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

Percentage Accurate: 74.3% → 83.2%

Time: 8.9s

Alternatives: 18

Speedup: 0.5×

• 57.8% 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: 74.3% 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: 83.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double 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 = fma(-t, x, (j * c)) * a;
	}
	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(fma(Float64(-t), x, Float64(j * c)) * a);
	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[(N[((-t) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 89.2%

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

   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 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 54.7

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

   5. Applied rewrites 54.7%

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

Alternative 2: 61.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, t, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{if}\;b \leq -2.9 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-86}:\\ \;\;\;\;\left(-c\right) \cdot \left(\mathsf{fma}\left(t, \frac{x}{c}, -j\right) \cdot a\right) - \left(c \cdot z\right) \cdot b\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-226}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+185}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \left(j \cdot c\right) \cdot a\right) - \left(c \cdot b\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma i t (* (- c) z)) b)))
   (if (<= b -2.9e+108)
     t_1
     (if (<= b -2.9e-86)
       (- (* (- c) (* (fma t (/ x c) (- j)) a)) (* (* c z) b))
       (if (<= b -1.2e-226)
         (+ (* (* z y) x) (* j (- (* c a) (* y i))))
         (if (<= b 2.3e+185)
           (- (fma (fma (- a) t (* z y)) x (* (* j c) a)) (* (* c b) z))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(i, t, (-c * z)) * b;
	double tmp;
	if (b <= -2.9e+108) {
		tmp = t_1;
	} else if (b <= -2.9e-86) {
		tmp = (-c * (fma(t, (x / c), -j) * a)) - ((c * z) * b);
	} else if (b <= -1.2e-226) {
		tmp = ((z * y) * x) + (j * ((c * a) - (y * i)));
	} else if (b <= 2.3e+185) {
		tmp = fma(fma(-a, t, (z * y)), x, ((j * c) * a)) - ((c * b) * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(i, t, Float64(Float64(-c) * z)) * b)
	tmp = 0.0
	if (b <= -2.9e+108)
		tmp = t_1;
	elseif (b <= -2.9e-86)
		tmp = Float64(Float64(Float64(-c) * Float64(fma(t, Float64(x / c), Float64(-j)) * a)) - Float64(Float64(c * z) * b));
	elseif (b <= -1.2e-226)
		tmp = Float64(Float64(Float64(z * y) * x) + Float64(j * Float64(Float64(c * a) - Float64(y * i))));
	elseif (b <= 2.3e+185)
		tmp = Float64(fma(fma(Float64(-a), t, Float64(z * y)), x, Float64(Float64(j * c) * a)) - Float64(Float64(c * b) * z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * t + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.9e+108], t$95$1, If[LessEqual[b, -2.9e-86], N[(N[((-c) * N[(N[(t * N[(x / c), $MachinePrecision] + (-j)), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(N[(c * z), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.2e-226], N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e+185], N[(N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x + N[(N[(j * c), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(N[(c * b), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.90000000000000007e108 or 2.3000000000000001e185 < b

   1. Initial program 77.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 83.6

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

   5. Applied rewrites 83.6%

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

   if -2.90000000000000007e108 < b < -2.8999999999999999e-86

   1. Initial program 62.1%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

   5. Applied rewrites 55.6%

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

   6. Taylor expanded in c around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lift-neg.f64 N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-neg.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-*.f64 57.6

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

   8. Applied rewrites 57.6%

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

   9. Taylor expanded in z around inf

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

       1. lift-*.f64 51.7

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

   11. Applied rewrites 51.7%

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

   12. Taylor expanded in a around 0

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. +-commutative N/A

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

       4. associate-/l* N/A

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

       5. lower-fma.f64 N/A

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

       6. lower-/.f64 N/A

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

       7. mul-1-neg N/A

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

       8. lower-neg.f64 56.2

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

   14. Applied rewrites 56.2%

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

   if -2.8999999999999999e-86 < b < -1.2e-226

   1. Initial program 89.3%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 82.9

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

   5. Applied rewrites 82.9%

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

   if -1.2e-226 < b < 2.3000000000000001e185

   1. Initial program 67.9%

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

   3. Taylor expanded in i around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 64.2%

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

Alternative 3: 61.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, t, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{if}\;b \leq -2.45 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(-t, x, j \cdot c\right) \cdot a - \left(c \cdot z\right) \cdot b\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-226}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+185}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \left(j \cdot c\right) \cdot a\right) - \left(c \cdot b\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma i t (* (- c) z)) b)))
   (if (<= b -2.45e+92)
     t_1
     (if (<= b -3e-17)
       (- (* (fma (- t) x (* j c)) a) (* (* c z) b))
       (if (<= b -1.2e-226)
         (+ (* (* z y) x) (* j (- (* c a) (* y i))))
         (if (<= b 2.3e+185)
           (- (fma (fma (- a) t (* z y)) x (* (* j c) a)) (* (* c b) z))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(i, t, (-c * z)) * b;
	double tmp;
	if (b <= -2.45e+92) {
		tmp = t_1;
	} else if (b <= -3e-17) {
		tmp = (fma(-t, x, (j * c)) * a) - ((c * z) * b);
	} else if (b <= -1.2e-226) {
		tmp = ((z * y) * x) + (j * ((c * a) - (y * i)));
	} else if (b <= 2.3e+185) {
		tmp = fma(fma(-a, t, (z * y)), x, ((j * c) * a)) - ((c * b) * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(i, t, Float64(Float64(-c) * z)) * b)
	tmp = 0.0
	if (b <= -2.45e+92)
		tmp = t_1;
	elseif (b <= -3e-17)
		tmp = Float64(Float64(fma(Float64(-t), x, Float64(j * c)) * a) - Float64(Float64(c * z) * b));
	elseif (b <= -1.2e-226)
		tmp = Float64(Float64(Float64(z * y) * x) + Float64(j * Float64(Float64(c * a) - Float64(y * i))));
	elseif (b <= 2.3e+185)
		tmp = Float64(fma(fma(Float64(-a), t, Float64(z * y)), x, Float64(Float64(j * c) * a)) - Float64(Float64(c * b) * z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * t + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.45e+92], t$95$1, If[LessEqual[b, -3e-17], N[(N[(N[((-t) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision] - N[(N[(c * z), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.2e-226], N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e+185], N[(N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x + N[(N[(j * c), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(N[(c * b), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.4500000000000001e92 or 2.3000000000000001e185 < b

   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 82.9

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

   5. Applied rewrites 82.9%

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

   if -2.4500000000000001e92 < b < -3.00000000000000006e-17

   1. Initial program 62.2%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

   5. Applied rewrites 61.0%

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

   6. Taylor expanded in c around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lift-neg.f64 N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-neg.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-*.f64 61.0

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

   8. Applied rewrites 61.0%

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

   9. Taylor expanded in z around inf

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

       1. lift-*.f64 53.8

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

   11. Applied rewrites 53.8%

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

   12. Taylor expanded in a around 0

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. associate-*r* N/A

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

       4. mul-1-neg N/A

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

       5. lower-fma.f64 N/A

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

       6. lift-neg.f64 N/A

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

       7. *-commutative N/A

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

       8. lift-*.f64 57.7

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

   14. Applied rewrites 57.7%

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

   if -3.00000000000000006e-17 < b < -1.2e-226

   1. Initial program 80.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 70.5

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

   5. Applied rewrites 70.5%

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

   if -1.2e-226 < b < 2.3000000000000001e185

   1. Initial program 67.9%

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

   3. Taylor expanded in i around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 64.2%

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

Alternative 4: 58.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot z\right) \cdot b\\ t_2 := \mathsf{fma}\left(i, t, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{if}\;b \leq -2.45 \cdot 10^{+92}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(-t, x, j \cdot c\right) \cdot a - t\_1\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-183}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+185}:\\ \;\;\;\;\mathsf{fma}\left(-a, t \cdot x, \left(j \cdot c\right) \cdot a\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* c z) b)) (t_2 (* (fma i t (* (- c) z)) b)))
   (if (<= b -2.45e+92)
     t_2
     (if (<= b -3e-17)
       (- (* (fma (- t) x (* j c)) a) t_1)
       (if (<= b 1.7e-183)
         (+ (* (* z y) x) (* j (- (* c a) (* y i))))
         (if (<= b 2.3e+185)
           (- (fma (- a) (* t x) (* (* j c) a)) t_1)
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (c * z) * b;
	double t_2 = fma(i, t, (-c * z)) * b;
	double tmp;
	if (b <= -2.45e+92) {
		tmp = t_2;
	} else if (b <= -3e-17) {
		tmp = (fma(-t, x, (j * c)) * a) - t_1;
	} else if (b <= 1.7e-183) {
		tmp = ((z * y) * x) + (j * ((c * a) - (y * i)));
	} else if (b <= 2.3e+185) {
		tmp = fma(-a, (t * x), ((j * c) * a)) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(c * z) * b)
	t_2 = Float64(fma(i, t, Float64(Float64(-c) * z)) * b)
	tmp = 0.0
	if (b <= -2.45e+92)
		tmp = t_2;
	elseif (b <= -3e-17)
		tmp = Float64(Float64(fma(Float64(-t), x, Float64(j * c)) * a) - t_1);
	elseif (b <= 1.7e-183)
		tmp = Float64(Float64(Float64(z * y) * x) + Float64(j * Float64(Float64(c * a) - Float64(y * i))));
	elseif (b <= 2.3e+185)
		tmp = Float64(fma(Float64(-a), Float64(t * x), Float64(Float64(j * c) * a)) - t_1);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(c * z), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * t + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.45e+92], t$95$2, If[LessEqual[b, -3e-17], N[(N[(N[((-t) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[b, 1.7e-183], N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e+185], N[(N[((-a) * N[(t * x), $MachinePrecision] + N[(N[(j * c), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.4500000000000001e92 or 2.3000000000000001e185 < b

   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 82.9

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

   5. Applied rewrites 82.9%

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

   if -2.4500000000000001e92 < b < -3.00000000000000006e-17

   1. Initial program 62.2%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

   5. Applied rewrites 61.0%

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

   6. Taylor expanded in c around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lift-neg.f64 N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-neg.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-*.f64 61.0

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

   8. Applied rewrites 61.0%

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

   9. Taylor expanded in z around inf

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

       1. lift-*.f64 53.8

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

   11. Applied rewrites 53.8%

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

   12. Taylor expanded in a around 0

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. associate-*r* N/A

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

       4. mul-1-neg N/A

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

       5. lower-fma.f64 N/A

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

       6. lift-neg.f64 N/A

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

       7. *-commutative N/A

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

       8. lift-*.f64 57.7

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

   14. Applied rewrites 57.7%

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

   if -3.00000000000000006e-17 < b < 1.70000000000000007e-183

   1. Initial program 67.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 65.7

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

   5. Applied rewrites 65.7%

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

   if 1.70000000000000007e-183 < b < 2.3000000000000001e185

   1. Initial program 77.4%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

   5. Applied rewrites 71.3%

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

   6. Taylor expanded in z around inf

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

      1. lift-*.f64 60.4

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

   8. Applied rewrites 60.4%

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

Alternative 5: 66.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(-a, t \cdot x, \left(j \cdot c\right) \cdot a\right) - \mathsf{fma}\left(-i, t, c \cdot z\right) \cdot b\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+130}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- i) j (* z x)) y)))
   (if (<= y -7.2e+75)
     t_1
     (if (<= y 1.7e-34)
       (- (fma (- a) (* t x) (* (* j c) a)) (* (fma (- i) t (* c z)) b))
       (if (<= y 2.5e+130) (+ (* (* z y) x) (* j (- (* c a) (* y i)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-i, j, (z * x)) * y;
	double tmp;
	if (y <= -7.2e+75) {
		tmp = t_1;
	} else if (y <= 1.7e-34) {
		tmp = fma(-a, (t * x), ((j * c) * a)) - (fma(-i, t, (c * z)) * b);
	} else if (y <= 2.5e+130) {
		tmp = ((z * y) * x) + (j * ((c * a) - (y * i)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-i), j, Float64(z * x)) * y)
	tmp = 0.0
	if (y <= -7.2e+75)
		tmp = t_1;
	elseif (y <= 1.7e-34)
		tmp = Float64(fma(Float64(-a), Float64(t * x), Float64(Float64(j * c) * a)) - Float64(fma(Float64(-i), t, Float64(c * z)) * b));
	elseif (y <= 2.5e+130)
		tmp = Float64(Float64(Float64(z * y) * x) + Float64(j * Float64(Float64(c * a) - Float64(y * i))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -7.2e+75], t$95$1, If[LessEqual[y, 1.7e-34], N[(N[((-a) * N[(t * x), $MachinePrecision] + N[(N[(j * c), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(N[((-i) * t + N[(c * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+130], N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.2e75 or 2.4999999999999998e130 < y

   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 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 72.2

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

   5. Applied rewrites 72.2%

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

   if -7.2e75 < y < 1.7e-34

   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 y around 0

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

      1. lower--.f64 N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

   5. Applied rewrites 72.6%

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

   if 1.7e-34 < y < 2.4999999999999998e130

   1. Initial program 88.4%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 71.8

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

   5. Applied rewrites 71.8%

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

Alternative 6: 58.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-t, x, j \cdot c\right) \cdot a - \left(c \cdot z\right) \cdot b\\ t_2 := \mathsf{fma}\left(i, t, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{if}\;b \leq -2.45 \cdot 10^{+92}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-184}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+185}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* (fma (- t) x (* j c)) a) (* (* c z) b)))
        (t_2 (* (fma i t (* (- c) z)) b)))
   (if (<= b -2.45e+92)
     t_2
     (if (<= b -3e-17)
       t_1
       (if (<= b 5e-184)
         (+ (* (* z y) x) (* j (- (* c a) (* y i))))
         (if (<= b 2.3e+185) 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(-t, x, (j * c)) * a) - ((c * z) * b);
	double t_2 = fma(i, t, (-c * z)) * b;
	double tmp;
	if (b <= -2.45e+92) {
		tmp = t_2;
	} else if (b <= -3e-17) {
		tmp = t_1;
	} else if (b <= 5e-184) {
		tmp = ((z * y) * x) + (j * ((c * a) - (y * i)));
	} else if (b <= 2.3e+185) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(fma(Float64(-t), x, Float64(j * c)) * a) - Float64(Float64(c * z) * b))
	t_2 = Float64(fma(i, t, Float64(Float64(-c) * z)) * b)
	tmp = 0.0
	if (b <= -2.45e+92)
		tmp = t_2;
	elseif (b <= -3e-17)
		tmp = t_1;
	elseif (b <= 5e-184)
		tmp = Float64(Float64(Float64(z * y) * x) + Float64(j * Float64(Float64(c * a) - Float64(y * i))));
	elseif (b <= 2.3e+185)
		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[(N[((-t) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision] - N[(N[(c * z), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * t + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.45e+92], t$95$2, If[LessEqual[b, -3e-17], t$95$1, If[LessEqual[b, 5e-184], N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e+185], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.4500000000000001e92 or 2.3000000000000001e185 < b

   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 82.9

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

   5. Applied rewrites 82.9%

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

   if -2.4500000000000001e92 < b < -3.00000000000000006e-17 or 5.00000000000000003e-184 < b < 2.3000000000000001e185

   1. Initial program 73.1%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

   5. Applied rewrites 68.4%

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

   6. Taylor expanded in c around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lift-neg.f64 N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-neg.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-*.f64 65.3

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

   8. Applied rewrites 65.3%

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

   9. Taylor expanded in z around inf

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

       1. lift-*.f64 56.4

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

   11. Applied rewrites 56.4%

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

   12. Taylor expanded in a around 0

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. associate-*r* N/A

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

       4. mul-1-neg N/A

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

       5. lower-fma.f64 N/A

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

       6. lift-neg.f64 N/A

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

       7. *-commutative N/A

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

       8. lift-*.f64 59.6

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

   14. Applied rewrites 59.6%

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

   if -3.00000000000000006e-17 < b < 5.00000000000000003e-184

   1. Initial program 67.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 65.7

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

   5. Applied rewrites 65.7%

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

Alternative 7: 58.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{if}\;y \leq -2.05 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-105}:\\ \;\;\;\;\mathsf{fma}\left(-t, x, j \cdot c\right) \cdot a - \left(c \cdot z\right) \cdot b\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(i, t, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- i) j (* z x)) y)))
   (if (<= y -2.05e+76)
     t_1
     (if (<= y 2.8e-105)
       (- (* (fma (- t) x (* j c)) a) (* (* c z) b))
       (if (<= y 6.4e+35) (* (fma i t (* (- c) z)) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-i, j, (z * x)) * y;
	double tmp;
	if (y <= -2.05e+76) {
		tmp = t_1;
	} else if (y <= 2.8e-105) {
		tmp = (fma(-t, x, (j * c)) * a) - ((c * z) * b);
	} else if (y <= 6.4e+35) {
		tmp = fma(i, t, (-c * z)) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-i), j, Float64(z * x)) * y)
	tmp = 0.0
	if (y <= -2.05e+76)
		tmp = t_1;
	elseif (y <= 2.8e-105)
		tmp = Float64(Float64(fma(Float64(-t), x, Float64(j * c)) * a) - Float64(Float64(c * z) * b));
	elseif (y <= 6.4e+35)
		tmp = Float64(fma(i, t, Float64(Float64(-c) * z)) * b);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -2.05e+76], t$95$1, If[LessEqual[y, 2.8e-105], N[(N[(N[((-t) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision] - N[(N[(c * z), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e+35], N[(N[(i * t + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.0499999999999999e76 or 6.39999999999999965e35 < y

   1. Initial program 66.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. 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 69.9

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

   5. Applied rewrites 69.9%

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

   if -2.0499999999999999e76 < y < 2.8e-105

   1. Initial program 74.5%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

   5. Applied rewrites 71.3%

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

   6. Taylor expanded in c around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lift-neg.f64 N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-neg.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-*.f64 68.4

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

   8. Applied rewrites 68.4%

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

   9. Taylor expanded in z around inf

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

       1. lift-*.f64 60.8

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

   11. Applied rewrites 60.8%

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

   12. Taylor expanded in a around 0

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. associate-*r* N/A

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

       4. mul-1-neg N/A

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

       5. lower-fma.f64 N/A

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

       6. lift-neg.f64 N/A

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

       7. *-commutative N/A

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

       8. lift-*.f64 61.6

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

   14. Applied rewrites 61.6%

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

   if 2.8e-105 < y < 6.39999999999999965e35

   1. Initial program 75.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 65.5

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

   5. Applied rewrites 65.5%

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

Alternative 8: 52.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, t, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8.6 \cdot 10^{-203}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot a\right) \cdot j\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-285}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(-t, x, j \cdot c\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma i t (* (- c) z)) b)))
   (if (<= b -3.2e+90)
     t_1
     (if (<= b -8.6e-203)
       (* (fma (- i) y (* c a)) j)
       (if (<= b -1.2e-285)
         (* (fma (- a) t (* z y)) x)
         (if (<= b 1.05e+38) (* (fma (- t) x (* j c)) a) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(i, t, (-c * z)) * b;
	double tmp;
	if (b <= -3.2e+90) {
		tmp = t_1;
	} else if (b <= -8.6e-203) {
		tmp = fma(-i, y, (c * a)) * j;
	} else if (b <= -1.2e-285) {
		tmp = fma(-a, t, (z * y)) * x;
	} else if (b <= 1.05e+38) {
		tmp = fma(-t, x, (j * c)) * a;
	} else {
		tmp = t_1;
	}
	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)
	tmp = 0.0
	if (b <= -3.2e+90)
		tmp = t_1;
	elseif (b <= -8.6e-203)
		tmp = Float64(fma(Float64(-i), y, Float64(c * a)) * j);
	elseif (b <= -1.2e-285)
		tmp = Float64(fma(Float64(-a), t, Float64(z * y)) * x);
	elseif (b <= 1.05e+38)
		tmp = Float64(fma(Float64(-t), x, Float64(j * c)) * a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * t + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -3.2e+90], t$95$1, If[LessEqual[b, -8.6e-203], N[(N[((-i) * y + N[(c * a), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[b, -1.2e-285], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[b, 1.05e+38], N[(N[((-t) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.19999999999999998e90 or 1.05e38 < b

   1. Initial program 76.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 72.9

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

   5. Applied rewrites 72.9%

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

   if -3.19999999999999998e90 < b < -8.60000000000000054e-203

   1. Initial program 71.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 51.5

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

   5. Applied rewrites 51.5%

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

   if -8.60000000000000054e-203 < b < -1.2e-285

   1. Initial program 77.6%

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

   3. Taylor expanded in 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 69.5

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

   5. Applied rewrites 69.5%

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

   if -1.2e-285 < b < 1.05e38

   1. Initial program 62.2%

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

   3. Taylor expanded in 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 55.2

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

   5. Applied rewrites 55.2%

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

Alternative 9: 41.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, t, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{if}\;b \leq -9 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{-179}:\\ \;\;\;\;\left(-i\right) \cdot \left(j \cdot y\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{-297}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+36}:\\ \;\;\;\;\left(-t\right) \cdot \left(a \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma i t (* (- c) z)) b)))
   (if (<= b -9e-20)
     t_1
     (if (<= b -3.7e-179)
       (* (- i) (* j y))
       (if (<= b 2.25e-297)
         (* (* z x) y)
         (if (<= b 7.2e+36) (* (- t) (* a x)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(i, t, (-c * z)) * b;
	double tmp;
	if (b <= -9e-20) {
		tmp = t_1;
	} else if (b <= -3.7e-179) {
		tmp = -i * (j * y);
	} else if (b <= 2.25e-297) {
		tmp = (z * x) * y;
	} else if (b <= 7.2e+36) {
		tmp = -t * (a * x);
	} else {
		tmp = t_1;
	}
	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)
	tmp = 0.0
	if (b <= -9e-20)
		tmp = t_1;
	elseif (b <= -3.7e-179)
		tmp = Float64(Float64(-i) * Float64(j * y));
	elseif (b <= 2.25e-297)
		tmp = Float64(Float64(z * x) * y);
	elseif (b <= 7.2e+36)
		tmp = Float64(Float64(-t) * Float64(a * x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * t + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -9e-20], t$95$1, If[LessEqual[b, -3.7e-179], N[((-i) * N[(j * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.25e-297], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[b, 7.2e+36], N[((-t) * N[(a * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.0000000000000003e-20 or 7.1999999999999995e36 < b

   1. Initial program 73.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. 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 65.5

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

   5. Applied rewrites 65.5%

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

   if -9.0000000000000003e-20 < b < -3.6999999999999999e-179

   1. Initial program 74.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. 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 48.4

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

   5. Applied rewrites 48.4%

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

   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 41.2

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

   8. Applied rewrites 41.2%

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

   if -3.6999999999999999e-179 < b < 2.24999999999999988e-297

   1. Initial program 74.4%

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

   3. Taylor expanded in 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 59.3

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

   5. Applied rewrites 59.3%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 50.0

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

   8. Applied rewrites 50.0%

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

   if 2.24999999999999988e-297 < b < 7.1999999999999995e36

   1. Initial program 64.6%

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

   3. Taylor expanded in t around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-neg.f64 44.7

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

   5. Applied rewrites 44.7%

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

   6. Taylor expanded in x around inf

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

      1. lower-*.f64 39.9

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

   8. Applied rewrites 39.9%

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

Alternative 10: 51.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, t, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8.6 \cdot 10^{-203}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot a\right) \cdot j\\ \mathbf{elif}\;b \leq 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma i t (* (- c) z)) b)))
   (if (<= b -3.2e+90)
     t_1
     (if (<= b -8.6e-203)
       (* (fma (- i) y (* c a)) j)
       (if (<= b 1e+38) (* (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 = fma(i, t, (-c * z)) * b;
	double tmp;
	if (b <= -3.2e+90) {
		tmp = t_1;
	} else if (b <= -8.6e-203) {
		tmp = fma(-i, y, (c * a)) * j;
	} else if (b <= 1e+38) {
		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(fma(i, t, Float64(Float64(-c) * z)) * b)
	tmp = 0.0
	if (b <= -3.2e+90)
		tmp = t_1;
	elseif (b <= -8.6e-203)
		tmp = Float64(fma(Float64(-i), y, Float64(c * a)) * j);
	elseif (b <= 1e+38)
		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[(N[(i * t + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -3.2e+90], t$95$1, If[LessEqual[b, -8.6e-203], N[(N[((-i) * y + N[(c * a), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[b, 1e+38], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.19999999999999998e90 or 9.99999999999999977e37 < b

   1. Initial program 76.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 72.9

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

   5. Applied rewrites 72.9%

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

   if -3.19999999999999998e90 < b < -8.60000000000000054e-203

   1. Initial program 71.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 51.5

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

   5. Applied rewrites 51.5%

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

   if -8.60000000000000054e-203 < b < 9.99999999999999977e37

   1. Initial program 66.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 54.1

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

   5. Applied rewrites 54.1%

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

Alternative 11: 52.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-237}:\\ \;\;\;\;\mathsf{fma}\left(j, a, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(i, t, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- i) j (* z x)) y)))
   (if (<= y -1.45e+116)
     t_1
     (if (<= y -7.5e-237)
       (* (fma j a (* (- b) z)) c)
       (if (<= y 6.4e+35) (* (fma i t (* (- c) z)) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-i, j, (z * x)) * y;
	double tmp;
	if (y <= -1.45e+116) {
		tmp = t_1;
	} else if (y <= -7.5e-237) {
		tmp = fma(j, a, (-b * z)) * c;
	} else if (y <= 6.4e+35) {
		tmp = fma(i, t, (-c * z)) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-i), j, Float64(z * x)) * y)
	tmp = 0.0
	if (y <= -1.45e+116)
		tmp = t_1;
	elseif (y <= -7.5e-237)
		tmp = Float64(fma(j, a, Float64(Float64(-b) * z)) * c);
	elseif (y <= 6.4e+35)
		tmp = Float64(fma(i, t, Float64(Float64(-c) * z)) * b);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.45e+116], t$95$1, If[LessEqual[y, -7.5e-237], N[(N[(j * a + N[((-b) * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[y, 6.4e+35], N[(N[(i * t + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4500000000000001e116 or 6.39999999999999965e35 < 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 71.2

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

   5. Applied rewrites 71.2%

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

   if -1.4500000000000001e116 < y < -7.50000000000000034e-237

   1. Initial program 73.3%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-neg.f64 53.1

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

   5. Applied rewrites 53.1%

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

   if -7.50000000000000034e-237 < y < 6.39999999999999965e35

   1. Initial program 73.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. 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 58.1

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

   5. Applied rewrites 58.1%

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

Alternative 12: 51.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -70000000 \lor \neg \left(b \leq 10^{+38}\right):\\ \;\;\;\;\mathsf{fma}\left(i, t, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -70000000.0) (not (<= b 1e+38)))
   (* (fma i t (* (- c) z)) b)
   (* (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 ((b <= -70000000.0) || !(b <= 1e+38)) {
		tmp = fma(i, t, (-c * z)) * b;
	} else {
		tmp = fma(-a, t, (z * y)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -70000000.0) || !(b <= 1e+38))
		tmp = Float64(fma(i, t, Float64(Float64(-c) * z)) * b);
	else
		tmp = 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[b, -70000000.0], N[Not[LessEqual[b, 1e+38]], $MachinePrecision]], N[(N[(i * t + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7e7 or 9.99999999999999977e37 < b

   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 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 68.5

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

   5. Applied rewrites 68.5%

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

   if -7e7 < b < 9.99999999999999977e37

   1. Initial program 68.8%

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

   3. Taylor expanded in 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 49.0

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

   5. Applied rewrites 49.0%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -70000000 \lor \neg \left(b \leq 10^{+38}\right):\\ \;\;\;\;\mathsf{fma}\left(i, t, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 45.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.65 \cdot 10^{+63} \lor \neg \left(j \leq 2.25 \cdot 10^{-39}\right):\\ \;\;\;\;\mathsf{fma}\left(j, a, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, t, \left(-c\right) \cdot z\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1.65e+63) (not (<= j 2.25e-39)))
   (* (fma j a (* (- b) z)) c)
   (* (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 ((j <= -1.65e+63) || !(j <= 2.25e-39)) {
		tmp = fma(j, a, (-b * z)) * c;
	} 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 ((j <= -1.65e+63) || !(j <= 2.25e-39))
		tmp = Float64(fma(j, a, Float64(Float64(-b) * z)) * c);
	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[j, -1.65e+63], N[Not[LessEqual[j, 2.25e-39]], $MachinePrecision]], N[(N[(j * a + N[((-b) * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], N[(N[(i * t + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.6500000000000001e63 or 2.25e-39 < j

   1. Initial program 68.9%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-neg.f64 53.2

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

   5. Applied rewrites 53.2%

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

   if -1.6500000000000001e63 < j < 2.25e-39

   1. Initial program 74.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 51.7

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

   5. Applied rewrites 51.7%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.65 \cdot 10^{+63} \lor \neg \left(j \leq 2.25 \cdot 10^{-39}\right):\\ \;\;\;\;\mathsf{fma}\left(j, a, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, t, \left(-c\right) \cdot z\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 28.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -9.5 \cdot 10^{+159}:\\ \;\;\;\;\left(\left(-c\right) \cdot z\right) \cdot b\\ \mathbf{elif}\;c \leq -3.05 \cdot 10^{-298}:\\ \;\;\;\;\left(\left(-a\right) \cdot t\right) \cdot x\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{-105}:\\ \;\;\;\;\left(i \cdot t\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot a\right) \cdot j\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -9.5e+159)
   (* (* (- c) z) b)
   (if (<= c -3.05e-298)
     (* (* (- a) t) x)
     (if (<= c 3.1e-105) (* (* i t) b) (* (* c a) j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -9.5e+159) {
		tmp = (-c * z) * b;
	} else if (c <= -3.05e-298) {
		tmp = (-a * t) * x;
	} else if (c <= 3.1e-105) {
		tmp = (i * t) * b;
	} else {
		tmp = (c * a) * j;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-9.5d+159)) then
        tmp = (-c * z) * b
    else if (c <= (-3.05d-298)) then
        tmp = (-a * t) * x
    else if (c <= 3.1d-105) then
        tmp = (i * t) * b
    else
        tmp = (c * a) * j
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -9.5e+159) {
		tmp = (-c * z) * b;
	} else if (c <= -3.05e-298) {
		tmp = (-a * t) * x;
	} else if (c <= 3.1e-105) {
		tmp = (i * t) * b;
	} else {
		tmp = (c * a) * j;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -9.5e+159:
		tmp = (-c * z) * b
	elif c <= -3.05e-298:
		tmp = (-a * t) * x
	elif c <= 3.1e-105:
		tmp = (i * t) * b
	else:
		tmp = (c * a) * j
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -9.5e+159)
		tmp = Float64(Float64(Float64(-c) * z) * b);
	elseif (c <= -3.05e-298)
		tmp = Float64(Float64(Float64(-a) * t) * x);
	elseif (c <= 3.1e-105)
		tmp = Float64(Float64(i * t) * b);
	else
		tmp = Float64(Float64(c * a) * j);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -9.5e+159)
		tmp = (-c * z) * b;
	elseif (c <= -3.05e-298)
		tmp = (-a * t) * x;
	elseif (c <= 3.1e-105)
		tmp = (i * t) * b;
	else
		tmp = (c * a) * j;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -9.5e+159], N[(N[((-c) * z), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[c, -3.05e-298], N[(N[((-a) * t), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[c, 3.1e-105], N[(N[(i * t), $MachinePrecision] * b), $MachinePrecision], N[(N[(c * a), $MachinePrecision] * j), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if c < -9.5000000000000003e159

   1. Initial program 58.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. 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 74.0

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

   5. Applied rewrites 74.0%

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

   6. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

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

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

      3. lift-*.f64 N/A

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

      4. lift-neg.f64 71.3

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

   8. Applied rewrites 71.3%

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

   if -9.5000000000000003e159 < c < -3.05000000000000006e-298

   1. Initial program 75.7%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

   5. Applied rewrites 60.9%

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

   6. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

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

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. lower-*.f64 N/A

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

      10. lift-neg.f64 38.4

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

   8. Applied rewrites 38.4%

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

   if -3.05000000000000006e-298 < c < 3.10000000000000014e-105

   1. Initial program 82.1%

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

   3. Taylor expanded in b around 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 42.3

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

   5. Applied rewrites 42.3%

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

   6. Taylor expanded in z around 0

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

      1. lift-*.f64 33.9

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

   8. Applied rewrites 33.9%

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

   if 3.10000000000000014e-105 < c

   1. Initial program 67.3%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

   5. Applied rewrites 60.8%

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

   6. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 32.0

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

   8. Applied rewrites 32.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 34.2

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

   10. Applied rewrites 34.2%

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

Alternative 15: 28.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot a\right) \cdot j\\ \mathbf{if}\;c \leq -1.1 \cdot 10^{+197}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -3.05 \cdot 10^{-298}:\\ \;\;\;\;\left(\left(-a\right) \cdot t\right) \cdot x\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{-105}:\\ \;\;\;\;\left(i \cdot t\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* c a) j)))
   (if (<= c -1.1e+197)
     t_1
     (if (<= c -3.05e-298)
       (* (* (- a) t) x)
       (if (<= c 3.1e-105) (* (* i t) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (c * a) * j;
	double tmp;
	if (c <= -1.1e+197) {
		tmp = t_1;
	} else if (c <= -3.05e-298) {
		tmp = (-a * t) * x;
	} else if (c <= 3.1e-105) {
		tmp = (i * t) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (c * a) * j
    if (c <= (-1.1d+197)) then
        tmp = t_1
    else if (c <= (-3.05d-298)) then
        tmp = (-a * t) * x
    else if (c <= 3.1d-105) then
        tmp = (i * t) * b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (c * a) * j;
	double tmp;
	if (c <= -1.1e+197) {
		tmp = t_1;
	} else if (c <= -3.05e-298) {
		tmp = (-a * t) * x;
	} else if (c <= 3.1e-105) {
		tmp = (i * t) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (c * a) * j
	tmp = 0
	if c <= -1.1e+197:
		tmp = t_1
	elif c <= -3.05e-298:
		tmp = (-a * t) * x
	elif c <= 3.1e-105:
		tmp = (i * t) * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(c * a) * j)
	tmp = 0.0
	if (c <= -1.1e+197)
		tmp = t_1;
	elseif (c <= -3.05e-298)
		tmp = Float64(Float64(Float64(-a) * t) * x);
	elseif (c <= 3.1e-105)
		tmp = Float64(Float64(i * t) * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (c * a) * j;
	tmp = 0.0;
	if (c <= -1.1e+197)
		tmp = t_1;
	elseif (c <= -3.05e-298)
		tmp = (-a * t) * x;
	elseif (c <= 3.1e-105)
		tmp = (i * t) * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(c * a), $MachinePrecision] * j), $MachinePrecision]}, If[LessEqual[c, -1.1e+197], t$95$1, If[LessEqual[c, -3.05e-298], N[(N[((-a) * t), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[c, 3.1e-105], N[(N[(i * t), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.09999999999999995e197 or 3.10000000000000014e-105 < c

   1. Initial program 65.4%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

   5. Applied rewrites 60.7%

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

   6. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 33.1

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

   8. Applied rewrites 33.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 38.8

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

   10. Applied rewrites 38.8%

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

   if -1.09999999999999995e197 < c < -3.05000000000000006e-298

   1. Initial program 74.4%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

   5. Applied rewrites 59.6%

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

   6. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

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

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. lower-*.f64 N/A

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

      10. lift-neg.f64 38.8

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

   8. Applied rewrites 38.8%

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

   if -3.05000000000000006e-298 < c < 3.10000000000000014e-105

   1. Initial program 82.1%

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

   3. Taylor expanded in b around 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 42.3

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

   5. Applied rewrites 42.3%

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

   6. Taylor expanded in z around 0

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

      1. lift-*.f64 33.9

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

   8. Applied rewrites 33.9%

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

Alternative 16: 28.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.65 \cdot 10^{+63} \lor \neg \left(j \leq 2.6 \cdot 10^{-36}\right):\\ \;\;\;\;\left(c \cdot a\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot t\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1.65e+63) (not (<= j 2.6e-36))) (* (* c a) 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 <= -1.65e+63) || !(j <= 2.6e-36)) {
		tmp = (c * a) * 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 <= (-1.65d+63)) .or. (.not. (j <= 2.6d-36))) then
        tmp = (c * a) * 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 <= -1.65e+63) || !(j <= 2.6e-36)) {
		tmp = (c * a) * j;
	} else {
		tmp = (i * t) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -1.65e+63) or not (j <= 2.6e-36):
		tmp = (c * a) * 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 <= -1.65e+63) || !(j <= 2.6e-36))
		tmp = Float64(Float64(c * a) * 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 <= -1.65e+63) || ~((j <= 2.6e-36)))
		tmp = (c * a) * 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, -1.65e+63], N[Not[LessEqual[j, 2.6e-36]], $MachinePrecision]], N[(N[(c * a), $MachinePrecision] * j), $MachinePrecision], N[(N[(i * t), $MachinePrecision] * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.6500000000000001e63 or 2.6e-36 < j

   1. Initial program 68.9%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

   5. Applied rewrites 47.5%

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

   6. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 35.9

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

   8. Applied rewrites 35.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 39.2

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

   10. Applied rewrites 39.2%

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

   if -1.6500000000000001e63 < j < 2.6e-36

   1. Initial program 74.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 51.7

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

   5. Applied rewrites 51.7%

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

   6. Taylor expanded in z around 0

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

      1. lift-*.f64 31.8

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

   8. Applied rewrites 31.8%

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

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.65 \cdot 10^{+63} \lor \neg \left(j \leq 2.6 \cdot 10^{-36}\right):\\ \;\;\;\;\left(c \cdot a\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot t\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+25} \lor \neg \left(y \leq 6.5 \cdot 10^{-27}\right):\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot a\right) \cdot j\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -4e+25) (not (<= y 6.5e-27))) (* (* z y) x) (* (* c a) j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -4e+25) || !(y <= 6.5e-27)) {
		tmp = (z * y) * x;
	} else {
		tmp = (c * a) * j;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((y <= (-4d+25)) .or. (.not. (y <= 6.5d-27))) then
        tmp = (z * y) * x
    else
        tmp = (c * a) * j
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -4e+25) || !(y <= 6.5e-27)) {
		tmp = (z * y) * x;
	} else {
		tmp = (c * a) * j;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (y <= -4e+25) or not (y <= 6.5e-27):
		tmp = (z * y) * x
	else:
		tmp = (c * a) * j
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -4e+25) || !(y <= 6.5e-27))
		tmp = Float64(Float64(z * y) * x);
	else
		tmp = Float64(Float64(c * a) * j);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((y <= -4e+25) || ~((y <= 6.5e-27)))
		tmp = (z * y) * x;
	else
		tmp = (c * a) * j;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[y, -4e+25], N[Not[LessEqual[y, 6.5e-27]], $MachinePrecision]], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], N[(N[(c * a), $MachinePrecision] * j), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.00000000000000036e25 or 6.50000000000000025e-27 < y

   1. Initial program 68.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 61.3

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

   5. Applied rewrites 61.3%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 35.4

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

   8. Applied rewrites 35.4%

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

   if -4.00000000000000036e25 < y < 6.50000000000000025e-27

   1. Initial program 74.6%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

   5. Applied rewrites 72.2%

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

   6. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 26.7

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

   8. Applied rewrites 26.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 30.8

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

   10. Applied rewrites 30.8%

       \[\leadsto \left(c \cdot a\right) \cdot j \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+25} \lor \neg \left(y \leq 6.5 \cdot 10^{-27}\right):\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot a\right) \cdot j\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 21.9% accurate, 5.5× speedup

Math

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

FPCore

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

C

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

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.8%

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

3. Taylor expanded in 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 37.5

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

5. Applied rewrites 37.5%

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

6. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. *-commutative N/A

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

   4. lower-*.f64 20.8

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

8. Applied rewrites 20.8%

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

Developer Target 1: 60.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) 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 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - 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 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - 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 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - 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 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - 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[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2025064 
(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)))))