \cdot y - t \cdot a\right) \cdot x \]

      7. *-commutative N/A

         \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x \]

      8. lower-*.f64 31.9

         \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x \]

   4. Applied rewrites 31.9%

      \[\leadsto \color{blue}{\left(z \cdot y - a \cdot t\right) \cdot x} \]

   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 25.8

         \[\leadsto \left(z \cdot y\right) \cdot x \]

   7. Applied rewrites 25.8%

      \[\leadsto \left(z \cdot y\right) \cdot x \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 20: 29.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{+14}:\\ \;\;\;\;\left(j \cdot c\right) \cdot a\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-156}:\\ \;\;\;\;\left(b \cdot t\right) \cdot i\\ \mathbf{elif}\;a \leq 7500000000000:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot a\right) \cdot j\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -6.6e+14)
   (* (* j c) a)
   (if (<= a -3.3e-156)
     (* (* b t) i)
     (if (<= a 7500000000000.0) (* (* z y) x) (* (* c a) j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -6.6e+14) {
		tmp = (j * c) * a;
	} else if (a <= -3.3e-156) {
		tmp = (b * t) * i;
	} else if (a <= 7500000000000.0) {
		tmp = (z * y) * x;
	} else {
		tmp = (c * a) * j;
	}
	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 (a <= (-6.6d+14)) then
        tmp = (j * c) * a
    else if (a <= (-3.3d-156)) then
        tmp = (b * t) * i
    else if (a <= 7500000000000.0d0) then
        tmp = (z * y) * x
    else
        tmp = (c * a) * j
    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 (a <= -6.6e+14) {
		tmp = (j * c) * a;
	} else if (a <= -3.3e-156) {
		tmp = (b * t) * i;
	} else if (a <= 7500000000000.0) {
		tmp = (z * y) * x;
	} else {
		tmp = (c * a) * j;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -6.6e+14:
		tmp = (j * c) * a
	elif a <= -3.3e-156:
		tmp = (b * t) * i
	elif a <= 7500000000000.0:
		tmp = (z * y) * x
	else:
		tmp = (c * a) * j
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -6.6e+14)
		tmp = Float64(Float64(j * c) * a);
	elseif (a <= -3.3e-156)
		tmp = Float64(Float64(b * t) * i);
	elseif (a <= 7500000000000.0)
		tmp = Float64(Float64(z * y) * x);
	else
		tmp = Float64(Float64(c * a) * j);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -6.6e+14)
		tmp = (j * c) * a;
	elseif (a <= -3.3e-156)
		tmp = (b * t) * i;
	elseif (a <= 7500000000000.0)
		tmp = (z * y) * x;
	else
		tmp = (c * a) * j;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -6.6e+14], N[(N[(j * c), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[a, -3.3e-156], N[(N[(b * t), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[a, 7500000000000.0], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], N[(N[(c * a), $MachinePrecision] * j), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.6e14

   1. Initial program 66.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot c - i \cdot y\right) \cdot \color{blue}{j} \]

      2. *-commutative N/A

         \[\leadsto \left(c \cdot a - i \cdot y\right) \cdot j \]

      3. *-commutative N/A

         \[\leadsto \left(c \cdot a - y \cdot i\right) \cdot j \]

      4. lower-*.f64 N/A

         \[\leadsto \left(c \cdot a - y \cdot i\right) \cdot \color{blue}{j} \]

      5. lift--.f64 N/A

         \[\leadsto \left(c \cdot a - y \cdot i\right) \cdot j \]

      6. lift-*.f64 N/A

         \[\leadsto \left(c \cdot a - y \cdot i\right) \cdot j \]

      7. *-commutative N/A

         \[\leadsto \left(c \cdot a - i \cdot y\right) \cdot j \]

      8. lower-*.f64 49.2

         \[\leadsto \left(c \cdot a - i \cdot y\right) \cdot j \]

   4. Applied rewrites 49.2%

      \[\leadsto \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j} \]

   5. Taylor expanded in y around 0

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(c \cdot j\right) \cdot a \]

      2. lower-*.f64 N/A

         \[\leadsto \left(c \cdot j\right) \cdot a \]

      3. *-commutative N/A

         \[\leadsto \left(j \cdot c\right) \cdot a \]

      4. lower-*.f64 36.6

         \[\leadsto \left(j \cdot c\right) \cdot a \]

   7. Applied rewrites 36.6%

      \[\leadsto \left(j \cdot c\right) \cdot \color{blue}{a} \]

   if -6.6e14 < a < -3.2999999999999999e-156

   1. Initial program 78.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around 0

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right) + \left(j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(i \cdot t - c \cdot z\right) \cdot b + \left(\color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, \color{blue}{b}, j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, \left(a \cdot c - i \cdot y\right) \cdot j + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, \left(c \cdot a - i \cdot y\right) \cdot j + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, \left(c \cdot a - y \cdot i\right) \cdot j + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      9. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, \mathsf{fma}\left(c \cdot a - y \cdot i, j, x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) \]

   4. Applied rewrites 81.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i \cdot t - c \cdot z, b, \mathsf{fma}\left(c \cdot a - i \cdot y, j, \left(z \cdot y - a \cdot t\right) \cdot x\right)\right)} \]

   5. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) \cdot \color{blue}{i} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) \cdot \color{blue}{i} \]

      3. associate-*r* N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - \left(-1 \cdot b\right) \cdot t\right) \cdot i \]

      4. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot t\right) \cdot i \]

      5. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right) \cdot i \]

      6. +-commutative N/A

         \[\leadsto \left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right) \cdot i \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, t, -1 \cdot \left(j \cdot y\right)\right) \cdot i \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(b, t, \mathsf{neg}\left(j \cdot y\right)\right) \cdot i \]

      9. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, t, -j \cdot y\right) \cdot i \]

      10. lower-*.f64 43.1

          \[\leadsto \mathsf{fma}\left(b, t, -j \cdot y\right) \cdot i \]

   7. Applied rewrites 43.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t, -j \cdot y\right) \cdot i} \]

   8. Taylor expanded in y around 0

      \[\leadsto \left(b \cdot t\right) \cdot i \]
   9. Step-by-step derivation

      1. lower-*.f64 23.0

         \[\leadsto \left(b \cdot t\right) \cdot i \]

   10. Applied rewrites 23.0%

       \[\leadsto \left(b \cdot t\right) \cdot i \]

   if -3.2999999999999999e-156 < a < 7.5e12

   1. Initial program 80.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   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

         \[\leadsto \left(z \cdot y - t \cdot a\right) \cdot x \]

      6. lower-*.f64 N/A

         \[\leadsto \left(z \cdot y - t \cdot a\right) \cdot x \]

      7. *-commutative N/A

         \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x \]

      8. lower-*.f64 31.9

         \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x \]

   4. Applied rewrites 31.9%

      \[\leadsto \color{blue}{\left(z \cdot y - a \cdot t\right) \cdot x} \]

   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 25.9

         \[\leadsto \left(z \cdot y\right) \cdot x \]

   7. Applied rewrites 25.9%

      \[\leadsto \left(z \cdot y\right) \cdot x \]

   if 7.5e12 < a

   1. Initial program 65.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot c - i \cdot y\right) \cdot \color{blue}{j} \]

      2. *-commutative N/A

         \[\leadsto \left(c \cdot a - i \cdot y\right) \cdot j \]

      3. *-commutative N/A

         \[\leadsto \left(c \cdot a - y \cdot i\right) \cdot j \]

      4. lower-*.f64 N/A

         \[\leadsto \left(c \cdot a - y \cdot i\right) \cdot \color{blue}{j} \]

      5. lift--.f64 N/A

         \[\leadsto \left(c \cdot a - y \cdot i\right) \cdot j \]

      6. lift-*.f64 N/A

         \[\leadsto \left(c \cdot a - y \cdot i\right) \cdot j \]

      7. *-commutative N/A

         \[\leadsto \left(c \cdot a - i \cdot y\right) \cdot j \]

      8. lower-*.f64 46.3

         \[\leadsto \left(c \cdot a - i \cdot y\right) \cdot j \]

   4. Applied rewrites 46.3%

      \[\leadsto \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j} \]

   5. Taylor expanded in y around 0

      \[\leadsto \left(a \cdot c\right) \cdot j \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(c \cdot a\right) \cdot j \]

      2. lift-*.f64 35.2

         \[\leadsto \left(c \cdot a\right) \cdot j \]

   7. Applied rewrites 35.2%

      \[\leadsto \left(c \cdot a\right) \cdot j \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 21: 29.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot a\right) \cdot j\\ \mathbf{if}\;c \leq -3 \cdot 10^{+171}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 12000:\\ \;\;\;\;\left(b \cdot t\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* c a) j)))
   (if (<= c -3e+171) t_1 (if (<= c 12000.0) (* (* b t) i) 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 * a) * j;
	double tmp;
	if (c <= -3e+171) {
		tmp = t_1;
	} else if (c <= 12000.0) {
		tmp = (b * t) * i;
	} 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 * a) * j
    if (c <= (-3d+171)) then
        tmp = t_1
    else if (c <= 12000.0d0) then
        tmp = (b * t) * i
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (c * a) * j;
	double tmp;
	if (c <= -3e+171) {
		tmp = t_1;
	} else if (c <= 12000.0) {
		tmp = (b * t) * i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (c * a) * j
	tmp = 0
	if c <= -3e+171:
		tmp = t_1
	elif c <= 12000.0:
		tmp = (b * t) * i
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(c * a) * j)
	tmp = 0.0
	if (c <= -3e+171)
		tmp = t_1;
	elseif (c <= 12000.0)
		tmp = Float64(Float64(b * t) * i);
	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 * a) * j;
	tmp = 0.0;
	if (c <= -3e+171)
		tmp = t_1;
	elseif (c <= 12000.0)
		tmp = (b * t) * i;
	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 * a), $MachinePrecision] * j), $MachinePrecision]}, If[LessEqual[c, -3e+171], t$95$1, If[LessEqual[c, 12000.0], N[(N[(b * t), $MachinePrecision] * i), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if c < -3.0000000000000001e171 or 12000 < c

   1. Initial program 64.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot c - i \cdot y\right) \cdot \color{blue}{j} \]

      2. *-commutative N/A

         \[\leadsto \left(c \cdot a - i \cdot y\right) \cdot j \]

      3. *-commutative N/A

         \[\leadsto \left(c \cdot a - y \cdot i\right) \cdot j \]

      4. lower-*.f64 N/A

         \[\leadsto \left(c \cdot a - y \cdot i\right) \cdot \color{blue}{j} \]

      5. lift--.f64 N/A

         \[\leadsto \left(c \cdot a - y \cdot i\right) \cdot j \]

      6. lift-*.f64 N/A

         \[\leadsto \left(c \cdot a - y \cdot i\right) \cdot j \]

      7. *-commutative N/A

         \[\leadsto \left(c \cdot a - i \cdot y\right) \cdot j \]

      8. lower-*.f64 46.9

         \[\leadsto \left(c \cdot a - i \cdot y\right) \cdot j \]

   4. Applied rewrites 46.9%

      \[\leadsto \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j} \]

   5. Taylor expanded in y around 0

      \[\leadsto \left(a \cdot c\right) \cdot j \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(c \cdot a\right) \cdot j \]

      2. lift-*.f64 37.9

         \[\leadsto \left(c \cdot a\right) \cdot j \]

   7. Applied rewrites 37.9%

      \[\leadsto \left(c \cdot a\right) \cdot j \]

   if -3.0000000000000001e171 < c < 12000

   1. Initial program 78.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around 0

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right) + \left(j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(i \cdot t - c \cdot z\right) \cdot b + \left(\color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, \color{blue}{b}, j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, \left(a \cdot c - i \cdot y\right) \cdot j + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, \left(c \cdot a - i \cdot y\right) \cdot j + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, \left(c \cdot a - y \cdot i\right) \cdot j + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      9. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot t - c \cdot z, b, \mathsf{fma}\left(c \cdot a - y \cdot i, j, x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) \]

   4. Applied rewrites 81.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i \cdot t - c \cdot z, b, \mathsf{fma}\left(c \cdot a - i \cdot y, j, \left(z \cdot y - a \cdot t\right) \cdot x\right)\right)} \]

   5. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) \cdot \color{blue}{i} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) \cdot \color{blue}{i} \]

      3. associate-*r* N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - \left(-1 \cdot b\right) \cdot t\right) \cdot i \]

      4. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot t\right) \cdot i \]

      5. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right) \cdot i \]

      6. +-commutative N/A

         \[\leadsto \left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right) \cdot i \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, t, -1 \cdot \left(j \cdot y\right)\right) \cdot i \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(b, t, \mathsf{neg}\left(j \cdot y\right)\right) \cdot i \]

      9. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, t, -j \cdot y\right) \cdot i \]

      10. lower-*.f64 45.2

          \[\leadsto \mathsf{fma}\left(b, t, -j \cdot y\right) \cdot i \]

   7. Applied rewrites 45.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t, -j \cdot y\right) \cdot i} \]

   8. Taylor expanded in y around 0

      \[\leadsto \left(b \cdot t\right) \cdot i \]
   9. Step-by-step derivation

      1. lower-*.f64 24.6

         \[\leadsto \left(b \cdot t\right) \cdot i \]

   10. Applied rewrites 24.6%

       \[\leadsto \left(b \cdot t\right) \cdot i \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 22: 28.9% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot c\right) \cdot a\\ \mathbf{if}\;j \leq -3200000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 9 \cdot 10^{-72}:\\ \;\;\;\;\left(i \cdot t\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* j c) a)))
   (if (<= j -3200000000000.0) t_1 (if (<= j 9e-72) (* (* i t) b) 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 = (j * c) * a;
	double tmp;
	if (j <= -3200000000000.0) {
		tmp = t_1;
	} else if (j <= 9e-72) {
		tmp = (i * t) * b;
	} 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 = (j * c) * a
    if (j <= (-3200000000000.0d0)) then
        tmp = t_1
    else if (j <= 9d-72) then
        tmp = (i * t) * b
    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 = (j * c) * a;
	double tmp;
	if (j <= -3200000000000.0) {
		tmp = t_1;
	} else if (j <= 9e-72) {
		tmp = (i * t) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * c) * a
	tmp = 0
	if j <= -3200000000000.0:
		tmp = t_1
	elif j <= 9e-72:
		tmp = (i * t) * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * c) * a)
	tmp = 0.0
	if (j <= -3200000000000.0)
		tmp = t_1;
	elseif (j <= 9e-72)
		tmp = Float64(Float64(i * t) * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * c) * a;
	tmp = 0.0;
	if (j <= -3200000000000.0)
		tmp = t_1;
	elseif (j <= 9e-72)
		tmp = (i * t) * b;
	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[(j * c), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[j, -3200000000000.0], t$95$1, If[LessEqual[j, 9e-72], N[(N[(i * t), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if j < -3.2e12 or 9e-72 < j

   1. Initial program 73.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot c - i \cdot y\right) \cdot \color{blue}{j} \]

      2. *-commutative N/A

         \[\leadsto \left(c \cdot a - i \cdot y\right) \cdot j \]

      3. *-commutative N/A

         \[\leadsto \left(c \cdot a - y \cdot i\right) \cdot j \]

      4. lower-*.f64 N/A

         \[\leadsto \left(c \cdot a - y \cdot i\right) \cdot \color{blue}{j} \]

      5. lift--.f64 N/A

         \[\leadsto \left(c \cdot a - y \cdot i\right) \cdot j \]

      6. lift-*.f64 N/A

         \[\leadsto \left(c \cdot a - y \cdot i\right) \cdot j \]

      7. *-commutative N/A

         \[\leadsto \left(c \cdot a - i \cdot y\right) \cdot j \]

      8. lower-*.f64 57.7

         \[\leadsto \left(c \cdot a - i \cdot y\right) \cdot j \]

   4. Applied rewrites 57.7%

      \[\leadsto \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j} \]

   5. Taylor expanded in y around 0

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(c \cdot j\right) \cdot a \]

      2. lower-*.f64 N/A

         \[\leadsto \left(c \cdot j\right) \cdot a \]

      3. *-commutative N/A

         \[\leadsto \left(j \cdot c\right) \cdot a \]

      4. lower-*.f64 32.9

         \[\leadsto \left(j \cdot c\right) \cdot a \]

   7. Applied rewrites 32.9%

      \[\leadsto \left(j \cdot c\right) \cdot \color{blue}{a} \]

   if -3.2e12 < j < 9e-72

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in j around 0

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) - \color{blue}{b \cdot \left(c \cdot z - i \cdot t\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x - \color{blue}{b} \cdot \left(c \cdot z - i \cdot t\right) \]

      3. *-commutative N/A

         \[\leadsto \left(y \cdot z - t \cdot a\right) \cdot x - b \cdot \left(c \cdot z - i \cdot t\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \left(y \cdot z - t \cdot a\right) \cdot x - \color{blue}{b} \cdot \left(c \cdot z - i \cdot t\right) \]

      5. lift--.f64 N/A

         \[\leadsto \left(y \cdot z - t \cdot a\right) \cdot x - b \cdot \left(c \cdot z - i \cdot t\right) \]

      6. *-commutative N/A

         \[\leadsto \left(z \cdot y - t \cdot a\right) \cdot x - b \cdot \left(c \cdot z - i \cdot t\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \left(z \cdot y - t \cdot a\right) \cdot x - b \cdot \left(c \cdot z - i \cdot t\right) \]

      8. *-commutative N/A

         \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - b \cdot \left(c \cdot z - i \cdot t\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - b \cdot \left(c \cdot z - i \cdot t\right) \]

      10. *-commutative N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot \color{blue}{b} \]

      11. *-commutative N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - t \cdot i\right) \cdot b \]

      12. lower-*.f64 N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - t \cdot i\right) \cdot \color{blue}{b} \]

      13. lift--.f64 N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - t \cdot i\right) \cdot b \]

      14. *-commutative N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b \]

      15. lift-*.f64 N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b \]

      16. lower-*.f64 71.5

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b \]

   4. Applied rewrites 71.5%

      \[\leadsto \color{blue}{\left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b} \]

   5. Taylor expanded in i around inf

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(i \cdot t\right) \cdot b \]

      2. lower-*.f64 N/A

         \[\leadsto \left(i \cdot t\right) \cdot b \]

      3. lift-*.f64 25.2

         \[\leadsto \left(i \cdot t\right) \cdot b \]

   7. Applied rewrites 25.2%

      \[\leadsto \left(i \cdot t\right) \cdot \color{blue}{b} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 22.7% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \left(j \cdot c\right) \cdot a \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* (* j c) a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return (j * c) * a;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, 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 * c) * a
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 * c) * a;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return (j * c) * a

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(j * c) * a)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = (j * c) * a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(j * c), $MachinePrecision] * a), $MachinePrecision]

Derivation

1. Initial program 73.4%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

2. Taylor expanded in j around inf

   \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
3. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \left(a \cdot c - i \cdot y\right) \cdot \color{blue}{j} \]

   2. *-commutative N/A

      \[\leadsto \left(c \cdot a - i \cdot y\right) \cdot j \]

   3. *-commutative N/A

      \[\leadsto \left(c \cdot a - y \cdot i\right) \cdot j \]

   4. lower-*.f64 N/A

      \[\leadsto \left(c \cdot a - y \cdot i\right) \cdot \color{blue}{j} \]

   5. lift--.f64 N/A

      \[\leadsto \left(c \cdot a - y \cdot i\right) \cdot j \]

   6. lift-*.f64 N/A

      \[\leadsto \left(c \cdot a - y \cdot i\right) \cdot j \]

   7. *-commutative N/A

      \[\leadsto \left(c \cdot a - i \cdot y\right) \cdot j \]

   8. lower-*.f64 40.4

      \[\leadsto \left(c \cdot a - i \cdot y\right) \cdot j \]

4. Applied rewrites 40.4%

   \[\leadsto \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j} \]

5. Taylor expanded in y around 0

   \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
6. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \left(c \cdot j\right) \cdot a \]

   2. lower-*.f64 N/A

      \[\leadsto \left(c \cdot j\right) \cdot a \]

   3. *-commutative N/A

      \[\leadsto \left(j \cdot c\right) \cdot a \]

   4. lower-*.f64 22.7

      \[\leadsto \left(j \cdot c\right) \cdot a \]

7. Applied rewrites 22.7%

   \[\leadsto \left(j \cdot c\right) \cdot \color{blue}{a} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025120 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64
  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))