Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.8% → 82.4%

Time: 9.2s

Alternatives: 25

Speedup: 0.5×

• 57.1% 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: 73.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.4% accurate, 0.5× speedup

Math

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

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 (- (* c t) (* i y))))))
   (if (<= t_1 INFINITY) t_1 (fma (- i) (* j y) (* b (fma (- c) z (* a i)))))))

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 * ((c * t) - (i * y)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(-i, (j * y), (b * fma(-c, z, (a * i))));
	}
	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(j * Float64(Float64(c * t) - Float64(i * y))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = fma(Float64(-i), Float64(j * y), Float64(b * fma(Float64(-c), z, Float64(a * i))));
	end
	return 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[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[((-i) * N[(j * y), $MachinePrecision] + N[(b * N[((-c) * z + N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 41.6%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 61.5%

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

4. Final simplification 87.1%

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

Alternative 2: 70.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-b\right) \cdot \mathsf{fma}\left(-a, i, c \cdot z\right)\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, t\_1\right)\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(-i, j \cdot y, b \cdot \mathsf{fma}\left(-c, z, a \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-142}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+40}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-a, t, y \cdot z\right), c \cdot \mathsf{fma}\left(-b, z, j \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- b) (fma (- a) i (* c z)))))
   (if (<= x -1.15e+106)
     (fma (fma (- a) t (* z y)) x t_1)
     (if (<= x -1.05e-11)
       (fma (- i) (* j y) (* b (fma (- c) z (* a i))))
       (if (<= x -5.5e-142)
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (* j (* c t)))
         (if (<= x 3.4e+40)
           (fma (fma (- i) y (* c t)) j t_1)
           (fma x (fma (- a) t (* y z)) (* c (fma (- b) z (* j t))))))))))

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 * fma(-a, i, (c * z));
	double tmp;
	if (x <= -1.15e+106) {
		tmp = fma(fma(-a, t, (z * y)), x, t_1);
	} else if (x <= -1.05e-11) {
		tmp = fma(-i, (j * y), (b * fma(-c, z, (a * i))));
	} else if (x <= -5.5e-142) {
		tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * (c * t));
	} else if (x <= 3.4e+40) {
		tmp = fma(fma(-i, y, (c * t)), j, t_1);
	} else {
		tmp = fma(x, fma(-a, t, (y * z)), (c * fma(-b, z, (j * t))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(-b) * fma(Float64(-a), i, Float64(c * z)))
	tmp = 0.0
	if (x <= -1.15e+106)
		tmp = fma(fma(Float64(-a), t, Float64(z * y)), x, t_1);
	elseif (x <= -1.05e-11)
		tmp = fma(Float64(-i), Float64(j * y), Float64(b * fma(Float64(-c), z, Float64(a * i))));
	elseif (x <= -5.5e-142)
		tmp = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(j * Float64(c * t)));
	elseif (x <= 3.4e+40)
		tmp = fma(fma(Float64(-i), y, Float64(c * t)), j, t_1);
	else
		tmp = fma(x, fma(Float64(-a), t, Float64(y * z)), Float64(c * fma(Float64(-b), z, Float64(j * t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-b) * N[((-a) * i + N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.15e+106], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x + t$95$1), $MachinePrecision], If[LessEqual[x, -1.05e-11], N[((-i) * N[(j * y), $MachinePrecision] + N[(b * N[((-c) * z + N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.5e-142], 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[(c * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.4e+40], N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j + t$95$1), $MachinePrecision], N[(x * N[((-a) * t + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(c * N[((-b) * z + N[(j * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.1500000000000001e106

   1. Initial program 81.7%

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

   3. Taylor expanded in j around 0

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

   5. Applied rewrites 89.1%

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

   if -1.1500000000000001e106 < x < -1.0499999999999999e-11

   1. Initial program 48.5%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 65.4%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 82.3%

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

   if -1.0499999999999999e-11 < x < -5.50000000000000023e-142

   1. Initial program 76.1%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 70.1%

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

   if -5.50000000000000023e-142 < x < 3.39999999999999989e40

   1. Initial program 83.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 85.8%

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

   if 3.39999999999999989e40 < x

   1. Initial program 80.6%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 92.2%

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

   6. Taylor expanded in i around 0

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

   8. Applied rewrites 86.9%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(-a, t, y \cdot z\right)}, c \cdot \mathsf{fma}\left(-b, z, j \cdot t\right)\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \left(-b\right) \cdot \mathsf{fma}\left(-a, i, c \cdot z\right)\right)\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(-i, j \cdot y, b \cdot \mathsf{fma}\left(-c, z, a \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-142}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+40}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \left(-b\right) \cdot \mathsf{fma}\left(-a, i, c \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-a, t, y \cdot z\right), c \cdot \mathsf{fma}\left(-b, z, j \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-b\right) \cdot \mathsf{fma}\left(-a, i, c \cdot z\right)\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, t\_1\right)\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(-i, j \cdot y, b \cdot \mathsf{fma}\left(-c, z, a \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-143}:\\ \;\;\;\;\left(-a\right) \cdot \mathsf{fma}\left(t, x, \left(-b\right) \cdot i\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+40}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-a, t, y \cdot z\right), c \cdot \mathsf{fma}\left(-b, z, j \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- b) (fma (- a) i (* c z)))))
   (if (<= x -1.15e+106)
     (fma (fma (- a) t (* z y)) x t_1)
     (if (<= x -1.05e-11)
       (fma (- i) (* j y) (* b (fma (- c) z (* a i))))
       (if (<= x -3.2e-143)
         (+ (* (- a) (fma t x (* (- b) i))) (* j (- (* c t) (* i y))))
         (if (<= x 3.4e+40)
           (fma (fma (- i) y (* c t)) j t_1)
           (fma x (fma (- a) t (* y z)) (* c (fma (- b) z (* j t))))))))))

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 * fma(-a, i, (c * z));
	double tmp;
	if (x <= -1.15e+106) {
		tmp = fma(fma(-a, t, (z * y)), x, t_1);
	} else if (x <= -1.05e-11) {
		tmp = fma(-i, (j * y), (b * fma(-c, z, (a * i))));
	} else if (x <= -3.2e-143) {
		tmp = (-a * fma(t, x, (-b * i))) + (j * ((c * t) - (i * y)));
	} else if (x <= 3.4e+40) {
		tmp = fma(fma(-i, y, (c * t)), j, t_1);
	} else {
		tmp = fma(x, fma(-a, t, (y * z)), (c * fma(-b, z, (j * t))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(-b) * fma(Float64(-a), i, Float64(c * z)))
	tmp = 0.0
	if (x <= -1.15e+106)
		tmp = fma(fma(Float64(-a), t, Float64(z * y)), x, t_1);
	elseif (x <= -1.05e-11)
		tmp = fma(Float64(-i), Float64(j * y), Float64(b * fma(Float64(-c), z, Float64(a * i))));
	elseif (x <= -3.2e-143)
		tmp = Float64(Float64(Float64(-a) * fma(t, x, Float64(Float64(-b) * i))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))));
	elseif (x <= 3.4e+40)
		tmp = fma(fma(Float64(-i), y, Float64(c * t)), j, t_1);
	else
		tmp = fma(x, fma(Float64(-a), t, Float64(y * z)), Float64(c * fma(Float64(-b), z, Float64(j * t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-b) * N[((-a) * i + N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.15e+106], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x + t$95$1), $MachinePrecision], If[LessEqual[x, -1.05e-11], N[((-i) * N[(j * y), $MachinePrecision] + N[(b * N[((-c) * z + N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.2e-143], N[(N[((-a) * N[(t * x + N[((-b) * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.4e+40], N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j + t$95$1), $MachinePrecision], N[(x * N[((-a) * t + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(c * N[((-b) * z + N[(j * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.1500000000000001e106

   1. Initial program 81.7%

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

   3. Taylor expanded in j around 0

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

   5. Applied rewrites 89.1%

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

   if -1.1500000000000001e106 < x < -1.0499999999999999e-11

   1. Initial program 48.5%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 65.4%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 82.3%

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

   if -1.0499999999999999e-11 < x < -3.1999999999999998e-143

   1. Initial program 76.1%

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

   3. Taylor expanded in a around -inf

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

   5. Applied rewrites 66.6%

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

   if -3.1999999999999998e-143 < x < 3.39999999999999989e40

   1. Initial program 83.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 85.8%

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

   if 3.39999999999999989e40 < x

   1. Initial program 80.6%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 92.2%

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

   6. Taylor expanded in i around 0

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

   8. Applied rewrites 86.9%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(-a, t, y \cdot z\right)}, c \cdot \mathsf{fma}\left(-b, z, j \cdot t\right)\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \left(-b\right) \cdot \mathsf{fma}\left(-a, i, c \cdot z\right)\right)\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(-i, j \cdot y, b \cdot \mathsf{fma}\left(-c, z, a \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-143}:\\ \;\;\;\;\left(-a\right) \cdot \mathsf{fma}\left(t, x, \left(-b\right) \cdot i\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+40}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \left(-b\right) \cdot \mathsf{fma}\left(-a, i, c \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-a, t, y \cdot z\right), c \cdot \mathsf{fma}\left(-b, z, j \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-b\right) \cdot \mathsf{fma}\left(-a, i, c \cdot z\right)\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, t\_1\right)\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(-i, j \cdot y, b \cdot \mathsf{fma}\left(-c, z, a \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+40}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-a, t, y \cdot z\right), c \cdot \mathsf{fma}\left(-b, z, j \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- b) (fma (- a) i (* c z)))))
   (if (<= x -1.15e+106)
     (fma (fma (- a) t (* z y)) x t_1)
     (if (<= x -1.05e-11)
       (fma (- i) (* j y) (* b (fma (- c) z (* a i))))
       (if (<= x 3.4e+40)
         (fma (fma (- i) y (* c t)) j t_1)
         (fma x (fma (- a) t (* y z)) (* c (fma (- b) z (* j t)))))))))

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 * fma(-a, i, (c * z));
	double tmp;
	if (x <= -1.15e+106) {
		tmp = fma(fma(-a, t, (z * y)), x, t_1);
	} else if (x <= -1.05e-11) {
		tmp = fma(-i, (j * y), (b * fma(-c, z, (a * i))));
	} else if (x <= 3.4e+40) {
		tmp = fma(fma(-i, y, (c * t)), j, t_1);
	} else {
		tmp = fma(x, fma(-a, t, (y * z)), (c * fma(-b, z, (j * t))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(-b) * fma(Float64(-a), i, Float64(c * z)))
	tmp = 0.0
	if (x <= -1.15e+106)
		tmp = fma(fma(Float64(-a), t, Float64(z * y)), x, t_1);
	elseif (x <= -1.05e-11)
		tmp = fma(Float64(-i), Float64(j * y), Float64(b * fma(Float64(-c), z, Float64(a * i))));
	elseif (x <= 3.4e+40)
		tmp = fma(fma(Float64(-i), y, Float64(c * t)), j, t_1);
	else
		tmp = fma(x, fma(Float64(-a), t, Float64(y * z)), Float64(c * fma(Float64(-b), z, Float64(j * t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-b) * N[((-a) * i + N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.15e+106], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x + t$95$1), $MachinePrecision], If[LessEqual[x, -1.05e-11], N[((-i) * N[(j * y), $MachinePrecision] + N[(b * N[((-c) * z + N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.4e+40], N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j + t$95$1), $MachinePrecision], N[(x * N[((-a) * t + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(c * N[((-b) * z + N[(j * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.1500000000000001e106

   1. Initial program 81.7%

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

   3. Taylor expanded in j around 0

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

   5. Applied rewrites 89.1%

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

   if -1.1500000000000001e106 < x < -1.0499999999999999e-11

   1. Initial program 48.5%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 65.4%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 82.3%

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

   if -1.0499999999999999e-11 < x < 3.39999999999999989e40

   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 x around 0

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

   5. Applied rewrites 78.2%

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

   if 3.39999999999999989e40 < x

   1. Initial program 80.6%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 92.2%

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

   6. Taylor expanded in i around 0

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

   8. Applied rewrites 86.9%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \left(-b\right) \cdot \mathsf{fma}\left(-a, i, c \cdot z\right)\right)\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(-i, j \cdot y, b \cdot \mathsf{fma}\left(-c, z, a \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+40}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \left(-b\right) \cdot \mathsf{fma}\left(-a, i, c \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-a, t, y \cdot z\right), c \cdot \mathsf{fma}\left(-b, z, j \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-i, j \cdot y, b \cdot \mathsf{fma}\left(-c, z, a \cdot i\right)\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \left(-b\right) \cdot \left(c \cdot z\right)\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-182}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-a, t, y \cdot z\right), c \cdot \left(\left(-b\right) \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (fma (- i) (* j y) (* b (fma (- c) z (* a i))))))
   (if (<= x -1.2e+106)
     (fma (fma (- a) t (* z y)) x (* (- b) (* c z)))
     (if (<= x -8.5e-12)
       t_1
       (if (<= x -5.6e-182)
         (+ (* (- a) (* t x)) (* j (- (* c t) (* i y))))
         (if (<= x 4.6e+49)
           t_1
           (fma x (fma (- a) t (* y z)) (* c (* (- b) z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-i, (j * y), (b * fma(-c, z, (a * i))));
	double tmp;
	if (x <= -1.2e+106) {
		tmp = fma(fma(-a, t, (z * y)), x, (-b * (c * z)));
	} else if (x <= -8.5e-12) {
		tmp = t_1;
	} else if (x <= -5.6e-182) {
		tmp = (-a * (t * x)) + (j * ((c * t) - (i * y)));
	} else if (x <= 4.6e+49) {
		tmp = t_1;
	} else {
		tmp = fma(x, fma(-a, t, (y * z)), (c * (-b * z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = fma(Float64(-i), Float64(j * y), Float64(b * fma(Float64(-c), z, Float64(a * i))))
	tmp = 0.0
	if (x <= -1.2e+106)
		tmp = fma(fma(Float64(-a), t, Float64(z * y)), x, Float64(Float64(-b) * Float64(c * z)));
	elseif (x <= -8.5e-12)
		tmp = t_1;
	elseif (x <= -5.6e-182)
		tmp = Float64(Float64(Float64(-a) * Float64(t * x)) + Float64(j * Float64(Float64(c * t) - Float64(i * y))));
	elseif (x <= 4.6e+49)
		tmp = t_1;
	else
		tmp = fma(x, fma(Float64(-a), t, Float64(y * z)), Float64(c * Float64(Float64(-b) * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-i) * N[(j * y), $MachinePrecision] + N[(b * N[((-c) * z + N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e+106], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x + N[((-b) * N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8.5e-12], t$95$1, If[LessEqual[x, -5.6e-182], N[(N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6e+49], t$95$1, N[(x * N[((-a) * t + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(c * N[((-b) * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.2e106

   1. Initial program 81.7%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 81.7%

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

   6. Taylor expanded in i around 0

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

   8. Applied rewrites 84.6%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 64.9%

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

   12. Taylor expanded in j around 0

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

   14. Applied rewrites 86.8%

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

   if -1.2e106 < x < -8.4999999999999997e-12 or -5.59999999999999986e-182 < x < 4.60000000000000004e49

   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 0

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

   5. Applied rewrites 72.6%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 70.1%

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

   if -8.4999999999999997e-12 < x < -5.59999999999999986e-182

   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 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 64.3%

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

   if 4.60000000000000004e49 < x

   1. Initial program 80.6%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 92.2%

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

   6. Taylor expanded in i around 0

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

   8. Applied rewrites 86.9%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 77.5%

       \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(-a, t, y \cdot z\right), c \cdot \left(-1 \cdot \left(b \cdot z\right)\right)\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \left(-b\right) \cdot \left(c \cdot z\right)\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(-i, j \cdot y, b \cdot \mathsf{fma}\left(-c, z, a \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-182}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+49}:\\ \;\;\;\;\mathsf{fma}\left(-i, j \cdot y, b \cdot \mathsf{fma}\left(-c, z, a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-a, t, y \cdot z\right), c \cdot \left(\left(-b\right) \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-i, j \cdot y, b \cdot \mathsf{fma}\left(-c, z, a \cdot i\right)\right)\\ t_2 := \mathsf{fma}\left(-a, t, z \cdot y\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(t\_2, x, \left(-b\right) \cdot \left(c \cdot z\right)\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-182}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (fma (- i) (* j y) (* b (fma (- c) z (* a i)))))
        (t_2 (fma (- a) t (* z y))))
   (if (<= x -1.2e+106)
     (fma t_2 x (* (- b) (* c z)))
     (if (<= x -8.5e-12)
       t_1
       (if (<= x -5.6e-182)
         (+ (* (- a) (* t x)) (* j (- (* c t) (* i y))))
         (if (<= x 8.8e+159) t_1 (* t_2 x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-i, (j * y), (b * fma(-c, z, (a * i))));
	double t_2 = fma(-a, t, (z * y));
	double tmp;
	if (x <= -1.2e+106) {
		tmp = fma(t_2, x, (-b * (c * z)));
	} else if (x <= -8.5e-12) {
		tmp = t_1;
	} else if (x <= -5.6e-182) {
		tmp = (-a * (t * x)) + (j * ((c * t) - (i * y)));
	} else if (x <= 8.8e+159) {
		tmp = t_1;
	} else {
		tmp = t_2 * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = fma(Float64(-i), Float64(j * y), Float64(b * fma(Float64(-c), z, Float64(a * i))))
	t_2 = fma(Float64(-a), t, Float64(z * y))
	tmp = 0.0
	if (x <= -1.2e+106)
		tmp = fma(t_2, x, Float64(Float64(-b) * Float64(c * z)));
	elseif (x <= -8.5e-12)
		tmp = t_1;
	elseif (x <= -5.6e-182)
		tmp = Float64(Float64(Float64(-a) * Float64(t * x)) + Float64(j * Float64(Float64(c * t) - Float64(i * y))));
	elseif (x <= 8.8e+159)
		tmp = t_1;
	else
		tmp = Float64(t_2 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-i) * N[(j * y), $MachinePrecision] + N[(b * N[((-c) * z + N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e+106], N[(t$95$2 * x + N[((-b) * N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8.5e-12], t$95$1, If[LessEqual[x, -5.6e-182], N[(N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.8e+159], t$95$1, N[(t$95$2 * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.2e106

   1. Initial program 81.7%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 81.7%

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

   6. Taylor expanded in i around 0

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

   8. Applied rewrites 84.6%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 64.9%

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

   12. Taylor expanded in j around 0

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

   14. Applied rewrites 86.8%

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

   if -1.2e106 < x < -8.4999999999999997e-12 or -5.59999999999999986e-182 < x < 8.7999999999999997e159

   1. Initial program 76.9%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 74.8%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 68.1%

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

   if -8.4999999999999997e-12 < x < -5.59999999999999986e-182

   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 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 64.3%

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

   if 8.7999999999999997e159 < x

   1. Initial program 79.2%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 85.5%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \left(-b\right) \cdot \left(c \cdot z\right)\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(-i, j \cdot y, b \cdot \mathsf{fma}\left(-c, z, a \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-182}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+159}:\\ \;\;\;\;\mathsf{fma}\left(-i, j \cdot y, b \cdot \mathsf{fma}\left(-c, z, a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-i, j \cdot y, b \cdot \mathsf{fma}\left(-c, z, a \cdot i\right)\right)\\ t_2 := \mathsf{fma}\left(-a, t, z \cdot y\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(t\_2, x, \left(-b\right) \cdot \left(c \cdot z\right)\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-181}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (fma (- i) (* j y) (* b (fma (- c) z (* a i)))))
        (t_2 (fma (- a) t (* z y))))
   (if (<= x -1.2e+106)
     (fma t_2 x (* (- b) (* c z)))
     (if (<= x -1.9e-27)
       t_1
       (if (<= x -1.5e-181)
         (+ (* (* z y) x) (* j (- (* c t) (* i y))))
         (if (<= x 8.8e+159) t_1 (* t_2 x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-i, (j * y), (b * fma(-c, z, (a * i))));
	double t_2 = fma(-a, t, (z * y));
	double tmp;
	if (x <= -1.2e+106) {
		tmp = fma(t_2, x, (-b * (c * z)));
	} else if (x <= -1.9e-27) {
		tmp = t_1;
	} else if (x <= -1.5e-181) {
		tmp = ((z * y) * x) + (j * ((c * t) - (i * y)));
	} else if (x <= 8.8e+159) {
		tmp = t_1;
	} else {
		tmp = t_2 * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = fma(Float64(-i), Float64(j * y), Float64(b * fma(Float64(-c), z, Float64(a * i))))
	t_2 = fma(Float64(-a), t, Float64(z * y))
	tmp = 0.0
	if (x <= -1.2e+106)
		tmp = fma(t_2, x, Float64(Float64(-b) * Float64(c * z)));
	elseif (x <= -1.9e-27)
		tmp = t_1;
	elseif (x <= -1.5e-181)
		tmp = Float64(Float64(Float64(z * y) * x) + Float64(j * Float64(Float64(c * t) - Float64(i * y))));
	elseif (x <= 8.8e+159)
		tmp = t_1;
	else
		tmp = Float64(t_2 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-i) * N[(j * y), $MachinePrecision] + N[(b * N[((-c) * z + N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e+106], N[(t$95$2 * x + N[((-b) * N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.9e-27], t$95$1, If[LessEqual[x, -1.5e-181], N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.8e+159], t$95$1, N[(t$95$2 * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.2e106

   1. Initial program 81.7%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 81.7%

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

   6. Taylor expanded in i around 0

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

   8. Applied rewrites 84.6%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 64.9%

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

   12. Taylor expanded in j around 0

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

   14. Applied rewrites 86.8%

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

   if -1.2e106 < x < -1.9e-27 or -1.49999999999999987e-181 < x < 8.7999999999999997e159

   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 c around 0

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

   5. Applied rewrites 74.6%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 66.9%

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

   if -1.9e-27 < x < -1.49999999999999987e-181

   1. Initial program 82.0%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 68.5%

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

   if 8.7999999999999997e159 < x

   1. Initial program 79.2%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 85.5%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \left(-b\right) \cdot \left(c \cdot z\right)\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-27}:\\ \;\;\;\;\mathsf{fma}\left(-i, j \cdot y, b \cdot \mathsf{fma}\left(-c, z, a \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-181}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+159}:\\ \;\;\;\;\mathsf{fma}\left(-i, j \cdot y, b \cdot \mathsf{fma}\left(-c, z, a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-i, j \cdot y, b \cdot \mathsf{fma}\left(-c, z, a \cdot i\right)\right)\\ t_2 := \mathsf{fma}\left(-a, t, z \cdot y\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(t\_2, x, \left(-b\right) \cdot \left(c \cdot z\right)\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-181}:\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot z, c \cdot \mathsf{fma}\left(-b, z, j \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (fma (- i) (* j y) (* b (fma (- c) z (* a i)))))
        (t_2 (fma (- a) t (* z y))))
   (if (<= x -1.2e+106)
     (fma t_2 x (* (- b) (* c z)))
     (if (<= x -2.3e-27)
       t_1
       (if (<= x -5.8e-181)
         (fma x (* y z) (* c (fma (- b) z (* j t))))
         (if (<= x 8.8e+159) t_1 (* t_2 x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-i, (j * y), (b * fma(-c, z, (a * i))));
	double t_2 = fma(-a, t, (z * y));
	double tmp;
	if (x <= -1.2e+106) {
		tmp = fma(t_2, x, (-b * (c * z)));
	} else if (x <= -2.3e-27) {
		tmp = t_1;
	} else if (x <= -5.8e-181) {
		tmp = fma(x, (y * z), (c * fma(-b, z, (j * t))));
	} else if (x <= 8.8e+159) {
		tmp = t_1;
	} else {
		tmp = t_2 * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = fma(Float64(-i), Float64(j * y), Float64(b * fma(Float64(-c), z, Float64(a * i))))
	t_2 = fma(Float64(-a), t, Float64(z * y))
	tmp = 0.0
	if (x <= -1.2e+106)
		tmp = fma(t_2, x, Float64(Float64(-b) * Float64(c * z)));
	elseif (x <= -2.3e-27)
		tmp = t_1;
	elseif (x <= -5.8e-181)
		tmp = fma(x, Float64(y * z), Float64(c * fma(Float64(-b), z, Float64(j * t))));
	elseif (x <= 8.8e+159)
		tmp = t_1;
	else
		tmp = Float64(t_2 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-i) * N[(j * y), $MachinePrecision] + N[(b * N[((-c) * z + N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e+106], N[(t$95$2 * x + N[((-b) * N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.3e-27], t$95$1, If[LessEqual[x, -5.8e-181], N[(x * N[(y * z), $MachinePrecision] + N[(c * N[((-b) * z + N[(j * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.8e+159], t$95$1, N[(t$95$2 * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.2e106

   1. Initial program 81.7%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 81.7%

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

   6. Taylor expanded in i around 0

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

   8. Applied rewrites 84.6%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 64.9%

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

   12. Taylor expanded in j around 0

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

   14. Applied rewrites 86.8%

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

   if -1.2e106 < x < -2.2999999999999999e-27 or -5.7999999999999996e-181 < x < 8.7999999999999997e159

   1. Initial program 76.4%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 74.4%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 66.6%

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

   if -2.2999999999999999e-27 < x < -5.7999999999999996e-181

   1. Initial program 82.6%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 70.5%

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

   6. Taylor expanded in i around 0

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

   8. Applied rewrites 67.9%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 63.4%

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

   if 8.7999999999999997e159 < x

   1. Initial program 79.2%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 85.5%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \left(-b\right) \cdot \left(c \cdot z\right)\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-27}:\\ \;\;\;\;\mathsf{fma}\left(-i, j \cdot y, b \cdot \mathsf{fma}\left(-c, z, a \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-181}:\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot z, c \cdot \mathsf{fma}\left(-b, z, j \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+159}:\\ \;\;\;\;\mathsf{fma}\left(-i, j \cdot y, b \cdot \mathsf{fma}\left(-c, z, a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ t_2 := \mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{+90}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -0.54:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-181}:\\ \;\;\;\;\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-229}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma i a (* (- c) z)) b)) (t_2 (* (fma (- a) t (* z y)) x)))
   (if (<= x -1.55e+90)
     t_2
     (if (<= x -0.54)
       t_1
       (if (<= x -5.5e-181)
         (* (fma (- a) x (* j c)) t)
         (if (<= x -1.35e-229)
           t_1
           (if (<= x 3.1e-25)
             (* (fma (- i) y (* c t)) j)
             (if (<= x 8e+63) 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(i, a, (-c * z)) * b;
	double t_2 = fma(-a, t, (z * y)) * x;
	double tmp;
	if (x <= -1.55e+90) {
		tmp = t_2;
	} else if (x <= -0.54) {
		tmp = t_1;
	} else if (x <= -5.5e-181) {
		tmp = fma(-a, x, (j * c)) * t;
	} else if (x <= -1.35e-229) {
		tmp = t_1;
	} else if (x <= 3.1e-25) {
		tmp = fma(-i, y, (c * t)) * j;
	} else if (x <= 8e+63) {
		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(i, a, Float64(Float64(-c) * z)) * b)
	t_2 = Float64(fma(Float64(-a), t, Float64(z * y)) * x)
	tmp = 0.0
	if (x <= -1.55e+90)
		tmp = t_2;
	elseif (x <= -0.54)
		tmp = t_1;
	elseif (x <= -5.5e-181)
		tmp = Float64(fma(Float64(-a), x, Float64(j * c)) * t);
	elseif (x <= -1.35e-229)
		tmp = t_1;
	elseif (x <= 3.1e-25)
		tmp = Float64(fma(Float64(-i), y, Float64(c * t)) * j);
	elseif (x <= 8e+63)
		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[(i * a + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.55e+90], t$95$2, If[LessEqual[x, -0.54], t$95$1, If[LessEqual[x, -5.5e-181], N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[x, -1.35e-229], t$95$1, If[LessEqual[x, 3.1e-25], N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[x, 8e+63], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.54999999999999994e90 or 8.00000000000000046e63 < x

   1. Initial program 80.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. 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 75.0%

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

   if -1.54999999999999994e90 < x < -0.54000000000000004 or -5.50000000000000033e-181 < x < -1.3499999999999999e-229 or 3.09999999999999995e-25 < x < 8.00000000000000046e63

   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 74.8%

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

   if -0.54000000000000004 < x < -5.50000000000000033e-181

   1. Initial program 76.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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 56.3%

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

   if -1.3499999999999999e-229 < x < 3.09999999999999995e-25

   1. Initial program 79.2%

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

   3. Taylor expanded in j around inf

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

   5. Applied rewrites 59.0%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+90}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq -0.54:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-181}:\\ \;\;\;\;\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-229}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -6 \cdot 10^{+70} \lor \neg \left(i \leq 2.15 \cdot 10^{+169}\right):\\ \;\;\;\;\mathsf{fma}\left(-i, j \cdot y, b \cdot \mathsf{fma}\left(-c, z, a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-a, t, y \cdot z\right), c \cdot \mathsf{fma}\left(-b, z, j \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -6e+70) (not (<= i 2.15e+169)))
   (fma (- i) (* j y) (* b (fma (- c) z (* a i))))
   (fma x (fma (- a) t (* y z)) (* c (fma (- b) z (* j t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -6e+70) || !(i <= 2.15e+169)) {
		tmp = fma(-i, (j * y), (b * fma(-c, z, (a * i))));
	} else {
		tmp = fma(x, fma(-a, t, (y * z)), (c * fma(-b, z, (j * t))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -6e+70) || !(i <= 2.15e+169))
		tmp = fma(Float64(-i), Float64(j * y), Float64(b * fma(Float64(-c), z, Float64(a * i))));
	else
		tmp = fma(x, fma(Float64(-a), t, Float64(y * z)), Float64(c * fma(Float64(-b), z, Float64(j * t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -6e+70], N[Not[LessEqual[i, 2.15e+169]], $MachinePrecision]], N[((-i) * N[(j * y), $MachinePrecision] + N[(b * N[((-c) * z + N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[((-a) * t + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(c * N[((-b) * z + N[(j * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -5.99999999999999952e70 or 2.1500000000000001e169 < i

   1. Initial program 64.8%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 70.0%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 82.8%

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

   if -5.99999999999999952e70 < i < 2.1500000000000001e169

   1. Initial program 83.8%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 80.7%

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

   6. Taylor expanded in i around 0

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

   8. Applied rewrites 73.8%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6 \cdot 10^{+70} \lor \neg \left(i \leq 2.15 \cdot 10^{+169}\right):\\ \;\;\;\;\mathsf{fma}\left(-i, j \cdot y, b \cdot \mathsf{fma}\left(-c, z, a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-a, t, y \cdot z\right), c \cdot \mathsf{fma}\left(-b, z, j \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ t_2 := \mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{+90}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -0.54:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-62}:\\ \;\;\;\;\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{elif}\;x \leq -1.36 \cdot 10^{-294}:\\ \;\;\;\;\mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma i a (* (- c) z)) b)) (t_2 (* (fma (- a) t (* z y)) x)))
   (if (<= x -1.55e+90)
     t_2
     (if (<= x -0.54)
       t_1
       (if (<= x -2.9e-62)
         (* (fma (- a) x (* j c)) t)
         (if (<= x -1.36e-294)
           (* (fma j t (* (- b) z)) c)
           (if (<= x 8e+63) 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(i, a, (-c * z)) * b;
	double t_2 = fma(-a, t, (z * y)) * x;
	double tmp;
	if (x <= -1.55e+90) {
		tmp = t_2;
	} else if (x <= -0.54) {
		tmp = t_1;
	} else if (x <= -2.9e-62) {
		tmp = fma(-a, x, (j * c)) * t;
	} else if (x <= -1.36e-294) {
		tmp = fma(j, t, (-b * z)) * c;
	} else if (x <= 8e+63) {
		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(i, a, Float64(Float64(-c) * z)) * b)
	t_2 = Float64(fma(Float64(-a), t, Float64(z * y)) * x)
	tmp = 0.0
	if (x <= -1.55e+90)
		tmp = t_2;
	elseif (x <= -0.54)
		tmp = t_1;
	elseif (x <= -2.9e-62)
		tmp = Float64(fma(Float64(-a), x, Float64(j * c)) * t);
	elseif (x <= -1.36e-294)
		tmp = Float64(fma(j, t, Float64(Float64(-b) * z)) * c);
	elseif (x <= 8e+63)
		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[(i * a + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.55e+90], t$95$2, If[LessEqual[x, -0.54], t$95$1, If[LessEqual[x, -2.9e-62], N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[x, -1.36e-294], N[(N[(j * t + N[((-b) * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[x, 8e+63], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.54999999999999994e90 or 8.00000000000000046e63 < x

   1. Initial program 80.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. 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 75.0%

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

   if -1.54999999999999994e90 < x < -0.54000000000000004 or -1.36000000000000003e-294 < x < 8.00000000000000046e63

   1. Initial program 76.2%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 50.6%

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

   if -0.54000000000000004 < x < -2.89999999999999986e-62

   1. Initial program 62.4%

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

   3. Taylor expanded in 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 56.4%

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

   if -2.89999999999999986e-62 < x < -1.36000000000000003e-294

   1. Initial program 84.8%

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

   3. Taylor expanded in c around inf

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

   5. Applied rewrites 64.2%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+90}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq -0.54:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-62}:\\ \;\;\;\;\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{elif}\;x \leq -1.36 \cdot 10^{-294}:\\ \;\;\;\;\mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 40.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{if}\;x \leq -1.22 \cdot 10^{+247}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{+97}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-182}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma i a (* (- c) z)) b)))
   (if (<= x -1.22e+247)
     (* (- a) (* t x))
     (if (<= x -4.8e+97)
       (* (* y x) z)
       (if (<= x -3.9e-54)
         t_1
         (if (<= x -5.8e-182)
           (* (* j t) c)
           (if (<= x 4.9e+160) t_1 (* (* x z) y))))))))

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(i, a, (-c * z)) * b;
	double tmp;
	if (x <= -1.22e+247) {
		tmp = -a * (t * x);
	} else if (x <= -4.8e+97) {
		tmp = (y * x) * z;
	} else if (x <= -3.9e-54) {
		tmp = t_1;
	} else if (x <= -5.8e-182) {
		tmp = (j * t) * c;
	} else if (x <= 4.9e+160) {
		tmp = t_1;
	} else {
		tmp = (x * z) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(i, a, Float64(Float64(-c) * z)) * b)
	tmp = 0.0
	if (x <= -1.22e+247)
		tmp = Float64(Float64(-a) * Float64(t * x));
	elseif (x <= -4.8e+97)
		tmp = Float64(Float64(y * x) * z);
	elseif (x <= -3.9e-54)
		tmp = t_1;
	elseif (x <= -5.8e-182)
		tmp = Float64(Float64(j * t) * c);
	elseif (x <= 4.9e+160)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * z) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * a + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[x, -1.22e+247], N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.8e+97], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[x, -3.9e-54], t$95$1, If[LessEqual[x, -5.8e-182], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[x, 4.9e+160], t$95$1, N[(N[(x * z), $MachinePrecision] * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.22000000000000006e247

   1. Initial program 68.6%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 81.3%

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

   6. Taylor expanded in i around 0

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

   8. Applied rewrites 93.8%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 69.2%

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

   12. Taylor expanded in a around inf

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

   14. Applied rewrites 68.9%

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

   if -1.22000000000000006e247 < x < -4.8e97

   1. Initial program 89.9%

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

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 64.6%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 52.5%

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

   10. Applied rewrites 58.8%

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

   if -4.8e97 < x < -3.9e-54 or -5.79999999999999974e-182 < x < 4.9000000000000002e160

   1. Initial program 75.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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 46.5%

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

   if -3.9e-54 < x < -5.79999999999999974e-182

   1. Initial program 88.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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 61.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 49.6%

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

   if 4.9000000000000002e160 < x

   1. Initial program 79.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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 59.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 59.5%

      \[\leadsto \left(x \cdot z\right) \cdot y \]
3. Recombined 5 regimes into one program.

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+247}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{+97}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-54}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-182}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{+160}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 53.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{if}\;x \leq -6.6 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-36}:\\ \;\;\;\;\left(-i\right) \cdot \mathsf{fma}\left(j, y, \left(-a\right) \cdot b\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- a) t (* z y)) x)))
   (if (<= x -6.6e+84)
     t_1
     (if (<= x -1.75e-36)
       (* (- i) (fma j y (* (- a) b)))
       (if (<= x 3.1e-25)
         (* (fma (- i) y (* c t)) j)
         (if (<= x 8e+63) (* (fma i a (* (- c) z)) 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, t, (z * y)) * x;
	double tmp;
	if (x <= -6.6e+84) {
		tmp = t_1;
	} else if (x <= -1.75e-36) {
		tmp = -i * fma(j, y, (-a * b));
	} else if (x <= 3.1e-25) {
		tmp = fma(-i, y, (c * t)) * j;
	} else if (x <= 8e+63) {
		tmp = fma(i, a, (-c * z)) * 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), t, Float64(z * y)) * x)
	tmp = 0.0
	if (x <= -6.6e+84)
		tmp = t_1;
	elseif (x <= -1.75e-36)
		tmp = Float64(Float64(-i) * fma(j, y, Float64(Float64(-a) * b)));
	elseif (x <= 3.1e-25)
		tmp = Float64(fma(Float64(-i), y, Float64(c * t)) * j);
	elseif (x <= 8e+63)
		tmp = Float64(fma(i, a, Float64(Float64(-c) * z)) * 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) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -6.6e+84], t$95$1, If[LessEqual[x, -1.75e-36], N[((-i) * N[(j * y + N[((-a) * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.1e-25], N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[x, 8e+63], N[(N[(i * a + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.60000000000000034e84 or 8.00000000000000046e63 < x

   1. Initial program 78.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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 74.5%

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

   if -6.60000000000000034e84 < x < -1.75e-36

   1. Initial program 54.6%

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

   3. Taylor expanded in i around -inf

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

   5. Applied rewrites 57.6%

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

   if -1.75e-36 < x < 3.09999999999999995e-25

   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 j around inf

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

   5. Applied rewrites 57.0%

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

   if 3.09999999999999995e-25 < x < 8.00000000000000046e63

   1. Initial program 99.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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 75.5%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+84}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-36}:\\ \;\;\;\;\left(-i\right) \cdot \mathsf{fma}\left(j, y, \left(-a\right) \cdot b\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 53.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{if}\;x \leq -6.6 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-37}:\\ \;\;\;\;\left(-a\right) \cdot \mathsf{fma}\left(t, x, \left(-b\right) \cdot i\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- a) t (* z y)) x)))
   (if (<= x -6.6e+84)
     t_1
     (if (<= x -2e-37)
       (* (- a) (fma t x (* (- b) i)))
       (if (<= x 3.1e-25)
         (* (fma (- i) y (* c t)) j)
         (if (<= x 8e+63) (* (fma i a (* (- c) z)) 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, t, (z * y)) * x;
	double tmp;
	if (x <= -6.6e+84) {
		tmp = t_1;
	} else if (x <= -2e-37) {
		tmp = -a * fma(t, x, (-b * i));
	} else if (x <= 3.1e-25) {
		tmp = fma(-i, y, (c * t)) * j;
	} else if (x <= 8e+63) {
		tmp = fma(i, a, (-c * z)) * 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), t, Float64(z * y)) * x)
	tmp = 0.0
	if (x <= -6.6e+84)
		tmp = t_1;
	elseif (x <= -2e-37)
		tmp = Float64(Float64(-a) * fma(t, x, Float64(Float64(-b) * i)));
	elseif (x <= 3.1e-25)
		tmp = Float64(fma(Float64(-i), y, Float64(c * t)) * j);
	elseif (x <= 8e+63)
		tmp = Float64(fma(i, a, Float64(Float64(-c) * z)) * 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) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -6.6e+84], t$95$1, If[LessEqual[x, -2e-37], N[((-a) * N[(t * x + N[((-b) * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.1e-25], N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[x, 8e+63], N[(N[(i * a + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.60000000000000034e84 or 8.00000000000000046e63 < x

   1. Initial program 78.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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 74.5%

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

   if -6.60000000000000034e84 < x < -2.00000000000000013e-37

   1. Initial program 54.6%

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

   3. Taylor expanded in a around -inf

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

   5. Applied rewrites 55.4%

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

   if -2.00000000000000013e-37 < x < 3.09999999999999995e-25

   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 j around inf

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

   5. Applied rewrites 57.0%

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

   if 3.09999999999999995e-25 < x < 8.00000000000000046e63

   1. Initial program 99.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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 75.5%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+84}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-37}:\\ \;\;\;\;\left(-a\right) \cdot \mathsf{fma}\left(t, x, \left(-b\right) \cdot i\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ t_2 := \mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{+90}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.36 \cdot 10^{-294}:\\ \;\;\;\;\mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma i a (* (- c) z)) b)) (t_2 (* (fma (- a) t (* z y)) x)))
   (if (<= x -1.55e+90)
     t_2
     (if (<= x -8e-52)
       t_1
       (if (<= x -1.36e-294)
         (* (fma j t (* (- b) z)) c)
         (if (<= x 8e+63) 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(i, a, (-c * z)) * b;
	double t_2 = fma(-a, t, (z * y)) * x;
	double tmp;
	if (x <= -1.55e+90) {
		tmp = t_2;
	} else if (x <= -8e-52) {
		tmp = t_1;
	} else if (x <= -1.36e-294) {
		tmp = fma(j, t, (-b * z)) * c;
	} else if (x <= 8e+63) {
		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(i, a, Float64(Float64(-c) * z)) * b)
	t_2 = Float64(fma(Float64(-a), t, Float64(z * y)) * x)
	tmp = 0.0
	if (x <= -1.55e+90)
		tmp = t_2;
	elseif (x <= -8e-52)
		tmp = t_1;
	elseif (x <= -1.36e-294)
		tmp = Float64(fma(j, t, Float64(Float64(-b) * z)) * c);
	elseif (x <= 8e+63)
		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[(i * a + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.55e+90], t$95$2, If[LessEqual[x, -8e-52], t$95$1, If[LessEqual[x, -1.36e-294], N[(N[(j * t + N[((-b) * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[x, 8e+63], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.54999999999999994e90 or 8.00000000000000046e63 < x

   1. Initial program 80.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. 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 75.0%

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

   if -1.54999999999999994e90 < x < -8.0000000000000001e-52 or -1.36000000000000003e-294 < x < 8.00000000000000046e63

   1. Initial program 73.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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 47.2%

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

   if -8.0000000000000001e-52 < x < -1.36000000000000003e-294

   1. Initial program 85.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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 63.7%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+90}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-52}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{elif}\;x \leq -1.36 \cdot 10^{-294}:\\ \;\;\;\;\mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 61.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+70}:\\ \;\;\;\;\left(-a\right) \cdot \mathsf{fma}\left(t, x, \left(-b\right) \cdot i\right)\\ \mathbf{elif}\;a \leq 1.86 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot z, c \cdot \mathsf{fma}\left(-b, z, j \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x - b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -3.2e+70)
   (* (- a) (fma t x (* (- b) i)))
   (if (<= a 1.86e+80)
     (fma x (* y z) (* c (fma (- b) z (* j t))))
     (* (- a) (- (* t x) (* b i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -3.2e+70) {
		tmp = -a * fma(t, x, (-b * i));
	} else if (a <= 1.86e+80) {
		tmp = fma(x, (y * z), (c * fma(-b, z, (j * t))));
	} else {
		tmp = -a * ((t * x) - (b * i));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -3.2e+70)
		tmp = Float64(Float64(-a) * fma(t, x, Float64(Float64(-b) * i)));
	elseif (a <= 1.86e+80)
		tmp = fma(x, Float64(y * z), Float64(c * fma(Float64(-b), z, Float64(j * t))));
	else
		tmp = Float64(Float64(-a) * Float64(Float64(t * x) - Float64(b * i)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -3.2e+70], N[((-a) * N[(t * x + N[((-b) * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.86e+80], N[(x * N[(y * z), $MachinePrecision] + N[(c * N[((-b) * z + N[(j * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-a) * N[(N[(t * x), $MachinePrecision] - N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.2000000000000002e70

   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 a around -inf

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

   5. Applied rewrites 76.5%

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

   if -3.2000000000000002e70 < a < 1.8599999999999999e80

   1. Initial program 83.2%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 79.1%

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

   6. Taylor expanded in i around 0

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

   8. Applied rewrites 70.6%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 65.0%

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

   if 1.8599999999999999e80 < a

   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 c around 0

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

   5. Applied rewrites 71.8%

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

   6. Taylor expanded in j around -inf

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

   8. Applied rewrites 74.2%

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

   9. Taylor expanded in a around -inf

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

   11. Applied rewrites 66.7%

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+70}:\\ \;\;\;\;\left(-a\right) \cdot \mathsf{fma}\left(t, x, \left(-b\right) \cdot i\right)\\ \mathbf{elif}\;a \leq 1.86 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot z, c \cdot \mathsf{fma}\left(-b, z, j \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x - b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 45.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.36 \cdot 10^{-294}:\\ \;\;\;\;\mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{+45}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma y x (* (- b) c)) z)))
   (if (<= x -7.5e+45)
     t_1
     (if (<= x -1.36e-294)
       (* (fma j t (* (- b) z)) c)
       (if (<= x 5.1e+45) (* (fma i a (* (- c) z)) 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(y, x, (-b * c)) * z;
	double tmp;
	if (x <= -7.5e+45) {
		tmp = t_1;
	} else if (x <= -1.36e-294) {
		tmp = fma(j, t, (-b * z)) * c;
	} else if (x <= 5.1e+45) {
		tmp = fma(i, a, (-c * z)) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(y, x, Float64(Float64(-b) * c)) * z)
	tmp = 0.0
	if (x <= -7.5e+45)
		tmp = t_1;
	elseif (x <= -1.36e-294)
		tmp = Float64(fma(j, t, Float64(Float64(-b) * z)) * c);
	elseif (x <= 5.1e+45)
		tmp = Float64(fma(i, a, Float64(Float64(-c) * z)) * 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[(y * x + N[((-b) * c), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[x, -7.5e+45], t$95$1, If[LessEqual[x, -1.36e-294], N[(N[(j * t + N[((-b) * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[x, 5.1e+45], N[(N[(i * a + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.50000000000000058e45 or 5.0999999999999997e45 < x

   1. Initial program 78.9%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 59.2%

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

   if -7.50000000000000058e45 < x < -1.36000000000000003e-294

   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 c around inf

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

   5. Applied rewrites 51.3%

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

   if -1.36000000000000003e-294 < x < 5.0999999999999997e45

   1. Initial program 82.0%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 47.0%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+45}:\\ \;\;\;\;\mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z\\ \mathbf{elif}\;x \leq -1.36 \cdot 10^{-294}:\\ \;\;\;\;\mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{+45}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 43.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{if}\;c \leq -1.06 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{-206}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{+130}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma j t (* (- b) z)) c)))
   (if (<= c -1.06e-169)
     t_1
     (if (<= c 3.4e-206)
       (* (* x z) y)
       (if (<= c 4.6e+130) (* (fma i a (* (- c) z)) 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(j, t, (-b * z)) * c;
	double tmp;
	if (c <= -1.06e-169) {
		tmp = t_1;
	} else if (c <= 3.4e-206) {
		tmp = (x * z) * y;
	} else if (c <= 4.6e+130) {
		tmp = fma(i, a, (-c * z)) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(j, t, Float64(Float64(-b) * z)) * c)
	tmp = 0.0
	if (c <= -1.06e-169)
		tmp = t_1;
	elseif (c <= 3.4e-206)
		tmp = Float64(Float64(x * z) * y);
	elseif (c <= 4.6e+130)
		tmp = Float64(fma(i, a, Float64(Float64(-c) * z)) * 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[(j * t + N[((-b) * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]}, If[LessEqual[c, -1.06e-169], t$95$1, If[LessEqual[c, 3.4e-206], N[(N[(x * z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[c, 4.6e+130], N[(N[(i * a + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.06e-169 or 4.60000000000000042e130 < c

   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 c around inf

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

   5. Applied rewrites 55.1%

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

   if -1.06e-169 < c < 3.39999999999999985e-206

   1. Initial program 90.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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 57.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 41.7%

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

   if 3.39999999999999985e-206 < c < 4.60000000000000042e130

   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 b around inf

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

   5. Applied rewrites 48.7%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.06 \cdot 10^{-169}:\\ \;\;\;\;\mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{-206}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{+130}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+247}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{+84}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-36}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+14}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -1.22e+247)
   (* (- a) (* t x))
   (if (<= x -6.6e+84)
     (* (* y x) z)
     (if (<= x -1.75e-36)
       (* a (* b i))
       (if (<= x 5.2e+14) (* (* j t) c) (* (* x z) 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 (x <= -1.22e+247) {
		tmp = -a * (t * x);
	} else if (x <= -6.6e+84) {
		tmp = (y * x) * z;
	} else if (x <= -1.75e-36) {
		tmp = a * (b * i);
	} else if (x <= 5.2e+14) {
		tmp = (j * t) * c;
	} else {
		tmp = (x * z) * y;
	}
	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 <= (-1.22d+247)) then
        tmp = -a * (t * x)
    else if (x <= (-6.6d+84)) then
        tmp = (y * x) * z
    else if (x <= (-1.75d-36)) then
        tmp = a * (b * i)
    else if (x <= 5.2d+14) then
        tmp = (j * t) * c
    else
        tmp = (x * z) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -1.22e+247) {
		tmp = -a * (t * x);
	} else if (x <= -6.6e+84) {
		tmp = (y * x) * z;
	} else if (x <= -1.75e-36) {
		tmp = a * (b * i);
	} else if (x <= 5.2e+14) {
		tmp = (j * t) * c;
	} else {
		tmp = (x * z) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -1.22e+247:
		tmp = -a * (t * x)
	elif x <= -6.6e+84:
		tmp = (y * x) * z
	elif x <= -1.75e-36:
		tmp = a * (b * i)
	elif x <= 5.2e+14:
		tmp = (j * t) * c
	else:
		tmp = (x * z) * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -1.22e+247)
		tmp = Float64(Float64(-a) * Float64(t * x));
	elseif (x <= -6.6e+84)
		tmp = Float64(Float64(y * x) * z);
	elseif (x <= -1.75e-36)
		tmp = Float64(a * Float64(b * i));
	elseif (x <= 5.2e+14)
		tmp = Float64(Float64(j * t) * c);
	else
		tmp = Float64(Float64(x * z) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -1.22e+247)
		tmp = -a * (t * x);
	elseif (x <= -6.6e+84)
		tmp = (y * x) * z;
	elseif (x <= -1.75e-36)
		tmp = a * (b * i);
	elseif (x <= 5.2e+14)
		tmp = (j * t) * c;
	else
		tmp = (x * z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -1.22e+247], N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.6e+84], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[x, -1.75e-36], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.2e+14], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], N[(N[(x * z), $MachinePrecision] * y), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.22000000000000006e247

   1. Initial program 68.6%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 81.3%

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

   6. Taylor expanded in i around 0

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

   8. Applied rewrites 93.8%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 69.2%

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

   12. Taylor expanded in a around inf

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

   14. Applied rewrites 68.9%

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

   if -1.22000000000000006e247 < x < -6.60000000000000034e84

   1. Initial program 81.9%

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

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 58.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 50.9%

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

   10. Applied rewrites 56.7%

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

   if -6.60000000000000034e84 < x < -1.75e-36

   1. Initial program 54.6%

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

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 57.8%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 38.3%

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

   if -1.75e-36 < x < 5.2e14

   1. Initial program 81.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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 50.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 36.9%

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

   if 5.2e14 < x

   1. Initial program 83.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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 51.2%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 44.6%

      \[\leadsto \left(x \cdot z\right) \cdot y \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+247}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{+84}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-36}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+14}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 31.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot z\right) \cdot y\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-36}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+14}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* x z) y)))
   (if (<= x -6.5e+84)
     t_1
     (if (<= x -1.75e-36)
       (* a (* b i))
       (if (<= x 5.2e+14) (* (* j t) c) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * z) * y;
	double tmp;
	if (x <= -6.5e+84) {
		tmp = t_1;
	} else if (x <= -1.75e-36) {
		tmp = a * (b * i);
	} else if (x <= 5.2e+14) {
		tmp = (j * t) * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * z) * y
    if (x <= (-6.5d+84)) then
        tmp = t_1
    else if (x <= (-1.75d-36)) then
        tmp = a * (b * i)
    else if (x <= 5.2d+14) then
        tmp = (j * t) * c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * z) * y;
	double tmp;
	if (x <= -6.5e+84) {
		tmp = t_1;
	} else if (x <= -1.75e-36) {
		tmp = a * (b * i);
	} else if (x <= 5.2e+14) {
		tmp = (j * t) * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * z) * y
	tmp = 0
	if x <= -6.5e+84:
		tmp = t_1
	elif x <= -1.75e-36:
		tmp = a * (b * i)
	elif x <= 5.2e+14:
		tmp = (j * t) * c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * z) * y)
	tmp = 0.0
	if (x <= -6.5e+84)
		tmp = t_1;
	elseif (x <= -1.75e-36)
		tmp = Float64(a * Float64(b * i));
	elseif (x <= 5.2e+14)
		tmp = Float64(Float64(j * t) * c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * z) * y;
	tmp = 0.0;
	if (x <= -6.5e+84)
		tmp = t_1;
	elseif (x <= -1.75e-36)
		tmp = a * (b * i);
	elseif (x <= 5.2e+14)
		tmp = (j * t) * c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[x, -6.5e+84], t$95$1, If[LessEqual[x, -1.75e-36], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.2e+14], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.50000000000000027e84 or 5.2e14 < x

   1. Initial program 80.7%

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

   3. Taylor expanded in 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 52.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 46.6%

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

   if -6.50000000000000027e84 < x < -1.75e-36

   1. Initial program 54.6%

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

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 57.8%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 38.3%

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

   if -1.75e-36 < x < 5.2e14

   1. Initial program 81.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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 50.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 36.9%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+84}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-36}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+14}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+84}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-36}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+14}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -6.6e+84)
   (* (* y x) z)
   (if (<= x -1.75e-36)
     (* a (* b i))
     (if (<= x 5.2e+14) (* (* j t) c) (* x (* y 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 <= -6.6e+84) {
		tmp = (y * x) * z;
	} else if (x <= -1.75e-36) {
		tmp = a * (b * i);
	} else if (x <= 5.2e+14) {
		tmp = (j * t) * c;
	} else {
		tmp = x * (y * 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 <= (-6.6d+84)) then
        tmp = (y * x) * z
    else if (x <= (-1.75d-36)) then
        tmp = a * (b * i)
    else if (x <= 5.2d+14) then
        tmp = (j * t) * c
    else
        tmp = x * (y * 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 <= -6.6e+84) {
		tmp = (y * x) * z;
	} else if (x <= -1.75e-36) {
		tmp = a * (b * i);
	} else if (x <= 5.2e+14) {
		tmp = (j * t) * c;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -6.6e+84:
		tmp = (y * x) * z
	elif x <= -1.75e-36:
		tmp = a * (b * i)
	elif x <= 5.2e+14:
		tmp = (j * t) * c
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -6.6e+84)
		tmp = Float64(Float64(y * x) * z);
	elseif (x <= -1.75e-36)
		tmp = Float64(a * Float64(b * i));
	elseif (x <= 5.2e+14)
		tmp = Float64(Float64(j * t) * c);
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -6.6e+84)
		tmp = (y * x) * z;
	elseif (x <= -1.75e-36)
		tmp = a * (b * i);
	elseif (x <= 5.2e+14)
		tmp = (j * t) * c;
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -6.6e+84], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[x, -1.75e-36], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.2e+14], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.60000000000000034e84

   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 t around 0

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

   5. Applied rewrites 58.6%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 43.1%

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

   10. Applied rewrites 46.9%

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

   if -6.60000000000000034e84 < x < -1.75e-36

   1. Initial program 54.6%

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

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 57.8%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 38.3%

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

   if -1.75e-36 < x < 5.2e14

   1. Initial program 81.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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 50.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 36.9%

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

   if 5.2e14 < x

   1. Initial program 83.2%

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

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 62.3%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 43.0%

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

4. Final simplification 40.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+84}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-36}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+14}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 30.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+70} \lor \neg \left(a \leq 1.1 \cdot 10^{-23}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -1.7e+70) (not (<= a 1.1e-23))) (* a (* b i)) (* x (* y 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 ((a <= -1.7e+70) || !(a <= 1.1e-23)) {
		tmp = a * (b * i);
	} else {
		tmp = x * (y * 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 ((a <= (-1.7d+70)) .or. (.not. (a <= 1.1d-23))) then
        tmp = a * (b * i)
    else
        tmp = x * (y * 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 ((a <= -1.7e+70) || !(a <= 1.1e-23)) {
		tmp = a * (b * i);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -1.7e+70) or not (a <= 1.1e-23):
		tmp = a * (b * i)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -1.7e+70) || !(a <= 1.1e-23))
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -1.7e+70) || ~((a <= 1.1e-23)))
		tmp = a * (b * i);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -1.7e+70], N[Not[LessEqual[a, 1.1e-23]], $MachinePrecision]], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.7e70 or 1.1e-23 < a

   1. Initial program 72.2%

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

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 56.3%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 39.9%

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

   if -1.7e70 < a < 1.1e-23

   1. Initial program 83.3%

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

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 60.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 30.0%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+70} \lor \neg \left(a \leq 1.1 \cdot 10^{-23}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 29.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+84}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+63}:\\ \;\;\;\;\left(a \cdot i\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -6.6e+84)
   (* (* y x) z)
   (if (<= x 8e+63) (* (* a i) b) (* x (* y 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 <= -6.6e+84) {
		tmp = (y * x) * z;
	} else if (x <= 8e+63) {
		tmp = (a * i) * b;
	} else {
		tmp = x * (y * 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 <= (-6.6d+84)) then
        tmp = (y * x) * z
    else if (x <= 8d+63) then
        tmp = (a * i) * b
    else
        tmp = x * (y * 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 <= -6.6e+84) {
		tmp = (y * x) * z;
	} else if (x <= 8e+63) {
		tmp = (a * i) * b;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -6.6e+84:
		tmp = (y * x) * z
	elif x <= 8e+63:
		tmp = (a * i) * b
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -6.6e+84)
		tmp = Float64(Float64(y * x) * z);
	elseif (x <= 8e+63)
		tmp = Float64(Float64(a * i) * b);
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -6.6e+84)
		tmp = (y * x) * z;
	elseif (x <= 8e+63)
		tmp = (a * i) * b;
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -6.6e+84], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[x, 8e+63], N[(N[(a * i), $MachinePrecision] * b), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.60000000000000034e84

   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 t around 0

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

   5. Applied rewrites 58.6%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 43.1%

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

   10. Applied rewrites 46.9%

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

   if -6.60000000000000034e84 < x < 8.00000000000000046e63

   1. Initial program 78.0%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 43.1%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 28.0%

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

   if 8.00000000000000046e63 < x

   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 t around 0

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

   5. Applied rewrites 59.5%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 46.4%

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

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+84}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+63}:\\ \;\;\;\;\left(a \cdot i\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+84}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+63}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -6.6e+84)
   (* (* y x) z)
   (if (<= x 8e+63) (* a (* b i)) (* x (* y 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 <= -6.6e+84) {
		tmp = (y * x) * z;
	} else if (x <= 8e+63) {
		tmp = a * (b * i);
	} else {
		tmp = x * (y * 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 <= (-6.6d+84)) then
        tmp = (y * x) * z
    else if (x <= 8d+63) then
        tmp = a * (b * i)
    else
        tmp = x * (y * 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 <= -6.6e+84) {
		tmp = (y * x) * z;
	} else if (x <= 8e+63) {
		tmp = a * (b * i);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -6.6e+84:
		tmp = (y * x) * z
	elif x <= 8e+63:
		tmp = a * (b * i)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -6.6e+84)
		tmp = Float64(Float64(y * x) * z);
	elseif (x <= 8e+63)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -6.6e+84)
		tmp = (y * x) * z;
	elseif (x <= 8e+63)
		tmp = a * (b * i);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -6.6e+84], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[x, 8e+63], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.60000000000000034e84

   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 t around 0

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

   5. Applied rewrites 58.6%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 43.1%

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

   10. Applied rewrites 46.9%

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

   if -6.60000000000000034e84 < x < 8.00000000000000046e63

   1. Initial program 78.0%

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

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 58.6%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 27.4%

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

   if 8.00000000000000046e63 < x

   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 t around 0

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

   5. Applied rewrites 59.5%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 46.4%

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

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+84}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+63}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 22.2% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.4%

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

3. Taylor expanded in t around 0

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

5. Applied rewrites 58.8%

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

6. Taylor expanded in a around inf

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

8. Applied rewrites 22.1%

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

9. Final simplification 22.1%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
10. 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 2025026 
(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)))))