Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.7% → 79.8%

Time: 15.3s

Alternatives: 30

Speedup: 1.0×

• 58.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 79.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+145}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-17} \lor \neg \left(z \leq 8 \cdot 10^{+116}\right):\\ \;\;\;\;\left(\mathsf{fma}\left(y, x, \frac{\mathsf{fma}\left(\mathsf{fma}\left(-x, t, i \cdot b\right), a, \mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\right)}{z}\right) - c \cdot b\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot a\right), b, \mathsf{fma}\left(\mathsf{fma}\left(-a, x, j \cdot c\right), t, \mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -2.3e+145)
   (* (fma (- b) c (* y x)) z)
   (if (or (<= z -1.2e-17) (not (<= z 8e+116)))
     (*
      (-
       (fma
        y
        x
        (/ (fma (fma (- x) t (* i b)) a (* (fma (- i) y (* c t)) j)) z))
       (* c b))
      z)
     (fma
      (fma (- c) z (* i a))
      b
      (fma (fma (- a) x (* j c)) t (* (fma (- j) i (* z x)) y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.3e+145) {
		tmp = fma(-b, c, (y * x)) * z;
	} else if ((z <= -1.2e-17) || !(z <= 8e+116)) {
		tmp = (fma(y, x, (fma(fma(-x, t, (i * b)), a, (fma(-i, y, (c * t)) * j)) / z)) - (c * b)) * z;
	} else {
		tmp = fma(fma(-c, z, (i * a)), b, fma(fma(-a, x, (j * c)), t, (fma(-j, i, (z * x)) * y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -2.3e+145)
		tmp = Float64(fma(Float64(-b), c, Float64(y * x)) * z);
	elseif ((z <= -1.2e-17) || !(z <= 8e+116))
		tmp = Float64(Float64(fma(y, x, Float64(fma(fma(Float64(-x), t, Float64(i * b)), a, Float64(fma(Float64(-i), y, Float64(c * t)) * j)) / z)) - Float64(c * b)) * z);
	else
		tmp = fma(fma(Float64(-c), z, Float64(i * a)), b, fma(fma(Float64(-a), x, Float64(j * c)), t, Float64(fma(Float64(-j), i, Float64(z * x)) * y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -2.3e+145], N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[Or[LessEqual[z, -1.2e-17], N[Not[LessEqual[z, 8e+116]], $MachinePrecision]], N[(N[(N[(y * x + N[(N[(N[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a + N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(N[((-c) * z + N[(i * a), $MachinePrecision]), $MachinePrecision] * b + N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t + N[(N[((-j) * i + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3e145

   1. Initial program 61.2%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 87.4%

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

   if -2.3e145 < z < -1.19999999999999993e-17 or 8.00000000000000012e116 < z

   1. Initial program 75.5%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 87.7%

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

   if -1.19999999999999993e-17 < z < 8.00000000000000012e116

   1. Initial program 74.8%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 90.7%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+145}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-17} \lor \neg \left(z \leq 8 \cdot 10^{+116}\right):\\ \;\;\;\;\left(\mathsf{fma}\left(y, x, \frac{\mathsf{fma}\left(\mathsf{fma}\left(-x, t, i \cdot b\right), a, \mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\right)}{z}\right) - c \cdot b\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot a\right), b, \mathsf{fma}\left(\mathsf{fma}\left(-a, x, j \cdot c\right), t, \mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+119}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-17}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot a\right), b, \mathsf{fma}\left(\mathsf{fma}\left(-a, x, j \cdot c\right), t, \mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -2.5e+119)
   (* (fma (- b) c (* y x)) z)
   (if (<= z -1.2e-17)
     (+
      (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
      (* j (- (* c t) (* i y))))
     (fma
      (fma (- c) z (* i a))
      b
      (fma (fma (- a) x (* j c)) t (* (fma (- j) i (* z x)) y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.5e+119) {
		tmp = fma(-b, c, (y * x)) * z;
	} else if (z <= -1.2e-17) {
		tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
	} else {
		tmp = fma(fma(-c, z, (i * a)), b, fma(fma(-a, x, (j * c)), t, (fma(-j, i, (z * x)) * y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -2.5e+119)
		tmp = Float64(fma(Float64(-b), c, Float64(y * x)) * z);
	elseif (z <= -1.2e-17)
		tmp = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))));
	else
		tmp = fma(fma(Float64(-c), z, Float64(i * a)), b, fma(fma(Float64(-a), x, Float64(j * c)), t, Float64(fma(Float64(-j), i, Float64(z * x)) * y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -2.5e+119], N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, -1.2e-17], N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-c) * z + N[(i * a), $MachinePrecision]), $MachinePrecision] * b + N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t + N[(N[((-j) * i + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5e119

   1. Initial program 60.2%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 80.9%

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

   if -2.5e119 < z < -1.19999999999999993e-17

   1. Initial program 91.2%

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

   if -1.19999999999999993e-17 < z

   1. Initial program 74.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 87.3%

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

Alternative 3: 77.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+142}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot a\right), b, \mathsf{fma}\left(\mathsf{fma}\left(-a, x, j \cdot c\right), t, \mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -9.6e+142)
   (* (fma (- b) c (* y x)) z)
   (fma
    (fma (- c) z (* i a))
    b
    (fma (fma (- a) x (* j c)) t (* (fma (- j) i (* z x)) y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -9.6e+142) {
		tmp = fma(-b, c, (y * x)) * z;
	} else {
		tmp = fma(fma(-c, z, (i * a)), b, fma(fma(-a, x, (j * c)), t, (fma(-j, i, (z * x)) * y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -9.6e+142)
		tmp = Float64(fma(Float64(-b), c, Float64(y * x)) * z);
	else
		tmp = fma(fma(Float64(-c), z, Float64(i * a)), b, fma(fma(Float64(-a), x, Float64(j * c)), t, Float64(fma(Float64(-j), i, Float64(z * x)) * y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -9.6e+142], N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(N[((-c) * z + N[(i * a), $MachinePrecision]), $MachinePrecision] * b + N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t + N[(N[((-j) * i + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.5999999999999996e142

   1. Initial program 61.2%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 87.4%

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

   if -9.5999999999999996e142 < z

   1. Initial program 75.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 84.6%

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

Alternative 4: 49.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{+132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-100}:\\ \;\;\;\;\mathsf{fma}\left(-x, t, i \cdot b\right) \cdot a\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{-142}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, \frac{j}{z}, x\right) \cdot y\right) \cdot z\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-186}:\\ \;\;\;\;\left(-t\right) \cdot \mathsf{fma}\left(-c, j, a \cdot x\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-79}:\\ \;\;\;\;\left(\left(j - \frac{b \cdot a}{y}\right) \cdot \left(-i\right)\right) \cdot y\\ \mathbf{elif}\;z \leq 9600000000:\\ \;\;\;\;\mathsf{fma}\left(\left(-a\right) \cdot t, x, \left(z \cdot y\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- b) c (* y x)) z)))
   (if (<= z -2.35e+132)
     t_1
     (if (<= z -9.5e-100)
       (* (fma (- x) t (* i b)) a)
       (if (<= z -5.7e-142)
         (* (* (fma (- i) (/ j z) x) y) z)
         (if (<= z 7.2e-186)
           (* (- t) (fma (- c) j (* a x)))
           (if (<= z 2.15e-79)
             (* (* (- j (/ (* b a) y)) (- i)) y)
             (if (<= z 9600000000.0)
               (fma (* (- a) t) x (* (* 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(-b, c, (y * x)) * z;
	double tmp;
	if (z <= -2.35e+132) {
		tmp = t_1;
	} else if (z <= -9.5e-100) {
		tmp = fma(-x, t, (i * b)) * a;
	} else if (z <= -5.7e-142) {
		tmp = (fma(-i, (j / z), x) * y) * z;
	} else if (z <= 7.2e-186) {
		tmp = -t * fma(-c, j, (a * x));
	} else if (z <= 2.15e-79) {
		tmp = ((j - ((b * a) / y)) * -i) * y;
	} else if (z <= 9600000000.0) {
		tmp = fma((-a * t), x, ((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(-b), c, Float64(y * x)) * z)
	tmp = 0.0
	if (z <= -2.35e+132)
		tmp = t_1;
	elseif (z <= -9.5e-100)
		tmp = Float64(fma(Float64(-x), t, Float64(i * b)) * a);
	elseif (z <= -5.7e-142)
		tmp = Float64(Float64(fma(Float64(-i), Float64(j / z), x) * y) * z);
	elseif (z <= 7.2e-186)
		tmp = Float64(Float64(-t) * fma(Float64(-c), j, Float64(a * x)));
	elseif (z <= 2.15e-79)
		tmp = Float64(Float64(Float64(j - Float64(Float64(b * a) / y)) * Float64(-i)) * y);
	elseif (z <= 9600000000.0)
		tmp = fma(Float64(Float64(-a) * t), x, 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[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -2.35e+132], t$95$1, If[LessEqual[z, -9.5e-100], N[(N[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[z, -5.7e-142], N[(N[(N[((-i) * N[(j / z), $MachinePrecision] + x), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 7.2e-186], N[((-t) * N[((-c) * j + N[(a * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e-79], N[(N[(N[(j - N[(N[(b * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, 9600000000.0], N[(N[((-a) * t), $MachinePrecision] * x + N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.35e132 or 9.6e9 < z

   1. Initial program 68.4%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 71.0%

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

   if -2.35e132 < z < -9.4999999999999992e-100

   1. Initial program 80.9%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 62.3%

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

   if -9.4999999999999992e-100 < z < -5.69999999999999995e-142

   1. Initial program 91.6%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 65.8%

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

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot \left(x + -1 \cdot \frac{i \cdot j}{z}\right)\right) \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 73.1%

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

   if -5.69999999999999995e-142 < z < 7.1999999999999997e-186

   1. Initial program 72.5%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 92.9%

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

   6. Taylor expanded in t around -inf

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

   8. Applied rewrites 63.0%

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

   if 7.1999999999999997e-186 < z < 2.14999999999999991e-79

   1. Initial program 68.8%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 80.1%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 63.5%

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

   9. Taylor expanded in i around -inf

      \[\leadsto \left(-1 \cdot \left(i \cdot \left(j - \frac{a \cdot b}{y}\right)\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 67.9%

       \[\leadsto \left(\left(j - \frac{b \cdot a}{y}\right) \cdot \left(-i\right)\right) \cdot y \]

   if 2.14999999999999991e-79 < z < 9.6e9

   1. Initial program 78.5%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 61.6%

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

   7. Applied rewrites 61.6%

      \[\leadsto \mathsf{fma}\left(\left(-a\right) \cdot t, \color{blue}{x}, \left(z \cdot y\right) \cdot x\right) \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 5: 49.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{+132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-100}:\\ \;\;\;\;\mathsf{fma}\left(-x, t, i \cdot b\right) \cdot a\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{-142}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, \frac{j}{z}, x\right) \cdot y\right) \cdot z\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{-186}:\\ \;\;\;\;\left(-t\right) \cdot \mathsf{fma}\left(-c, j, a \cdot x\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-79}:\\ \;\;\;\;\mathsf{fma}\left(-y, j, b \cdot a\right) \cdot i\\ \mathbf{elif}\;z \leq 9600000000:\\ \;\;\;\;\mathsf{fma}\left(\left(-a\right) \cdot t, x, \left(z \cdot y\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- b) c (* y x)) z)))
   (if (<= z -2.35e+132)
     t_1
     (if (<= z -9.5e-100)
       (* (fma (- x) t (* i b)) a)
       (if (<= z -5.7e-142)
         (* (* (fma (- i) (/ j z) x) y) z)
         (if (<= z 3.35e-186)
           (* (- t) (fma (- c) j (* a x)))
           (if (<= z 2.15e-79)
             (* (fma (- y) j (* b a)) i)
             (if (<= z 9600000000.0)
               (fma (* (- a) t) x (* (* 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(-b, c, (y * x)) * z;
	double tmp;
	if (z <= -2.35e+132) {
		tmp = t_1;
	} else if (z <= -9.5e-100) {
		tmp = fma(-x, t, (i * b)) * a;
	} else if (z <= -5.7e-142) {
		tmp = (fma(-i, (j / z), x) * y) * z;
	} else if (z <= 3.35e-186) {
		tmp = -t * fma(-c, j, (a * x));
	} else if (z <= 2.15e-79) {
		tmp = fma(-y, j, (b * a)) * i;
	} else if (z <= 9600000000.0) {
		tmp = fma((-a * t), x, ((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(-b), c, Float64(y * x)) * z)
	tmp = 0.0
	if (z <= -2.35e+132)
		tmp = t_1;
	elseif (z <= -9.5e-100)
		tmp = Float64(fma(Float64(-x), t, Float64(i * b)) * a);
	elseif (z <= -5.7e-142)
		tmp = Float64(Float64(fma(Float64(-i), Float64(j / z), x) * y) * z);
	elseif (z <= 3.35e-186)
		tmp = Float64(Float64(-t) * fma(Float64(-c), j, Float64(a * x)));
	elseif (z <= 2.15e-79)
		tmp = Float64(fma(Float64(-y), j, Float64(b * a)) * i);
	elseif (z <= 9600000000.0)
		tmp = fma(Float64(Float64(-a) * t), x, 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[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -2.35e+132], t$95$1, If[LessEqual[z, -9.5e-100], N[(N[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[z, -5.7e-142], N[(N[(N[((-i) * N[(j / z), $MachinePrecision] + x), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 3.35e-186], N[((-t) * N[((-c) * j + N[(a * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e-79], N[(N[((-y) * j + N[(b * a), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[z, 9600000000.0], N[(N[((-a) * t), $MachinePrecision] * x + N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.35e132 or 9.6e9 < z

   1. Initial program 68.4%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 71.0%

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

   if -2.35e132 < z < -9.4999999999999992e-100

   1. Initial program 80.9%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 62.3%

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

   if -9.4999999999999992e-100 < z < -5.69999999999999995e-142

   1. Initial program 91.6%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 65.8%

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

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot \left(x + -1 \cdot \frac{i \cdot j}{z}\right)\right) \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 73.1%

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

   if -5.69999999999999995e-142 < z < 3.35000000000000017e-186

   1. Initial program 72.5%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 92.9%

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

   6. Taylor expanded in t around -inf

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

   8. Applied rewrites 63.0%

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

   if 3.35000000000000017e-186 < z < 2.14999999999999991e-79

   1. Initial program 68.8%

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

   3. Taylor expanded in i around inf

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

   5. Applied rewrites 65.0%

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

   if 2.14999999999999991e-79 < z < 9.6e9

   1. Initial program 78.5%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 61.6%

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

   7. Applied rewrites 61.6%

      \[\leadsto \mathsf{fma}\left(\left(-a\right) \cdot t, \color{blue}{x}, \left(z \cdot y\right) \cdot x\right) \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 6: 49.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ t_2 := \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{+132}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-85}:\\ \;\;\;\;\mathsf{fma}\left(-x, t, i \cdot b\right) \cdot a\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{-186}:\\ \;\;\;\;\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-79}:\\ \;\;\;\;\mathsf{fma}\left(-y, j, b \cdot a\right) \cdot i\\ \mathbf{elif}\;z \leq 9600000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- a) t (* z y)) x)) (t_2 (* (fma (- b) c (* y x)) z)))
   (if (<= z -2.35e+132)
     t_2
     (if (<= z -2.8e-85)
       (* (fma (- x) t (* i b)) a)
       (if (<= z -7.5e-137)
         t_1
         (if (<= z 3.35e-186)
           (* (fma (- a) x (* j c)) t)
           (if (<= z 2.15e-79)
             (* (fma (- y) j (* b a)) i)
             (if (<= z 9600000000.0) 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 = fma(-a, t, (z * y)) * x;
	double t_2 = fma(-b, c, (y * x)) * z;
	double tmp;
	if (z <= -2.35e+132) {
		tmp = t_2;
	} else if (z <= -2.8e-85) {
		tmp = fma(-x, t, (i * b)) * a;
	} else if (z <= -7.5e-137) {
		tmp = t_1;
	} else if (z <= 3.35e-186) {
		tmp = fma(-a, x, (j * c)) * t;
	} else if (z <= 2.15e-79) {
		tmp = fma(-y, j, (b * a)) * i;
	} else if (z <= 9600000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-a), t, Float64(z * y)) * x)
	t_2 = Float64(fma(Float64(-b), c, Float64(y * x)) * z)
	tmp = 0.0
	if (z <= -2.35e+132)
		tmp = t_2;
	elseif (z <= -2.8e-85)
		tmp = Float64(fma(Float64(-x), t, Float64(i * b)) * a);
	elseif (z <= -7.5e-137)
		tmp = t_1;
	elseif (z <= 3.35e-186)
		tmp = Float64(fma(Float64(-a), x, Float64(j * c)) * t);
	elseif (z <= 2.15e-79)
		tmp = Float64(fma(Float64(-y), j, Float64(b * a)) * i);
	elseif (z <= 9600000000.0)
		tmp = t_1;
	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[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -2.35e+132], t$95$2, If[LessEqual[z, -2.8e-85], N[(N[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[z, -7.5e-137], t$95$1, If[LessEqual[z, 3.35e-186], N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 2.15e-79], N[(N[((-y) * j + N[(b * a), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[z, 9600000000.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.35e132 or 9.6e9 < z

   1. Initial program 68.4%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 71.0%

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

   if -2.35e132 < z < -2.80000000000000017e-85

   1. Initial program 79.0%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 64.3%

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

   if -2.80000000000000017e-85 < z < -7.4999999999999995e-137 or 2.14999999999999991e-79 < z < 9.6e9

   1. Initial program 86.1%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 63.6%

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

   if -7.4999999999999995e-137 < z < 3.35000000000000017e-186

   1. Initial program 72.0%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 61.1%

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

   if 3.35000000000000017e-186 < z < 2.14999999999999991e-79

   1. Initial program 68.8%

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

   3. Taylor expanded in i around inf

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

   5. Applied rewrites 65.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, j, b \cdot a\right) \cdot i} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 7: 64.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{if}\;c \leq -1.56 \cdot 10^{+29}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right) + t\_1\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \mathsf{fma}\left(-y, j, b \cdot a\right) \cdot i\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{+146}:\\ \;\;\;\;\left(\left(-c\right) \cdot z\right) \cdot b + t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, b, j \cdot t\right) \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c t) (* i y)))))
   (if (<= c -1.56e+29)
     (+ (* (- a) (* t x)) t_1)
     (if (<= c 1.85e-12)
       (fma (fma (- a) t (* z y)) x (* (fma (- y) j (* b a)) i))
       (if (<= c 1.5e+146)
         (+ (* (* (- c) z) b) t_1)
         (* (fma (- z) b (* j t)) c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * t) - (i * y));
	double tmp;
	if (c <= -1.56e+29) {
		tmp = (-a * (t * x)) + t_1;
	} else if (c <= 1.85e-12) {
		tmp = fma(fma(-a, t, (z * y)), x, (fma(-y, j, (b * a)) * i));
	} else if (c <= 1.5e+146) {
		tmp = ((-c * z) * b) + t_1;
	} else {
		tmp = fma(-z, b, (j * t)) * c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * t) - Float64(i * y)))
	tmp = 0.0
	if (c <= -1.56e+29)
		tmp = Float64(Float64(Float64(-a) * Float64(t * x)) + t_1);
	elseif (c <= 1.85e-12)
		tmp = fma(fma(Float64(-a), t, Float64(z * y)), x, Float64(fma(Float64(-y), j, Float64(b * a)) * i));
	elseif (c <= 1.5e+146)
		tmp = Float64(Float64(Float64(Float64(-c) * z) * b) + t_1);
	else
		tmp = Float64(fma(Float64(-z), b, Float64(j * t)) * c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.56e+29], N[(N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[c, 1.85e-12], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x + N[(N[((-y) * j + N[(b * a), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.5e+146], N[(N[(N[((-c) * z), $MachinePrecision] * b), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[((-z) * b + N[(j * t), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.5599999999999999e29

   1. Initial program 69.9%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 62.1%

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

   if -1.5599999999999999e29 < c < 1.84999999999999999e-12

   1. Initial program 80.9%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 76.2%

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

   if 1.84999999999999999e-12 < c < 1.50000000000000001e146

   1. Initial program 75.8%

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

   3. Taylor expanded in c around inf

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

   5. Applied rewrites 70.0%

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

   if 1.50000000000000001e146 < c

   1. Initial program 51.1%

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

   3. Taylor expanded in c around inf

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

   5. Applied rewrites 78.8%

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

Alternative 8: 51.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+62}:\\ \;\;\;\;\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-41}:\\ \;\;\;\;\mathsf{fma}\left(-x, t, i \cdot b\right) \cdot a\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-104}:\\ \;\;\;\;\mathsf{fma}\left(-z, b, j \cdot t\right) \cdot c\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-280}:\\ \;\;\;\;\mathsf{fma}\left(z, x, \left(-j\right) \cdot i\right) \cdot y\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-94}:\\ \;\;\;\;\mathsf{fma}\left(-c, z, i \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot \mathsf{fma}\left(-c, j, a \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -4e+62)
   (* (fma (- a) x (* j c)) t)
   (if (<= t -1.75e-41)
     (* (fma (- x) t (* i b)) a)
     (if (<= t -3e-104)
       (* (fma (- z) b (* j t)) c)
       (if (<= t 7.2e-280)
         (* (fma z x (* (- j) i)) y)
         (if (<= t 1.08e-94)
           (* (fma (- c) z (* i a)) b)
           (* (- t) (fma (- c) j (* a x)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -4e+62) {
		tmp = fma(-a, x, (j * c)) * t;
	} else if (t <= -1.75e-41) {
		tmp = fma(-x, t, (i * b)) * a;
	} else if (t <= -3e-104) {
		tmp = fma(-z, b, (j * t)) * c;
	} else if (t <= 7.2e-280) {
		tmp = fma(z, x, (-j * i)) * y;
	} else if (t <= 1.08e-94) {
		tmp = fma(-c, z, (i * a)) * b;
	} else {
		tmp = -t * fma(-c, j, (a * x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -4e+62)
		tmp = Float64(fma(Float64(-a), x, Float64(j * c)) * t);
	elseif (t <= -1.75e-41)
		tmp = Float64(fma(Float64(-x), t, Float64(i * b)) * a);
	elseif (t <= -3e-104)
		tmp = Float64(fma(Float64(-z), b, Float64(j * t)) * c);
	elseif (t <= 7.2e-280)
		tmp = Float64(fma(z, x, Float64(Float64(-j) * i)) * y);
	elseif (t <= 1.08e-94)
		tmp = Float64(fma(Float64(-c), z, Float64(i * a)) * b);
	else
		tmp = Float64(Float64(-t) * fma(Float64(-c), j, Float64(a * x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -4e+62], N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, -1.75e-41], N[(N[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t, -3e-104], N[(N[((-z) * b + N[(j * t), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[t, 7.2e-280], N[(N[(z * x + N[((-j) * i), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 1.08e-94], N[(N[((-c) * z + N[(i * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], N[((-t) * N[((-c) * j + N[(a * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -4.00000000000000014e62

   1. Initial program 62.2%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 62.5%

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

   if -4.00000000000000014e62 < t < -1.75e-41

   1. Initial program 68.3%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 68.5%

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

   if -1.75e-41 < t < -3.0000000000000002e-104

   1. Initial program 67.2%

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

   3. Taylor expanded in c around inf

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

   5. Applied rewrites 75.1%

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

   if -3.0000000000000002e-104 < t < 7.19999999999999989e-280

   1. Initial program 79.5%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 65.6%

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

   7. Applied rewrites 67.7%

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

   if 7.19999999999999989e-280 < t < 1.08e-94

   1. Initial program 85.7%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 62.2%

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

   if 1.08e-94 < t

   1. Initial program 73.1%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 87.5%

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

   6. Taylor expanded in t around -inf

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

   8. Applied rewrites 62.3%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \mathsf{fma}\left(-c, j, a \cdot x\right)} \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 9: 29.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(-t\right) \cdot a\right) \cdot x\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+143}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(\left(-c\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-243}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-171}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-62}:\\ \;\;\;\;\left(\left(-i\right) \cdot y\right) \cdot j\\ \mathbf{elif}\;z \leq 9600000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-z\right) \cdot b\right) \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* (- t) a) x)))
   (if (<= z -1.8e+143)
     (* (* z x) y)
     (if (<= z -2.6e+110)
       (* b (* (- c) z))
       (if (<= z -3.2e-243)
         t_1
         (if (<= z 3.7e-171)
           (* (* j t) c)
           (if (<= z 1.5e-62)
             (* (* (- i) y) j)
             (if (<= z 9600000000.0) t_1 (* (* (- z) b) c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (-t * a) * x;
	double tmp;
	if (z <= -1.8e+143) {
		tmp = (z * x) * y;
	} else if (z <= -2.6e+110) {
		tmp = b * (-c * z);
	} else if (z <= -3.2e-243) {
		tmp = t_1;
	} else if (z <= 3.7e-171) {
		tmp = (j * t) * c;
	} else if (z <= 1.5e-62) {
		tmp = (-i * y) * j;
	} else if (z <= 9600000000.0) {
		tmp = t_1;
	} else {
		tmp = (-z * b) * c;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i, 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 = (-t * a) * x
    if (z <= (-1.8d+143)) then
        tmp = (z * x) * y
    else if (z <= (-2.6d+110)) then
        tmp = b * (-c * z)
    else if (z <= (-3.2d-243)) then
        tmp = t_1
    else if (z <= 3.7d-171) then
        tmp = (j * t) * c
    else if (z <= 1.5d-62) then
        tmp = (-i * y) * j
    else if (z <= 9600000000.0d0) then
        tmp = t_1
    else
        tmp = (-z * b) * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (-t * a) * x;
	double tmp;
	if (z <= -1.8e+143) {
		tmp = (z * x) * y;
	} else if (z <= -2.6e+110) {
		tmp = b * (-c * z);
	} else if (z <= -3.2e-243) {
		tmp = t_1;
	} else if (z <= 3.7e-171) {
		tmp = (j * t) * c;
	} else if (z <= 1.5e-62) {
		tmp = (-i * y) * j;
	} else if (z <= 9600000000.0) {
		tmp = t_1;
	} else {
		tmp = (-z * b) * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (-t * a) * x
	tmp = 0
	if z <= -1.8e+143:
		tmp = (z * x) * y
	elif z <= -2.6e+110:
		tmp = b * (-c * z)
	elif z <= -3.2e-243:
		tmp = t_1
	elif z <= 3.7e-171:
		tmp = (j * t) * c
	elif z <= 1.5e-62:
		tmp = (-i * y) * j
	elif z <= 9600000000.0:
		tmp = t_1
	else:
		tmp = (-z * b) * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(-t) * a) * x)
	tmp = 0.0
	if (z <= -1.8e+143)
		tmp = Float64(Float64(z * x) * y);
	elseif (z <= -2.6e+110)
		tmp = Float64(b * Float64(Float64(-c) * z));
	elseif (z <= -3.2e-243)
		tmp = t_1;
	elseif (z <= 3.7e-171)
		tmp = Float64(Float64(j * t) * c);
	elseif (z <= 1.5e-62)
		tmp = Float64(Float64(Float64(-i) * y) * j);
	elseif (z <= 9600000000.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(-z) * b) * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (-t * a) * x;
	tmp = 0.0;
	if (z <= -1.8e+143)
		tmp = (z * x) * y;
	elseif (z <= -2.6e+110)
		tmp = b * (-c * z);
	elseif (z <= -3.2e-243)
		tmp = t_1;
	elseif (z <= 3.7e-171)
		tmp = (j * t) * c;
	elseif (z <= 1.5e-62)
		tmp = (-i * y) * j;
	elseif (z <= 9600000000.0)
		tmp = t_1;
	else
		tmp = (-z * b) * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-t) * a), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -1.8e+143], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, -2.6e+110], N[(b * N[((-c) * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.2e-243], t$95$1, If[LessEqual[z, 3.7e-171], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[z, 1.5e-62], N[(N[((-i) * y), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[z, 9600000000.0], t$95$1, N[(N[((-z) * b), $MachinePrecision] * c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.8e143

   1. Initial program 61.2%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 74.8%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot z\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 71.6%

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

   if -1.8e143 < z < -2.6e110

   1. Initial program 60.9%

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

   3. Taylor expanded in c around inf

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

   5. Applied rewrites 61.8%

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

   7. Applied rewrites 51.8%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 53.4%

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

   if -2.6e110 < z < -3.1999999999999998e-243 or 1.5000000000000001e-62 < z < 9.6e9

   1. Initial program 84.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 54.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 42.5%

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

   if -3.1999999999999998e-243 < z < 3.70000000000000012e-171

   1. Initial program 65.7%

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

   3. Taylor expanded in c around inf

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

   5. Applied rewrites 43.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 38.3%

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

   if 3.70000000000000012e-171 < z < 1.5000000000000001e-62

   1. Initial program 71.5%

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

   3. Taylor expanded in j around inf

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

   5. Applied rewrites 55.1%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 44.8%

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

   if 9.6e9 < z

   1. Initial program 72.0%

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

   3. Taylor expanded in c around inf

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

   5. Applied rewrites 58.7%

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

   6. Taylor expanded in z around inf

      \[\leadsto \left(-1 \cdot \left(b \cdot z\right)\right) \cdot c \]
   7. Step-by-step derivation

   8. Applied rewrites 47.3%

      \[\leadsto \left(\left(-z\right) \cdot b\right) \cdot c \]
3. Recombined 6 regimes into one program.

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+143}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(\left(-c\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-243}:\\ \;\;\;\;\left(\left(-t\right) \cdot a\right) \cdot x\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-171}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-62}:\\ \;\;\;\;\left(\left(-i\right) \cdot y\right) \cdot j\\ \mathbf{elif}\;z \leq 9600000000:\\ \;\;\;\;\left(\left(-t\right) \cdot a\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-z\right) \cdot b\right) \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 28.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(-c\right) \cdot z\right)\\ t_2 := \left(\left(-t\right) \cdot a\right) \cdot x\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+143}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-243}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-171}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-62}:\\ \;\;\;\;\left(\left(-i\right) \cdot y\right) \cdot j\\ \mathbf{elif}\;z \leq 9600000000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* (- c) z))) (t_2 (* (* (- t) a) x)))
   (if (<= z -1.8e+143)
     (* (* z x) y)
     (if (<= z -2.6e+110)
       t_1
       (if (<= z -3.2e-243)
         t_2
         (if (<= z 3.7e-171)
           (* (* j t) c)
           (if (<= z 1.5e-62)
             (* (* (- i) y) j)
             (if (<= z 9600000000.0) t_2 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 t_2 = (-t * a) * x;
	double tmp;
	if (z <= -1.8e+143) {
		tmp = (z * x) * y;
	} else if (z <= -2.6e+110) {
		tmp = t_1;
	} else if (z <= -3.2e-243) {
		tmp = t_2;
	} else if (z <= 3.7e-171) {
		tmp = (j * t) * c;
	} else if (z <= 1.5e-62) {
		tmp = (-i * y) * j;
	} else if (z <= 9600000000.0) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = b * (-c * z)
    t_2 = (-t * a) * x
    if (z <= (-1.8d+143)) then
        tmp = (z * x) * y
    else if (z <= (-2.6d+110)) then
        tmp = t_1
    else if (z <= (-3.2d-243)) then
        tmp = t_2
    else if (z <= 3.7d-171) then
        tmp = (j * t) * c
    else if (z <= 1.5d-62) then
        tmp = (-i * y) * j
    else if (z <= 9600000000.0d0) then
        tmp = t_2
    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 t_2 = (-t * a) * x;
	double tmp;
	if (z <= -1.8e+143) {
		tmp = (z * x) * y;
	} else if (z <= -2.6e+110) {
		tmp = t_1;
	} else if (z <= -3.2e-243) {
		tmp = t_2;
	} else if (z <= 3.7e-171) {
		tmp = (j * t) * c;
	} else if (z <= 1.5e-62) {
		tmp = (-i * y) * j;
	} else if (z <= 9600000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (-c * z)
	t_2 = (-t * a) * x
	tmp = 0
	if z <= -1.8e+143:
		tmp = (z * x) * y
	elif z <= -2.6e+110:
		tmp = t_1
	elif z <= -3.2e-243:
		tmp = t_2
	elif z <= 3.7e-171:
		tmp = (j * t) * c
	elif z <= 1.5e-62:
		tmp = (-i * y) * j
	elif z <= 9600000000.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(-c) * z))
	t_2 = Float64(Float64(Float64(-t) * a) * x)
	tmp = 0.0
	if (z <= -1.8e+143)
		tmp = Float64(Float64(z * x) * y);
	elseif (z <= -2.6e+110)
		tmp = t_1;
	elseif (z <= -3.2e-243)
		tmp = t_2;
	elseif (z <= 3.7e-171)
		tmp = Float64(Float64(j * t) * c);
	elseif (z <= 1.5e-62)
		tmp = Float64(Float64(Float64(-i) * y) * j);
	elseif (z <= 9600000000.0)
		tmp = t_2;
	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);
	t_2 = (-t * a) * x;
	tmp = 0.0;
	if (z <= -1.8e+143)
		tmp = (z * x) * y;
	elseif (z <= -2.6e+110)
		tmp = t_1;
	elseif (z <= -3.2e-243)
		tmp = t_2;
	elseif (z <= 3.7e-171)
		tmp = (j * t) * c;
	elseif (z <= 1.5e-62)
		tmp = (-i * y) * j;
	elseif (z <= 9600000000.0)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[((-t) * a), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -1.8e+143], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, -2.6e+110], t$95$1, If[LessEqual[z, -3.2e-243], t$95$2, If[LessEqual[z, 3.7e-171], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[z, 1.5e-62], N[(N[((-i) * y), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[z, 9600000000.0], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.8e143

   1. Initial program 61.2%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 74.8%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot z\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 71.6%

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

   if -1.8e143 < z < -2.6e110 or 9.6e9 < z

   1. Initial program 70.2%

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

   3. Taylor expanded in c around inf

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

   5. Applied rewrites 59.2%

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

   7. Applied rewrites 57.6%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 43.9%

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

   if -2.6e110 < z < -3.1999999999999998e-243 or 1.5000000000000001e-62 < z < 9.6e9

   1. Initial program 84.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 54.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 42.5%

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

   if -3.1999999999999998e-243 < z < 3.70000000000000012e-171

   1. Initial program 65.7%

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

   3. Taylor expanded in c around inf

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

   5. Applied rewrites 43.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 38.3%

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

   if 3.70000000000000012e-171 < z < 1.5000000000000001e-62

   1. Initial program 71.5%

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

   3. Taylor expanded in j around inf

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

   5. Applied rewrites 55.1%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 44.8%

      \[\leadsto \left(\left(-i\right) \cdot y\right) \cdot j \]
3. Recombined 5 regimes into one program.

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+143}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(\left(-c\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-243}:\\ \;\;\;\;\left(\left(-t\right) \cdot a\right) \cdot x\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-171}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-62}:\\ \;\;\;\;\left(\left(-i\right) \cdot y\right) \cdot j\\ \mathbf{elif}\;z \leq 9600000000:\\ \;\;\;\;\left(\left(-t\right) \cdot a\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(-c\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(-c\right) \cdot z\right)\\ t_2 := \left(\left(-t\right) \cdot a\right) \cdot x\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+143}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-243}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-159}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-79}:\\ \;\;\;\;\left(\left(-j\right) \cdot y\right) \cdot i\\ \mathbf{elif}\;z \leq 9600000000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* (- c) z))) (t_2 (* (* (- t) a) x)))
   (if (<= z -1.8e+143)
     (* (* z x) y)
     (if (<= z -2.6e+110)
       t_1
       (if (<= z -3.2e-243)
         t_2
         (if (<= z 8.2e-159)
           (* (* j t) c)
           (if (<= z 2.05e-79)
             (* (* (- j) y) i)
             (if (<= z 9600000000.0) t_2 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 t_2 = (-t * a) * x;
	double tmp;
	if (z <= -1.8e+143) {
		tmp = (z * x) * y;
	} else if (z <= -2.6e+110) {
		tmp = t_1;
	} else if (z <= -3.2e-243) {
		tmp = t_2;
	} else if (z <= 8.2e-159) {
		tmp = (j * t) * c;
	} else if (z <= 2.05e-79) {
		tmp = (-j * y) * i;
	} else if (z <= 9600000000.0) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = b * (-c * z)
    t_2 = (-t * a) * x
    if (z <= (-1.8d+143)) then
        tmp = (z * x) * y
    else if (z <= (-2.6d+110)) then
        tmp = t_1
    else if (z <= (-3.2d-243)) then
        tmp = t_2
    else if (z <= 8.2d-159) then
        tmp = (j * t) * c
    else if (z <= 2.05d-79) then
        tmp = (-j * y) * i
    else if (z <= 9600000000.0d0) then
        tmp = t_2
    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 t_2 = (-t * a) * x;
	double tmp;
	if (z <= -1.8e+143) {
		tmp = (z * x) * y;
	} else if (z <= -2.6e+110) {
		tmp = t_1;
	} else if (z <= -3.2e-243) {
		tmp = t_2;
	} else if (z <= 8.2e-159) {
		tmp = (j * t) * c;
	} else if (z <= 2.05e-79) {
		tmp = (-j * y) * i;
	} else if (z <= 9600000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (-c * z)
	t_2 = (-t * a) * x
	tmp = 0
	if z <= -1.8e+143:
		tmp = (z * x) * y
	elif z <= -2.6e+110:
		tmp = t_1
	elif z <= -3.2e-243:
		tmp = t_2
	elif z <= 8.2e-159:
		tmp = (j * t) * c
	elif z <= 2.05e-79:
		tmp = (-j * y) * i
	elif z <= 9600000000.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(-c) * z))
	t_2 = Float64(Float64(Float64(-t) * a) * x)
	tmp = 0.0
	if (z <= -1.8e+143)
		tmp = Float64(Float64(z * x) * y);
	elseif (z <= -2.6e+110)
		tmp = t_1;
	elseif (z <= -3.2e-243)
		tmp = t_2;
	elseif (z <= 8.2e-159)
		tmp = Float64(Float64(j * t) * c);
	elseif (z <= 2.05e-79)
		tmp = Float64(Float64(Float64(-j) * y) * i);
	elseif (z <= 9600000000.0)
		tmp = t_2;
	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);
	t_2 = (-t * a) * x;
	tmp = 0.0;
	if (z <= -1.8e+143)
		tmp = (z * x) * y;
	elseif (z <= -2.6e+110)
		tmp = t_1;
	elseif (z <= -3.2e-243)
		tmp = t_2;
	elseif (z <= 8.2e-159)
		tmp = (j * t) * c;
	elseif (z <= 2.05e-79)
		tmp = (-j * y) * i;
	elseif (z <= 9600000000.0)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[((-t) * a), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -1.8e+143], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, -2.6e+110], t$95$1, If[LessEqual[z, -3.2e-243], t$95$2, If[LessEqual[z, 8.2e-159], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[z, 2.05e-79], N[(N[((-j) * y), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[z, 9600000000.0], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.8e143

   1. Initial program 61.2%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 74.8%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot z\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 71.6%

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

   if -1.8e143 < z < -2.6e110 or 9.6e9 < z

   1. Initial program 70.2%

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

   3. Taylor expanded in c around inf

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

   5. Applied rewrites 59.2%

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

   7. Applied rewrites 57.6%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 43.9%

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

   if -2.6e110 < z < -3.1999999999999998e-243 or 2.04999999999999997e-79 < z < 9.6e9

   1. Initial program 83.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 54.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 41.2%

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

   if -3.1999999999999998e-243 < z < 8.20000000000000029e-159

   1. Initial program 67.4%

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

   3. Taylor expanded in c around inf

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

   5. Applied rewrites 40.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 36.3%

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

   if 8.20000000000000029e-159 < z < 2.04999999999999997e-79

   1. Initial program 70.7%

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

   3. Taylor expanded in j around inf

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

   5. Applied rewrites 54.5%

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

   6. Taylor expanded in y around inf

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 47.6%

      \[\leadsto \left(\left(-j\right) \cdot y\right) \cdot \color{blue}{i} \]
3. Recombined 5 regimes into one program.

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+143}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(\left(-c\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-243}:\\ \;\;\;\;\left(\left(-t\right) \cdot a\right) \cdot x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-159}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-79}:\\ \;\;\;\;\left(\left(-j\right) \cdot y\right) \cdot i\\ \mathbf{elif}\;z \leq 9600000000:\\ \;\;\;\;\left(\left(-t\right) \cdot a\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(-c\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{if}\;t \leq -4 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-41}:\\ \;\;\;\;\mathsf{fma}\left(-x, t, i \cdot b\right) \cdot a\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-104}:\\ \;\;\;\;\mathsf{fma}\left(-z, b, j \cdot t\right) \cdot c\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-280}:\\ \;\;\;\;\mathsf{fma}\left(z, x, \left(-j\right) \cdot i\right) \cdot y\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-94}:\\ \;\;\;\;\mathsf{fma}\left(-c, z, i \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- a) x (* j c)) t)))
   (if (<= t -4e+62)
     t_1
     (if (<= t -1.75e-41)
       (* (fma (- x) t (* i b)) a)
       (if (<= t -3e-104)
         (* (fma (- z) b (* j t)) c)
         (if (<= t 7.2e-280)
           (* (fma z x (* (- j) i)) y)
           (if (<= t 1.08e-94) (* (fma (- c) z (* i a)) 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 = fma(-a, x, (j * c)) * t;
	double tmp;
	if (t <= -4e+62) {
		tmp = t_1;
	} else if (t <= -1.75e-41) {
		tmp = fma(-x, t, (i * b)) * a;
	} else if (t <= -3e-104) {
		tmp = fma(-z, b, (j * t)) * c;
	} else if (t <= 7.2e-280) {
		tmp = fma(z, x, (-j * i)) * y;
	} else if (t <= 1.08e-94) {
		tmp = fma(-c, z, (i * a)) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-a), x, Float64(j * c)) * t)
	tmp = 0.0
	if (t <= -4e+62)
		tmp = t_1;
	elseif (t <= -1.75e-41)
		tmp = Float64(fma(Float64(-x), t, Float64(i * b)) * a);
	elseif (t <= -3e-104)
		tmp = Float64(fma(Float64(-z), b, Float64(j * t)) * c);
	elseif (t <= 7.2e-280)
		tmp = Float64(fma(z, x, Float64(Float64(-j) * i)) * y);
	elseif (t <= 1.08e-94)
		tmp = Float64(fma(Float64(-c), z, Float64(i * a)) * b);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -4e+62], t$95$1, If[LessEqual[t, -1.75e-41], N[(N[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t, -3e-104], N[(N[((-z) * b + N[(j * t), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[t, 7.2e-280], N[(N[(z * x + N[((-j) * i), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 1.08e-94], N[(N[((-c) * z + N[(i * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.00000000000000014e62 or 1.08e-94 < t

   1. Initial program 68.7%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 62.4%

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

   if -4.00000000000000014e62 < t < -1.75e-41

   1. Initial program 68.3%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 68.5%

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

   if -1.75e-41 < t < -3.0000000000000002e-104

   1. Initial program 67.2%

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

   3. Taylor expanded in c around inf

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

   5. Applied rewrites 75.1%

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

   if -3.0000000000000002e-104 < t < 7.19999999999999989e-280

   1. Initial program 79.5%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 65.6%

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

   7. Applied rewrites 67.7%

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

   if 7.19999999999999989e-280 < t < 1.08e-94

   1. Initial program 85.7%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 62.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-c, z, i \cdot a\right) \cdot b} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 13: 51.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-c, z, i \cdot a\right) \cdot b\\ t_2 := \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{if}\;t \leq -4 \cdot 10^{+62}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-41}:\\ \;\;\;\;\mathsf{fma}\left(-x, t, i \cdot b\right) \cdot a\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-280}:\\ \;\;\;\;\mathsf{fma}\left(z, x, \left(-j\right) \cdot i\right) \cdot y\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-94}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- c) z (* i a)) b)) (t_2 (* (fma (- a) x (* j c)) t)))
   (if (<= t -4e+62)
     t_2
     (if (<= t -7.5e-41)
       (* (fma (- x) t (* i b)) a)
       (if (<= t -1.8e-105)
         t_1
         (if (<= t 7.2e-280)
           (* (fma z x (* (- j) i)) y)
           (if (<= t 1.08e-94) 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 = fma(-c, z, (i * a)) * b;
	double t_2 = fma(-a, x, (j * c)) * t;
	double tmp;
	if (t <= -4e+62) {
		tmp = t_2;
	} else if (t <= -7.5e-41) {
		tmp = fma(-x, t, (i * b)) * a;
	} else if (t <= -1.8e-105) {
		tmp = t_1;
	} else if (t <= 7.2e-280) {
		tmp = fma(z, x, (-j * i)) * y;
	} else if (t <= 1.08e-94) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-c), z, Float64(i * a)) * b)
	t_2 = Float64(fma(Float64(-a), x, Float64(j * c)) * t)
	tmp = 0.0
	if (t <= -4e+62)
		tmp = t_2;
	elseif (t <= -7.5e-41)
		tmp = Float64(fma(Float64(-x), t, Float64(i * b)) * a);
	elseif (t <= -1.8e-105)
		tmp = t_1;
	elseif (t <= 7.2e-280)
		tmp = Float64(fma(z, x, Float64(Float64(-j) * i)) * y);
	elseif (t <= 1.08e-94)
		tmp = t_1;
	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[((-c) * z + N[(i * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -4e+62], t$95$2, If[LessEqual[t, -7.5e-41], N[(N[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t, -1.8e-105], t$95$1, If[LessEqual[t, 7.2e-280], N[(N[(z * x + N[((-j) * i), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 1.08e-94], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.00000000000000014e62 or 1.08e-94 < t

   1. Initial program 68.7%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 62.4%

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

   if -4.00000000000000014e62 < t < -7.50000000000000049e-41

   1. Initial program 68.3%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 68.5%

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

   if -7.50000000000000049e-41 < t < -1.79999999999999982e-105 or 7.19999999999999989e-280 < t < 1.08e-94

   1. Initial program 81.5%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 63.2%

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

   if -1.79999999999999982e-105 < t < 7.19999999999999989e-280

   1. Initial program 79.5%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 65.6%

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

   7. Applied rewrites 67.7%

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

Alternative 14: 48.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ t_2 := \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+111}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-158}:\\ \;\;\;\;\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{elif}\;z \leq 10^{-62}:\\ \;\;\;\;\mathsf{fma}\left(z, x, \left(-j\right) \cdot i\right) \cdot y\\ \mathbf{elif}\;z \leq 9600000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- a) t (* z y)) x)) (t_2 (* (fma (- b) c (* y x)) z)))
   (if (<= z -3.5e+111)
     t_2
     (if (<= z -7.5e-137)
       t_1
       (if (<= z 1.5e-158)
         (* (fma (- a) x (* j c)) t)
         (if (<= z 1e-62)
           (* (fma z x (* (- j) i)) y)
           (if (<= z 9600000000.0) 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 = fma(-a, t, (z * y)) * x;
	double t_2 = fma(-b, c, (y * x)) * z;
	double tmp;
	if (z <= -3.5e+111) {
		tmp = t_2;
	} else if (z <= -7.5e-137) {
		tmp = t_1;
	} else if (z <= 1.5e-158) {
		tmp = fma(-a, x, (j * c)) * t;
	} else if (z <= 1e-62) {
		tmp = fma(z, x, (-j * i)) * y;
	} else if (z <= 9600000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-a), t, Float64(z * y)) * x)
	t_2 = Float64(fma(Float64(-b), c, Float64(y * x)) * z)
	tmp = 0.0
	if (z <= -3.5e+111)
		tmp = t_2;
	elseif (z <= -7.5e-137)
		tmp = t_1;
	elseif (z <= 1.5e-158)
		tmp = Float64(fma(Float64(-a), x, Float64(j * c)) * t);
	elseif (z <= 1e-62)
		tmp = Float64(fma(z, x, Float64(Float64(-j) * i)) * y);
	elseif (z <= 9600000000.0)
		tmp = t_1;
	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[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -3.5e+111], t$95$2, If[LessEqual[z, -7.5e-137], t$95$1, If[LessEqual[z, 1.5e-158], N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 1e-62], N[(N[(z * x + N[((-j) * i), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, 9600000000.0], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.5000000000000002e111 or 9.6e9 < z

   1. Initial program 67.2%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 69.7%

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

   if -3.5000000000000002e111 < z < -7.4999999999999995e-137 or 1e-62 < z < 9.6e9

   1. Initial program 86.9%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 58.6%

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

   if -7.4999999999999995e-137 < z < 1.5e-158

   1. Initial program 70.9%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 58.5%

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

   if 1.5e-158 < z < 1e-62

   1. Initial program 70.2%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 60.4%

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

   7. Applied rewrites 60.4%

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

Alternative 15: 58.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+111} \lor \neg \left(z \leq 4.8 \cdot 10^{+26}\right):\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -2.7e+111) (not (<= z 4.8e+26)))
   (* (fma (- b) c (* y x)) z)
   (+ (* (- a) (* t x)) (* j (- (* c t) (* i y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -2.7e+111) || !(z <= 4.8e+26)) {
		tmp = fma(-b, c, (y * x)) * z;
	} else {
		tmp = (-a * (t * x)) + (j * ((c * t) - (i * y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -2.7e+111) || !(z <= 4.8e+26))
		tmp = Float64(fma(Float64(-b), c, Float64(y * x)) * z);
	else
		tmp = Float64(Float64(Float64(-a) * Float64(t * x)) + Float64(j * Float64(Float64(c * t) - Float64(i * y))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -2.7e+111], N[Not[LessEqual[z, 4.8e+26]], $MachinePrecision]], N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6999999999999999e111 or 4.80000000000000009e26 < z

   1. Initial program 67.1%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 70.8%

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

   if -2.6999999999999999e111 < z < 4.80000000000000009e26

   1. Initial program 76.7%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 59.4%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+111} \lor \neg \left(z \leq 4.8 \cdot 10^{+26}\right):\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 28.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot x\right) \cdot y\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-205}:\\ \;\;\;\;\left(i \cdot a\right) \cdot b\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-159}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-79}:\\ \;\;\;\;\left(\left(-j\right) \cdot y\right) \cdot i\\ \mathbf{elif}\;z \leq 0.00048:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(-c\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z x) y)))
   (if (<= z -1.45e+138)
     t_1
     (if (<= z -2.7e-205)
       (* (* i a) b)
       (if (<= z 8.2e-159)
         (* (* j t) c)
         (if (<= z 3.1e-79)
           (* (* (- j) y) i)
           (if (<= z 0.00048) t_1 (* b (* (- c) z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * x) * y;
	double tmp;
	if (z <= -1.45e+138) {
		tmp = t_1;
	} else if (z <= -2.7e-205) {
		tmp = (i * a) * b;
	} else if (z <= 8.2e-159) {
		tmp = (j * t) * c;
	} else if (z <= 3.1e-79) {
		tmp = (-j * y) * i;
	} else if (z <= 0.00048) {
		tmp = t_1;
	} else {
		tmp = b * (-c * z);
	}
	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 = (z * x) * y
    if (z <= (-1.45d+138)) then
        tmp = t_1
    else if (z <= (-2.7d-205)) then
        tmp = (i * a) * b
    else if (z <= 8.2d-159) then
        tmp = (j * t) * c
    else if (z <= 3.1d-79) then
        tmp = (-j * y) * i
    else if (z <= 0.00048d0) then
        tmp = t_1
    else
        tmp = b * (-c * z)
    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 = (z * x) * y;
	double tmp;
	if (z <= -1.45e+138) {
		tmp = t_1;
	} else if (z <= -2.7e-205) {
		tmp = (i * a) * b;
	} else if (z <= 8.2e-159) {
		tmp = (j * t) * c;
	} else if (z <= 3.1e-79) {
		tmp = (-j * y) * i;
	} else if (z <= 0.00048) {
		tmp = t_1;
	} else {
		tmp = b * (-c * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * x) * y
	tmp = 0
	if z <= -1.45e+138:
		tmp = t_1
	elif z <= -2.7e-205:
		tmp = (i * a) * b
	elif z <= 8.2e-159:
		tmp = (j * t) * c
	elif z <= 3.1e-79:
		tmp = (-j * y) * i
	elif z <= 0.00048:
		tmp = t_1
	else:
		tmp = b * (-c * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * x) * y)
	tmp = 0.0
	if (z <= -1.45e+138)
		tmp = t_1;
	elseif (z <= -2.7e-205)
		tmp = Float64(Float64(i * a) * b);
	elseif (z <= 8.2e-159)
		tmp = Float64(Float64(j * t) * c);
	elseif (z <= 3.1e-79)
		tmp = Float64(Float64(Float64(-j) * y) * i);
	elseif (z <= 0.00048)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(Float64(-c) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (z * x) * y;
	tmp = 0.0;
	if (z <= -1.45e+138)
		tmp = t_1;
	elseif (z <= -2.7e-205)
		tmp = (i * a) * b;
	elseif (z <= 8.2e-159)
		tmp = (j * t) * c;
	elseif (z <= 3.1e-79)
		tmp = (-j * y) * i;
	elseif (z <= 0.00048)
		tmp = t_1;
	else
		tmp = b * (-c * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[z, -1.45e+138], t$95$1, If[LessEqual[z, -2.7e-205], N[(N[(i * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[z, 8.2e-159], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[z, 3.1e-79], N[(N[((-j) * y), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[z, 0.00048], t$95$1, N[(b * N[((-c) * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.45000000000000005e138 or 3.0999999999999999e-79 < z < 4.80000000000000012e-4

   1. Initial program 69.3%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 61.7%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot z\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 55.7%

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

   if -1.45000000000000005e138 < z < -2.7000000000000001e-205

   1. Initial program 80.3%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 44.2%

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

   6. Taylor expanded in z around 0

      \[\leadsto \left(a \cdot i\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 37.4%

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

   if -2.7000000000000001e-205 < z < 8.20000000000000029e-159

   1. Initial program 71.0%

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

   3. Taylor expanded in c around inf

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

   5. Applied rewrites 41.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 36.2%

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

   if 8.20000000000000029e-159 < z < 3.0999999999999999e-79

   1. Initial program 70.7%

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

   3. Taylor expanded in j around inf

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

   5. Applied rewrites 54.5%

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

   6. Taylor expanded in y around inf

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 47.6%

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

   if 4.80000000000000012e-4 < z

   1. Initial program 72.7%

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

   3. Taylor expanded in c around inf

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

   5. Applied rewrites 57.1%

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

   7. Applied rewrites 57.1%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 42.0%

       \[\leadsto \left(-b\right) \cdot \color{blue}{\left(c \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+138}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-205}:\\ \;\;\;\;\left(i \cdot a\right) \cdot b\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-159}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-79}:\\ \;\;\;\;\left(\left(-j\right) \cdot y\right) \cdot i\\ \mathbf{elif}\;z \leq 0.00048:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(-c\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 28.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot x\right) \cdot y\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-205}:\\ \;\;\;\;\left(i \cdot a\right) \cdot b\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-159}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-79}:\\ \;\;\;\;\left(\left(-j\right) \cdot y\right) \cdot i\\ \mathbf{elif}\;z \leq 0.00048:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-b\right) \cdot c\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z x) y)))
   (if (<= z -1.45e+138)
     t_1
     (if (<= z -2.7e-205)
       (* (* i a) b)
       (if (<= z 8.2e-159)
         (* (* j t) c)
         (if (<= z 3.1e-79)
           (* (* (- j) y) i)
           (if (<= z 0.00048) t_1 (* (* (- b) c) z))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * x) * y;
	double tmp;
	if (z <= -1.45e+138) {
		tmp = t_1;
	} else if (z <= -2.7e-205) {
		tmp = (i * a) * b;
	} else if (z <= 8.2e-159) {
		tmp = (j * t) * c;
	} else if (z <= 3.1e-79) {
		tmp = (-j * y) * i;
	} else if (z <= 0.00048) {
		tmp = t_1;
	} else {
		tmp = (-b * c) * z;
	}
	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 = (z * x) * y
    if (z <= (-1.45d+138)) then
        tmp = t_1
    else if (z <= (-2.7d-205)) then
        tmp = (i * a) * b
    else if (z <= 8.2d-159) then
        tmp = (j * t) * c
    else if (z <= 3.1d-79) then
        tmp = (-j * y) * i
    else if (z <= 0.00048d0) then
        tmp = t_1
    else
        tmp = (-b * c) * z
    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 = (z * x) * y;
	double tmp;
	if (z <= -1.45e+138) {
		tmp = t_1;
	} else if (z <= -2.7e-205) {
		tmp = (i * a) * b;
	} else if (z <= 8.2e-159) {
		tmp = (j * t) * c;
	} else if (z <= 3.1e-79) {
		tmp = (-j * y) * i;
	} else if (z <= 0.00048) {
		tmp = t_1;
	} else {
		tmp = (-b * c) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * x) * y
	tmp = 0
	if z <= -1.45e+138:
		tmp = t_1
	elif z <= -2.7e-205:
		tmp = (i * a) * b
	elif z <= 8.2e-159:
		tmp = (j * t) * c
	elif z <= 3.1e-79:
		tmp = (-j * y) * i
	elif z <= 0.00048:
		tmp = t_1
	else:
		tmp = (-b * c) * z
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * x) * y)
	tmp = 0.0
	if (z <= -1.45e+138)
		tmp = t_1;
	elseif (z <= -2.7e-205)
		tmp = Float64(Float64(i * a) * b);
	elseif (z <= 8.2e-159)
		tmp = Float64(Float64(j * t) * c);
	elseif (z <= 3.1e-79)
		tmp = Float64(Float64(Float64(-j) * y) * i);
	elseif (z <= 0.00048)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(-b) * c) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (z * x) * y;
	tmp = 0.0;
	if (z <= -1.45e+138)
		tmp = t_1;
	elseif (z <= -2.7e-205)
		tmp = (i * a) * b;
	elseif (z <= 8.2e-159)
		tmp = (j * t) * c;
	elseif (z <= 3.1e-79)
		tmp = (-j * y) * i;
	elseif (z <= 0.00048)
		tmp = t_1;
	else
		tmp = (-b * c) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[z, -1.45e+138], t$95$1, If[LessEqual[z, -2.7e-205], N[(N[(i * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[z, 8.2e-159], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[z, 3.1e-79], N[(N[((-j) * y), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[z, 0.00048], t$95$1, N[(N[((-b) * c), $MachinePrecision] * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.45000000000000005e138 or 3.0999999999999999e-79 < z < 4.80000000000000012e-4

   1. Initial program 69.3%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 61.7%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot z\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 55.7%

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

   if -1.45000000000000005e138 < z < -2.7000000000000001e-205

   1. Initial program 80.3%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 44.2%

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

   6. Taylor expanded in z around 0

      \[\leadsto \left(a \cdot i\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 37.4%

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

   if -2.7000000000000001e-205 < z < 8.20000000000000029e-159

   1. Initial program 71.0%

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

   3. Taylor expanded in c around inf

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

   5. Applied rewrites 41.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 36.2%

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

   if 8.20000000000000029e-159 < z < 3.0999999999999999e-79

   1. Initial program 70.7%

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

   3. Taylor expanded in j around inf

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

   5. Applied rewrites 54.5%

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

   6. Taylor expanded in y around inf

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 47.6%

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

   if 4.80000000000000012e-4 < z

   1. Initial program 72.7%

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

   3. Taylor expanded in c around inf

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

   5. Applied rewrites 57.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 41.9%

      \[\leadsto \left(\left(-b\right) \cdot c\right) \cdot \color{blue}{z} \]
3. Recombined 5 regimes into one program.

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+138}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-205}:\\ \;\;\;\;\left(i \cdot a\right) \cdot b\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-159}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-79}:\\ \;\;\;\;\left(\left(-j\right) \cdot y\right) \cdot i\\ \mathbf{elif}\;z \leq 0.00048:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-b\right) \cdot c\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+62}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-81}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-192}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-287}:\\ \;\;\;\;\left(\left(-j\right) \cdot y\right) \cdot i\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-95}:\\ \;\;\;\;\left(i \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -4e+62)
   (* (* j t) c)
   (if (<= t -3e-81)
     (* (* i b) a)
     (if (<= t -5.8e-192)
       (* (* z x) y)
       (if (<= t 2e-287)
         (* (* (- j) y) i)
         (if (<= t 4.5e-95) (* (* i a) b) (* (- a) (* t x))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -4e+62) {
		tmp = (j * t) * c;
	} else if (t <= -3e-81) {
		tmp = (i * b) * a;
	} else if (t <= -5.8e-192) {
		tmp = (z * x) * y;
	} else if (t <= 2e-287) {
		tmp = (-j * y) * i;
	} else if (t <= 4.5e-95) {
		tmp = (i * a) * b;
	} else {
		tmp = -a * (t * x);
	}
	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 (t <= (-4d+62)) then
        tmp = (j * t) * c
    else if (t <= (-3d-81)) then
        tmp = (i * b) * a
    else if (t <= (-5.8d-192)) then
        tmp = (z * x) * y
    else if (t <= 2d-287) then
        tmp = (-j * y) * i
    else if (t <= 4.5d-95) then
        tmp = (i * a) * b
    else
        tmp = -a * (t * x)
    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 (t <= -4e+62) {
		tmp = (j * t) * c;
	} else if (t <= -3e-81) {
		tmp = (i * b) * a;
	} else if (t <= -5.8e-192) {
		tmp = (z * x) * y;
	} else if (t <= 2e-287) {
		tmp = (-j * y) * i;
	} else if (t <= 4.5e-95) {
		tmp = (i * a) * b;
	} else {
		tmp = -a * (t * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -4e+62:
		tmp = (j * t) * c
	elif t <= -3e-81:
		tmp = (i * b) * a
	elif t <= -5.8e-192:
		tmp = (z * x) * y
	elif t <= 2e-287:
		tmp = (-j * y) * i
	elif t <= 4.5e-95:
		tmp = (i * a) * b
	else:
		tmp = -a * (t * x)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -4e+62)
		tmp = Float64(Float64(j * t) * c);
	elseif (t <= -3e-81)
		tmp = Float64(Float64(i * b) * a);
	elseif (t <= -5.8e-192)
		tmp = Float64(Float64(z * x) * y);
	elseif (t <= 2e-287)
		tmp = Float64(Float64(Float64(-j) * y) * i);
	elseif (t <= 4.5e-95)
		tmp = Float64(Float64(i * a) * b);
	else
		tmp = Float64(Float64(-a) * Float64(t * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -4e+62)
		tmp = (j * t) * c;
	elseif (t <= -3e-81)
		tmp = (i * b) * a;
	elseif (t <= -5.8e-192)
		tmp = (z * x) * y;
	elseif (t <= 2e-287)
		tmp = (-j * y) * i;
	elseif (t <= 4.5e-95)
		tmp = (i * a) * b;
	else
		tmp = -a * (t * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -4e+62], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[t, -3e-81], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t, -5.8e-192], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 2e-287], N[(N[((-j) * y), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[t, 4.5e-95], N[(N[(i * a), $MachinePrecision] * b), $MachinePrecision], N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -4.00000000000000014e62

   1. Initial program 62.2%

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

   3. Taylor expanded in c around inf

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

   5. Applied rewrites 60.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 49.5%

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

   if -4.00000000000000014e62 < t < -2.9999999999999999e-81

   1. Initial program 68.9%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 45.1%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 42.1%

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

   if -2.9999999999999999e-81 < t < -5.80000000000000033e-192

   1. Initial program 73.3%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 54.9%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot z\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 46.9%

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

   if -5.80000000000000033e-192 < t < 2.00000000000000004e-287

   1. Initial program 82.1%

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

   3. Taylor expanded in j around inf

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

   5. Applied rewrites 51.9%

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

   6. Taylor expanded in y around inf

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 48.1%

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

   if 2.00000000000000004e-287 < t < 4.5e-95

   1. Initial program 85.7%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 62.2%

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

   6. Taylor expanded in z around 0

      \[\leadsto \left(a \cdot i\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 36.0%

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

   if 4.5e-95 < t

   1. Initial program 73.1%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 49.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 38.2%

      \[\leadsto \left(-a\right) \cdot \color{blue}{\left(t \cdot x\right)} \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 19: 44.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+236}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{+78} \lor \neg \left(t \leq 6 \cdot 10^{-164}\right):\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, \left(-j\right) \cdot i\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -1.6e+236)
   (* (* j t) c)
   (if (or (<= t -3.3e+78) (not (<= t 6e-164)))
     (* (fma (- a) t (* z y)) x)
     (* (fma z x (* (- j) i)) y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -1.6e+236) {
		tmp = (j * t) * c;
	} else if ((t <= -3.3e+78) || !(t <= 6e-164)) {
		tmp = fma(-a, t, (z * y)) * x;
	} else {
		tmp = fma(z, x, (-j * i)) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -1.6e+236)
		tmp = Float64(Float64(j * t) * c);
	elseif ((t <= -3.3e+78) || !(t <= 6e-164))
		tmp = Float64(fma(Float64(-a), t, Float64(z * y)) * x);
	else
		tmp = Float64(fma(z, x, Float64(Float64(-j) * i)) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -1.6e+236], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], If[Or[LessEqual[t, -3.3e+78], N[Not[LessEqual[t, 6e-164]], $MachinePrecision]], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(z * x + N[((-j) * i), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6000000000000001e236

   1. Initial program 50.4%

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

   3. Taylor expanded in c around inf

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

   5. Applied rewrites 71.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 71.8%

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

   if -1.6000000000000001e236 < t < -3.3e78 or 6.0000000000000002e-164 < t

   1. Initial program 73.1%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 51.1%

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

   if -3.3e78 < t < 6.0000000000000002e-164

   1. Initial program 76.5%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 51.6%

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

   7. Applied rewrites 52.5%

      \[\leadsto \mathsf{fma}\left(z, x, \left(-j\right) \cdot i\right) \cdot y \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+236}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{+78} \lor \neg \left(t \leq 6 \cdot 10^{-164}\right):\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, \left(-j\right) \cdot i\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 30.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+62}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-81}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{-137}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-95}:\\ \;\;\;\;\left(i \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -4e+62)
   (* (* j t) c)
   (if (<= t -3e-81)
     (* (* i b) a)
     (if (<= t 5.9e-137)
       (* (* z x) y)
       (if (<= t 4.5e-95) (* (* i a) b) (* (- a) (* t x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -4e+62) {
		tmp = (j * t) * c;
	} else if (t <= -3e-81) {
		tmp = (i * b) * a;
	} else if (t <= 5.9e-137) {
		tmp = (z * x) * y;
	} else if (t <= 4.5e-95) {
		tmp = (i * a) * b;
	} else {
		tmp = -a * (t * x);
	}
	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 (t <= (-4d+62)) then
        tmp = (j * t) * c
    else if (t <= (-3d-81)) then
        tmp = (i * b) * a
    else if (t <= 5.9d-137) then
        tmp = (z * x) * y
    else if (t <= 4.5d-95) then
        tmp = (i * a) * b
    else
        tmp = -a * (t * x)
    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 (t <= -4e+62) {
		tmp = (j * t) * c;
	} else if (t <= -3e-81) {
		tmp = (i * b) * a;
	} else if (t <= 5.9e-137) {
		tmp = (z * x) * y;
	} else if (t <= 4.5e-95) {
		tmp = (i * a) * b;
	} else {
		tmp = -a * (t * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -4e+62:
		tmp = (j * t) * c
	elif t <= -3e-81:
		tmp = (i * b) * a
	elif t <= 5.9e-137:
		tmp = (z * x) * y
	elif t <= 4.5e-95:
		tmp = (i * a) * b
	else:
		tmp = -a * (t * x)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -4e+62)
		tmp = Float64(Float64(j * t) * c);
	elseif (t <= -3e-81)
		tmp = Float64(Float64(i * b) * a);
	elseif (t <= 5.9e-137)
		tmp = Float64(Float64(z * x) * y);
	elseif (t <= 4.5e-95)
		tmp = Float64(Float64(i * a) * b);
	else
		tmp = Float64(Float64(-a) * Float64(t * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -4e+62)
		tmp = (j * t) * c;
	elseif (t <= -3e-81)
		tmp = (i * b) * a;
	elseif (t <= 5.9e-137)
		tmp = (z * x) * y;
	elseif (t <= 4.5e-95)
		tmp = (i * a) * b;
	else
		tmp = -a * (t * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -4e+62], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[t, -3e-81], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t, 5.9e-137], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 4.5e-95], N[(N[(i * a), $MachinePrecision] * b), $MachinePrecision], N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.00000000000000014e62

   1. Initial program 62.2%

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

   3. Taylor expanded in c around inf

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

   5. Applied rewrites 60.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 49.5%

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

   if -4.00000000000000014e62 < t < -2.9999999999999999e-81

   1. Initial program 68.9%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 45.1%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 42.1%

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

   if -2.9999999999999999e-81 < t < 5.9000000000000001e-137

   1. Initial program 81.6%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 54.0%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot z\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 34.5%

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

   if 5.9000000000000001e-137 < t < 4.5e-95

   1. Initial program 77.6%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 68.4%

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

   6. Taylor expanded in z around 0

      \[\leadsto \left(a \cdot i\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 68.4%

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

   if 4.5e-95 < t

   1. Initial program 73.1%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 49.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 38.2%

      \[\leadsto \left(-a\right) \cdot \color{blue}{\left(t \cdot x\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 21: 51.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-280}:\\ \;\;\;\;\mathsf{fma}\left(z, x, \left(-j\right) \cdot i\right) \cdot y\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-94}:\\ \;\;\;\;\mathsf{fma}\left(-c, z, i \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- a) x (* j c)) t)))
   (if (<= t -3.8e+71)
     t_1
     (if (<= t 7.2e-280)
       (* (fma z x (* (- j) i)) y)
       (if (<= t 1.08e-94) (* (fma (- c) z (* i a)) 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 = fma(-a, x, (j * c)) * t;
	double tmp;
	if (t <= -3.8e+71) {
		tmp = t_1;
	} else if (t <= 7.2e-280) {
		tmp = fma(z, x, (-j * i)) * y;
	} else if (t <= 1.08e-94) {
		tmp = fma(-c, z, (i * a)) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-a), x, Float64(j * c)) * t)
	tmp = 0.0
	if (t <= -3.8e+71)
		tmp = t_1;
	elseif (t <= 7.2e-280)
		tmp = Float64(fma(z, x, Float64(Float64(-j) * i)) * y);
	elseif (t <= 1.08e-94)
		tmp = Float64(fma(Float64(-c), z, Float64(i * a)) * b);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -3.8e+71], t$95$1, If[LessEqual[t, 7.2e-280], N[(N[(z * x + N[((-j) * i), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 1.08e-94], N[(N[((-c) * z + N[(i * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.8000000000000001e71 or 1.08e-94 < t

   1. Initial program 68.8%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 63.1%

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

   if -3.8000000000000001e71 < t < 7.19999999999999989e-280

   1. Initial program 74.2%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 55.7%

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

   7. Applied rewrites 56.8%

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

   if 7.19999999999999989e-280 < t < 1.08e-94

   1. Initial program 85.7%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 62.2%

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

Alternative 22: 29.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+62}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-81}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{-137}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-93}:\\ \;\;\;\;\left(i \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot t\right) \cdot j\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -4e+62)
   (* (* j t) c)
   (if (<= t -3e-81)
     (* (* i b) a)
     (if (<= t 5.9e-137)
       (* (* z x) y)
       (if (<= t 2.9e-93) (* (* i a) b) (* (* c t) 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 (t <= -4e+62) {
		tmp = (j * t) * c;
	} else if (t <= -3e-81) {
		tmp = (i * b) * a;
	} else if (t <= 5.9e-137) {
		tmp = (z * x) * y;
	} else if (t <= 2.9e-93) {
		tmp = (i * a) * b;
	} else {
		tmp = (c * t) * 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 (t <= (-4d+62)) then
        tmp = (j * t) * c
    else if (t <= (-3d-81)) then
        tmp = (i * b) * a
    else if (t <= 5.9d-137) then
        tmp = (z * x) * y
    else if (t <= 2.9d-93) then
        tmp = (i * a) * b
    else
        tmp = (c * t) * 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 (t <= -4e+62) {
		tmp = (j * t) * c;
	} else if (t <= -3e-81) {
		tmp = (i * b) * a;
	} else if (t <= 5.9e-137) {
		tmp = (z * x) * y;
	} else if (t <= 2.9e-93) {
		tmp = (i * a) * b;
	} else {
		tmp = (c * t) * j;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -4e+62:
		tmp = (j * t) * c
	elif t <= -3e-81:
		tmp = (i * b) * a
	elif t <= 5.9e-137:
		tmp = (z * x) * y
	elif t <= 2.9e-93:
		tmp = (i * a) * b
	else:
		tmp = (c * t) * j
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -4e+62)
		tmp = Float64(Float64(j * t) * c);
	elseif (t <= -3e-81)
		tmp = Float64(Float64(i * b) * a);
	elseif (t <= 5.9e-137)
		tmp = Float64(Float64(z * x) * y);
	elseif (t <= 2.9e-93)
		tmp = Float64(Float64(i * a) * b);
	else
		tmp = Float64(Float64(c * t) * j);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -4e+62)
		tmp = (j * t) * c;
	elseif (t <= -3e-81)
		tmp = (i * b) * a;
	elseif (t <= 5.9e-137)
		tmp = (z * x) * y;
	elseif (t <= 2.9e-93)
		tmp = (i * a) * b;
	else
		tmp = (c * t) * j;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -4e+62], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[t, -3e-81], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t, 5.9e-137], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 2.9e-93], N[(N[(i * a), $MachinePrecision] * b), $MachinePrecision], N[(N[(c * t), $MachinePrecision] * j), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.00000000000000014e62

   1. Initial program 62.2%

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

   3. Taylor expanded in c around inf

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

   5. Applied rewrites 60.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 49.5%

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

   if -4.00000000000000014e62 < t < -2.9999999999999999e-81

   1. Initial program 68.9%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 45.1%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 42.1%

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

   if -2.9999999999999999e-81 < t < 5.9000000000000001e-137

   1. Initial program 81.6%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 54.0%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot z\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 34.5%

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

   if 5.9000000000000001e-137 < t < 2.8999999999999998e-93

   1. Initial program 79.9%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 61.9%

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

   6. Taylor expanded in z around 0

      \[\leadsto \left(a \cdot i\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 61.9%

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

   if 2.8999999999999998e-93 < t

   1. Initial program 72.7%

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

   3. Taylor expanded in j around inf

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

   5. Applied rewrites 38.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 30.0%

      \[\leadsto \left(c \cdot t\right) \cdot j \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 23: 51.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+71} \lor \neg \left(t \leq 1.1 \cdot 10^{-68}\right):\\ \;\;\;\;\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, \left(-j\right) \cdot i\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -3.8e+71) (not (<= t 1.1e-68)))
   (* (fma (- a) x (* j c)) t)
   (* (fma z x (* (- j) i)) y)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -3.8e+71) || !(t <= 1.1e-68)) {
		tmp = fma(-a, x, (j * c)) * t;
	} else {
		tmp = fma(z, x, (-j * i)) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -3.8e+71) || !(t <= 1.1e-68))
		tmp = Float64(fma(Float64(-a), x, Float64(j * c)) * t);
	else
		tmp = Float64(fma(z, x, Float64(Float64(-j) * i)) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -3.8e+71], N[Not[LessEqual[t, 1.1e-68]], $MachinePrecision]], N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(z * x + N[((-j) * i), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.8000000000000001e71 or 1.10000000000000001e-68 < t

   1. Initial program 68.3%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 63.2%

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

   if -3.8000000000000001e71 < t < 1.10000000000000001e-68

   1. Initial program 77.9%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 51.2%

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

   7. Applied rewrites 51.9%

      \[\leadsto \mathsf{fma}\left(z, x, \left(-j\right) \cdot i\right) \cdot y \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+71} \lor \neg \left(t \leq 1.1 \cdot 10^{-68}\right):\\ \;\;\;\;\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, \left(-j\right) \cdot i\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 42.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+76}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+46}:\\ \;\;\;\;\mathsf{fma}\left(z, x, \left(-j\right) \cdot i\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-t\right) \cdot a\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -8e+76)
   (* (* j t) c)
   (if (<= t 2.05e+46) (* (fma z x (* (- j) i)) y) (* (* (- t) a) x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -8e+76) {
		tmp = (j * t) * c;
	} else if (t <= 2.05e+46) {
		tmp = fma(z, x, (-j * i)) * y;
	} else {
		tmp = (-t * a) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -8e+76)
		tmp = Float64(Float64(j * t) * c);
	elseif (t <= 2.05e+46)
		tmp = Float64(fma(z, x, Float64(Float64(-j) * i)) * y);
	else
		tmp = Float64(Float64(Float64(-t) * a) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -8e+76], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[t, 2.05e+46], N[(N[(z * x + N[((-j) * i), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[(N[((-t) * a), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.0000000000000004e76

   1. Initial program 61.9%

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

   3. Taylor expanded in c around inf

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

   5. Applied rewrites 62.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 50.3%

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

   if -8.0000000000000004e76 < t < 2.05e46

   1. Initial program 77.8%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 48.4%

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

   7. Applied rewrites 49.0%

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

   if 2.05e46 < t

   1. Initial program 71.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 55.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 46.9%

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

Alternative 25: 29.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot x\right) \cdot y\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.06 \cdot 10^{-273}:\\ \;\;\;\;\left(i \cdot a\right) \cdot b\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{-33}:\\ \;\;\;\;\left(c \cdot t\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z x) y)))
   (if (<= x -1.2e+17)
     t_1
     (if (<= x -1.06e-273)
       (* (* i a) b)
       (if (<= x 6.1e-33) (* (* c t) j) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * x) * y;
	double tmp;
	if (x <= -1.2e+17) {
		tmp = t_1;
	} else if (x <= -1.06e-273) {
		tmp = (i * a) * b;
	} else if (x <= 6.1e-33) {
		tmp = (c * t) * j;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * x) * y
    if (x <= (-1.2d+17)) then
        tmp = t_1
    else if (x <= (-1.06d-273)) then
        tmp = (i * a) * b
    else if (x <= 6.1d-33) then
        tmp = (c * t) * j
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * x) * y;
	double tmp;
	if (x <= -1.2e+17) {
		tmp = t_1;
	} else if (x <= -1.06e-273) {
		tmp = (i * a) * b;
	} else if (x <= 6.1e-33) {
		tmp = (c * t) * j;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * x) * y
	tmp = 0
	if x <= -1.2e+17:
		tmp = t_1
	elif x <= -1.06e-273:
		tmp = (i * a) * b
	elif x <= 6.1e-33:
		tmp = (c * t) * j
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * x) * y)
	tmp = 0.0
	if (x <= -1.2e+17)
		tmp = t_1;
	elseif (x <= -1.06e-273)
		tmp = Float64(Float64(i * a) * b);
	elseif (x <= 6.1e-33)
		tmp = Float64(Float64(c * t) * j);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (z * x) * y;
	tmp = 0.0;
	if (x <= -1.2e+17)
		tmp = t_1;
	elseif (x <= -1.06e-273)
		tmp = (i * a) * b;
	elseif (x <= 6.1e-33)
		tmp = (c * t) * j;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[x, -1.2e+17], t$95$1, If[LessEqual[x, -1.06e-273], N[(N[(i * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[x, 6.1e-33], N[(N[(c * t), $MachinePrecision] * j), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.2e17 or 6.1000000000000001e-33 < x

   1. Initial program 73.9%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 46.7%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot z\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 39.2%

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

   if -1.2e17 < x < -1.0600000000000001e-273

   1. Initial program 79.4%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 49.9%

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

   6. Taylor expanded in z around 0

      \[\leadsto \left(a \cdot i\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 32.0%

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

   if -1.0600000000000001e-273 < x < 6.1000000000000001e-33

   1. Initial program 66.7%

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

   3. Taylor expanded in j around inf

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

   5. Applied rewrites 51.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 34.4%

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

Alternative 26: 29.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+17}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq -1.06 \cdot 10^{-273}:\\ \;\;\;\;\left(i \cdot a\right) \cdot b\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{-33}:\\ \;\;\;\;\left(c \cdot t\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -1.2e+17)
   (* (* z y) x)
   (if (<= x -1.06e-273)
     (* (* i a) b)
     (if (<= x 6.1e-33) (* (* c t) j) (* (* y x) z)))))

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 <= -1.2e+17) {
		tmp = (z * y) * x;
	} else if (x <= -1.06e-273) {
		tmp = (i * a) * b;
	} else if (x <= 6.1e-33) {
		tmp = (c * t) * j;
	} else {
		tmp = (y * x) * z;
	}
	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 (x <= (-1.2d+17)) then
        tmp = (z * y) * x
    else if (x <= (-1.06d-273)) then
        tmp = (i * a) * b
    else if (x <= 6.1d-33) then
        tmp = (c * t) * j
    else
        tmp = (y * x) * z
    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 (x <= -1.2e+17) {
		tmp = (z * y) * x;
	} else if (x <= -1.06e-273) {
		tmp = (i * a) * b;
	} else if (x <= 6.1e-33) {
		tmp = (c * t) * j;
	} else {
		tmp = (y * x) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -1.2e+17:
		tmp = (z * y) * x
	elif x <= -1.06e-273:
		tmp = (i * a) * b
	elif x <= 6.1e-33:
		tmp = (c * t) * j
	else:
		tmp = (y * x) * z
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -1.2e+17)
		tmp = Float64(Float64(z * y) * x);
	elseif (x <= -1.06e-273)
		tmp = Float64(Float64(i * a) * b);
	elseif (x <= 6.1e-33)
		tmp = Float64(Float64(c * t) * j);
	else
		tmp = Float64(Float64(y * x) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -1.2e+17)
		tmp = (z * y) * x;
	elseif (x <= -1.06e-273)
		tmp = (i * a) * b;
	elseif (x <= 6.1e-33)
		tmp = (c * t) * j;
	else
		tmp = (y * x) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -1.2e+17], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, -1.06e-273], N[(N[(i * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[x, 6.1e-33], N[(N[(c * t), $MachinePrecision] * j), $MachinePrecision], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.2e17

   1. Initial program 77.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 71.1%

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

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot z\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 38.9%

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

   if -1.2e17 < x < -1.0600000000000001e-273

   1. Initial program 79.4%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 49.9%

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

   6. Taylor expanded in z around 0

      \[\leadsto \left(a \cdot i\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 32.0%

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

   if -1.0600000000000001e-273 < x < 6.1000000000000001e-33

   1. Initial program 66.7%

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

   3. Taylor expanded in j around inf

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

   5. Applied rewrites 51.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 34.4%

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

   if 6.1000000000000001e-33 < x

   1. Initial program 71.8%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 64.0%

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

   6. Taylor expanded in t around inf

      \[\leadsto \left(t \cdot \left(-1 \cdot a + \frac{y \cdot z}{t}\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 65.2%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 37.4%

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

Alternative 27: 30.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+90} \lor \neg \left(x \leq 1.85 \cdot 10^{-60}\right):\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= x -7e+90) (not (<= x 1.85e-60))) (* (* y x) z) (* (* i b) 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 <= -7e+90) || !(x <= 1.85e-60)) {
		tmp = (y * x) * z;
	} else {
		tmp = (i * b) * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i, 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 ((x <= (-7d+90)) .or. (.not. (x <= 1.85d-60))) then
        tmp = (y * x) * z
    else
        tmp = (i * b) * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -7e+90) || !(x <= 1.85e-60)) {
		tmp = (y * x) * z;
	} else {
		tmp = (i * b) * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (x <= -7e+90) or not (x <= 1.85e-60):
		tmp = (y * x) * z
	else:
		tmp = (i * b) * a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((x <= -7e+90) || !(x <= 1.85e-60))
		tmp = Float64(Float64(y * x) * z);
	else
		tmp = Float64(Float64(i * b) * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((x <= -7e+90) || ~((x <= 1.85e-60)))
		tmp = (y * x) * z;
	else
		tmp = (i * b) * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[x, -7e+90], N[Not[LessEqual[x, 1.85e-60]], $MachinePrecision]], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.9999999999999997e90 or 1.85000000000000012e-60 < x

   1. Initial program 72.9%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 65.9%

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

   6. Taylor expanded in t around inf

      \[\leadsto \left(t \cdot \left(-1 \cdot a + \frac{y \cdot z}{t}\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 66.6%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 36.7%

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

   if -6.9999999999999997e90 < x < 1.85000000000000012e-60

   1. Initial program 73.7%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 49.1%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 27.1%

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

4. Final simplification 31.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+90} \lor \neg \left(x \leq 1.85 \cdot 10^{-60}\right):\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 29.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+138}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;z \leq 10^{-81}:\\ \;\;\;\;\left(i \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -1.45e+138)
   (* (* z y) x)
   (if (<= z 1e-81) (* (* i a) b) (* (* y x) z))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.45e+138) {
		tmp = (z * y) * x;
	} else if (z <= 1e-81) {
		tmp = (i * a) * b;
	} else {
		tmp = (y * x) * z;
	}
	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 (z <= (-1.45d+138)) then
        tmp = (z * y) * x
    else if (z <= 1d-81) then
        tmp = (i * a) * b
    else
        tmp = (y * x) * z
    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 (z <= -1.45e+138) {
		tmp = (z * y) * x;
	} else if (z <= 1e-81) {
		tmp = (i * a) * b;
	} else {
		tmp = (y * x) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -1.45e+138:
		tmp = (z * y) * x
	elif z <= 1e-81:
		tmp = (i * a) * b
	else:
		tmp = (y * x) * z
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -1.45e+138)
		tmp = Float64(Float64(z * y) * x);
	elseif (z <= 1e-81)
		tmp = Float64(Float64(i * a) * b);
	else
		tmp = Float64(Float64(y * x) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -1.45e+138)
		tmp = (z * y) * x;
	elseif (z <= 1e-81)
		tmp = (i * a) * b;
	else
		tmp = (y * x) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -1.45e+138], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 1e-81], N[(N[(i * a), $MachinePrecision] * b), $MachinePrecision], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45000000000000005e138

   1. Initial program 64.6%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 63.3%

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

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot z\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 60.3%

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

   if -1.45000000000000005e138 < z < 9.9999999999999996e-82

   1. Initial program 74.5%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 37.4%

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

   6. Taylor expanded in z around 0

      \[\leadsto \left(a \cdot i\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 30.8%

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

   if 9.9999999999999996e-82 < z

   1. Initial program 75.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 40.9%

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

   6. Taylor expanded in t around inf

      \[\leadsto \left(t \cdot \left(-1 \cdot a + \frac{y \cdot z}{t}\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 43.5%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 25.9%

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

Alternative 29: 29.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{+90}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-60}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -5.7e+90)
   (* (* z y) x)
   (if (<= x 1.85e-60) (* (* i b) a) (* (* y x) z))))

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 <= -5.7e+90) {
		tmp = (z * y) * x;
	} else if (x <= 1.85e-60) {
		tmp = (i * b) * a;
	} else {
		tmp = (y * x) * z;
	}
	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 (x <= (-5.7d+90)) then
        tmp = (z * y) * x
    else if (x <= 1.85d-60) then
        tmp = (i * b) * a
    else
        tmp = (y * x) * z
    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 (x <= -5.7e+90) {
		tmp = (z * y) * x;
	} else if (x <= 1.85e-60) {
		tmp = (i * b) * a;
	} else {
		tmp = (y * x) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -5.7e+90:
		tmp = (z * y) * x
	elif x <= 1.85e-60:
		tmp = (i * b) * a
	else:
		tmp = (y * x) * z
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -5.7e+90)
		tmp = Float64(Float64(z * y) * x);
	elseif (x <= 1.85e-60)
		tmp = Float64(Float64(i * b) * a);
	else
		tmp = Float64(Float64(y * x) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -5.7e+90)
		tmp = (z * y) * x;
	elseif (x <= 1.85e-60)
		tmp = (i * b) * a;
	else
		tmp = (y * x) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -5.7e+90], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 1.85e-60], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.70000000000000018e90

   1. Initial program 73.8%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 72.1%

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

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot z\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 41.7%

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

   if -5.70000000000000018e90 < x < 1.85000000000000012e-60

   1. Initial program 73.7%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 49.1%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 27.1%

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

   if 1.85000000000000012e-60 < x

   1. Initial program 72.4%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 62.4%

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

   6. Taylor expanded in t around inf

      \[\leadsto \left(t \cdot \left(-1 \cdot a + \frac{y \cdot z}{t}\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 63.6%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 35.1%

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

Alternative 30: 22.3% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \left(y \cdot x\right) \cdot z \end{array} \]

FPCore

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

C

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

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 = (y * x) * z
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 (y * x) * z;
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision]

Derivation

1. Initial program 73.3%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 40.4%

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

6. Taylor expanded in t around inf

   \[\leadsto \left(t \cdot \left(-1 \cdot a + \frac{y \cdot z}{t}\right)\right) \cdot x \]
7. Step-by-step derivation

8. Applied rewrites 41.4%

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

9. Taylor expanded in y around inf

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

11. Applied rewrites 22.2%

    \[\leadsto \left(y \cdot x\right) \cdot \color{blue}{z} \]
12. Add Preprocessing

Developer Target 1: 69.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) 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 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		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 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) 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 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		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(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		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 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2025018 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -1015122364899489/125000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -942510763643697/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (if (< t -238547917063487/3125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 10535888557455487/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))