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

Percentage Accurate: 73.7% → 81.6%

Time: 12.6s

Alternatives: 19

Speedup: 0.5×

• 57.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 89.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

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

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

      5. +-commutative N/A

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

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

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

      7. *-commutative N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 54.3

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

   5. Applied rewrites 54.3%

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

Alternative 2: 71.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 89.6%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 81.8

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

   5. Applied rewrites 81.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

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

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

      5. +-commutative N/A

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

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

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

      7. *-commutative N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 54.3

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

   5. Applied rewrites 54.3%

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

Alternative 3: 66.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -6 \cdot 10^{+70} \lor \neg \left(i \leq 4 \cdot 10^{+197}\right):\\ \;\;\;\;\mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-t, a, z \cdot y\right), x, \mathsf{fma}\left(-z, b, j \cdot a\right) \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -6e+70) (not (<= i 4e+197)))
   (* (fma (- y) j (* b t)) i)
   (fma (fma (- t) a (* z y)) x (* (fma (- z) b (* j a)) 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 ((i <= -6e+70) || !(i <= 4e+197)) {
		tmp = fma(-y, j, (b * t)) * i;
	} else {
		tmp = fma(fma(-t, a, (z * y)), x, (fma(-z, b, (j * a)) * c));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -6e+70) || !(i <= 4e+197))
		tmp = Float64(fma(Float64(-y), j, Float64(b * t)) * i);
	else
		tmp = fma(fma(Float64(-t), a, Float64(z * y)), x, Float64(fma(Float64(-z), b, Float64(j * a)) * c));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -6e+70], N[Not[LessEqual[i, 4e+197]], $MachinePrecision]], N[(N[((-y) * j + N[(b * t), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision], N[(N[((-t) * a + N[(z * y), $MachinePrecision]), $MachinePrecision] * x + N[(N[((-z) * b + N[(j * a), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -5.99999999999999952e70 or 3.9999999999999998e197 < i

   1. Initial program 61.4%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 74.6

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

   5. Applied rewrites 74.6%

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

   if -5.99999999999999952e70 < i < 3.9999999999999998e197

   1. Initial program 81.4%

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

   3. Taylor expanded in i around 0

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

   5. Applied rewrites 76.8%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6 \cdot 10^{+70} \lor \neg \left(i \leq 4 \cdot 10^{+197}\right):\\ \;\;\;\;\mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-t, a, z \cdot y\right), x, \mathsf{fma}\left(-z, b, j \cdot a\right) \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-55}:\\ \;\;\;\;\mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-226}:\\ \;\;\;\;\mathsf{fma}\left(-z, b, j \cdot a\right) \cdot c\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-253}:\\ \;\;\;\;\mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot a\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- t) a (* z y)) x)))
   (if (<= x -1.55e+83)
     t_1
     (if (<= x -6e-55)
       (* (fma (- a) x (* i b)) t)
       (if (<= x -2.5e-226)
         (* (fma (- z) b (* j a)) c)
         (if (<= x 6.2e-253)
           (* (fma (- y) j (* b t)) i)
           (if (<= x 2.05e-17) (* (fma (- i) y (* c a)) j) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-t, a, (z * y)) * x;
	double tmp;
	if (x <= -1.55e+83) {
		tmp = t_1;
	} else if (x <= -6e-55) {
		tmp = fma(-a, x, (i * b)) * t;
	} else if (x <= -2.5e-226) {
		tmp = fma(-z, b, (j * a)) * c;
	} else if (x <= 6.2e-253) {
		tmp = fma(-y, j, (b * t)) * i;
	} else if (x <= 2.05e-17) {
		tmp = fma(-i, y, (c * a)) * j;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-t), a, Float64(z * y)) * x)
	tmp = 0.0
	if (x <= -1.55e+83)
		tmp = t_1;
	elseif (x <= -6e-55)
		tmp = Float64(fma(Float64(-a), x, Float64(i * b)) * t);
	elseif (x <= -2.5e-226)
		tmp = Float64(fma(Float64(-z), b, Float64(j * a)) * c);
	elseif (x <= 6.2e-253)
		tmp = Float64(fma(Float64(-y), j, Float64(b * t)) * i);
	elseif (x <= 2.05e-17)
		tmp = Float64(fma(Float64(-i), y, Float64(c * a)) * j);
	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[((-t) * a + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.55e+83], t$95$1, If[LessEqual[x, -6e-55], N[(N[((-a) * x + N[(i * b), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[x, -2.5e-226], N[(N[((-z) * b + N[(j * a), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[x, 6.2e-253], N[(N[((-y) * j + N[(b * t), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[x, 2.05e-17], N[(N[((-i) * y + N[(c * a), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.54999999999999996e83 or 2.05e-17 < x

   1. Initial program 78.5%

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

   3. Taylor expanded in 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. mul-1-neg N/A

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

      10. *-commutative N/A

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

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

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

      12. lower-fma.f64 N/A

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

      13. lower-neg.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 72.5

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

   5. Applied rewrites 72.5%

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

   if -1.54999999999999996e83 < x < -6.00000000000000033e-55

   1. Initial program 66.3%

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

   3. Taylor expanded in t around inf

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

      1. distribute-lft-out-- N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

   5. Applied rewrites 53.2%

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

   if -6.00000000000000033e-55 < x < -2.4999999999999999e-226

   1. Initial program 80.4%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 61.5

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

   5. Applied rewrites 61.5%

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

   if -2.4999999999999999e-226 < x < 6.19999999999999991e-253

   1. Initial program 64.5%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 68.8

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

   5. Applied rewrites 68.8%

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

   if 6.19999999999999991e-253 < x < 2.05e-17

   1. Initial program 79.2%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

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

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

      5. +-commutative N/A

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

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

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

      7. *-commutative N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 60.8

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

   5. Applied rewrites 60.8%

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

Alternative 5: 53.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-55}:\\ \;\;\;\;\mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-226}:\\ \;\;\;\;\mathsf{fma}\left(j, a, \left(-z\right) \cdot b\right) \cdot c\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-253}:\\ \;\;\;\;\mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot a\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- t) a (* z y)) x)))
   (if (<= x -1.55e+83)
     t_1
     (if (<= x -6e-55)
       (* (fma (- a) x (* i b)) t)
       (if (<= x -2.5e-226)
         (* (fma j a (* (- z) b)) c)
         (if (<= x 6.2e-253)
           (* (fma (- y) j (* b t)) i)
           (if (<= x 2.05e-17) (* (fma (- i) y (* c a)) j) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-t, a, (z * y)) * x;
	double tmp;
	if (x <= -1.55e+83) {
		tmp = t_1;
	} else if (x <= -6e-55) {
		tmp = fma(-a, x, (i * b)) * t;
	} else if (x <= -2.5e-226) {
		tmp = fma(j, a, (-z * b)) * c;
	} else if (x <= 6.2e-253) {
		tmp = fma(-y, j, (b * t)) * i;
	} else if (x <= 2.05e-17) {
		tmp = fma(-i, y, (c * a)) * j;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-t), a, Float64(z * y)) * x)
	tmp = 0.0
	if (x <= -1.55e+83)
		tmp = t_1;
	elseif (x <= -6e-55)
		tmp = Float64(fma(Float64(-a), x, Float64(i * b)) * t);
	elseif (x <= -2.5e-226)
		tmp = Float64(fma(j, a, Float64(Float64(-z) * b)) * c);
	elseif (x <= 6.2e-253)
		tmp = Float64(fma(Float64(-y), j, Float64(b * t)) * i);
	elseif (x <= 2.05e-17)
		tmp = Float64(fma(Float64(-i), y, Float64(c * a)) * j);
	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[((-t) * a + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.55e+83], t$95$1, If[LessEqual[x, -6e-55], N[(N[((-a) * x + N[(i * b), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[x, -2.5e-226], N[(N[(j * a + N[((-z) * b), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[x, 6.2e-253], N[(N[((-y) * j + N[(b * t), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[x, 2.05e-17], N[(N[((-i) * y + N[(c * a), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.54999999999999996e83 or 2.05e-17 < x

   1. Initial program 78.5%

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

   3. Taylor expanded in 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. mul-1-neg N/A

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

      10. *-commutative N/A

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

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

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

      12. lower-fma.f64 N/A

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

      13. lower-neg.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 72.5

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

   5. Applied rewrites 72.5%

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

   if -1.54999999999999996e83 < x < -6.00000000000000033e-55

   1. Initial program 66.3%

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

   3. Taylor expanded in t around inf

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

      1. distribute-lft-out-- N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

   5. Applied rewrites 53.2%

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

   if -6.00000000000000033e-55 < x < -2.4999999999999999e-226

   1. Initial program 80.4%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

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

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

      5. distribute-lft-neg-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. *-lft-identity N/A

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

      10. lower--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower-*.f64 74.0

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

   5. Applied rewrites 74.0%

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

   6. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. *-commutative N/A

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

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

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

      11. mul-1-neg N/A

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

      12. lower-*.f64 N/A

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

      13. mul-1-neg N/A

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

      14. lower-neg.f64 61.5

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

   8. Applied rewrites 61.5%

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

   if -2.4999999999999999e-226 < x < 6.19999999999999991e-253

   1. Initial program 64.5%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 68.8

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

   5. Applied rewrites 68.8%

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

   if 6.19999999999999991e-253 < x < 2.05e-17

   1. Initial program 79.2%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

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

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

      5. +-commutative N/A

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

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

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

      7. *-commutative N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 60.8

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

   5. Applied rewrites 60.8%

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

Alternative 6: 60.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+72}:\\ \;\;\;\;\left(\mathsf{fma}\left(b, \frac{i}{a}, -x\right) \cdot a\right) \cdot t\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+78}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -3.3e+72)
   (* (* (fma b (/ i a) (- x)) a) t)
   (if (<= t 7.2e+78)
     (+ (* (* z y) x) (* j (- (* c a) (* y i))))
     (* (fma (- a) x (* i b)) 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 (t <= -3.3e+72) {
		tmp = (fma(b, (i / a), -x) * a) * t;
	} else if (t <= 7.2e+78) {
		tmp = ((z * y) * x) + (j * ((c * a) - (y * i)));
	} else {
		tmp = fma(-a, x, (i * b)) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -3.3e+72)
		tmp = Float64(Float64(fma(b, Float64(i / a), Float64(-x)) * a) * t);
	elseif (t <= 7.2e+78)
		tmp = Float64(Float64(Float64(z * y) * x) + Float64(j * Float64(Float64(c * a) - Float64(y * i))));
	else
		tmp = Float64(fma(Float64(-a), x, Float64(i * b)) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -3.3e+72], N[(N[(N[(b * N[(i / a), $MachinePrecision] + (-x)), $MachinePrecision] * a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, 7.2e+78], N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-a) * x + N[(i * b), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.3e72

   1. Initial program 73.0%

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

   3. Taylor expanded in t around inf

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

      1. distribute-lft-out-- N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

   5. Applied rewrites 66.9%

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

   6. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 68.7

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

   8. Applied rewrites 68.7%

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

   if -3.3e72 < t < 7.20000000000000039e78

   1. Initial program 80.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

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

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

      5. distribute-lft-neg-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. *-lft-identity N/A

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

      10. lower--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower-*.f64 79.0

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

   5. Applied rewrites 79.0%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 68.0

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

   8. Applied rewrites 68.0%

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

   if 7.20000000000000039e78 < t

   1. Initial program 64.0%

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

   3. Taylor expanded in t around inf

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

      1. distribute-lft-out-- N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

   5. Applied rewrites 65.7%

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

Alternative 7: 60.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+72}:\\ \;\;\;\;\left(\mathsf{fma}\left(b, \frac{i}{a}, -x\right) \cdot a\right) \cdot t\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+78}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -3.5e+72)
   (* (* (fma b (/ i a) (- x)) a) t)
   (if (<= t 7.2e+78)
     (+ (* (* z x) y) (* j (- (* c a) (* y i))))
     (* (fma (- a) x (* i b)) 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 (t <= -3.5e+72) {
		tmp = (fma(b, (i / a), -x) * a) * t;
	} else if (t <= 7.2e+78) {
		tmp = ((z * x) * y) + (j * ((c * a) - (y * i)));
	} else {
		tmp = fma(-a, x, (i * b)) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -3.5e+72)
		tmp = Float64(Float64(fma(b, Float64(i / a), Float64(-x)) * a) * t);
	elseif (t <= 7.2e+78)
		tmp = Float64(Float64(Float64(z * x) * y) + Float64(j * Float64(Float64(c * a) - Float64(y * i))));
	else
		tmp = Float64(fma(Float64(-a), x, Float64(i * b)) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -3.5e+72], N[(N[(N[(b * N[(i / a), $MachinePrecision] + (-x)), $MachinePrecision] * a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, 7.2e+78], N[(N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-a) * x + N[(i * b), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.5000000000000001e72

   1. Initial program 73.0%

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

   3. Taylor expanded in t around inf

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

      1. distribute-lft-out-- N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

   5. Applied rewrites 66.9%

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

   6. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 68.7

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

   8. Applied rewrites 68.7%

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

   if -3.5000000000000001e72 < t < 7.20000000000000039e78

   1. Initial program 80.3%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 67.4

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

   5. Applied rewrites 67.4%

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

   if 7.20000000000000039e78 < t

   1. Initial program 64.0%

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

   3. Taylor expanded in t around inf

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

      1. distribute-lft-out-- N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

   5. Applied rewrites 65.7%

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

Alternative 8: 51.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-t, x, j \cdot c\right) \cdot a\\ t_2 := \mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{+84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-205}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-200}:\\ \;\;\;\;\mathsf{fma}\left(j, a, \left(-z\right) \cdot b\right) \cdot c\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- t) x (* j c)) a)) (t_2 (* (fma (- j) i (* z x)) y)))
   (if (<= y -1.95e+84)
     t_2
     (if (<= y -1.02e-205)
       t_1
       (if (<= y 3.5e-200)
         (* (fma j a (* (- z) b)) c)
         (if (<= y 1.85e-29) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-t, x, (j * c)) * a;
	double t_2 = fma(-j, i, (z * x)) * y;
	double tmp;
	if (y <= -1.95e+84) {
		tmp = t_2;
	} else if (y <= -1.02e-205) {
		tmp = t_1;
	} else if (y <= 3.5e-200) {
		tmp = fma(j, a, (-z * b)) * c;
	} else if (y <= 1.85e-29) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-t), x, Float64(j * c)) * a)
	t_2 = Float64(fma(Float64(-j), i, Float64(z * x)) * y)
	tmp = 0.0
	if (y <= -1.95e+84)
		tmp = t_2;
	elseif (y <= -1.02e-205)
		tmp = t_1;
	elseif (y <= 3.5e-200)
		tmp = Float64(fma(j, a, Float64(Float64(-z) * b)) * c);
	elseif (y <= 1.85e-29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-t) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-j) * i + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.95e+84], t$95$2, If[LessEqual[y, -1.02e-205], t$95$1, If[LessEqual[y, 3.5e-200], N[(N[(j * a + N[((-z) * b), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[y, 1.85e-29], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.95000000000000008e84 or 1.8499999999999999e-29 < y

   1. Initial program 73.2%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

      5. distribute-lft-neg-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 67.8

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

   5. Applied rewrites 67.8%

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

   if -1.95000000000000008e84 < y < -1.02000000000000001e-205 or 3.50000000000000023e-200 < y < 1.8499999999999999e-29

   1. Initial program 74.6%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 57.5

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

   5. Applied rewrites 57.5%

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

   if -1.02000000000000001e-205 < y < 3.50000000000000023e-200

   1. Initial program 84.7%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

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

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

      5. distribute-lft-neg-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. *-lft-identity N/A

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

      10. lower--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower-*.f64 84.7

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

   5. Applied rewrites 84.7%

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

   6. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. *-commutative N/A

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

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

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

      11. mul-1-neg N/A

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

      12. lower-*.f64 N/A

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

      13. mul-1-neg N/A

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

      14. lower-neg.f64 63.2

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

   8. Applied rewrites 63.2%

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

Alternative 9: 53.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-55}:\\ \;\;\;\;\mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-229}:\\ \;\;\;\;\mathsf{fma}\left(j, a, \left(-z\right) \cdot b\right) \cdot c\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot a\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- t) a (* z y)) x)))
   (if (<= x -1.55e+83)
     t_1
     (if (<= x -6e-55)
       (* (fma (- a) x (* i b)) t)
       (if (<= x -3.5e-229)
         (* (fma j a (* (- z) b)) c)
         (if (<= x 2.05e-17) (* (fma (- i) y (* c a)) j) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-t, a, (z * y)) * x;
	double tmp;
	if (x <= -1.55e+83) {
		tmp = t_1;
	} else if (x <= -6e-55) {
		tmp = fma(-a, x, (i * b)) * t;
	} else if (x <= -3.5e-229) {
		tmp = fma(j, a, (-z * b)) * c;
	} else if (x <= 2.05e-17) {
		tmp = fma(-i, y, (c * a)) * j;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-t), a, Float64(z * y)) * x)
	tmp = 0.0
	if (x <= -1.55e+83)
		tmp = t_1;
	elseif (x <= -6e-55)
		tmp = Float64(fma(Float64(-a), x, Float64(i * b)) * t);
	elseif (x <= -3.5e-229)
		tmp = Float64(fma(j, a, Float64(Float64(-z) * b)) * c);
	elseif (x <= 2.05e-17)
		tmp = Float64(fma(Float64(-i), y, Float64(c * a)) * j);
	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[((-t) * a + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.55e+83], t$95$1, If[LessEqual[x, -6e-55], N[(N[((-a) * x + N[(i * b), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[x, -3.5e-229], N[(N[(j * a + N[((-z) * b), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[x, 2.05e-17], N[(N[((-i) * y + N[(c * a), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.54999999999999996e83 or 2.05e-17 < x

   1. Initial program 78.5%

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

   3. Taylor expanded in 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. mul-1-neg N/A

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

      10. *-commutative N/A

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

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

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

      12. lower-fma.f64 N/A

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

      13. lower-neg.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 72.5

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

   5. Applied rewrites 72.5%

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

   if -1.54999999999999996e83 < x < -6.00000000000000033e-55

   1. Initial program 66.3%

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

   3. Taylor expanded in t around inf

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

      1. distribute-lft-out-- N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

   5. Applied rewrites 53.2%

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

   if -6.00000000000000033e-55 < x < -3.5000000000000003e-229

   1. Initial program 81.1%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

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

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

      5. distribute-lft-neg-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. *-lft-identity N/A

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

      10. lower--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower-*.f64 71.6

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

   5. Applied rewrites 71.6%

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

   6. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. *-commutative N/A

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

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

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

      11. mul-1-neg N/A

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

      12. lower-*.f64 N/A

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

      13. mul-1-neg N/A

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

      14. lower-neg.f64 59.5

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

   8. Applied rewrites 59.5%

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

   if -3.5000000000000003e-229 < x < 2.05e-17

   1. Initial program 74.4%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

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

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

      5. +-commutative N/A

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

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

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

      7. *-commutative N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 55.6

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

   5. Applied rewrites 55.6%

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

Alternative 10: 51.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y\\ \mathbf{if}\;y \leq -1 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-37}:\\ \;\;\;\;\mathsf{fma}\left(j, a, \left(-z\right) \cdot b\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- j) i (* z x)) y)))
   (if (<= y -1e+74)
     t_1
     (if (<= y -1e+18)
       (* (fma (- a) x (* i b)) t)
       (if (<= y 7.5e-37) (* (fma j a (* (- z) b)) 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 = fma(-j, i, (z * x)) * y;
	double tmp;
	if (y <= -1e+74) {
		tmp = t_1;
	} else if (y <= -1e+18) {
		tmp = fma(-a, x, (i * b)) * t;
	} else if (y <= 7.5e-37) {
		tmp = fma(j, a, (-z * b)) * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-j), i, Float64(z * x)) * y)
	tmp = 0.0
	if (y <= -1e+74)
		tmp = t_1;
	elseif (y <= -1e+18)
		tmp = Float64(fma(Float64(-a), x, Float64(i * b)) * t);
	elseif (y <= 7.5e-37)
		tmp = Float64(fma(j, a, Float64(Float64(-z) * b)) * c);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-j) * i + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1e+74], t$95$1, If[LessEqual[y, -1e+18], N[(N[((-a) * x + N[(i * b), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 7.5e-37], N[(N[(j * a + N[((-z) * b), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.99999999999999952e73 or 7.5000000000000004e-37 < y

   1. Initial program 72.3%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   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. mul-1-neg N/A

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

      4. *-commutative N/A

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

      5. distribute-lft-neg-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 65.7

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

   5. Applied rewrites 65.7%

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

   if -9.99999999999999952e73 < y < -1e18

   1. Initial program 78.7%

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

   3. Taylor expanded in t around inf

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

      1. distribute-lft-out-- N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

   5. Applied rewrites 78.9%

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

   if -1e18 < y < 7.5000000000000004e-37

   1. Initial program 79.6%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

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

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

      5. distribute-lft-neg-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. *-lft-identity N/A

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

      10. lower--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower-*.f64 78.7

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

   5. Applied rewrites 78.7%

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

   6. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. *-commutative N/A

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

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

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

      11. mul-1-neg N/A

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

      12. lower-*.f64 N/A

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

      13. mul-1-neg N/A

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

      14. lower-neg.f64 55.9

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

   8. Applied rewrites 55.9%

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

Alternative 11: 50.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-86}:\\ \;\;\;\;\mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+58}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot a\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- c) b (* y x)) z)))
   (if (<= z -7.5e+135)
     t_1
     (if (<= z -8.5e-86)
       (* (fma (- a) x (* i b)) t)
       (if (<= z 3.4e+58) (* (fma (- i) y (* c a)) j) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-c, b, (y * x)) * z;
	double tmp;
	if (z <= -7.5e+135) {
		tmp = t_1;
	} else if (z <= -8.5e-86) {
		tmp = fma(-a, x, (i * b)) * t;
	} else if (z <= 3.4e+58) {
		tmp = fma(-i, y, (c * a)) * j;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-c), b, Float64(y * x)) * z)
	tmp = 0.0
	if (z <= -7.5e+135)
		tmp = t_1;
	elseif (z <= -8.5e-86)
		tmp = Float64(fma(Float64(-a), x, Float64(i * b)) * t);
	elseif (z <= 3.4e+58)
		tmp = Float64(fma(Float64(-i), y, Float64(c * a)) * j);
	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[((-c) * b + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -7.5e+135], t$95$1, If[LessEqual[z, -8.5e-86], N[(N[((-a) * x + N[(i * b), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 3.4e+58], N[(N[((-i) * y + N[(c * a), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.49999999999999947e135 or 3.4000000000000001e58 < z

   1. Initial program 69.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-neg.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 73.3

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

   5. Applied rewrites 73.3%

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

   if -7.49999999999999947e135 < z < -8.499999999999999e-86

   1. Initial program 73.6%

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

   3. Taylor expanded in t around inf

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

      1. distribute-lft-out-- N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

   5. Applied rewrites 51.2%

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

   if -8.499999999999999e-86 < z < 3.4000000000000001e58

   1. Initial program 81.8%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

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

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

      5. +-commutative N/A

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

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

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

      7. *-commutative N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 54.3

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

   5. Applied rewrites 54.3%

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

Alternative 12: 52.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-301}:\\ \;\;\;\;\mathsf{fma}\left(j, a, \left(-z\right) \cdot b\right) \cdot c\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- a) x (* i b)) t)))
   (if (<= t -4.8e+28)
     t_1
     (if (<= t 8e-301)
       (* (fma j a (* (- z) b)) c)
       (if (<= t 1.1e+18) (* (fma (- c) b (* y x)) 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(-a, x, (i * b)) * t;
	double tmp;
	if (t <= -4.8e+28) {
		tmp = t_1;
	} else if (t <= 8e-301) {
		tmp = fma(j, a, (-z * b)) * c;
	} else if (t <= 1.1e+18) {
		tmp = fma(-c, b, (y * x)) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-a), x, Float64(i * b)) * t)
	tmp = 0.0
	if (t <= -4.8e+28)
		tmp = t_1;
	elseif (t <= 8e-301)
		tmp = Float64(fma(j, a, Float64(Float64(-z) * b)) * c);
	elseif (t <= 1.1e+18)
		tmp = Float64(fma(Float64(-c), b, Float64(y * x)) * 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[((-a) * x + N[(i * b), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -4.8e+28], t$95$1, If[LessEqual[t, 8e-301], N[(N[(j * a + N[((-z) * b), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[t, 1.1e+18], N[(N[((-c) * b + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.79999999999999962e28 or 1.1e18 < t

   1. Initial program 70.8%

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

   3. Taylor expanded in t around inf

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

      1. distribute-lft-out-- N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

   5. Applied rewrites 63.0%

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

   if -4.79999999999999962e28 < t < 8.00000000000000053e-301

   1. Initial program 79.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

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

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

      5. distribute-lft-neg-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. *-lft-identity N/A

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

      10. lower--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower-*.f64 77.8

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

   5. Applied rewrites 77.8%

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

   6. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. *-commutative N/A

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

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

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

      11. mul-1-neg N/A

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

      12. lower-*.f64 N/A

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

      13. mul-1-neg N/A

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

      14. lower-neg.f64 53.7

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

   8. Applied rewrites 53.7%

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

   if 8.00000000000000053e-301 < t < 1.1e18

   1. Initial program 81.6%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-neg.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 51.4

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

   5. Applied rewrites 51.4%

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

Alternative 13: 51.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-79}:\\ \;\;\;\;\mathsf{fma}\left(j, a, \left(-z\right) \cdot b\right) \cdot c\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+17}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- a) x (* i b)) t)))
   (if (<= t -4.8e+28)
     t_1
     (if (<= t 2.6e-79)
       (* (fma j a (* (- z) b)) c)
       (if (<= t 9.2e+17) (* (* 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(-a, x, (i * b)) * t;
	double tmp;
	if (t <= -4.8e+28) {
		tmp = t_1;
	} else if (t <= 2.6e-79) {
		tmp = fma(j, a, (-z * b)) * c;
	} else if (t <= 9.2e+17) {
		tmp = (z * y) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-a), x, Float64(i * b)) * t)
	tmp = 0.0
	if (t <= -4.8e+28)
		tmp = t_1;
	elseif (t <= 2.6e-79)
		tmp = Float64(fma(j, a, Float64(Float64(-z) * b)) * c);
	elseif (t <= 9.2e+17)
		tmp = Float64(Float64(z * y) * x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-a) * x + N[(i * b), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -4.8e+28], t$95$1, If[LessEqual[t, 2.6e-79], N[(N[(j * a + N[((-z) * b), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[t, 9.2e+17], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.79999999999999962e28 or 9.2e17 < t

   1. Initial program 70.8%

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

   3. Taylor expanded in t around inf

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

      1. distribute-lft-out-- N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

   5. Applied rewrites 63.0%

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

   if -4.79999999999999962e28 < t < 2.59999999999999994e-79

   1. Initial program 83.2%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

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

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

      5. distribute-lft-neg-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. *-lft-identity N/A

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

      10. lower--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower-*.f64 82.3

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

   5. Applied rewrites 82.3%

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

   6. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. *-commutative N/A

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

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

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

      11. mul-1-neg N/A

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

      12. lower-*.f64 N/A

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

      13. mul-1-neg N/A

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

      14. lower-neg.f64 49.0

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

   8. Applied rewrites 49.0%

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

   if 2.59999999999999994e-79 < t < 9.2e17

   1. Initial program 65.1%

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

   3. Taylor expanded in y around 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. mul-1-neg N/A

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

      4. *-commutative N/A

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

      5. distribute-lft-neg-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 61.1

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

   5. Applied rewrites 61.1%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 60.7

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

   8. Applied rewrites 60.7%

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

Alternative 14: 42.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3600000000000 \lor \neg \left(c \leq 2.45 \cdot 10^{-55}\right):\\ \;\;\;\;\mathsf{fma}\left(j, a, \left(-z\right) \cdot b\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -3600000000000.0) (not (<= c 2.45e-55)))
   (* (fma j a (* (- z) b)) c)
   (* (* z y) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -3600000000000.0) || !(c <= 2.45e-55)) {
		tmp = fma(j, a, (-z * b)) * c;
	} else {
		tmp = (z * y) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -3600000000000.0) || !(c <= 2.45e-55))
		tmp = Float64(fma(j, a, Float64(Float64(-z) * b)) * c);
	else
		tmp = Float64(Float64(z * y) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -3600000000000.0], N[Not[LessEqual[c, 2.45e-55]], $MachinePrecision]], N[(N[(j * a + N[((-z) * b), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.6e12 or 2.45000000000000018e-55 < c

   1. Initial program 70.4%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

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

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

      5. distribute-lft-neg-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. *-lft-identity N/A

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

      10. lower--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower-*.f64 67.5

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

   5. Applied rewrites 67.5%

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

   6. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. *-commutative N/A

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

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

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

      11. mul-1-neg N/A

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

      12. lower-*.f64 N/A

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

      13. mul-1-neg N/A

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

      14. lower-neg.f64 59.4

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

   8. Applied rewrites 59.4%

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

   if -3.6e12 < c < 2.45000000000000018e-55

   1. Initial program 82.5%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

      5. distribute-lft-neg-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 55.7

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

   5. Applied rewrites 55.7%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 36.1

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

   8. Applied rewrites 36.1%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3600000000000 \lor \neg \left(c \leq 2.45 \cdot 10^{-55}\right):\\ \;\;\;\;\mathsf{fma}\left(j, a, \left(-z\right) \cdot b\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.1 \cdot 10^{+143}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-74}:\\ \;\;\;\;\left(\left(-x\right) \cdot a\right) \cdot t\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+59}:\\ \;\;\;\;\left(j \cdot a\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -7.1e+143)
   (* (* z y) x)
   (if (<= z -4.1e-74)
     (* (* (- x) a) t)
     (if (<= z 1.85e+59) (* (* j a) c) (* (* z x) y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -7.1e+143) {
		tmp = (z * y) * x;
	} else if (z <= -4.1e-74) {
		tmp = (-x * a) * t;
	} else if (z <= 1.85e+59) {
		tmp = (j * a) * c;
	} else {
		tmp = (z * x) * y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-7.1d+143)) then
        tmp = (z * y) * x
    else if (z <= (-4.1d-74)) then
        tmp = (-x * a) * t
    else if (z <= 1.85d+59) then
        tmp = (j * a) * c
    else
        tmp = (z * x) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -7.1e+143) {
		tmp = (z * y) * x;
	} else if (z <= -4.1e-74) {
		tmp = (-x * a) * t;
	} else if (z <= 1.85e+59) {
		tmp = (j * a) * c;
	} else {
		tmp = (z * x) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -7.1e+143:
		tmp = (z * y) * x
	elif z <= -4.1e-74:
		tmp = (-x * a) * t
	elif z <= 1.85e+59:
		tmp = (j * a) * c
	else:
		tmp = (z * x) * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -7.1e+143)
		tmp = Float64(Float64(z * y) * x);
	elseif (z <= -4.1e-74)
		tmp = Float64(Float64(Float64(-x) * a) * t);
	elseif (z <= 1.85e+59)
		tmp = Float64(Float64(j * a) * c);
	else
		tmp = Float64(Float64(z * x) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -7.1e+143)
		tmp = (z * y) * x;
	elseif (z <= -4.1e-74)
		tmp = (-x * a) * t;
	elseif (z <= 1.85e+59)
		tmp = (j * a) * c;
	else
		tmp = (z * x) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -7.1e+143], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, -4.1e-74], N[(N[((-x) * a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 1.85e+59], N[(N[(j * a), $MachinePrecision] * c), $MachinePrecision], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.10000000000000043e143

   1. Initial program 73.2%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

      5. distribute-lft-neg-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 60.8

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

   5. Applied rewrites 60.8%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 60.6

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

   8. Applied rewrites 60.6%

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

   if -7.10000000000000043e143 < z < -4.10000000000000032e-74

   1. Initial program 72.5%

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

   3. Taylor expanded in t around inf

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

      1. distribute-lft-out-- N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

   5. Applied rewrites 51.2%

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

   6. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. mul-1-neg N/A

         \[\leadsto \left(\left(-1 \cdot x\right) \cdot a\right) \cdot t \]

      5. lower-*.f64 N/A

         \[\leadsto \left(\left(-1 \cdot x\right) \cdot a\right) \cdot t \]

      6. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(x\right)\right) \cdot a\right) \cdot t \]

      7. lower-neg.f64 34.6

         \[\leadsto \left(\left(-x\right) \cdot a\right) \cdot t \]

   8. Applied rewrites 34.6%

      \[\leadsto \left(\left(-x\right) \cdot a\right) \cdot t \]

   if -4.10000000000000032e-74 < z < 1.84999999999999999e59

   1. Initial program 81.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \left(x \cdot \color{blue}{\left(z \cdot \left(y + -1 \cdot \frac{a \cdot t}{z}\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(x \cdot \left(\left(y + -1 \cdot \frac{a \cdot t}{z}\right) \cdot \color{blue}{z}\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(\left(y + -1 \cdot \frac{a \cdot t}{z}\right) \cdot \color{blue}{z}\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative N/A

         \[\leadsto \left(x \cdot \left(\left(y + \frac{a \cdot t}{z} \cdot -1\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(x \cdot \left(\left(y - \left(\mathsf{neg}\left(\frac{a \cdot t}{z}\right)\right) \cdot -1\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \left(x \cdot \left(\left(y - \left(\mathsf{neg}\left(\frac{a \cdot t}{z} \cdot -1\right)\right)\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. *-commutative N/A

         \[\leadsto \left(x \cdot \left(\left(y - \left(\mathsf{neg}\left(-1 \cdot \frac{a \cdot t}{z}\right)\right)\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      7. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(\left(y - \left(\mathsf{neg}\left(-1\right)\right) \cdot \frac{a \cdot t}{z}\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      8. metadata-eval N/A

         \[\leadsto \left(x \cdot \left(\left(y - 1 \cdot \frac{a \cdot t}{z}\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      9. *-lft-identity N/A

         \[\leadsto \left(x \cdot \left(\left(y - \frac{a \cdot t}{z}\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      10. lower--.f64 N/A

          \[\leadsto \left(x \cdot \left(\left(y - \frac{a \cdot t}{z}\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      11. lower-/.f64 N/A

          \[\leadsto \left(x \cdot \left(\left(y - \frac{a \cdot t}{z}\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      12. lower-*.f64 75.2

          \[\leadsto \left(x \cdot \left(\left(y - \frac{a \cdot t}{z}\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Applied rewrites 75.2%

      \[\leadsto \left(x \cdot \color{blue}{\left(\left(y - \frac{a \cdot t}{z}\right) \cdot z\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot j - b \cdot z\right) \cdot \color{blue}{c} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot j - b \cdot z\right) \cdot \color{blue}{c} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(a \cdot j + \left(\mathsf{neg}\left(b\right)\right) \cdot z\right) \cdot c \]

      4. mul-1-neg N/A

         \[\leadsto \left(a \cdot j + \left(-1 \cdot b\right) \cdot z\right) \cdot c \]

      5. associate-*r* N/A

         \[\leadsto \left(a \cdot j + -1 \cdot \left(b \cdot z\right)\right) \cdot c \]

      6. *-commutative N/A

         \[\leadsto \left(j \cdot a + -1 \cdot \left(b \cdot z\right)\right) \cdot c \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(j, a, -1 \cdot \left(b \cdot z\right)\right) \cdot c \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(j, a, \mathsf{neg}\left(b \cdot z\right)\right) \cdot c \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(j, a, \mathsf{neg}\left(z \cdot b\right)\right) \cdot c \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{fma}\left(j, a, \left(\mathsf{neg}\left(z\right)\right) \cdot b\right) \cdot c \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(j, a, \left(-1 \cdot z\right) \cdot b\right) \cdot c \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(j, a, \left(-1 \cdot z\right) \cdot b\right) \cdot c \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(j, a, \left(\mathsf{neg}\left(z\right)\right) \cdot b\right) \cdot c \]

      14. lower-neg.f64 42.6

          \[\leadsto \mathsf{fma}\left(j, a, \left(-z\right) \cdot b\right) \cdot c \]

   8. Applied rewrites 42.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a, \left(-z\right) \cdot b\right) \cdot c} \]

   9. Taylor expanded in z around 0

      \[\leadsto \left(a \cdot j\right) \cdot c \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \left(j \cdot a\right) \cdot c \]

       2. lower-*.f64 37.1

          \[\leadsto \left(j \cdot a\right) \cdot c \]

   11. Applied rewrites 37.1%

       \[\leadsto \left(j \cdot a\right) \cdot c \]

   if 1.84999999999999999e59 < z

   1. Initial program 67.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right) \cdot \color{blue}{y} \]

      3. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(i \cdot j\right)\right) + x \cdot z\right) \cdot y \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(j \cdot i\right)\right) + x \cdot z\right) \cdot y \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(j\right)\right) \cdot i + x \cdot z\right) \cdot y \]

      6. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(j\right), i, x \cdot z\right) \cdot y \]

      7. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-j, i, x \cdot z\right) \cdot y \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y \]

      9. lower-*.f64 56.7

         \[\leadsto \mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y \]

   5. Applied rewrites 56.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y} \]

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot z\right) \cdot y \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(z \cdot x\right) \cdot y \]

      2. lower-*.f64 49.1

         \[\leadsto \left(z \cdot x\right) \cdot y \]

   8. Applied rewrites 49.1%

      \[\leadsto \left(z \cdot x\right) \cdot y \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 16: 30.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-60} \lor \neg \left(z \leq 2 \cdot 10^{-33}\right):\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot a\right) \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -6.6e-60) (not (<= z 2e-33))) (* (* z y) x) (* (* j a) 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 ((z <= -6.6e-60) || !(z <= 2e-33)) {
		tmp = (z * y) * x;
	} else {
		tmp = (j * a) * c;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((z <= (-6.6d-60)) .or. (.not. (z <= 2d-33))) then
        tmp = (z * y) * x
    else
        tmp = (j * a) * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -6.6e-60) || !(z <= 2e-33)) {
		tmp = (z * y) * x;
	} else {
		tmp = (j * a) * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -6.6e-60) or not (z <= 2e-33):
		tmp = (z * y) * x
	else:
		tmp = (j * a) * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -6.6e-60) || !(z <= 2e-33))
		tmp = Float64(Float64(z * y) * x);
	else
		tmp = Float64(Float64(j * a) * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -6.6e-60) || ~((z <= 2e-33)))
		tmp = (z * y) * x;
	else
		tmp = (j * a) * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -6.6e-60], N[Not[LessEqual[z, 2e-33]], $MachinePrecision]], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], N[(N[(j * a), $MachinePrecision] * c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5999999999999996e-60 or 2.0000000000000001e-33 < z

   1. Initial program 69.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   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. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(i \cdot j\right)\right) + x \cdot z\right) \cdot y \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(j \cdot i\right)\right) + x \cdot z\right) \cdot y \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(j\right)\right) \cdot i + x \cdot z\right) \cdot y \]

      6. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(j\right), i, x \cdot z\right) \cdot y \]

      7. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-j, i, x \cdot z\right) \cdot y \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y \]

      9. lower-*.f64 50.8

         \[\leadsto \mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y \]

   5. Applied rewrites 50.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y} \]

   6. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(y \cdot z\right) \cdot x \]

      2. lower-*.f64 N/A

         \[\leadsto \left(y \cdot z\right) \cdot x \]

      3. *-commutative N/A

         \[\leadsto \left(z \cdot y\right) \cdot x \]

      4. lower-*.f64 36.8

         \[\leadsto \left(z \cdot y\right) \cdot x \]

   8. Applied rewrites 36.8%

      \[\leadsto \left(z \cdot y\right) \cdot \color{blue}{x} \]

   if -6.5999999999999996e-60 < z < 2.0000000000000001e-33

   1. Initial program 85.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \left(x \cdot \color{blue}{\left(z \cdot \left(y + -1 \cdot \frac{a \cdot t}{z}\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(x \cdot \left(\left(y + -1 \cdot \frac{a \cdot t}{z}\right) \cdot \color{blue}{z}\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(\left(y + -1 \cdot \frac{a \cdot t}{z}\right) \cdot \color{blue}{z}\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative N/A

         \[\leadsto \left(x \cdot \left(\left(y + \frac{a \cdot t}{z} \cdot -1\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(x \cdot \left(\left(y - \left(\mathsf{neg}\left(\frac{a \cdot t}{z}\right)\right) \cdot -1\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \left(x \cdot \left(\left(y - \left(\mathsf{neg}\left(\frac{a \cdot t}{z} \cdot -1\right)\right)\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. *-commutative N/A

         \[\leadsto \left(x \cdot \left(\left(y - \left(\mathsf{neg}\left(-1 \cdot \frac{a \cdot t}{z}\right)\right)\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      7. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(\left(y - \left(\mathsf{neg}\left(-1\right)\right) \cdot \frac{a \cdot t}{z}\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      8. metadata-eval N/A

         \[\leadsto \left(x \cdot \left(\left(y - 1 \cdot \frac{a \cdot t}{z}\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      9. *-lft-identity N/A

         \[\leadsto \left(x \cdot \left(\left(y - \frac{a \cdot t}{z}\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      10. lower--.f64 N/A

          \[\leadsto \left(x \cdot \left(\left(y - \frac{a \cdot t}{z}\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      11. lower-/.f64 N/A

          \[\leadsto \left(x \cdot \left(\left(y - \frac{a \cdot t}{z}\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      12. lower-*.f64 78.0

          \[\leadsto \left(x \cdot \left(\left(y - \frac{a \cdot t}{z}\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Applied rewrites 78.0%

      \[\leadsto \left(x \cdot \color{blue}{\left(\left(y - \frac{a \cdot t}{z}\right) \cdot z\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot j - b \cdot z\right) \cdot \color{blue}{c} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot j - b \cdot z\right) \cdot \color{blue}{c} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(a \cdot j + \left(\mathsf{neg}\left(b\right)\right) \cdot z\right) \cdot c \]

      4. mul-1-neg N/A

         \[\leadsto \left(a \cdot j + \left(-1 \cdot b\right) \cdot z\right) \cdot c \]

      5. associate-*r* N/A

         \[\leadsto \left(a \cdot j + -1 \cdot \left(b \cdot z\right)\right) \cdot c \]

      6. *-commutative N/A

         \[\leadsto \left(j \cdot a + -1 \cdot \left(b \cdot z\right)\right) \cdot c \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(j, a, -1 \cdot \left(b \cdot z\right)\right) \cdot c \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(j, a, \mathsf{neg}\left(b \cdot z\right)\right) \cdot c \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(j, a, \mathsf{neg}\left(z \cdot b\right)\right) \cdot c \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{fma}\left(j, a, \left(\mathsf{neg}\left(z\right)\right) \cdot b\right) \cdot c \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(j, a, \left(-1 \cdot z\right) \cdot b\right) \cdot c \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(j, a, \left(-1 \cdot z\right) \cdot b\right) \cdot c \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(j, a, \left(\mathsf{neg}\left(z\right)\right) \cdot b\right) \cdot c \]

      14. lower-neg.f64 44.5

          \[\leadsto \mathsf{fma}\left(j, a, \left(-z\right) \cdot b\right) \cdot c \]

   8. Applied rewrites 44.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a, \left(-z\right) \cdot b\right) \cdot c} \]

   9. Taylor expanded in z around 0

      \[\leadsto \left(a \cdot j\right) \cdot c \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \left(j \cdot a\right) \cdot c \]

       2. lower-*.f64 40.6

          \[\leadsto \left(j \cdot a\right) \cdot c \]

   11. Applied rewrites 40.6%

       \[\leadsto \left(j \cdot a\right) \cdot c \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-60} \lor \neg \left(z \leq 2 \cdot 10^{-33}\right):\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot a\right) \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.06 \cdot 10^{+83} \lor \neg \left(x \leq 1.25 \cdot 10^{-83}\right):\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot t\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= x -2.06e+83) (not (<= x 1.25e-83))) (* (* z y) x) (* (* i t) b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -2.06e+83) || !(x <= 1.25e-83)) {
		tmp = (z * y) * x;
	} else {
		tmp = (i * t) * b;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((x <= (-2.06d+83)) .or. (.not. (x <= 1.25d-83))) then
        tmp = (z * y) * x
    else
        tmp = (i * t) * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -2.06e+83) || !(x <= 1.25e-83)) {
		tmp = (z * y) * x;
	} else {
		tmp = (i * t) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (x <= -2.06e+83) or not (x <= 1.25e-83):
		tmp = (z * y) * x
	else:
		tmp = (i * t) * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((x <= -2.06e+83) || !(x <= 1.25e-83))
		tmp = Float64(Float64(z * y) * x);
	else
		tmp = Float64(Float64(i * t) * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((x <= -2.06e+83) || ~((x <= 1.25e-83)))
		tmp = (z * y) * x;
	else
		tmp = (i * t) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[x, -2.06e+83], N[Not[LessEqual[x, 1.25e-83]], $MachinePrecision]], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], N[(N[(i * t), $MachinePrecision] * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.06e83 or 1.25e-83 < x

   1. Initial program 77.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 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. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(i \cdot j\right)\right) + x \cdot z\right) \cdot y \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(j \cdot i\right)\right) + x \cdot z\right) \cdot y \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(j\right)\right) \cdot i + x \cdot z\right) \cdot y \]

      6. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(j\right), i, x \cdot z\right) \cdot y \]

      7. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-j, i, x \cdot z\right) \cdot y \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y \]

      9. lower-*.f64 52.3

         \[\leadsto \mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y \]

   5. Applied rewrites 52.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y} \]

   6. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(y \cdot z\right) \cdot x \]

      2. lower-*.f64 N/A

         \[\leadsto \left(y \cdot z\right) \cdot x \]

      3. *-commutative N/A

         \[\leadsto \left(z \cdot y\right) \cdot x \]

      4. lower-*.f64 40.8

         \[\leadsto \left(z \cdot y\right) \cdot x \]

   8. Applied rewrites 40.8%

      \[\leadsto \left(z \cdot y\right) \cdot \color{blue}{x} \]

   if -2.06e83 < x < 1.25e-83

   1. Initial program 74.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(t \cdot -1\right) \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot t\right) \cdot \left(\color{blue}{a \cdot x} - b \cdot i\right) \]

      4. associate-*r* N/A

         \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      5. *-commutative N/A

         \[\leadsto -1 \cdot \left(\left(a \cdot x - b \cdot i\right) \cdot \color{blue}{t}\right) \]

      6. associate-*r* N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right) \cdot \color{blue}{t} \]

      7. distribute-lft-out-- N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot t \]

      8. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot \color{blue}{t} \]

   5. Applied rewrites 38.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t} \]

   6. Taylor expanded in x around 0

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(i \cdot t\right) \cdot b \]

      2. lower-*.f64 N/A

         \[\leadsto \left(i \cdot t\right) \cdot b \]

      3. lower-*.f64 29.7

         \[\leadsto \left(i \cdot t\right) \cdot b \]

   8. Applied rewrites 29.7%

      \[\leadsto \left(i \cdot t\right) \cdot \color{blue}{b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.06 \cdot 10^{+83} \lor \neg \left(x \leq 1.25 \cdot 10^{-83}\right):\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot t\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-60}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+59}:\\ \;\;\;\;\left(j \cdot a\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -6.6e-60)
   (* (* z y) x)
   (if (<= z 1.85e+59) (* (* j a) c) (* (* z x) y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -6.6e-60) {
		tmp = (z * y) * x;
	} else if (z <= 1.85e+59) {
		tmp = (j * a) * c;
	} else {
		tmp = (z * x) * y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-6.6d-60)) then
        tmp = (z * y) * x
    else if (z <= 1.85d+59) then
        tmp = (j * a) * c
    else
        tmp = (z * x) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -6.6e-60) {
		tmp = (z * y) * x;
	} else if (z <= 1.85e+59) {
		tmp = (j * a) * c;
	} else {
		tmp = (z * x) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -6.6e-60:
		tmp = (z * y) * x
	elif z <= 1.85e+59:
		tmp = (j * a) * c
	else:
		tmp = (z * x) * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -6.6e-60)
		tmp = Float64(Float64(z * y) * x);
	elseif (z <= 1.85e+59)
		tmp = Float64(Float64(j * a) * c);
	else
		tmp = Float64(Float64(z * x) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -6.6e-60)
		tmp = (z * y) * x;
	elseif (z <= 1.85e+59)
		tmp = (j * a) * c;
	else
		tmp = (z * x) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -6.6e-60], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 1.85e+59], N[(N[(j * a), $MachinePrecision] * c), $MachinePrecision], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5999999999999996e-60

   1. Initial program 72.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 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. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(i \cdot j\right)\right) + x \cdot z\right) \cdot y \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(j \cdot i\right)\right) + x \cdot z\right) \cdot y \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(j\right)\right) \cdot i + x \cdot z\right) \cdot y \]

      6. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(j\right), i, x \cdot z\right) \cdot y \]

      7. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-j, i, x \cdot z\right) \cdot y \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y \]

      9. lower-*.f64 48.1

         \[\leadsto \mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y \]

   5. Applied rewrites 48.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y} \]

   6. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(y \cdot z\right) \cdot x \]

      2. lower-*.f64 N/A

         \[\leadsto \left(y \cdot z\right) \cdot x \]

      3. *-commutative N/A

         \[\leadsto \left(z \cdot y\right) \cdot x \]

      4. lower-*.f64 36.2

         \[\leadsto \left(z \cdot y\right) \cdot x \]

   8. Applied rewrites 36.2%

      \[\leadsto \left(z \cdot y\right) \cdot \color{blue}{x} \]

   if -6.5999999999999996e-60 < z < 1.84999999999999999e59

   1. Initial program 81.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \left(x \cdot \color{blue}{\left(z \cdot \left(y + -1 \cdot \frac{a \cdot t}{z}\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(x \cdot \left(\left(y + -1 \cdot \frac{a \cdot t}{z}\right) \cdot \color{blue}{z}\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(\left(y + -1 \cdot \frac{a \cdot t}{z}\right) \cdot \color{blue}{z}\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative N/A

         \[\leadsto \left(x \cdot \left(\left(y + \frac{a \cdot t}{z} \cdot -1\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(x \cdot \left(\left(y - \left(\mathsf{neg}\left(\frac{a \cdot t}{z}\right)\right) \cdot -1\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \left(x \cdot \left(\left(y - \left(\mathsf{neg}\left(\frac{a \cdot t}{z} \cdot -1\right)\right)\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. *-commutative N/A

         \[\leadsto \left(x \cdot \left(\left(y - \left(\mathsf{neg}\left(-1 \cdot \frac{a \cdot t}{z}\right)\right)\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      7. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(\left(y - \left(\mathsf{neg}\left(-1\right)\right) \cdot \frac{a \cdot t}{z}\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      8. metadata-eval N/A

         \[\leadsto \left(x \cdot \left(\left(y - 1 \cdot \frac{a \cdot t}{z}\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      9. *-lft-identity N/A

         \[\leadsto \left(x \cdot \left(\left(y - \frac{a \cdot t}{z}\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      10. lower--.f64 N/A

          \[\leadsto \left(x \cdot \left(\left(y - \frac{a \cdot t}{z}\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      11. lower-/.f64 N/A

          \[\leadsto \left(x \cdot \left(\left(y - \frac{a \cdot t}{z}\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      12. lower-*.f64 75.6

          \[\leadsto \left(x \cdot \left(\left(y - \frac{a \cdot t}{z}\right) \cdot z\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Applied rewrites 75.6%

      \[\leadsto \left(x \cdot \color{blue}{\left(\left(y - \frac{a \cdot t}{z}\right) \cdot z\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot j - b \cdot z\right) \cdot \color{blue}{c} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot j - b \cdot z\right) \cdot \color{blue}{c} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(a \cdot j + \left(\mathsf{neg}\left(b\right)\right) \cdot z\right) \cdot c \]

      4. mul-1-neg N/A

         \[\leadsto \left(a \cdot j + \left(-1 \cdot b\right) \cdot z\right) \cdot c \]

      5. associate-*r* N/A

         \[\leadsto \left(a \cdot j + -1 \cdot \left(b \cdot z\right)\right) \cdot c \]

      6. *-commutative N/A

         \[\leadsto \left(j \cdot a + -1 \cdot \left(b \cdot z\right)\right) \cdot c \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(j, a, -1 \cdot \left(b \cdot z\right)\right) \cdot c \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(j, a, \mathsf{neg}\left(b \cdot z\right)\right) \cdot c \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(j, a, \mathsf{neg}\left(z \cdot b\right)\right) \cdot c \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{fma}\left(j, a, \left(\mathsf{neg}\left(z\right)\right) \cdot b\right) \cdot c \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(j, a, \left(-1 \cdot z\right) \cdot b\right) \cdot c \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(j, a, \left(-1 \cdot z\right) \cdot b\right) \cdot c \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(j, a, \left(\mathsf{neg}\left(z\right)\right) \cdot b\right) \cdot c \]

      14. lower-neg.f64 42.8

          \[\leadsto \mathsf{fma}\left(j, a, \left(-z\right) \cdot b\right) \cdot c \]

   8. Applied rewrites 42.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a, \left(-z\right) \cdot b\right) \cdot c} \]

   9. Taylor expanded in z around 0

      \[\leadsto \left(a \cdot j\right) \cdot c \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \left(j \cdot a\right) \cdot c \]

       2. lower-*.f64 37.4

          \[\leadsto \left(j \cdot a\right) \cdot c \]

   11. Applied rewrites 37.4%

       \[\leadsto \left(j \cdot a\right) \cdot c \]

   if 1.84999999999999999e59 < z

   1. Initial program 67.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right) \cdot \color{blue}{y} \]

      3. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(i \cdot j\right)\right) + x \cdot z\right) \cdot y \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(j \cdot i\right)\right) + x \cdot z\right) \cdot y \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(j\right)\right) \cdot i + x \cdot z\right) \cdot y \]

      6. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(j\right), i, x \cdot z\right) \cdot y \]

      7. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-j, i, x \cdot z\right) \cdot y \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y \]

      9. lower-*.f64 56.7

         \[\leadsto \mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y \]

   5. Applied rewrites 56.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y} \]

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot z\right) \cdot y \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(z \cdot x\right) \cdot y \]

      2. lower-*.f64 49.1

         \[\leadsto \left(z \cdot x\right) \cdot y \]

   8. Applied rewrites 49.1%

      \[\leadsto \left(z \cdot x\right) \cdot y \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 22.3% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \left(i \cdot t\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* (* i t) b))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return (i * t) * b;
}

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 = (i * t) * b
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 (i * t) * b;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return (i * t) * b

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(i * t) * b)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = (i * t) * b;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(i * t), $MachinePrecision] * b), $MachinePrecision]

Derivation

1. Initial program 76.0%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Add Preprocessing

3. Taylor expanded in t around inf

   \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
4. Step-by-step derivation

   1. distribute-lft-out-- N/A

      \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)}\right) \]

   2. associate-*r* N/A

      \[\leadsto \left(t \cdot -1\right) \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)} \]

   3. *-commutative N/A

      \[\leadsto \left(-1 \cdot t\right) \cdot \left(\color{blue}{a \cdot x} - b \cdot i\right) \]

   4. associate-*r* N/A

      \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

   5. *-commutative N/A

      \[\leadsto -1 \cdot \left(\left(a \cdot x - b \cdot i\right) \cdot \color{blue}{t}\right) \]

   6. associate-*r* N/A

      \[\leadsto \left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right) \cdot \color{blue}{t} \]

   7. distribute-lft-out-- N/A

      \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot t \]

   8. lower-*.f64 N/A

      \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot \color{blue}{t} \]

5. Applied rewrites 38.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t} \]

6. Taylor expanded in x around 0

   \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
7. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \left(i \cdot t\right) \cdot b \]

   2. lower-*.f64 N/A

      \[\leadsto \left(i \cdot t\right) \cdot b \]

   3. lower-*.f64 20.8

      \[\leadsto \left(i \cdot t\right) \cdot b \]

8. Applied rewrites 20.8%

   \[\leadsto \left(i \cdot t\right) \cdot \color{blue}{b} \]
9. Add Preprocessing

Developer Target 1: 59.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2025026 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -293938859355541/2000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 32113527362226803/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))