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

Percentage Accurate: 73.5% → 82.3%

Time: 7.4s

Alternatives: 13

Speedup: 0.5×

• 58.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.3% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i))))
          (* j (- (* c a) (* y i))))))
   (if (<= t_1 INFINITY) t_1 (* (- i) (fma j y (* (- b) 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 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = -i * fma(j, y, (-b * t));
	}
	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(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(-i) * fma(j, y, Float64(Float64(-b) * t)));
	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[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[((-i) * N[(j * y + N[((-b) * t), $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 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 93.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in i around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-neg.f64 62.0

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

   5. Applied rewrites 62.0%

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

Alternative 2: 52.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-i\right) \cdot \mathsf{fma}\left(j, y, \left(-b\right) \cdot t\right)\\ \mathbf{if}\;i \leq -6.8 \cdot 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -5.4 \cdot 10^{+50}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot a\right) \cdot j\\ \mathbf{elif}\;i \leq -8.2 \cdot 10^{-208}:\\ \;\;\;\;\mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z\\ \mathbf{elif}\;i \leq -1.9 \cdot 10^{-267}:\\ \;\;\;\;\mathsf{fma}\left(-t, x, j \cdot c\right) \cdot a\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- i) (fma j y (* (- b) t)))))
   (if (<= i -6.8e+140)
     t_1
     (if (<= i -5.4e+50)
       (* (fma (- i) y (* c a)) j)
       (if (<= i -8.2e-208)
         (* (fma y x (* (- b) c)) z)
         (if (<= i -1.9e-267)
           (* (fma (- t) x (* j c)) a)
           (if (<= i 3e-8) (* (fma (- a) t (* z y)) x) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -i * fma(j, y, (-b * t));
	double tmp;
	if (i <= -6.8e+140) {
		tmp = t_1;
	} else if (i <= -5.4e+50) {
		tmp = fma(-i, y, (c * a)) * j;
	} else if (i <= -8.2e-208) {
		tmp = fma(y, x, (-b * c)) * z;
	} else if (i <= -1.9e-267) {
		tmp = fma(-t, x, (j * c)) * a;
	} else if (i <= 3e-8) {
		tmp = fma(-a, t, (z * y)) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(-i) * fma(j, y, Float64(Float64(-b) * t)))
	tmp = 0.0
	if (i <= -6.8e+140)
		tmp = t_1;
	elseif (i <= -5.4e+50)
		tmp = Float64(fma(Float64(-i), y, Float64(c * a)) * j);
	elseif (i <= -8.2e-208)
		tmp = Float64(fma(y, x, Float64(Float64(-b) * c)) * z);
	elseif (i <= -1.9e-267)
		tmp = Float64(fma(Float64(-t), x, Float64(j * c)) * a);
	elseif (i <= 3e-8)
		tmp = Float64(fma(Float64(-a), t, Float64(z * y)) * x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-i) * N[(j * y + N[((-b) * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -6.8e+140], t$95$1, If[LessEqual[i, -5.4e+50], N[(N[((-i) * y + N[(c * a), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[i, -8.2e-208], N[(N[(y * x + N[((-b) * c), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[i, -1.9e-267], N[(N[((-t) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[i, 3e-8], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -6.8e140 or 2.99999999999999973e-8 < i

   1. Initial program 58.7%

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

   3. Taylor expanded in i around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-neg.f64 73.0

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

   5. Applied rewrites 73.0%

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

   if -6.8e140 < i < -5.4e50

   1. Initial program 86.7%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. +-commutative N/A

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

      11. associate-*r* N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 77.5

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

   5. Applied rewrites 77.5%

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

   if -5.4e50 < i < -8.1999999999999998e-208

   1. Initial program 85.1%

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-neg.f64 68.6

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

   5. Applied rewrites 68.6%

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

   if -8.1999999999999998e-208 < i < -1.90000000000000001e-267

   1. Initial program 86.5%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 79.3

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

   5. Applied rewrites 79.3%

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

   if -1.90000000000000001e-267 < i < 2.99999999999999973e-8

   1. Initial program 90.1%

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. +-commutative N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-neg.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 56.3

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

   5. Applied rewrites 56.3%

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

Alternative 3: 63.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -6.5 \cdot 10^{+170} \lor \neg \left(i \leq 5.9 \cdot 10^{-8}\right):\\ \;\;\;\;\left(-i\right) \cdot \mathsf{fma}\left(j, y, \left(-b\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot a\right), j, \mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -6.5e+170) (not (<= i 5.9e-8)))
   (* (- i) (fma j y (* (- b) t)))
   (fma (fma (- i) y (* c a)) j (* (fma (- a) t (* z y)) x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -6.5e+170) || !(i <= 5.9e-8)) {
		tmp = -i * fma(j, y, (-b * t));
	} else {
		tmp = fma(fma(-i, y, (c * a)), j, (fma(-a, t, (z * y)) * x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -6.5e+170) || !(i <= 5.9e-8))
		tmp = Float64(Float64(-i) * fma(j, y, Float64(Float64(-b) * t)));
	else
		tmp = fma(fma(Float64(-i), y, Float64(c * a)), j, Float64(fma(Float64(-a), t, Float64(z * y)) * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -6.5e+170], N[Not[LessEqual[i, 5.9e-8]], $MachinePrecision]], N[((-i) * N[(j * y + N[((-b) * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-i) * y + N[(c * a), $MachinePrecision]), $MachinePrecision] * j + N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -6.5e170 or 5.8999999999999999e-8 < i

   1. Initial program 58.5%

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

   3. Taylor expanded in i around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-neg.f64 73.7

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

   5. Applied rewrites 73.7%

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

   if -6.5e170 < i < 5.8999999999999999e-8

   1. Initial program 87.1%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. +-commutative N/A

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

      11. associate-*r* N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

   5. Applied rewrites 72.6%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6.5 \cdot 10^{+170} \lor \neg \left(i \leq 5.9 \cdot 10^{-8}\right):\\ \;\;\;\;\left(-i\right) \cdot \mathsf{fma}\left(j, y, \left(-b\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot a\right), j, \mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, t, \left(-c\right) \cdot z\right) \cdot b\\ t_2 := \mathsf{fma}\left(-i, y, c \cdot a\right) \cdot j\\ \mathbf{if}\;j \leq -1.4 \cdot 10^{+65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -9.2 \cdot 10^{-122}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{elif}\;j \leq -7.3 \cdot 10^{-298}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{-194}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{elif}\;j \leq 9 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma i t (* (- c) z)) b)) (t_2 (* (fma (- i) y (* c a)) j)))
   (if (<= j -1.4e+65)
     t_2
     (if (<= j -9.2e-122)
       (* (fma (- i) j (* z x)) y)
       (if (<= j -7.3e-298)
         t_1
         (if (<= j 1.2e-194)
           (* (fma (- a) t (* z y)) x)
           (if (<= j 9e+27) 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, t, (-c * z)) * b;
	double t_2 = fma(-i, y, (c * a)) * j;
	double tmp;
	if (j <= -1.4e+65) {
		tmp = t_2;
	} else if (j <= -9.2e-122) {
		tmp = fma(-i, j, (z * x)) * y;
	} else if (j <= -7.3e-298) {
		tmp = t_1;
	} else if (j <= 1.2e-194) {
		tmp = fma(-a, t, (z * y)) * x;
	} else if (j <= 9e+27) {
		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, t, Float64(Float64(-c) * z)) * b)
	t_2 = Float64(fma(Float64(-i), y, Float64(c * a)) * j)
	tmp = 0.0
	if (j <= -1.4e+65)
		tmp = t_2;
	elseif (j <= -9.2e-122)
		tmp = Float64(fma(Float64(-i), j, Float64(z * x)) * y);
	elseif (j <= -7.3e-298)
		tmp = t_1;
	elseif (j <= 1.2e-194)
		tmp = Float64(fma(Float64(-a), t, Float64(z * y)) * x);
	elseif (j <= 9e+27)
		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 * t + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-i) * y + N[(c * a), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]}, If[LessEqual[j, -1.4e+65], t$95$2, If[LessEqual[j, -9.2e-122], N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[j, -7.3e-298], t$95$1, If[LessEqual[j, 1.2e-194], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[j, 9e+27], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.3999999999999999e65 or 8.9999999999999998e27 < j

   1. Initial program 77.8%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. +-commutative N/A

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

      11. associate-*r* N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 70.5

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

   5. Applied rewrites 70.5%

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

   if -1.3999999999999999e65 < j < -9.20000000000000028e-122

   1. Initial program 78.5%

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 52.9

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

   5. Applied rewrites 52.9%

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

   if -9.20000000000000028e-122 < j < -7.3000000000000003e-298 or 1.2e-194 < j < 8.9999999999999998e27

   1. Initial program 78.8%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 57.0

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

   5. Applied rewrites 57.0%

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

   if -7.3000000000000003e-298 < j < 1.2e-194

   1. Initial program 61.0%

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. +-commutative N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-neg.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 71.4

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

   5. Applied rewrites 71.4%

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

Alternative 5: 59.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+17} \lor \neg \left(z \leq 5.4 \cdot 10^{+86}\right):\\ \;\;\;\;\mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot t\right) \cdot b + j \cdot \left(c \cdot a - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -5.5e+17) (not (<= z 5.4e+86)))
   (* (fma y x (* (- b) c)) z)
   (+ (* (* i t) b) (* j (- (* c a) (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -5.5e+17) || !(z <= 5.4e+86)) {
		tmp = fma(y, x, (-b * c)) * z;
	} else {
		tmp = ((i * t) * b) + (j * ((c * a) - (y * i)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -5.5e+17) || !(z <= 5.4e+86))
		tmp = Float64(fma(y, x, Float64(Float64(-b) * c)) * z);
	else
		tmp = Float64(Float64(Float64(i * t) * b) + Float64(j * Float64(Float64(c * a) - Float64(y * i))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -5.5e+17], N[Not[LessEqual[z, 5.4e+86]], $MachinePrecision]], N[(N[(y * x + N[((-b) * c), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(N[(N[(i * t), $MachinePrecision] * b), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5e17 or 5.40000000000000036e86 < z

   1. Initial program 72.2%

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-neg.f64 69.4

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

   5. Applied rewrites 69.4%

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

   if -5.5e17 < z < 5.40000000000000036e86

   1. Initial program 79.2%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 62.2

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

   5. Applied rewrites 62.2%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+17} \lor \neg \left(z \leq 5.4 \cdot 10^{+86}\right):\\ \;\;\;\;\mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot t\right) \cdot b + j \cdot \left(c \cdot a - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 29.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := \left(i \cdot t\right) \cdot b\\ \mathbf{if}\;i \leq -3.8 \cdot 10^{+164}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -8.5 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{-128}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* (* i t) b)))
   (if (<= i -3.8e+164)
     t_2
     (if (<= i -8.5e+67)
       t_1
       (if (<= i 2.4e-128) (* (* y x) z) (if (<= i 3.2e-7) 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 = a * (c * j);
	double t_2 = (i * t) * b;
	double tmp;
	if (i <= -3.8e+164) {
		tmp = t_2;
	} else if (i <= -8.5e+67) {
		tmp = t_1;
	} else if (i <= 2.4e-128) {
		tmp = (y * x) * z;
	} else if (i <= 3.2e-7) {
		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 = a * (c * j)
    t_2 = (i * t) * b
    if (i <= (-3.8d+164)) then
        tmp = t_2
    else if (i <= (-8.5d+67)) then
        tmp = t_1
    else if (i <= 2.4d-128) then
        tmp = (y * x) * z
    else if (i <= 3.2d-7) 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 = a * (c * j);
	double t_2 = (i * t) * b;
	double tmp;
	if (i <= -3.8e+164) {
		tmp = t_2;
	} else if (i <= -8.5e+67) {
		tmp = t_1;
	} else if (i <= 2.4e-128) {
		tmp = (y * x) * z;
	} else if (i <= 3.2e-7) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = (i * t) * b
	tmp = 0
	if i <= -3.8e+164:
		tmp = t_2
	elif i <= -8.5e+67:
		tmp = t_1
	elif i <= 2.4e-128:
		tmp = (y * x) * z
	elif i <= 3.2e-7:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(Float64(i * t) * b)
	tmp = 0.0
	if (i <= -3.8e+164)
		tmp = t_2;
	elseif (i <= -8.5e+67)
		tmp = t_1;
	elseif (i <= 2.4e-128)
		tmp = Float64(Float64(y * x) * z);
	elseif (i <= 3.2e-7)
		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 = a * (c * j);
	t_2 = (i * t) * b;
	tmp = 0.0;
	if (i <= -3.8e+164)
		tmp = t_2;
	elseif (i <= -8.5e+67)
		tmp = t_1;
	elseif (i <= 2.4e-128)
		tmp = (y * x) * z;
	elseif (i <= 3.2e-7)
		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[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * t), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[i, -3.8e+164], t$95$2, If[LessEqual[i, -8.5e+67], t$95$1, If[LessEqual[i, 2.4e-128], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[i, 3.2e-7], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -3.80000000000000021e164 or 3.2000000000000001e-7 < i

   1. Initial program 58.5%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 53.3

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

   5. Applied rewrites 53.3%

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

   6. Taylor expanded in z around 0

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

      1. lower-*.f64 43.0

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

   8. Applied rewrites 43.0%

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

   if -3.80000000000000021e164 < i < -8.50000000000000038e67 or 2.3999999999999998e-128 < i < 3.2000000000000001e-7

   1. Initial program 85.5%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. +-commutative N/A

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

      11. associate-*r* N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 51.0

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

   5. Applied rewrites 51.0%

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

   6. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 46.5

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

   8. Applied rewrites 46.5%

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

   if -8.50000000000000038e67 < i < 2.3999999999999998e-128

   1. Initial program 87.8%

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-neg.f64 56.2

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

   5. Applied rewrites 56.2%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 37.2

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

   8. Applied rewrites 37.2%

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

Alternative 7: 51.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{-38} \lor \neg \left(y \leq 58000000000000\right):\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, t, \left(-c\right) \cdot z\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -1.36e-38) (not (<= y 58000000000000.0)))
   (* (fma (- i) j (* z x)) y)
   (* (fma i t (* (- c) z)) b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -1.36e-38) || !(y <= 58000000000000.0)) {
		tmp = fma(-i, j, (z * x)) * y;
	} else {
		tmp = fma(i, t, (-c * z)) * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -1.36e-38) || !(y <= 58000000000000.0))
		tmp = Float64(fma(Float64(-i), j, Float64(z * x)) * y);
	else
		tmp = Float64(fma(i, t, Float64(Float64(-c) * z)) * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[y, -1.36e-38], N[Not[LessEqual[y, 58000000000000.0]], $MachinePrecision]], N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[(N[(i * t + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.36e-38 or 5.8e13 < y

   1. Initial program 69.2%

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 59.9

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

   5. Applied rewrites 59.9%

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

   if -1.36e-38 < y < 5.8e13

   1. Initial program 85.2%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 53.5

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

   5. Applied rewrites 53.5%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{-38} \lor \neg \left(y \leq 58000000000000\right):\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, t, \left(-c\right) \cdot z\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-13} \lor \neg \left(x \leq 5 \cdot 10^{-36}\right):\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, t, \left(-c\right) \cdot z\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= x -1.15e-13) (not (<= x 5e-36)))
   (* (fma (- a) t (* z y)) x)
   (* (fma i t (* (- c) z)) b)))

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 <= -1.15e-13) || !(x <= 5e-36)) {
		tmp = fma(-a, t, (z * y)) * x;
	} else {
		tmp = fma(i, t, (-c * z)) * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((x <= -1.15e-13) || !(x <= 5e-36))
		tmp = Float64(fma(Float64(-a), t, Float64(z * y)) * x);
	else
		tmp = Float64(fma(i, t, Float64(Float64(-c) * z)) * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[x, -1.15e-13], N[Not[LessEqual[x, 5e-36]], $MachinePrecision]], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(i * t + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1499999999999999e-13 or 5.00000000000000004e-36 < x

   1. Initial program 78.7%

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. +-commutative N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-neg.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 61.7

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

   5. Applied rewrites 61.7%

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

   if -1.1499999999999999e-13 < x < 5.00000000000000004e-36

   1. Initial program 73.6%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 49.8

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

   5. Applied rewrites 49.8%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-13} \lor \neg \left(x \leq 5 \cdot 10^{-36}\right):\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, t, \left(-c\right) \cdot z\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 44.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2.8 \cdot 10^{+52}:\\ \;\;\;\;\left(\left(-i\right) \cdot y\right) \cdot j\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, t, \left(-c\right) \cdot z\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -2.8e+52)
   (* (* (- i) y) j)
   (if (<= i 3.5e-7) (* (fma y x (* (- b) c)) z) (* (fma i t (* (- c) z)) b))))

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 <= -2.8e+52) {
		tmp = (-i * y) * j;
	} else if (i <= 3.5e-7) {
		tmp = fma(y, x, (-b * c)) * z;
	} else {
		tmp = fma(i, t, (-c * z)) * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -2.8e+52)
		tmp = Float64(Float64(Float64(-i) * y) * j);
	elseif (i <= 3.5e-7)
		tmp = Float64(fma(y, x, Float64(Float64(-b) * c)) * z);
	else
		tmp = Float64(fma(i, t, Float64(Float64(-c) * z)) * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -2.8e+52], N[(N[((-i) * y), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[i, 3.5e-7], N[(N[(y * x + N[((-b) * c), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(N[(i * t + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -2.8e52

   1. Initial program 61.2%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. +-commutative N/A

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

      11. associate-*r* N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 55.4

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

   5. Applied rewrites 55.4%

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

   6. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 44.6

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

   8. Applied rewrites 44.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. distribute-lft-neg-out N/A

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

      5. lower-*.f64 N/A

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

      6. lift-neg.f64 44.6

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

   10. Applied rewrites 44.6%

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

   if -2.8e52 < i < 3.49999999999999984e-7

   1. Initial program 88.2%

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-neg.f64 54.4

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

   5. Applied rewrites 54.4%

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

   if 3.49999999999999984e-7 < i

   1. Initial program 62.6%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 57.3

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

   5. Applied rewrites 57.3%

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

Alternative 10: 41.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.35 \cdot 10^{+72}:\\ \;\;\;\;\left(a \cdot c\right) \cdot j\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{+28}:\\ \;\;\;\;\mathsf{fma}\left(i, t, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(-i\right) \cdot \left(j \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.35e+72)
   (* (* a c) j)
   (if (<= j 1.15e+28) (* (fma i t (* (- c) z)) b) (* (- i) (* j 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 (j <= -1.35e+72) {
		tmp = (a * c) * j;
	} else if (j <= 1.15e+28) {
		tmp = fma(i, t, (-c * z)) * b;
	} else {
		tmp = -i * (j * y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.35e+72)
		tmp = Float64(Float64(a * c) * j);
	elseif (j <= 1.15e+28)
		tmp = Float64(fma(i, t, Float64(Float64(-c) * z)) * b);
	else
		tmp = Float64(Float64(-i) * Float64(j * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1.35e+72], N[(N[(a * c), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[j, 1.15e+28], N[(N[(i * t + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], N[((-i) * N[(j * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.35e72

   1. Initial program 75.0%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. +-commutative N/A

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

      11. associate-*r* N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 69.9

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

   5. Applied rewrites 69.9%

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

   6. Taylor expanded in y around 0

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

      1. lower-*.f64 50.5

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

   8. Applied rewrites 50.5%

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

   if -1.35e72 < j < 1.14999999999999992e28

   1. Initial program 75.4%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 47.2

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

   5. Applied rewrites 47.2%

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

   if 1.14999999999999992e28 < j

   1. Initial program 80.0%

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

   3. Taylor expanded in i around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-neg.f64 56.0

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

   5. Applied rewrites 56.0%

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

   6. Taylor expanded in y around inf

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

      1. lower-*.f64 46.2

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

   8. Applied rewrites 46.2%

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

Alternative 11: 30.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -5.4 \cdot 10^{+50}:\\ \;\;\;\;\left(\left(-i\right) \cdot y\right) \cdot j\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{-128}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{-7}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot t\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -5.4e+50)
   (* (* (- i) y) j)
   (if (<= i 2.4e-128)
     (* (* y x) z)
     (if (<= i 3.2e-7) (* a (* c j)) (* (* i t) b)))))

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 <= -5.4e+50) {
		tmp = (-i * y) * j;
	} else if (i <= 2.4e-128) {
		tmp = (y * x) * z;
	} else if (i <= 3.2e-7) {
		tmp = a * (c * j);
	} else {
		tmp = (i * t) * b;
	}
	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 (i <= (-5.4d+50)) then
        tmp = (-i * y) * j
    else if (i <= 2.4d-128) then
        tmp = (y * x) * z
    else if (i <= 3.2d-7) then
        tmp = a * (c * j)
    else
        tmp = (i * t) * b
    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 (i <= -5.4e+50) {
		tmp = (-i * y) * j;
	} else if (i <= 2.4e-128) {
		tmp = (y * x) * z;
	} else if (i <= 3.2e-7) {
		tmp = a * (c * j);
	} else {
		tmp = (i * t) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -5.4e+50:
		tmp = (-i * y) * j
	elif i <= 2.4e-128:
		tmp = (y * x) * z
	elif i <= 3.2e-7:
		tmp = a * (c * j)
	else:
		tmp = (i * t) * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -5.4e+50)
		tmp = Float64(Float64(Float64(-i) * y) * j);
	elseif (i <= 2.4e-128)
		tmp = Float64(Float64(y * x) * z);
	elseif (i <= 3.2e-7)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(Float64(i * t) * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -5.4e+50)
		tmp = (-i * y) * j;
	elseif (i <= 2.4e-128)
		tmp = (y * x) * z;
	elseif (i <= 3.2e-7)
		tmp = a * (c * j);
	else
		tmp = (i * t) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -5.4e+50], N[(N[((-i) * y), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[i, 2.4e-128], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[i, 3.2e-7], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(N[(i * t), $MachinePrecision] * b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if i < -5.4e50

   1. Initial program 61.2%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. +-commutative N/A

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

      11. associate-*r* N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 55.4

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

   5. Applied rewrites 55.4%

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

   6. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 44.6

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

   8. Applied rewrites 44.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. distribute-lft-neg-out N/A

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

      5. lower-*.f64 N/A

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

      6. lift-neg.f64 44.6

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

   10. Applied rewrites 44.6%

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

   if -5.4e50 < i < 2.3999999999999998e-128

   1. Initial program 87.5%

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-neg.f64 57.6

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

   5. Applied rewrites 57.6%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 38.1

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

   8. Applied rewrites 38.1%

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

   if 2.3999999999999998e-128 < i < 3.2000000000000001e-7

   1. Initial program 90.6%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. +-commutative N/A

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

      11. associate-*r* N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 45.8

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

   5. Applied rewrites 45.8%

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

   6. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 45.5

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

   8. Applied rewrites 45.5%

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

   if 3.2000000000000001e-7 < i

   1. Initial program 62.6%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 57.3

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

   5. Applied rewrites 57.3%

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

   6. Taylor expanded in z around 0

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

      1. lower-*.f64 46.4

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

   8. Applied rewrites 46.4%

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

Alternative 12: 29.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -7.6 \cdot 10^{+45} \lor \neg \left(j \leq 3.5 \cdot 10^{+28}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot t\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -7.6e+45) (not (<= j 3.5e+28))) (* a (* c j)) (* (* i t) b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -7.6e+45) || !(j <= 3.5e+28)) {
		tmp = a * (c * j);
	} else {
		tmp = (i * t) * b;
	}
	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 ((j <= (-7.6d+45)) .or. (.not. (j <= 3.5d+28))) then
        tmp = a * (c * j)
    else
        tmp = (i * t) * b
    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 ((j <= -7.6e+45) || !(j <= 3.5e+28)) {
		tmp = a * (c * j);
	} else {
		tmp = (i * t) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -7.6e+45) or not (j <= 3.5e+28):
		tmp = a * (c * j)
	else:
		tmp = (i * t) * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -7.6e+45) || !(j <= 3.5e+28))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(Float64(i * t) * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -7.6e+45) || ~((j <= 3.5e+28)))
		tmp = a * (c * j);
	else
		tmp = (i * t) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -7.6e+45], N[Not[LessEqual[j, 3.5e+28]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(N[(i * t), $MachinePrecision] * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -7.6000000000000004e45 or 3.5e28 < j

   1. Initial program 77.8%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. +-commutative N/A

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

      11. associate-*r* N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 67.8

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

   5. Applied rewrites 67.8%

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

   6. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 42.3

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

   8. Applied rewrites 42.3%

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

   if -7.6000000000000004e45 < j < 3.5e28

   1. Initial program 75.5%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 48.0

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

   5. Applied rewrites 48.0%

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

   6. Taylor expanded in z around 0

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

      1. lower-*.f64 30.1

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

   8. Applied rewrites 30.1%

      \[\leadsto \left(i \cdot t\right) \cdot b \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.6 \cdot 10^{+45} \lor \neg \left(j \leq 3.5 \cdot 10^{+28}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot t\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 22.3% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

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

C

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

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 * (c * j)
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 * (c * j);
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.4%

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

3. Taylor expanded in j around inf

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

   1. *-commutative N/A

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

   2. *-commutative N/A

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

   3. *-commutative N/A

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

   4. lower-*.f64 N/A

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

   5. *-commutative N/A

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

   6. *-commutative N/A

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

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

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

   8. mul-1-neg N/A

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

   9. associate-*r* N/A

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

   10. +-commutative N/A

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

   11. associate-*r* N/A

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

   12. mul-1-neg N/A

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

   13. lower-fma.f64 N/A

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

   14. lower-neg.f64 N/A

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

   15. *-commutative N/A

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

   16. lift-*.f64 37.4

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

5. Applied rewrites 37.4%

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

6. Taylor expanded in y around 0

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

   1. lower-*.f64 N/A

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

   2. lower-*.f64 21.7

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

8. Applied rewrites 21.7%

   \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2025085 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -293938859355541/2000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 32113527362226803/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))))))

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