Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 74.5% → 83.8%

Time: 8.5s

Alternatives: 21

Speedup: 0.5×

• 57.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 74.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 83.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 87.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

   5. Applied rewrites 32.7%

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

   6. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

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

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

      8. *-commutative N/A

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

      9. +-commutative N/A

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

      10. mul-1-neg N/A

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

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

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

   8. Applied rewrites 60.0%

      \[\leadsto \mathsf{fma}\left(-a, \color{blue}{t \cdot x}, \mathsf{fma}\left(\mathsf{fma}\left(-b, z, j \cdot t\right), c, 1 \cdot \left(\left(i \cdot b\right) \cdot a\right)\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.5%

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

Alternative 2: 73.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * t) - (i * y));
	double tmp;
	if ((((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + t_1) <= ((double) INFINITY)) {
		tmp = fma(-a, (t * x), (-b * fma(-a, i, (c * z)))) + t_1;
	} else {
		tmp = fma(-a, (t * x), fma(fma(-b, z, (j * t)), c, ((i * b) * a)));
	}
	return tmp;
}

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 87.4%

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

   3. Taylor expanded in y around 0

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

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

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

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

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

      12. mul-1-neg N/A

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

      13. associate-*r* N/A

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

      14. +-commutative N/A

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

      15. associate-*r* N/A

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

      16. mul-1-neg N/A

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

      17. lower-fma.f64 N/A

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

      18. lower-neg.f64 N/A

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

      19. lift-*.f64 80.2

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

   5. Applied rewrites 80.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

   5. Applied rewrites 32.7%

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

   6. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

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

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

      8. *-commutative N/A

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

      9. +-commutative N/A

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

      10. mul-1-neg N/A

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

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

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

   8. Applied rewrites 60.0%

      \[\leadsto \mathsf{fma}\left(-a, \color{blue}{t \cdot x}, \mathsf{fma}\left(\mathsf{fma}\left(-b, z, j \cdot t\right), c, 1 \cdot \left(\left(i \cdot b\right) \cdot a\right)\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.8%

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

Alternative 3: 67.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-45}:\\ \;\;\;\;\mathsf{fma}\left(-a, t \cdot x, \mathsf{fma}\left(\mathsf{fma}\left(-b, z, j \cdot t\right), c, \left(i \cdot b\right) \cdot a\right)\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \left(-b\right) \cdot \mathsf{fma}\left(-a, i, c \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- i) j (* z x)) y)))
   (if (<= y -1.55e+144)
     t_1
     (if (<= y 6.2e-45)
       (fma (- a) (* t x) (fma (fma (- b) z (* j t)) c (* (* i b) a)))
       (if (<= y 8e+35)
         (fma (fma (- a) t (* z y)) x (* (- b) (fma (- a) i (* c 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, j, (z * x)) * y;
	double tmp;
	if (y <= -1.55e+144) {
		tmp = t_1;
	} else if (y <= 6.2e-45) {
		tmp = fma(-a, (t * x), fma(fma(-b, z, (j * t)), c, ((i * b) * a)));
	} else if (y <= 8e+35) {
		tmp = fma(fma(-a, t, (z * y)), x, (-b * fma(-a, i, (c * z))));
	} 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 <= -1.55e+144)
		tmp = t_1;
	elseif (y <= 6.2e-45)
		tmp = fma(Float64(-a), Float64(t * x), fma(fma(Float64(-b), z, Float64(j * t)), c, Float64(Float64(i * b) * a)));
	elseif (y <= 8e+35)
		tmp = fma(fma(Float64(-a), t, Float64(z * y)), x, Float64(Float64(-b) * fma(Float64(-a), i, Float64(c * 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) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.55e+144], t$95$1, If[LessEqual[y, 6.2e-45], N[((-a) * N[(t * x), $MachinePrecision] + N[(N[((-b) * z + N[(j * t), $MachinePrecision]), $MachinePrecision] * c + N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+35], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x + N[((-b) * N[((-a) * i + N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5500000000000001e144 or 7.9999999999999997e35 < y

   1. Initial program 62.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   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 69.7

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

   5. Applied rewrites 69.7%

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

   if -1.5500000000000001e144 < y < 6.2000000000000002e-45

   1. Initial program 72.2%

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

   3. Taylor expanded in c around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

   5. Applied rewrites 73.2%

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

   6. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

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

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

      8. *-commutative N/A

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

      9. +-commutative N/A

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

      10. mul-1-neg N/A

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

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

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

   8. Applied rewrites 74.7%

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

   if 6.2000000000000002e-45 < y < 7.9999999999999997e35

   1. Initial program 70.3%

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

   3. Taylor expanded in j around 0

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

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

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. associate-*r* N/A

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

      9. +-commutative N/A

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

      10. associate-*r* N/A

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

      11. mul-1-neg N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-neg.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

   5. Applied rewrites 85.7%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+144}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-45}:\\ \;\;\;\;\mathsf{fma}\left(-a, t \cdot x, \mathsf{fma}\left(\mathsf{fma}\left(-b, z, j \cdot t\right), c, \left(i \cdot b\right) \cdot a\right)\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \left(-b\right) \cdot \mathsf{fma}\left(-a, i, c \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-45}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot c, t, \left(-a\right) \cdot \left(t \cdot x\right)\right) - \mathsf{fma}\left(c, z, \left(-i\right) \cdot a\right) \cdot b\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \left(-b\right) \cdot \mathsf{fma}\left(-a, i, c \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- i) j (* z x)) y)))
   (if (<= y -3.4e+147)
     t_1
     (if (<= y 5e-45)
       (- (fma (* j c) t (* (- a) (* t x))) (* (fma c z (* (- i) a)) b))
       (if (<= y 8e+35)
         (fma (fma (- a) t (* z y)) x (* (- b) (fma (- a) i (* c 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, j, (z * x)) * y;
	double tmp;
	if (y <= -3.4e+147) {
		tmp = t_1;
	} else if (y <= 5e-45) {
		tmp = fma((j * c), t, (-a * (t * x))) - (fma(c, z, (-i * a)) * b);
	} else if (y <= 8e+35) {
		tmp = fma(fma(-a, t, (z * y)), x, (-b * fma(-a, i, (c * z))));
	} 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 <= -3.4e+147)
		tmp = t_1;
	elseif (y <= 5e-45)
		tmp = Float64(fma(Float64(j * c), t, Float64(Float64(-a) * Float64(t * x))) - Float64(fma(c, z, Float64(Float64(-i) * a)) * b));
	elseif (y <= 8e+35)
		tmp = fma(fma(Float64(-a), t, Float64(z * y)), x, Float64(Float64(-b) * fma(Float64(-a), i, Float64(c * 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) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -3.4e+147], t$95$1, If[LessEqual[y, 5e-45], N[(N[(N[(j * c), $MachinePrecision] * t + N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(c * z + N[((-i) * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+35], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x + N[((-b) * N[((-a) * i + N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.4e147 or 7.9999999999999997e35 < y

   1. Initial program 61.6%

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

   3. Taylor expanded in y around inf

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

      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 69.4

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

   5. Applied rewrites 69.4%

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

   if -3.4e147 < y < 4.99999999999999976e-45

   1. Initial program 72.4%

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

   3. Taylor expanded in c around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

   5. Applied rewrites 73.3%

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

   6. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. lower-*.f64 N/A

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

      10. lift-neg.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

   8. Applied rewrites 71.0%

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

   if 4.99999999999999976e-45 < y < 7.9999999999999997e35

   1. Initial program 70.3%

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

   3. Taylor expanded in j around 0

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

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

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. associate-*r* N/A

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

      9. +-commutative N/A

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

      10. associate-*r* N/A

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

      11. mul-1-neg N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-neg.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

   5. Applied rewrites 85.7%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+147}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-45}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot c, t, \left(-a\right) \cdot \left(t \cdot x\right)\right) - \mathsf{fma}\left(c, z, \left(-i\right) \cdot a\right) \cdot b\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \left(-b\right) \cdot \mathsf{fma}\left(-a, i, c \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, i, c \cdot z\right)\\ t_2 := \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+147}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-45}:\\ \;\;\;\;\mathsf{fma}\left(-a, t \cdot x, \left(j \cdot t\right) \cdot c\right) - t\_1 \cdot b\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \left(-b\right) \cdot t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (fma (- a) i (* c z))) (t_2 (* (fma (- i) j (* z x)) y)))
   (if (<= y -3.4e+147)
     t_2
     (if (<= y 3.2e-45)
       (- (fma (- a) (* t x) (* (* j t) c)) (* t_1 b))
       (if (<= y 8e+35) (fma (fma (- a) t (* z y)) x (* (- 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 = fma(-a, i, (c * z));
	double t_2 = fma(-i, j, (z * x)) * y;
	double tmp;
	if (y <= -3.4e+147) {
		tmp = t_2;
	} else if (y <= 3.2e-45) {
		tmp = fma(-a, (t * x), ((j * t) * c)) - (t_1 * b);
	} else if (y <= 8e+35) {
		tmp = fma(fma(-a, t, (z * y)), x, (-b * t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = fma(Float64(-a), i, Float64(c * z))
	t_2 = Float64(fma(Float64(-i), j, Float64(z * x)) * y)
	tmp = 0.0
	if (y <= -3.4e+147)
		tmp = t_2;
	elseif (y <= 3.2e-45)
		tmp = Float64(fma(Float64(-a), Float64(t * x), Float64(Float64(j * t) * c)) - Float64(t_1 * b));
	elseif (y <= 8e+35)
		tmp = fma(fma(Float64(-a), t, Float64(z * y)), x, Float64(Float64(-b) * 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[((-a) * i + N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -3.4e+147], t$95$2, If[LessEqual[y, 3.2e-45], N[(N[((-a) * N[(t * x), $MachinePrecision] + N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+35], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x + N[((-b) * t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.4e147 or 7.9999999999999997e35 < y

   1. Initial program 61.6%

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

   3. Taylor expanded in y around inf

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

      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 69.4

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

   5. Applied rewrites 69.4%

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

   if -3.4e147 < y < 3.20000000000000007e-45

   1. Initial program 72.4%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

   5. Applied rewrites 70.4%

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

   if 3.20000000000000007e-45 < y < 7.9999999999999997e35

   1. Initial program 70.3%

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

   3. Taylor expanded in j around 0

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

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

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. associate-*r* N/A

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

      9. +-commutative N/A

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

      10. associate-*r* N/A

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

      11. mul-1-neg N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-neg.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

   5. Applied rewrites 85.7%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+147}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-45}:\\ \;\;\;\;\mathsf{fma}\left(-a, t \cdot x, \left(j \cdot t\right) \cdot c\right) - \mathsf{fma}\left(-a, i, c \cdot z\right) \cdot b\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \left(-b\right) \cdot \mathsf{fma}\left(-a, i, c \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.75 \cdot 10^{+44} \lor \neg \left(j \leq 5.4 \cdot 10^{+216}\right):\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \left(-b\right) \cdot \mathsf{fma}\left(-a, i, c \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1.75e+44) (not (<= j 5.4e+216)))
   (* (fma (- i) y (* c t)) j)
   (fma (fma (- a) t (* z y)) x (* (- b) (fma (- a) i (* c z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.75e+44) || !(j <= 5.4e+216)) {
		tmp = fma(-i, y, (c * t)) * j;
	} else {
		tmp = fma(fma(-a, t, (z * y)), x, (-b * fma(-a, i, (c * z))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -1.75e+44) || !(j <= 5.4e+216))
		tmp = Float64(fma(Float64(-i), y, Float64(c * t)) * j);
	else
		tmp = fma(fma(Float64(-a), t, Float64(z * y)), x, Float64(Float64(-b) * fma(Float64(-a), i, Float64(c * z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -1.75e+44], N[Not[LessEqual[j, 5.4e+216]], $MachinePrecision]], N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x + N[((-b) * N[((-a) * i + N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.75e44 or 5.4000000000000003e216 < j

   1. Initial program 74.1%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. +-commutative N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lift-*.f64 72.1

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

   5. Applied rewrites 72.1%

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

   if -1.75e44 < j < 5.4000000000000003e216

   1. Initial program 66.7%

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

   3. Taylor expanded in j around 0

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

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

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. associate-*r* N/A

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

      9. +-commutative N/A

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

      10. associate-*r* N/A

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

      11. mul-1-neg N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-neg.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

   5. Applied rewrites 67.0%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.75 \cdot 10^{+44} \lor \neg \left(j \leq 5.4 \cdot 10^{+216}\right):\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \left(-b\right) \cdot \mathsf{fma}\left(-a, i, c \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot \mathsf{fma}\left(t, x, \left(-b\right) \cdot i\right)\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-81}:\\ \;\;\;\;\mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+101}:\\ \;\;\;\;\mathsf{fma}\left(-a, t \cdot x, b \cdot \left(\left(-c\right) \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- a) (fma t x (* (- b) i)))))
   (if (<= a -1.3e+25)
     t_1
     (if (<= a 4.8e-81)
       (* (fma j t (* (- b) z)) c)
       (if (<= a 1.02e+101) (fma (- a) (* t x) (* b (* (- c) 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 = -a * fma(t, x, (-b * i));
	double tmp;
	if (a <= -1.3e+25) {
		tmp = t_1;
	} else if (a <= 4.8e-81) {
		tmp = fma(j, t, (-b * z)) * c;
	} else if (a <= 1.02e+101) {
		tmp = fma(-a, (t * x), (b * (-c * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(-a) * fma(t, x, Float64(Float64(-b) * i)))
	tmp = 0.0
	if (a <= -1.3e+25)
		tmp = t_1;
	elseif (a <= 4.8e-81)
		tmp = Float64(fma(j, t, Float64(Float64(-b) * z)) * c);
	elseif (a <= 1.02e+101)
		tmp = fma(Float64(-a), Float64(t * x), Float64(b * Float64(Float64(-c) * 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[((-a) * N[(t * x + N[((-b) * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.3e+25], t$95$1, If[LessEqual[a, 4.8e-81], N[(N[(j * t + N[((-b) * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[a, 1.02e+101], N[((-a) * N[(t * x), $MachinePrecision] + N[(b * N[((-c) * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.2999999999999999e25 or 1.02000000000000002e101 < a

   1. Initial program 56.7%

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

   3. Taylor expanded in a around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-neg.f64 70.0

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

   5. Applied rewrites 70.0%

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

   if -1.2999999999999999e25 < a < 4.7999999999999998e-81

   1. Initial program 75.8%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 53.2

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

   5. Applied rewrites 53.2%

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

   if 4.7999999999999998e-81 < a < 1.02000000000000002e101

   1. Initial program 83.9%

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

   3. Taylor expanded in c around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

   5. Applied rewrites 71.4%

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

   6. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

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

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

      8. *-commutative N/A

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

      9. +-commutative N/A

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

      10. mul-1-neg N/A

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

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

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

   8. Applied rewrites 55.6%

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

   9. Taylor expanded in z around inf

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

       1. associate-*r* N/A

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

       2. mul-1-neg N/A

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

       3. lower-*.f64 N/A

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

       4. lift-neg.f64 N/A

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

       5. lower-*.f64 60.7

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

   11. Applied rewrites 60.7%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+25}:\\ \;\;\;\;\left(-a\right) \cdot \mathsf{fma}\left(t, x, \left(-b\right) \cdot i\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-81}:\\ \;\;\;\;\mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+101}:\\ \;\;\;\;\mathsf{fma}\left(-a, t \cdot x, b \cdot \left(\left(-c\right) \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \mathsf{fma}\left(t, x, \left(-b\right) \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -5.2 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(-i, j \cdot y, \left(z \cdot y\right) \cdot x + a \cdot \left(i \cdot b\right)\right)\\ \mathbf{elif}\;i \leq 7.5 \cdot 10^{+100}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-b, z, j \cdot t\right), c, \left(\left(-a\right) \cdot t\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-i\right) \cdot \mathsf{fma}\left(j, y, \left(-a\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -5.2e+16)
   (fma (- i) (* j y) (+ (* (* z y) x) (* a (* i b))))
   (if (<= i 7.5e+100)
     (fma (fma (- b) z (* j t)) c (* (* (- a) t) x))
     (* (- i) (fma j y (* (- a) b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -5.2e+16) {
		tmp = fma(-i, (j * y), (((z * y) * x) + (a * (i * b))));
	} else if (i <= 7.5e+100) {
		tmp = fma(fma(-b, z, (j * t)), c, ((-a * t) * x));
	} else {
		tmp = -i * fma(j, y, (-a * b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -5.2e+16)
		tmp = fma(Float64(-i), Float64(j * y), Float64(Float64(Float64(z * y) * x) + Float64(a * Float64(i * b))));
	elseif (i <= 7.5e+100)
		tmp = fma(fma(Float64(-b), z, Float64(j * t)), c, Float64(Float64(Float64(-a) * t) * x));
	else
		tmp = Float64(Float64(-i) * fma(j, y, Float64(Float64(-a) * b)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -5.2e+16], N[((-i) * N[(j * y), $MachinePrecision] + N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] + N[(a * N[(i * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.5e+100], N[(N[((-b) * z + N[(j * t), $MachinePrecision]), $MachinePrecision] * c + N[(N[((-a) * t), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[((-i) * N[(j * y + N[((-a) * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -5.2e16

   1. Initial program 58.1%

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

   3. Taylor expanded in c around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

   5. Applied rewrites 65.9%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 73.7

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

   8. Applied rewrites 73.7%

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

   if -5.2e16 < i < 7.49999999999999983e100

   1. Initial program 75.4%

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

   3. Taylor expanded in c around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

   5. Applied rewrites 73.9%

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

   6. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

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

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

      8. *-commutative N/A

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

      9. +-commutative N/A

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

      10. mul-1-neg N/A

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

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

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

   8. Applied rewrites 67.3%

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

   9. Taylor expanded in i around 0

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

       1. +-commutative N/A

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

       2. mul-1-neg N/A

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

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

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

       4. *-commutative N/A

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

       5. lower-fma.f64 N/A

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

       6. lift-fma.f64 N/A

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

       7. lift-neg.f64 N/A

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

       8. lift-*.f64 N/A

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

       9. mul-1-neg N/A

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

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

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

       11. associate-*r* N/A

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

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

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

       13. mul-1-neg N/A

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

       14. lower-*.f64 N/A

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

       15. mul-1-neg N/A

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

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

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

       17. lower-*.f64 N/A

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

       18. lift-neg.f64 62.2

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

   11. Applied rewrites 62.2%

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

   if 7.49999999999999983e100 < i

   1. Initial program 55.0%

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

   3. Taylor expanded in i around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

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

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 61.9

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

   5. Applied rewrites 61.9%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.2 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(-i, j \cdot y, \left(z \cdot y\right) \cdot x + a \cdot \left(i \cdot b\right)\right)\\ \mathbf{elif}\;i \leq 7.5 \cdot 10^{+100}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-b, z, j \cdot t\right), c, \left(\left(-a\right) \cdot t\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-i\right) \cdot \mathsf{fma}\left(j, y, \left(-a\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-105}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-b, z, j \cdot t\right), c, \left(\left(-a\right) \cdot t\right) \cdot x\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+52}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- i) j (* z x)) y)))
   (if (<= y -2.1e+120)
     t_1
     (if (<= y 1.9e-105)
       (fma (fma (- b) z (* j t)) c (* (* (- a) t) x))
       (if (<= y 1.85e+52) (* (fma i a (* (- c) z)) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-i, j, (z * x)) * y;
	double tmp;
	if (y <= -2.1e+120) {
		tmp = t_1;
	} else if (y <= 1.9e-105) {
		tmp = fma(fma(-b, z, (j * t)), c, ((-a * t) * x));
	} else if (y <= 1.85e+52) {
		tmp = fma(i, a, (-c * z)) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-i), j, Float64(z * x)) * y)
	tmp = 0.0
	if (y <= -2.1e+120)
		tmp = t_1;
	elseif (y <= 1.9e-105)
		tmp = fma(fma(Float64(-b), z, Float64(j * t)), c, Float64(Float64(Float64(-a) * t) * x));
	elseif (y <= 1.85e+52)
		tmp = Float64(fma(i, a, Float64(Float64(-c) * z)) * b);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -2.1e+120], t$95$1, If[LessEqual[y, 1.9e-105], N[(N[((-b) * z + N[(j * t), $MachinePrecision]), $MachinePrecision] * c + N[(N[((-a) * t), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e+52], N[(N[(i * a + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1e120 or 1.85e52 < y

   1. Initial program 61.3%

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

   3. Taylor expanded in y around inf

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

      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 68.9

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

   5. Applied rewrites 68.9%

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

   if -2.1e120 < y < 1.8999999999999999e-105

   1. Initial program 72.8%

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

   3. Taylor expanded in c around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

   5. Applied rewrites 73.9%

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

   6. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

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

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

      8. *-commutative N/A

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

      9. +-commutative N/A

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

      10. mul-1-neg N/A

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

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

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

   8. Applied rewrites 75.5%

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

   9. Taylor expanded in i around 0

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

       1. +-commutative N/A

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

       2. mul-1-neg N/A

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

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

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

       4. *-commutative N/A

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

       5. lower-fma.f64 N/A

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

       6. lift-fma.f64 N/A

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

       7. lift-neg.f64 N/A

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

       8. lift-*.f64 N/A

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

       9. mul-1-neg N/A

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

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

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

       11. associate-*r* N/A

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

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

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

       13. mul-1-neg N/A

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

       14. lower-*.f64 N/A

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

       15. mul-1-neg N/A

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

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

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

       17. lower-*.f64 N/A

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

       18. lift-neg.f64 65.2

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

   11. Applied rewrites 65.2%

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

   if 1.8999999999999999e-105 < y < 1.85e52

   1. Initial program 70.4%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 59.6

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

   5. Applied rewrites 59.6%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+120}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-105}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-b, z, j \cdot t\right), c, \left(\left(-a\right) \cdot t\right) \cdot x\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+52}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 29.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(-c\right) \cdot z\right) \cdot b\\ \mathbf{if}\;b \leq -4.2 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8.9 \cdot 10^{-72}:\\ \;\;\;\;\left(\left(-i\right) \cdot y\right) \cdot j\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-186}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-286}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+37}:\\ \;\;\;\;\left(\left(-a\right) \cdot t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* (- c) z) b)))
   (if (<= b -4.2e+62)
     t_1
     (if (<= b -8.9e-72)
       (* (* (- i) y) j)
       (if (<= b -2.9e-186)
         (* (* j t) c)
         (if (<= b -1.5e-286)
           (* (* z y) x)
           (if (<= b 1.5e+37) (* (* (- a) t) x) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (-c * z) * b;
	double tmp;
	if (b <= -4.2e+62) {
		tmp = t_1;
	} else if (b <= -8.9e-72) {
		tmp = (-i * y) * j;
	} else if (b <= -2.9e-186) {
		tmp = (j * t) * c;
	} else if (b <= -1.5e-286) {
		tmp = (z * y) * x;
	} else if (b <= 1.5e+37) {
		tmp = (-a * t) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-c * z) * b
    if (b <= (-4.2d+62)) then
        tmp = t_1
    else if (b <= (-8.9d-72)) then
        tmp = (-i * y) * j
    else if (b <= (-2.9d-186)) then
        tmp = (j * t) * c
    else if (b <= (-1.5d-286)) then
        tmp = (z * y) * x
    else if (b <= 1.5d+37) then
        tmp = (-a * t) * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (-c * z) * b;
	double tmp;
	if (b <= -4.2e+62) {
		tmp = t_1;
	} else if (b <= -8.9e-72) {
		tmp = (-i * y) * j;
	} else if (b <= -2.9e-186) {
		tmp = (j * t) * c;
	} else if (b <= -1.5e-286) {
		tmp = (z * y) * x;
	} else if (b <= 1.5e+37) {
		tmp = (-a * t) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (-c * z) * b
	tmp = 0
	if b <= -4.2e+62:
		tmp = t_1
	elif b <= -8.9e-72:
		tmp = (-i * y) * j
	elif b <= -2.9e-186:
		tmp = (j * t) * c
	elif b <= -1.5e-286:
		tmp = (z * y) * x
	elif b <= 1.5e+37:
		tmp = (-a * t) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(-c) * z) * b)
	tmp = 0.0
	if (b <= -4.2e+62)
		tmp = t_1;
	elseif (b <= -8.9e-72)
		tmp = Float64(Float64(Float64(-i) * y) * j);
	elseif (b <= -2.9e-186)
		tmp = Float64(Float64(j * t) * c);
	elseif (b <= -1.5e-286)
		tmp = Float64(Float64(z * y) * x);
	elseif (b <= 1.5e+37)
		tmp = Float64(Float64(Float64(-a) * t) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (-c * z) * b;
	tmp = 0.0;
	if (b <= -4.2e+62)
		tmp = t_1;
	elseif (b <= -8.9e-72)
		tmp = (-i * y) * j;
	elseif (b <= -2.9e-186)
		tmp = (j * t) * c;
	elseif (b <= -1.5e-286)
		tmp = (z * y) * x;
	elseif (b <= 1.5e+37)
		tmp = (-a * t) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-c) * z), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -4.2e+62], t$95$1, If[LessEqual[b, -8.9e-72], N[(N[((-i) * y), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[b, -2.9e-186], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[b, -1.5e-286], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[b, 1.5e+37], N[(N[((-a) * t), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.2e62 or 1.50000000000000011e37 < b

   1. Initial program 71.3%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 67.2

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

   5. Applied rewrites 67.2%

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

   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 42.6

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

   8. Applied rewrites 42.6%

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

   if -4.2e62 < b < -8.8999999999999998e-72

   1. Initial program 70.4%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. +-commutative N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lift-*.f64 41.0

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

   5. Applied rewrites 41.0%

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

   6. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

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

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

      3. lower-*.f64 N/A

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

      4. lift-neg.f64 34.6

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

   8. Applied rewrites 34.6%

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

   if -8.8999999999999998e-72 < b < -2.90000000000000019e-186

   1. Initial program 76.1%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. +-commutative N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lift-*.f64 63.1

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

   5. Applied rewrites 63.1%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 49.1

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

   8. Applied rewrites 49.1%

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

   if -2.90000000000000019e-186 < b < -1.5e-286

   1. Initial program 72.4%

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

   3. Taylor expanded in x around inf

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

      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 69.0

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

   5. Applied rewrites 69.0%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 57.1

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

   8. Applied rewrites 57.1%

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

   if -1.5e-286 < b < 1.50000000000000011e37

   1. Initial program 59.2%

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

   3. Taylor expanded in x around inf

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

      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 51.7

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

   5. Applied rewrites 51.7%

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

   6. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

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

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

      3. lower-*.f64 N/A

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

      4. lift-neg.f64 40.8

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

   8. Applied rewrites 40.8%

      \[\leadsto \left(\left(-a\right) \cdot t\right) \cdot x \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+62}:\\ \;\;\;\;\left(\left(-c\right) \cdot z\right) \cdot b\\ \mathbf{elif}\;b \leq -8.9 \cdot 10^{-72}:\\ \;\;\;\;\left(\left(-i\right) \cdot y\right) \cdot j\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-186}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-286}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+37}:\\ \;\;\;\;\left(\left(-a\right) \cdot t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-c\right) \cdot z\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 28.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(-c\right) \cdot z\right) \cdot b\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-52}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-186}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-286}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+37}:\\ \;\;\;\;\left(\left(-a\right) \cdot t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* (- c) z) b)))
   (if (<= b -3.4e+88)
     t_1
     (if (<= b -6.8e-52)
       (* (* i b) a)
       (if (<= b -2.9e-186)
         (* (* j t) c)
         (if (<= b -1.5e-286)
           (* (* z y) x)
           (if (<= b 1.5e+37) (* (* (- a) t) x) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (-c * z) * b;
	double tmp;
	if (b <= -3.4e+88) {
		tmp = t_1;
	} else if (b <= -6.8e-52) {
		tmp = (i * b) * a;
	} else if (b <= -2.9e-186) {
		tmp = (j * t) * c;
	} else if (b <= -1.5e-286) {
		tmp = (z * y) * x;
	} else if (b <= 1.5e+37) {
		tmp = (-a * t) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-c * z) * b
    if (b <= (-3.4d+88)) then
        tmp = t_1
    else if (b <= (-6.8d-52)) then
        tmp = (i * b) * a
    else if (b <= (-2.9d-186)) then
        tmp = (j * t) * c
    else if (b <= (-1.5d-286)) then
        tmp = (z * y) * x
    else if (b <= 1.5d+37) then
        tmp = (-a * t) * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (-c * z) * b;
	double tmp;
	if (b <= -3.4e+88) {
		tmp = t_1;
	} else if (b <= -6.8e-52) {
		tmp = (i * b) * a;
	} else if (b <= -2.9e-186) {
		tmp = (j * t) * c;
	} else if (b <= -1.5e-286) {
		tmp = (z * y) * x;
	} else if (b <= 1.5e+37) {
		tmp = (-a * t) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (-c * z) * b
	tmp = 0
	if b <= -3.4e+88:
		tmp = t_1
	elif b <= -6.8e-52:
		tmp = (i * b) * a
	elif b <= -2.9e-186:
		tmp = (j * t) * c
	elif b <= -1.5e-286:
		tmp = (z * y) * x
	elif b <= 1.5e+37:
		tmp = (-a * t) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(-c) * z) * b)
	tmp = 0.0
	if (b <= -3.4e+88)
		tmp = t_1;
	elseif (b <= -6.8e-52)
		tmp = Float64(Float64(i * b) * a);
	elseif (b <= -2.9e-186)
		tmp = Float64(Float64(j * t) * c);
	elseif (b <= -1.5e-286)
		tmp = Float64(Float64(z * y) * x);
	elseif (b <= 1.5e+37)
		tmp = Float64(Float64(Float64(-a) * t) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (-c * z) * b;
	tmp = 0.0;
	if (b <= -3.4e+88)
		tmp = t_1;
	elseif (b <= -6.8e-52)
		tmp = (i * b) * a;
	elseif (b <= -2.9e-186)
		tmp = (j * t) * c;
	elseif (b <= -1.5e-286)
		tmp = (z * y) * x;
	elseif (b <= 1.5e+37)
		tmp = (-a * t) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-c) * z), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -3.4e+88], t$95$1, If[LessEqual[b, -6.8e-52], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[b, -2.9e-186], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[b, -1.5e-286], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[b, 1.5e+37], N[(N[((-a) * t), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.40000000000000004e88 or 1.50000000000000011e37 < b

   1. Initial program 73.4%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 67.2

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

   5. Applied rewrites 67.2%

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

   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 44.0

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

   8. Applied rewrites 44.0%

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

   if -3.40000000000000004e88 < b < -6.80000000000000035e-52

   1. Initial program 63.5%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 39.3

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

   5. Applied rewrites 39.3%

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

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 33.1

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

   8. Applied rewrites 33.1%

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

   if -6.80000000000000035e-52 < b < -2.90000000000000019e-186

   1. Initial program 74.2%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. +-commutative N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lift-*.f64 60.5

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

   5. Applied rewrites 60.5%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 42.6

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

   8. Applied rewrites 42.6%

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

   if -2.90000000000000019e-186 < b < -1.5e-286

   1. Initial program 72.4%

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

   3. Taylor expanded in x around inf

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

      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 69.0

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

   5. Applied rewrites 69.0%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 57.1

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

   8. Applied rewrites 57.1%

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

   if -1.5e-286 < b < 1.50000000000000011e37

   1. Initial program 59.2%

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

   3. Taylor expanded in x around inf

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

      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 51.7

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

   5. Applied rewrites 51.7%

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

   6. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

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

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

      3. lower-*.f64 N/A

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

      4. lift-neg.f64 40.8

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

   8. Applied rewrites 40.8%

      \[\leadsto \left(\left(-a\right) \cdot t\right) \cdot x \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+88}:\\ \;\;\;\;\left(\left(-c\right) \cdot z\right) \cdot b\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-52}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-186}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-286}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+37}:\\ \;\;\;\;\left(\left(-a\right) \cdot t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-c\right) \cdot z\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 28.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(-c\right) \cdot z\right) \cdot b\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-52}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-186}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-276}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+37}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* (- c) z) b)))
   (if (<= b -3.4e+88)
     t_1
     (if (<= b -6.8e-52)
       (* (* i b) a)
       (if (<= b -2.9e-186)
         (* (* j t) c)
         (if (<= b 4.2e-276)
           (* (* z y) x)
           (if (<= b 1.5e+37) (* (- a) (* t x)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (-c * z) * b;
	double tmp;
	if (b <= -3.4e+88) {
		tmp = t_1;
	} else if (b <= -6.8e-52) {
		tmp = (i * b) * a;
	} else if (b <= -2.9e-186) {
		tmp = (j * t) * c;
	} else if (b <= 4.2e-276) {
		tmp = (z * y) * x;
	} else if (b <= 1.5e+37) {
		tmp = -a * (t * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-c * z) * b
    if (b <= (-3.4d+88)) then
        tmp = t_1
    else if (b <= (-6.8d-52)) then
        tmp = (i * b) * a
    else if (b <= (-2.9d-186)) then
        tmp = (j * t) * c
    else if (b <= 4.2d-276) then
        tmp = (z * y) * x
    else if (b <= 1.5d+37) then
        tmp = -a * (t * x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (-c * z) * b;
	double tmp;
	if (b <= -3.4e+88) {
		tmp = t_1;
	} else if (b <= -6.8e-52) {
		tmp = (i * b) * a;
	} else if (b <= -2.9e-186) {
		tmp = (j * t) * c;
	} else if (b <= 4.2e-276) {
		tmp = (z * y) * x;
	} else if (b <= 1.5e+37) {
		tmp = -a * (t * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (-c * z) * b
	tmp = 0
	if b <= -3.4e+88:
		tmp = t_1
	elif b <= -6.8e-52:
		tmp = (i * b) * a
	elif b <= -2.9e-186:
		tmp = (j * t) * c
	elif b <= 4.2e-276:
		tmp = (z * y) * x
	elif b <= 1.5e+37:
		tmp = -a * (t * x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(-c) * z) * b)
	tmp = 0.0
	if (b <= -3.4e+88)
		tmp = t_1;
	elseif (b <= -6.8e-52)
		tmp = Float64(Float64(i * b) * a);
	elseif (b <= -2.9e-186)
		tmp = Float64(Float64(j * t) * c);
	elseif (b <= 4.2e-276)
		tmp = Float64(Float64(z * y) * x);
	elseif (b <= 1.5e+37)
		tmp = Float64(Float64(-a) * Float64(t * x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (-c * z) * b;
	tmp = 0.0;
	if (b <= -3.4e+88)
		tmp = t_1;
	elseif (b <= -6.8e-52)
		tmp = (i * b) * a;
	elseif (b <= -2.9e-186)
		tmp = (j * t) * c;
	elseif (b <= 4.2e-276)
		tmp = (z * y) * x;
	elseif (b <= 1.5e+37)
		tmp = -a * (t * x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-c) * z), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -3.4e+88], t$95$1, If[LessEqual[b, -6.8e-52], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[b, -2.9e-186], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[b, 4.2e-276], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[b, 1.5e+37], N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.40000000000000004e88 or 1.50000000000000011e37 < b

   1. Initial program 73.4%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 67.2

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

   5. Applied rewrites 67.2%

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

   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 44.0

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

   8. Applied rewrites 44.0%

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

   if -3.40000000000000004e88 < b < -6.80000000000000035e-52

   1. Initial program 63.5%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 39.3

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

   5. Applied rewrites 39.3%

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

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 33.1

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

   8. Applied rewrites 33.1%

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

   if -6.80000000000000035e-52 < b < -2.90000000000000019e-186

   1. Initial program 74.2%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. +-commutative N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lift-*.f64 60.5

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

   5. Applied rewrites 60.5%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 42.6

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

   8. Applied rewrites 42.6%

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

   if -2.90000000000000019e-186 < b < 4.2e-276

   1. Initial program 64.9%

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

   3. Taylor expanded in x around inf

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

      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 57.7

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

   5. Applied rewrites 57.7%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 47.1

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

   8. Applied rewrites 47.1%

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

   if 4.2e-276 < b < 1.50000000000000011e37

   1. Initial program 61.3%

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

   3. Taylor expanded in x around inf

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

      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 55.6

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

   5. Applied rewrites 55.6%

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

   6. Taylor expanded in y around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lift-neg.f64 N/A

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

      5. lower-*.f64 38.6

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

   8. Applied rewrites 38.6%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+88}:\\ \;\;\;\;\left(\left(-c\right) \cdot z\right) \cdot b\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-52}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-186}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-276}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+37}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-c\right) \cdot z\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{if}\;b \leq -1.1 \cdot 10^{-47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-186}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-286}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-71}:\\ \;\;\;\;\left(\left(-a\right) \cdot t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma i a (* (- c) z)) b)))
   (if (<= b -1.1e-47)
     t_1
     (if (<= b -2.9e-186)
       (* (* j t) c)
       (if (<= b -1.5e-286)
         (* (* z y) x)
         (if (<= b 5.6e-71) (* (* (- a) t) x) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(i, a, (-c * z)) * b;
	double tmp;
	if (b <= -1.1e-47) {
		tmp = t_1;
	} else if (b <= -2.9e-186) {
		tmp = (j * t) * c;
	} else if (b <= -1.5e-286) {
		tmp = (z * y) * x;
	} else if (b <= 5.6e-71) {
		tmp = (-a * t) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(i, a, Float64(Float64(-c) * z)) * b)
	tmp = 0.0
	if (b <= -1.1e-47)
		tmp = t_1;
	elseif (b <= -2.9e-186)
		tmp = Float64(Float64(j * t) * c);
	elseif (b <= -1.5e-286)
		tmp = Float64(Float64(z * y) * x);
	elseif (b <= 5.6e-71)
		tmp = Float64(Float64(Float64(-a) * t) * 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 * a + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.1e-47], t$95$1, If[LessEqual[b, -2.9e-186], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[b, -1.5e-286], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[b, 5.6e-71], N[(N[((-a) * t), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.10000000000000009e-47 or 5.60000000000000001e-71 < b

   1. Initial program 71.6%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 57.7

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

   5. Applied rewrites 57.7%

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

   if -1.10000000000000009e-47 < b < -2.90000000000000019e-186

   1. Initial program 71.6%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. +-commutative N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lift-*.f64 58.3

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

   5. Applied rewrites 58.3%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 41.2

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

   8. Applied rewrites 41.2%

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

   if -2.90000000000000019e-186 < b < -1.5e-286

   1. Initial program 72.4%

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

   3. Taylor expanded in x around inf

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

      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 69.0

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

   5. Applied rewrites 69.0%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 57.1

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

   8. Applied rewrites 57.1%

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

   if -1.5e-286 < b < 5.60000000000000001e-71

   1. Initial program 55.1%

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

   3. Taylor expanded in x around inf

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

      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 55.2

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

   5. Applied rewrites 55.2%

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

   6. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

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

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

      3. lower-*.f64 N/A

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

      4. lift-neg.f64 46.3

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

   8. Applied rewrites 46.3%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{-47}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-186}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-286}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-71}:\\ \;\;\;\;\left(\left(-a\right) \cdot t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+72}:\\ \;\;\;\;\left(b \cdot a\right) \cdot i\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-81}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+113} \lor \neg \left(a \leq 1.8 \cdot 10^{+173}\right):\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot a\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.9e+72)
   (* (* b a) i)
   (if (<= a 4.8e-81)
     (* (* j t) c)
     (if (or (<= a 1.15e+113) (not (<= a 1.8e+173)))
       (* (- a) (* t x))
       (* (* i a) 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 (a <= -1.9e+72) {
		tmp = (b * a) * i;
	} else if (a <= 4.8e-81) {
		tmp = (j * t) * c;
	} else if ((a <= 1.15e+113) || !(a <= 1.8e+173)) {
		tmp = -a * (t * x);
	} else {
		tmp = (i * a) * 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 (a <= (-1.9d+72)) then
        tmp = (b * a) * i
    else if (a <= 4.8d-81) then
        tmp = (j * t) * c
    else if ((a <= 1.15d+113) .or. (.not. (a <= 1.8d+173))) then
        tmp = -a * (t * x)
    else
        tmp = (i * a) * 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 (a <= -1.9e+72) {
		tmp = (b * a) * i;
	} else if (a <= 4.8e-81) {
		tmp = (j * t) * c;
	} else if ((a <= 1.15e+113) || !(a <= 1.8e+173)) {
		tmp = -a * (t * x);
	} else {
		tmp = (i * a) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.9e+72:
		tmp = (b * a) * i
	elif a <= 4.8e-81:
		tmp = (j * t) * c
	elif (a <= 1.15e+113) or not (a <= 1.8e+173):
		tmp = -a * (t * x)
	else:
		tmp = (i * a) * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.9e+72)
		tmp = Float64(Float64(b * a) * i);
	elseif (a <= 4.8e-81)
		tmp = Float64(Float64(j * t) * c);
	elseif ((a <= 1.15e+113) || !(a <= 1.8e+173))
		tmp = Float64(Float64(-a) * Float64(t * x));
	else
		tmp = Float64(Float64(i * a) * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.9e+72)
		tmp = (b * a) * i;
	elseif (a <= 4.8e-81)
		tmp = (j * t) * c;
	elseif ((a <= 1.15e+113) || ~((a <= 1.8e+173)))
		tmp = -a * (t * x);
	else
		tmp = (i * a) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.9e+72], N[(N[(b * a), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[a, 4.8e-81], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], If[Or[LessEqual[a, 1.15e+113], N[Not[LessEqual[a, 1.8e+173]], $MachinePrecision]], N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision], N[(N[(i * a), $MachinePrecision] * b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.90000000000000003e72

   1. Initial program 57.4%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 46.7

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

   5. Applied rewrites 46.7%

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

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 38.2

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

   8. Applied rewrites 38.2%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 44.8

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

   10. Applied rewrites 44.8%

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

   if -1.90000000000000003e72 < a < 4.7999999999999998e-81

   1. Initial program 75.1%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. +-commutative N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lift-*.f64 47.9

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

   5. Applied rewrites 47.9%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 30.7

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

   8. Applied rewrites 30.7%

      \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{c} \]

   if 4.7999999999999998e-81 < a < 1.14999999999999998e113 or 1.8000000000000001e173 < a

   1. Initial program 65.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   4. Step-by-step derivation

      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 45.6

          \[\leadsto \mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x \]

   5. Applied rewrites 45.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x} \]

   6. Taylor expanded in y around 0

      \[\leadsto -1 \cdot \color{blue}{\left(a \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \left(t \cdot \color{blue}{x}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t \cdot x\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t \cdot \color{blue}{x}\right) \]

      4. lift-neg.f64 N/A

         \[\leadsto \left(-a\right) \cdot \left(t \cdot x\right) \]

      5. lower-*.f64 42.7

         \[\leadsto \left(-a\right) \cdot \left(t \cdot x\right) \]

   8. Applied rewrites 42.7%

      \[\leadsto \left(-a\right) \cdot \color{blue}{\left(t \cdot x\right)} \]

   if 1.14999999999999998e113 < a < 1.8000000000000001e173

   1. Initial program 74.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(a \cdot i + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      4. *-commutative N/A

         \[\leadsto \left(i \cdot a + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      9. lower-neg.f64 75.0

         \[\leadsto \mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b \]

   5. Applied rewrites 75.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b} \]

   6. Taylor expanded in z around 0

      \[\leadsto \left(a \cdot i\right) \cdot b \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(i \cdot a\right) \cdot b \]

      2. lower-*.f64 66.6

         \[\leadsto \left(i \cdot a\right) \cdot b \]

   8. Applied rewrites 66.6%

      \[\leadsto \left(i \cdot a\right) \cdot b \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+72}:\\ \;\;\;\;\left(b \cdot a\right) \cdot i\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-81}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+113} \lor \neg \left(a \leq 1.8 \cdot 10^{+173}\right):\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot a\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{if}\;b \leq -0.01:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-190}:\\ \;\;\;\;\mathsf{fma}\left(j, c, \left(-a\right) \cdot x\right) \cdot t\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+37}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma i a (* (- c) z)) b)))
   (if (<= b -0.01)
     t_1
     (if (<= b -9.2e-190)
       (* (fma j c (* (- a) x)) t)
       (if (<= b 4.5e+37) (* (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, a, (-c * z)) * b;
	double tmp;
	if (b <= -0.01) {
		tmp = t_1;
	} else if (b <= -9.2e-190) {
		tmp = fma(j, c, (-a * x)) * t;
	} else if (b <= 4.5e+37) {
		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, a, Float64(Float64(-c) * z)) * b)
	tmp = 0.0
	if (b <= -0.01)
		tmp = t_1;
	elseif (b <= -9.2e-190)
		tmp = Float64(fma(j, c, Float64(Float64(-a) * x)) * t);
	elseif (b <= 4.5e+37)
		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 * a + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -0.01], t$95$1, If[LessEqual[b, -9.2e-190], N[(N[(j * c + N[((-a) * x), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[b, 4.5e+37], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -0.0100000000000000002 or 4.49999999999999962e37 < b

   1. Initial program 71.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(a \cdot i + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      4. *-commutative N/A

         \[\leadsto \left(i \cdot a + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      9. lower-neg.f64 64.9

         \[\leadsto \mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b \]

   5. Applied rewrites 64.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b} \]

   if -0.0100000000000000002 < b < -9.19999999999999968e-190

   1. Initial program 72.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot \color{blue}{t} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot \color{blue}{t} \]

      3. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot a\right) \cdot x + c \cdot j\right) \cdot t \]

      4. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(a\right)\right) \cdot x + c \cdot j\right) \cdot t \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(a\right), x, c \cdot j\right) \cdot t \]

      6. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-a, x, c \cdot j\right) \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t \]

      8. lower-*.f64 52.6

         \[\leadsto \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t \]

   5. Applied rewrites 52.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]
   6. Step-by-step derivation

      1. lift-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(a\right), x, j \cdot c\right) \cdot t \]

      2. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(a\right), x, j \cdot c\right) \cdot t \]

      3. lift-fma.f64 N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(a\right)\right) \cdot x + j \cdot c\right) \cdot t \]

      4. distribute-lft-neg-out N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(a \cdot x\right)\right) + j \cdot c\right) \cdot t \]

      5. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) + j \cdot c\right) \cdot t \]

      6. +-commutative N/A

         \[\leadsto \left(j \cdot c + -1 \cdot \left(a \cdot x\right)\right) \cdot t \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(j, c, -1 \cdot \left(a \cdot x\right)\right) \cdot t \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(j, c, \mathsf{neg}\left(a \cdot x\right)\right) \cdot t \]

      9. distribute-lft-neg-out N/A

         \[\leadsto \mathsf{fma}\left(j, c, \left(\mathsf{neg}\left(a\right)\right) \cdot x\right) \cdot t \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(j, c, \left(\mathsf{neg}\left(a\right)\right) \cdot x\right) \cdot t \]

      11. lift-neg.f64 52.6

          \[\leadsto \mathsf{fma}\left(j, c, \left(-a\right) \cdot x\right) \cdot t \]

   7. Applied rewrites 52.6%

      \[\leadsto \mathsf{fma}\left(j, c, \left(-a\right) \cdot x\right) \cdot t \]

   if -9.19999999999999968e-190 < b < 4.49999999999999962e37

   1. Initial program 62.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot \color{blue}{x} \]

      2. *-commutative N/A

         \[\leadsto \left(y \cdot z - t \cdot a\right) \cdot x \]

      3. lower-*.f64 N/A

         \[\leadsto \left(y \cdot z - t \cdot a\right) \cdot \color{blue}{x} \]

      4. *-commutative N/A

         \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x \]

      5. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(y \cdot z + \left(\mathsf{neg}\left(a\right)\right) \cdot t\right) \cdot x \]

      6. mul-1-neg N/A

         \[\leadsto \left(y \cdot z + \left(-1 \cdot a\right) \cdot t\right) \cdot x \]

      7. associate-*r* N/A

         \[\leadsto \left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right) \cdot x \]

      8. +-commutative N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right) \cdot x \]

      9. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot a\right) \cdot t + y \cdot z\right) \cdot x \]

      10. mul-1-neg N/A

          \[\leadsto \left(\left(\mathsf{neg}\left(a\right)\right) \cdot t + y \cdot z\right) \cdot x \]

      11. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(a\right), t, y \cdot z\right) \cdot x \]

      12. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(-a, t, y \cdot z\right) \cdot x \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x \]

      14. lower-*.f64 56.5

          \[\leadsto \mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x \]

   5. Applied rewrites 56.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.01:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-190}:\\ \;\;\;\;\mathsf{fma}\left(j, c, \left(-a\right) \cdot x\right) \cdot t\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+37}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+25} \lor \neg \left(a \leq 4.8 \cdot 10^{-81}\right):\\ \;\;\;\;\left(-a\right) \cdot \mathsf{fma}\left(t, x, \left(-b\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -1.3e+25) (not (<= a 4.8e-81)))
   (* (- a) (fma t x (* (- b) i)))
   (* (fma j t (* (- b) z)) c)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.3e+25) || !(a <= 4.8e-81)) {
		tmp = -a * fma(t, x, (-b * i));
	} else {
		tmp = fma(j, t, (-b * z)) * c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -1.3e+25) || !(a <= 4.8e-81))
		tmp = Float64(Float64(-a) * fma(t, x, Float64(Float64(-b) * i)));
	else
		tmp = Float64(fma(j, t, Float64(Float64(-b) * z)) * c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -1.3e+25], N[Not[LessEqual[a, 4.8e-81]], $MachinePrecision]], N[((-a) * N[(t * x + N[((-b) * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * t + N[((-b) * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.2999999999999999e25 or 4.7999999999999998e-81 < a

   1. Initial program 63.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(t \cdot x - b \cdot i\right)} \]

      2. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(a\right)\right) \cdot \left(\color{blue}{t \cdot x} - b \cdot i\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(a\right)\right) \cdot \color{blue}{\left(t \cdot x - b \cdot i\right)} \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(-a\right) \cdot \left(\color{blue}{t \cdot x} - b \cdot i\right) \]

      5. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(-a\right) \cdot \left(t \cdot x + \color{blue}{\left(\mathsf{neg}\left(b\right)\right) \cdot i}\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \left(-a\right) \cdot \mathsf{fma}\left(t, \color{blue}{x}, \left(\mathsf{neg}\left(b\right)\right) \cdot i\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \left(-a\right) \cdot \mathsf{fma}\left(t, x, \left(\mathsf{neg}\left(b\right)\right) \cdot i\right) \]

      8. lower-neg.f64 63.7

         \[\leadsto \left(-a\right) \cdot \mathsf{fma}\left(t, x, \left(-b\right) \cdot i\right) \]

   5. Applied rewrites 63.7%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \mathsf{fma}\left(t, x, \left(-b\right) \cdot i\right)} \]

   if -1.2999999999999999e25 < a < 4.7999999999999998e-81

   1. Initial program 75.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(j \cdot t - b \cdot z\right) \cdot \color{blue}{c} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(j \cdot t - b \cdot z\right) \cdot \color{blue}{c} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(j \cdot t + \left(\mathsf{neg}\left(b\right)\right) \cdot z\right) \cdot c \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(j, t, \left(\mathsf{neg}\left(b\right)\right) \cdot z\right) \cdot c \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(j, t, \left(\mathsf{neg}\left(b\right)\right) \cdot z\right) \cdot c \]

      6. lower-neg.f64 53.2

         \[\leadsto \mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c \]

   5. Applied rewrites 53.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+25} \lor \neg \left(a \leq 4.8 \cdot 10^{-81}\right):\\ \;\;\;\;\left(-a\right) \cdot \mathsf{fma}\left(t, x, \left(-b\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 52.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.01 \lor \neg \left(b \leq 4.5 \cdot 10^{+37}\right):\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, c, \left(-a\right) \cdot x\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -0.01) (not (<= b 4.5e+37)))
   (* (fma i a (* (- c) z)) b)
   (* (fma j c (* (- a) x)) t)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -0.01) || !(b <= 4.5e+37)) {
		tmp = fma(i, a, (-c * z)) * b;
	} else {
		tmp = fma(j, c, (-a * x)) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -0.01) || !(b <= 4.5e+37))
		tmp = Float64(fma(i, a, Float64(Float64(-c) * z)) * b);
	else
		tmp = Float64(fma(j, c, Float64(Float64(-a) * x)) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -0.01], N[Not[LessEqual[b, 4.5e+37]], $MachinePrecision]], N[(N[(i * a + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], N[(N[(j * c + N[((-a) * x), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -0.0100000000000000002 or 4.49999999999999962e37 < b

   1. Initial program 71.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(a \cdot i + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      4. *-commutative N/A

         \[\leadsto \left(i \cdot a + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      9. lower-neg.f64 64.9

         \[\leadsto \mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b \]

   5. Applied rewrites 64.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b} \]

   if -0.0100000000000000002 < b < 4.49999999999999962e37

   1. Initial program 65.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot \color{blue}{t} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot \color{blue}{t} \]

      3. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot a\right) \cdot x + c \cdot j\right) \cdot t \]

      4. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(a\right)\right) \cdot x + c \cdot j\right) \cdot t \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(a\right), x, c \cdot j\right) \cdot t \]

      6. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-a, x, c \cdot j\right) \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t \]

      8. lower-*.f64 49.0

         \[\leadsto \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t \]

   5. Applied rewrites 49.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]
   6. Step-by-step derivation

      1. lift-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(a\right), x, j \cdot c\right) \cdot t \]

      2. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(a\right), x, j \cdot c\right) \cdot t \]

      3. lift-fma.f64 N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(a\right)\right) \cdot x + j \cdot c\right) \cdot t \]

      4. distribute-lft-neg-out N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(a \cdot x\right)\right) + j \cdot c\right) \cdot t \]

      5. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) + j \cdot c\right) \cdot t \]

      6. +-commutative N/A

         \[\leadsto \left(j \cdot c + -1 \cdot \left(a \cdot x\right)\right) \cdot t \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(j, c, -1 \cdot \left(a \cdot x\right)\right) \cdot t \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(j, c, \mathsf{neg}\left(a \cdot x\right)\right) \cdot t \]

      9. distribute-lft-neg-out N/A

         \[\leadsto \mathsf{fma}\left(j, c, \left(\mathsf{neg}\left(a\right)\right) \cdot x\right) \cdot t \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(j, c, \left(\mathsf{neg}\left(a\right)\right) \cdot x\right) \cdot t \]

      11. lift-neg.f64 49.0

          \[\leadsto \mathsf{fma}\left(j, c, \left(-a\right) \cdot x\right) \cdot t \]

   7. Applied rewrites 49.0%

      \[\leadsto \mathsf{fma}\left(j, c, \left(-a\right) \cdot x\right) \cdot t \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.01 \lor \neg \left(b \leq 4.5 \cdot 10^{+37}\right):\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, c, \left(-a\right) \cdot x\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot x\\ \mathbf{if}\;x \leq -0.034:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-152}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{elif}\;x \leq 680000:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z y) x)))
   (if (<= x -0.034)
     t_1
     (if (<= x 1.1e-152)
       (* (* i b) a)
       (if (<= x 680000.0) (* (* j t) c) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * y) * x;
	double tmp;
	if (x <= -0.034) {
		tmp = t_1;
	} else if (x <= 1.1e-152) {
		tmp = (i * b) * a;
	} else if (x <= 680000.0) {
		tmp = (j * t) * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * y) * x
    if (x <= (-0.034d0)) then
        tmp = t_1
    else if (x <= 1.1d-152) then
        tmp = (i * b) * a
    else if (x <= 680000.0d0) then
        tmp = (j * t) * c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * y) * x;
	double tmp;
	if (x <= -0.034) {
		tmp = t_1;
	} else if (x <= 1.1e-152) {
		tmp = (i * b) * a;
	} else if (x <= 680000.0) {
		tmp = (j * t) * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * y) * x
	tmp = 0
	if x <= -0.034:
		tmp = t_1
	elif x <= 1.1e-152:
		tmp = (i * b) * a
	elif x <= 680000.0:
		tmp = (j * t) * c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * y) * x)
	tmp = 0.0
	if (x <= -0.034)
		tmp = t_1;
	elseif (x <= 1.1e-152)
		tmp = Float64(Float64(i * b) * a);
	elseif (x <= 680000.0)
		tmp = Float64(Float64(j * t) * c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (z * y) * x;
	tmp = 0.0;
	if (x <= -0.034)
		tmp = t_1;
	elseif (x <= 1.1e-152)
		tmp = (i * b) * a;
	elseif (x <= 680000.0)
		tmp = (j * t) * c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -0.034], t$95$1, If[LessEqual[x, 1.1e-152], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[x, 680000.0], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.034000000000000002 or 6.8e5 < x

   1. Initial program 68.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 58.8

          \[\leadsto \mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x \]

   5. Applied rewrites 58.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x} \]

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot z\right) \cdot x \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(z \cdot y\right) \cdot x \]

      2. lift-*.f64 35.2

         \[\leadsto \left(z \cdot y\right) \cdot x \]

   8. Applied rewrites 35.2%

      \[\leadsto \left(z \cdot y\right) \cdot x \]

   if -0.034000000000000002 < x < 1.09999999999999992e-152

   1. Initial program 68.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(a \cdot i + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      4. *-commutative N/A

         \[\leadsto \left(i \cdot a + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      9. lower-neg.f64 52.9

         \[\leadsto \mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b \]

   5. Applied rewrites 52.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b} \]

   6. Taylor expanded in z around 0

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b \cdot i\right) \cdot a \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b \cdot i\right) \cdot a \]

      3. *-commutative N/A

         \[\leadsto \left(i \cdot b\right) \cdot a \]

      4. lift-*.f64 37.1

         \[\leadsto \left(i \cdot b\right) \cdot a \]

   8. Applied rewrites 37.1%

      \[\leadsto \left(i \cdot b\right) \cdot \color{blue}{a} \]

   if 1.09999999999999992e-152 < x < 6.8e5

   1. Initial program 69.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(c \cdot t + \left(\mathsf{neg}\left(i\right)\right) \cdot y\right) \cdot j \]

      4. mul-1-neg N/A

         \[\leadsto \left(c \cdot t + \left(-1 \cdot i\right) \cdot y\right) \cdot j \]

      5. associate-*r* N/A

         \[\leadsto \left(c \cdot t + -1 \cdot \left(i \cdot y\right)\right) \cdot j \]

      6. +-commutative N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot y\right) + c \cdot t\right) \cdot j \]

      7. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot i\right) \cdot y + c \cdot t\right) \cdot j \]

      8. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(i\right)\right) \cdot y + c \cdot t\right) \cdot j \]

      9. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(i\right), y, c \cdot t\right) \cdot j \]

      10. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j \]

      11. lift-*.f64 52.6

          \[\leadsto \mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j \]

   5. Applied rewrites 52.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j} \]

   6. Taylor expanded in y around 0

      \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(j \cdot t\right) \cdot c \]

      2. lower-*.f64 N/A

         \[\leadsto \left(j \cdot t\right) \cdot c \]

      3. lower-*.f64 35.8

         \[\leadsto \left(j \cdot t\right) \cdot c \]

   8. Applied rewrites 35.8%

      \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.034:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-152}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{elif}\;x \leq 680000:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+72}:\\ \;\;\;\;\left(b \cdot a\right) \cdot i\\ \mathbf{elif}\;a \leq 7.9 \cdot 10^{-10}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot a\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.9e+72)
   (* (* b a) i)
   (if (<= a 7.9e-10) (* (* j t) c) (* (* i a) 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 (a <= -1.9e+72) {
		tmp = (b * a) * i;
	} else if (a <= 7.9e-10) {
		tmp = (j * t) * c;
	} else {
		tmp = (i * a) * 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 (a <= (-1.9d+72)) then
        tmp = (b * a) * i
    else if (a <= 7.9d-10) then
        tmp = (j * t) * c
    else
        tmp = (i * a) * 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 (a <= -1.9e+72) {
		tmp = (b * a) * i;
	} else if (a <= 7.9e-10) {
		tmp = (j * t) * c;
	} else {
		tmp = (i * a) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.9e+72:
		tmp = (b * a) * i
	elif a <= 7.9e-10:
		tmp = (j * t) * c
	else:
		tmp = (i * a) * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.9e+72)
		tmp = Float64(Float64(b * a) * i);
	elseif (a <= 7.9e-10)
		tmp = Float64(Float64(j * t) * c);
	else
		tmp = Float64(Float64(i * a) * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.9e+72)
		tmp = (b * a) * i;
	elseif (a <= 7.9e-10)
		tmp = (j * t) * c;
	else
		tmp = (i * a) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.9e+72], N[(N[(b * a), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[a, 7.9e-10], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], N[(N[(i * a), $MachinePrecision] * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.90000000000000003e72

   1. Initial program 57.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(a \cdot i + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      4. *-commutative N/A

         \[\leadsto \left(i \cdot a + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      9. lower-neg.f64 46.7

         \[\leadsto \mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b \]

   5. Applied rewrites 46.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b} \]

   6. Taylor expanded in z around 0

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b \cdot i\right) \cdot a \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b \cdot i\right) \cdot a \]

      3. *-commutative N/A

         \[\leadsto \left(i \cdot b\right) \cdot a \]

      4. lift-*.f64 38.2

         \[\leadsto \left(i \cdot b\right) \cdot a \]

   8. Applied rewrites 38.2%

      \[\leadsto \left(i \cdot b\right) \cdot \color{blue}{a} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(i \cdot b\right) \cdot a \]

      2. lift-*.f64 N/A

         \[\leadsto \left(i \cdot b\right) \cdot a \]

      3. *-commutative N/A

         \[\leadsto \left(b \cdot i\right) \cdot a \]

      4. *-commutative N/A

         \[\leadsto a \cdot \left(b \cdot \color{blue}{i}\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(a \cdot b\right) \cdot i \]

      6. lower-*.f64 N/A

         \[\leadsto \left(a \cdot b\right) \cdot i \]

      7. *-commutative N/A

         \[\leadsto \left(b \cdot a\right) \cdot i \]

      8. lower-*.f64 44.8

         \[\leadsto \left(b \cdot a\right) \cdot i \]

   10. Applied rewrites 44.8%

       \[\leadsto \left(b \cdot a\right) \cdot i \]

   if -1.90000000000000003e72 < a < 7.8999999999999996e-10

   1. Initial program 75.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(c \cdot t + \left(\mathsf{neg}\left(i\right)\right) \cdot y\right) \cdot j \]

      4. mul-1-neg N/A

         \[\leadsto \left(c \cdot t + \left(-1 \cdot i\right) \cdot y\right) \cdot j \]

      5. associate-*r* N/A

         \[\leadsto \left(c \cdot t + -1 \cdot \left(i \cdot y\right)\right) \cdot j \]

      6. +-commutative N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot y\right) + c \cdot t\right) \cdot j \]

      7. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot i\right) \cdot y + c \cdot t\right) \cdot j \]

      8. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(i\right)\right) \cdot y + c \cdot t\right) \cdot j \]

      9. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(i\right), y, c \cdot t\right) \cdot j \]

      10. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j \]

      11. lift-*.f64 45.1

          \[\leadsto \mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j \]

   5. Applied rewrites 45.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j} \]

   6. Taylor expanded in y around 0

      \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(j \cdot t\right) \cdot c \]

      2. lower-*.f64 N/A

         \[\leadsto \left(j \cdot t\right) \cdot c \]

      3. lower-*.f64 28.4

         \[\leadsto \left(j \cdot t\right) \cdot c \]

   8. Applied rewrites 28.4%

      \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{c} \]

   if 7.8999999999999996e-10 < a

   1. Initial program 65.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(a \cdot i + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      4. *-commutative N/A

         \[\leadsto \left(i \cdot a + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      9. lower-neg.f64 48.7

         \[\leadsto \mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b \]

   5. Applied rewrites 48.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b} \]

   6. Taylor expanded in z around 0

      \[\leadsto \left(a \cdot i\right) \cdot b \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(i \cdot a\right) \cdot b \]

      2. lower-*.f64 33.9

         \[\leadsto \left(i \cdot a\right) \cdot b \]

   8. Applied rewrites 33.9%

      \[\leadsto \left(i \cdot a\right) \cdot b \]
3. Recombined 3 regimes into one program.

4. Final simplification 33.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+72}:\\ \;\;\;\;\left(b \cdot a\right) \cdot i\\ \mathbf{elif}\;a \leq 7.9 \cdot 10^{-10}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot a\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+72}:\\ \;\;\;\;\left(b \cdot a\right) \cdot i\\ \mathbf{elif}\;a \leq 7.9 \cdot 10^{-10}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.9e+72)
   (* (* b a) i)
   (if (<= a 7.9e-10) (* (* j t) c) (* (* i b) a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.9e+72) {
		tmp = (b * a) * i;
	} else if (a <= 7.9e-10) {
		tmp = (j * t) * c;
	} else {
		tmp = (i * b) * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-1.9d+72)) then
        tmp = (b * a) * i
    else if (a <= 7.9d-10) then
        tmp = (j * t) * c
    else
        tmp = (i * b) * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.9e+72) {
		tmp = (b * a) * i;
	} else if (a <= 7.9e-10) {
		tmp = (j * t) * c;
	} else {
		tmp = (i * b) * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.9e+72:
		tmp = (b * a) * i
	elif a <= 7.9e-10:
		tmp = (j * t) * c
	else:
		tmp = (i * b) * a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.9e+72)
		tmp = Float64(Float64(b * a) * i);
	elseif (a <= 7.9e-10)
		tmp = Float64(Float64(j * t) * c);
	else
		tmp = Float64(Float64(i * b) * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.9e+72)
		tmp = (b * a) * i;
	elseif (a <= 7.9e-10)
		tmp = (j * t) * c;
	else
		tmp = (i * b) * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.9e+72], N[(N[(b * a), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[a, 7.9e-10], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.90000000000000003e72

   1. Initial program 57.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(a \cdot i + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      4. *-commutative N/A

         \[\leadsto \left(i \cdot a + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      9. lower-neg.f64 46.7

         \[\leadsto \mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b \]

   5. Applied rewrites 46.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b} \]

   6. Taylor expanded in z around 0

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b \cdot i\right) \cdot a \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b \cdot i\right) \cdot a \]

      3. *-commutative N/A

         \[\leadsto \left(i \cdot b\right) \cdot a \]

      4. lift-*.f64 38.2

         \[\leadsto \left(i \cdot b\right) \cdot a \]

   8. Applied rewrites 38.2%

      \[\leadsto \left(i \cdot b\right) \cdot \color{blue}{a} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(i \cdot b\right) \cdot a \]

      2. lift-*.f64 N/A

         \[\leadsto \left(i \cdot b\right) \cdot a \]

      3. *-commutative N/A

         \[\leadsto \left(b \cdot i\right) \cdot a \]

      4. *-commutative N/A

         \[\leadsto a \cdot \left(b \cdot \color{blue}{i}\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(a \cdot b\right) \cdot i \]

      6. lower-*.f64 N/A

         \[\leadsto \left(a \cdot b\right) \cdot i \]

      7. *-commutative N/A

         \[\leadsto \left(b \cdot a\right) \cdot i \]

      8. lower-*.f64 44.8

         \[\leadsto \left(b \cdot a\right) \cdot i \]

   10. Applied rewrites 44.8%

       \[\leadsto \left(b \cdot a\right) \cdot i \]

   if -1.90000000000000003e72 < a < 7.8999999999999996e-10

   1. Initial program 75.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(c \cdot t - i \cdot y\right) \cdot \color{blue}{j} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(c \cdot t + \left(\mathsf{neg}\left(i\right)\right) \cdot y\right) \cdot j \]

      4. mul-1-neg N/A

         \[\leadsto \left(c \cdot t + \left(-1 \cdot i\right) \cdot y\right) \cdot j \]

      5. associate-*r* N/A

         \[\leadsto \left(c \cdot t + -1 \cdot \left(i \cdot y\right)\right) \cdot j \]

      6. +-commutative N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot y\right) + c \cdot t\right) \cdot j \]

      7. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot i\right) \cdot y + c \cdot t\right) \cdot j \]

      8. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(i\right)\right) \cdot y + c \cdot t\right) \cdot j \]

      9. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(i\right), y, c \cdot t\right) \cdot j \]

      10. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j \]

      11. lift-*.f64 45.1

          \[\leadsto \mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j \]

   5. Applied rewrites 45.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j} \]

   6. Taylor expanded in y around 0

      \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(j \cdot t\right) \cdot c \]

      2. lower-*.f64 N/A

         \[\leadsto \left(j \cdot t\right) \cdot c \]

      3. lower-*.f64 28.4

         \[\leadsto \left(j \cdot t\right) \cdot c \]

   8. Applied rewrites 28.4%

      \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{c} \]

   if 7.8999999999999996e-10 < a

   1. Initial program 65.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(a \cdot i + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      4. *-commutative N/A

         \[\leadsto \left(i \cdot a + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      9. lower-neg.f64 48.7

         \[\leadsto \mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b \]

   5. Applied rewrites 48.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b} \]

   6. Taylor expanded in z around 0

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b \cdot i\right) \cdot a \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b \cdot i\right) \cdot a \]

      3. *-commutative N/A

         \[\leadsto \left(i \cdot b\right) \cdot a \]

      4. lift-*.f64 32.5

         \[\leadsto \left(i \cdot b\right) \cdot a \]

   8. Applied rewrites 32.5%

      \[\leadsto \left(i \cdot b\right) \cdot \color{blue}{a} \]
3. Recombined 3 regimes into one program.

4. Final simplification 33.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+72}:\\ \;\;\;\;\left(b \cdot a\right) \cdot i\\ \mathbf{elif}\;a \leq 7.9 \cdot 10^{-10}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 21.9% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \left(b \cdot a\right) \cdot i \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* (* b a) i))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return (b * a) * 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 = (b * a) * 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 (b * a) * i;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return (b * a) * i

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(b * a) * i)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = (b * a) * i;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(b * a), $MachinePrecision] * i), $MachinePrecision]

Derivation

1. Initial program 68.6%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Add Preprocessing

3. Taylor expanded in b around inf

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

   2. lower-*.f64 N/A

      \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

   3. fp-cancel-sub-sign-inv N/A

      \[\leadsto \left(a \cdot i + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

   4. *-commutative N/A

      \[\leadsto \left(i \cdot a + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

   5. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

   6. mul-1-neg N/A

      \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

   7. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

   8. mul-1-neg N/A

      \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

   9. lower-neg.f64 40.4

      \[\leadsto \mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b \]

5. Applied rewrites 40.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b} \]

6. Taylor expanded in z around 0

   \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
7. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \left(b \cdot i\right) \cdot a \]

   2. lower-*.f64 N/A

      \[\leadsto \left(b \cdot i\right) \cdot a \]

   3. *-commutative N/A

      \[\leadsto \left(i \cdot b\right) \cdot a \]

   4. lift-*.f64 21.9

      \[\leadsto \left(i \cdot b\right) \cdot a \]

8. Applied rewrites 21.9%

   \[\leadsto \left(i \cdot b\right) \cdot \color{blue}{a} \]
9. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(i \cdot b\right) \cdot a \]

   2. lift-*.f64 N/A

      \[\leadsto \left(i \cdot b\right) \cdot a \]

   3. *-commutative N/A

      \[\leadsto \left(b \cdot i\right) \cdot a \]

   4. *-commutative N/A

      \[\leadsto a \cdot \left(b \cdot \color{blue}{i}\right) \]

   5. associate-*r* N/A

      \[\leadsto \left(a \cdot b\right) \cdot i \]

   6. lower-*.f64 N/A

      \[\leadsto \left(a \cdot b\right) \cdot i \]

   7. *-commutative N/A

      \[\leadsto \left(b \cdot a\right) \cdot i \]

   8. lower-*.f64 22.6

      \[\leadsto \left(b \cdot a\right) \cdot i \]

10. Applied rewrites 22.6%

    \[\leadsto \left(b \cdot a\right) \cdot i \]

11. Final simplification 22.6%

    \[\leadsto \left(b \cdot a\right) \cdot i \]
12. Add Preprocessing

Developer Target 1: 70.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2025064 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -1015122364899489/125000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -942510763643697/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (if (< t -238547917063487/3125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 10535888557455487/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))