Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.3% → 82.1%

Time: 7.7s

Alternatives: 23

Speedup: 0.5×

• 58.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 23.9%

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

   6. Taylor expanded in x around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-*.f64 55.1

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

   8. Applied rewrites 55.1%

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

   9. Taylor expanded in z around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. mul-1-neg N/A

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

       4. +-commutative N/A

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

       5. associate-/l* N/A

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

       6. lower-fma.f64 N/A

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

       7. lower-/.f64 N/A

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

       8. lift-neg.f64 59.2

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

   11. Applied rewrites 59.2%

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

4. Final simplification 88.2%

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

Alternative 2: 72.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.6%

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

   3. Taylor expanded in y around 0

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

      1. lift-*.f64 84.5

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

   5. Applied rewrites 84.5%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 23.9%

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

   6. Taylor expanded in x around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-*.f64 55.1

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

   8. Applied rewrites 55.1%

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

   9. Taylor expanded in z around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. mul-1-neg N/A

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

       4. +-commutative N/A

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

       5. associate-/l* N/A

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

       6. lower-fma.f64 N/A

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

       7. lower-/.f64 N/A

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

       8. lift-neg.f64 59.2

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

   11. Applied rewrites 59.2%

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

4. Final simplification 79.9%

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

Alternative 3: 66.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(-i\right) \cdot j, y, \mathsf{fma}\left(\mathsf{fma}\left(-a, x, j \cdot c\right), t, \left(z \cdot y\right) \cdot x\right)\right)\\ t_2 := \mathsf{fma}\left(-a, i, c \cdot z\right)\\ \mathbf{if}\;j \leq -3.2 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(-a, t \cdot x, \left(j \cdot t\right) \cdot c\right) - t\_2 \cdot b\\ \mathbf{elif}\;j \leq -5.4 \cdot 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 4800:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \left(-b\right) \cdot t\_2\right)\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{+182}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (fma (* (- i) j) y (fma (fma (- a) x (* j c)) t (* (* z y) x))))
        (t_2 (fma (- a) i (* c z))))
   (if (<= j -3.2e+31)
     (- (fma (- a) (* t x) (* (* j t) c)) (* t_2 b))
     (if (<= j -5.4e-46)
       t_1
       (if (<= j 4800.0)
         (fma (fma (- a) t (* z y)) x (* (- b) t_2))
         (if (<= j 1.85e+182) t_1 (* (fma (- i) y (* c t)) 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 = fma((-i * j), y, fma(fma(-a, x, (j * c)), t, ((z * y) * x)));
	double t_2 = fma(-a, i, (c * z));
	double tmp;
	if (j <= -3.2e+31) {
		tmp = fma(-a, (t * x), ((j * t) * c)) - (t_2 * b);
	} else if (j <= -5.4e-46) {
		tmp = t_1;
	} else if (j <= 4800.0) {
		tmp = fma(fma(-a, t, (z * y)), x, (-b * t_2));
	} else if (j <= 1.85e+182) {
		tmp = t_1;
	} else {
		tmp = fma(-i, y, (c * t)) * j;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = fma(Float64(Float64(-i) * j), y, fma(fma(Float64(-a), x, Float64(j * c)), t, Float64(Float64(z * y) * x)))
	t_2 = fma(Float64(-a), i, Float64(c * z))
	tmp = 0.0
	if (j <= -3.2e+31)
		tmp = Float64(fma(Float64(-a), Float64(t * x), Float64(Float64(j * t) * c)) - Float64(t_2 * b));
	elseif (j <= -5.4e-46)
		tmp = t_1;
	elseif (j <= 4800.0)
		tmp = fma(fma(Float64(-a), t, Float64(z * y)), x, Float64(Float64(-b) * t_2));
	elseif (j <= 1.85e+182)
		tmp = t_1;
	else
		tmp = Float64(fma(Float64(-i), y, Float64(c * t)) * j);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-i) * j), $MachinePrecision] * y + N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t + N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-a) * i + N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.2e+31], N[(N[((-a) * N[(t * x), $MachinePrecision] + N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision] - N[(t$95$2 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -5.4e-46], t$95$1, If[LessEqual[j, 4800.0], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x + N[((-b) * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.85e+182], t$95$1, N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.2000000000000001e31

   1. Initial program 72.1%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

   5. Applied rewrites 63.6%

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

   if -3.2000000000000001e31 < j < -5.4e-46 or 4800 < j < 1.84999999999999988e182

   1. Initial program 76.5%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 74.9%

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

   6. Taylor expanded in b around 0

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

      1. mul-1-neg N/A

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

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

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. associate-*r* N/A

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

   8. Applied rewrites 86.8%

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

   if -5.4e-46 < j < 4800

   1. Initial program 78.4%

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

   3. Taylor expanded in j around 0

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

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

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. associate-*r* N/A

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

      9. +-commutative N/A

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

      10. associate-*r* N/A

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

      11. mul-1-neg N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-neg.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

   5. Applied rewrites 80.1%

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

   if 1.84999999999999988e182 < j

   1. Initial program 86.9%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. +-commutative N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lift-*.f64 90.0

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

   5. Applied rewrites 90.0%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.2 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(-a, t \cdot x, \left(j \cdot t\right) \cdot c\right) - \mathsf{fma}\left(-a, i, c \cdot z\right) \cdot b\\ \mathbf{elif}\;j \leq -5.4 \cdot 10^{-46}:\\ \;\;\;\;\mathsf{fma}\left(\left(-i\right) \cdot j, y, \mathsf{fma}\left(\mathsf{fma}\left(-a, x, j \cdot c\right), t, \left(z \cdot y\right) \cdot x\right)\right)\\ \mathbf{elif}\;j \leq 4800:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \left(-b\right) \cdot \mathsf{fma}\left(-a, i, c \cdot z\right)\right)\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{+182}:\\ \;\;\;\;\mathsf{fma}\left(\left(-i\right) \cdot j, y, \mathsf{fma}\left(\mathsf{fma}\left(-a, x, j \cdot c\right), t, \left(z \cdot y\right) \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-11}:\\ \;\;\;\;\left(-x\right) \cdot \left(\mathsf{fma}\left(a, \frac{t}{z}, -y\right) \cdot z\right)\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-274}:\\ \;\;\;\;\mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-237}:\\ \;\;\;\;\left(-i\right) \cdot \mathsf{fma}\left(j, y, \left(-a\right) \cdot b\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-83}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{elif}\;x \leq 5600000000:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(\mathsf{fma}\left(a, \frac{t}{y}, -z\right) \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -4e-11)
   (* (- x) (* (fma a (/ t z) (- y)) z))
   (if (<= x -1.15e-274)
     (* (fma j t (* (- b) z)) c)
     (if (<= x 1.9e-237)
       (* (- i) (fma j y (* (- a) b)))
       (if (<= x 1.85e-83)
         (* (fma i a (* (- c) z)) b)
         (if (<= x 5600000000.0)
           (* (fma (- i) j (* z x)) y)
           (* (- x) (* (fma a (/ t y) (- z)) y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -4e-11) {
		tmp = -x * (fma(a, (t / z), -y) * z);
	} else if (x <= -1.15e-274) {
		tmp = fma(j, t, (-b * z)) * c;
	} else if (x <= 1.9e-237) {
		tmp = -i * fma(j, y, (-a * b));
	} else if (x <= 1.85e-83) {
		tmp = fma(i, a, (-c * z)) * b;
	} else if (x <= 5600000000.0) {
		tmp = fma(-i, j, (z * x)) * y;
	} else {
		tmp = -x * (fma(a, (t / y), -z) * y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -4e-11)
		tmp = Float64(Float64(-x) * Float64(fma(a, Float64(t / z), Float64(-y)) * z));
	elseif (x <= -1.15e-274)
		tmp = Float64(fma(j, t, Float64(Float64(-b) * z)) * c);
	elseif (x <= 1.9e-237)
		tmp = Float64(Float64(-i) * fma(j, y, Float64(Float64(-a) * b)));
	elseif (x <= 1.85e-83)
		tmp = Float64(fma(i, a, Float64(Float64(-c) * z)) * b);
	elseif (x <= 5600000000.0)
		tmp = Float64(fma(Float64(-i), j, Float64(z * x)) * y);
	else
		tmp = Float64(Float64(-x) * Float64(fma(a, Float64(t / y), Float64(-z)) * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -4e-11], N[((-x) * N[(N[(a * N[(t / z), $MachinePrecision] + (-y)), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.15e-274], N[(N[(j * t + N[((-b) * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[x, 1.9e-237], N[((-i) * N[(j * y + N[((-a) * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.85e-83], N[(N[(i * a + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[x, 5600000000.0], N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[((-x) * N[(N[(a * N[(t / y), $MachinePrecision] + (-z)), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -3.99999999999999976e-11

   1. Initial program 76.4%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 79.5%

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

   6. Taylor expanded in x around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-*.f64 62.1

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

   8. Applied rewrites 62.1%

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

   9. Taylor expanded in z around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. mul-1-neg N/A

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

       4. +-commutative N/A

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

       5. associate-/l* N/A

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

       6. lower-fma.f64 N/A

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

       7. lower-/.f64 N/A

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

       8. lift-neg.f64 65.1

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

   11. Applied rewrites 65.1%

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

   if -3.99999999999999976e-11 < x < -1.14999999999999998e-274

   1. Initial program 88.0%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 60.1

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

   5. Applied rewrites 60.1%

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

   if -1.14999999999999998e-274 < x < 1.90000000000000012e-237

   1. Initial program 70.7%

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

   3. Taylor expanded in i around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

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

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 71.0

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

   5. Applied rewrites 71.0%

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

   if 1.90000000000000012e-237 < x < 1.84999999999999997e-83

   1. Initial program 70.3%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 74.4

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

   5. Applied rewrites 74.4%

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

   if 1.84999999999999997e-83 < x < 5.6e9

   1. Initial program 78.8%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 66.2

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

   5. Applied rewrites 66.2%

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

   if 5.6e9 < x

   1. Initial program 74.3%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 67.1%

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

   6. Taylor expanded in x around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-*.f64 69.6

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

   8. Applied rewrites 69.6%

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

   9. Taylor expanded in y around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. +-commutative N/A

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

       4. associate-/l* N/A

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

       5. lower-fma.f64 N/A

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

       6. lower-/.f64 N/A

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

       7. mul-1-neg N/A

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

       8. lower-neg.f64 72.4

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

   11. Applied rewrites 72.4%

       \[\leadsto \left(-x\right) \cdot \left(\mathsf{fma}\left(a, \frac{t}{y}, -z\right) \cdot y\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-11}:\\ \;\;\;\;\left(-x\right) \cdot \left(\mathsf{fma}\left(a, \frac{t}{z}, -y\right) \cdot z\right)\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-274}:\\ \;\;\;\;\mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-237}:\\ \;\;\;\;\left(-i\right) \cdot \mathsf{fma}\left(j, y, \left(-a\right) \cdot b\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-83}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{elif}\;x \leq 5600000000:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(\mathsf{fma}\left(a, \frac{t}{y}, -z\right) \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-x\right) \cdot \left(\mathsf{fma}\left(a, \frac{t}{y}, -z\right) \cdot y\right)\\ \mathbf{if}\;x \leq -2.06 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-274}:\\ \;\;\;\;\mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-237}:\\ \;\;\;\;\left(-i\right) \cdot \mathsf{fma}\left(j, y, \left(-a\right) \cdot b\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-83}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{elif}\;x \leq 5600000000:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- x) (* (fma a (/ t y) (- z)) y))))
   (if (<= x -2.06e-53)
     t_1
     (if (<= x -1.15e-274)
       (* (fma j t (* (- b) z)) c)
       (if (<= x 1.9e-237)
         (* (- i) (fma j y (* (- a) b)))
         (if (<= x 1.85e-83)
           (* (fma i a (* (- c) z)) b)
           (if (<= x 5600000000.0) (* (fma (- i) j (* z x)) y) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -x * (fma(a, (t / y), -z) * y);
	double tmp;
	if (x <= -2.06e-53) {
		tmp = t_1;
	} else if (x <= -1.15e-274) {
		tmp = fma(j, t, (-b * z)) * c;
	} else if (x <= 1.9e-237) {
		tmp = -i * fma(j, y, (-a * b));
	} else if (x <= 1.85e-83) {
		tmp = fma(i, a, (-c * z)) * b;
	} else if (x <= 5600000000.0) {
		tmp = fma(-i, j, (z * x)) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(-x) * Float64(fma(a, Float64(t / y), Float64(-z)) * y))
	tmp = 0.0
	if (x <= -2.06e-53)
		tmp = t_1;
	elseif (x <= -1.15e-274)
		tmp = Float64(fma(j, t, Float64(Float64(-b) * z)) * c);
	elseif (x <= 1.9e-237)
		tmp = Float64(Float64(-i) * fma(j, y, Float64(Float64(-a) * b)));
	elseif (x <= 1.85e-83)
		tmp = Float64(fma(i, a, Float64(Float64(-c) * z)) * b);
	elseif (x <= 5600000000.0)
		tmp = Float64(fma(Float64(-i), j, Float64(z * x)) * y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-x) * N[(N[(a * N[(t / y), $MachinePrecision] + (-z)), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.06e-53], t$95$1, If[LessEqual[x, -1.15e-274], N[(N[(j * t + N[((-b) * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[x, 1.9e-237], N[((-i) * N[(j * y + N[((-a) * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.85e-83], N[(N[(i * a + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[x, 5600000000.0], N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.06000000000000003e-53 or 5.6e9 < x

   1. Initial program 76.6%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 74.5%

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

   6. Taylor expanded in x around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-*.f64 64.0

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

   8. Applied rewrites 64.0%

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

   9. Taylor expanded in y around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. +-commutative N/A

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

       4. associate-/l* N/A

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

       5. lower-fma.f64 N/A

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

       6. lower-/.f64 N/A

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

       7. mul-1-neg N/A

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

       8. lower-neg.f64 67.5

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

   11. Applied rewrites 67.5%

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

   if -2.06000000000000003e-53 < x < -1.14999999999999998e-274

   1. Initial program 86.5%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 62.3

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

   5. Applied rewrites 62.3%

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

   if -1.14999999999999998e-274 < x < 1.90000000000000012e-237

   1. Initial program 70.7%

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

   3. Taylor expanded in i around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

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

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 71.0

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

   5. Applied rewrites 71.0%

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

   if 1.90000000000000012e-237 < x < 1.84999999999999997e-83

   1. Initial program 70.3%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 74.4

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

   5. Applied rewrites 74.4%

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

   if 1.84999999999999997e-83 < x < 5.6e9

   1. Initial program 78.8%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 66.2

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

   5. Applied rewrites 66.2%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.06 \cdot 10^{-53}:\\ \;\;\;\;\left(-x\right) \cdot \left(\mathsf{fma}\left(a, \frac{t}{y}, -z\right) \cdot y\right)\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-274}:\\ \;\;\;\;\mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-237}:\\ \;\;\;\;\left(-i\right) \cdot \mathsf{fma}\left(j, y, \left(-a\right) \cdot b\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-83}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{elif}\;x \leq 5600000000:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(\mathsf{fma}\left(a, \frac{t}{y}, -z\right) \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+53} \lor \neg \left(t \leq 1.65 \cdot 10^{+176}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(-i\right) \cdot j, y, \mathsf{fma}\left(\mathsf{fma}\left(-a, x, j \cdot c\right), t, \left(z \cdot y\right) \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \left(-b\right) \cdot \mathsf{fma}\left(-a, i, c \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -2.4e+53) (not (<= t 1.65e+176)))
   (fma (* (- i) j) y (fma (fma (- a) x (* j c)) t (* (* z y) x)))
   (fma (fma (- a) t (* z y)) x (* (- b) (fma (- a) i (* c z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -2.4e+53) || !(t <= 1.65e+176)) {
		tmp = fma((-i * j), y, fma(fma(-a, x, (j * c)), t, ((z * y) * x)));
	} else {
		tmp = fma(fma(-a, t, (z * y)), x, (-b * fma(-a, i, (c * z))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -2.4e+53) || !(t <= 1.65e+176))
		tmp = fma(Float64(Float64(-i) * j), y, fma(fma(Float64(-a), x, Float64(j * c)), t, Float64(Float64(z * y) * x)));
	else
		tmp = fma(fma(Float64(-a), t, Float64(z * y)), x, Float64(Float64(-b) * fma(Float64(-a), i, Float64(c * z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -2.4e+53], N[Not[LessEqual[t, 1.65e+176]], $MachinePrecision]], N[(N[((-i) * j), $MachinePrecision] * y + N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t + N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x + N[((-b) * N[((-a) * i + N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.4e53 or 1.65000000000000012e176 < t

   1. Initial program 64.7%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 74.4%

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

   6. Taylor expanded in b around 0

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

      1. mul-1-neg N/A

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

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

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. associate-*r* N/A

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

   8. Applied rewrites 82.5%

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

   if -2.4e53 < t < 1.65000000000000012e176

   1. Initial program 84.5%

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

   3. Taylor expanded in j around 0

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

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

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. associate-*r* N/A

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

      9. +-commutative N/A

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

      10. associate-*r* N/A

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

      11. mul-1-neg N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-neg.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

   5. Applied rewrites 73.0%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+53} \lor \neg \left(t \leq 1.65 \cdot 10^{+176}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(-i\right) \cdot j, y, \mathsf{fma}\left(\mathsf{fma}\left(-a, x, j \cdot c\right), t, \left(z \cdot y\right) \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \left(-b\right) \cdot \mathsf{fma}\left(-a, i, c \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.1 \cdot 10^{+101}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{+89}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \left(-b\right) \cdot \mathsf{fma}\left(-a, i, c \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -2.1e+101)
   (+ (* (* z y) x) (* j (- (* c t) (* i y))))
   (if (<= j 4e+89)
     (fma (fma (- a) t (* z y)) x (* (- b) (fma (- a) i (* c z))))
     (* (fma (- i) y (* c t)) j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2.1e+101) {
		tmp = ((z * y) * x) + (j * ((c * t) - (i * y)));
	} else if (j <= 4e+89) {
		tmp = fma(fma(-a, t, (z * y)), x, (-b * fma(-a, i, (c * z))));
	} else {
		tmp = fma(-i, y, (c * t)) * j;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -2.1e+101)
		tmp = Float64(Float64(Float64(z * y) * x) + Float64(j * Float64(Float64(c * t) - Float64(i * y))));
	elseif (j <= 4e+89)
		tmp = fma(fma(Float64(-a), t, Float64(z * y)), x, Float64(Float64(-b) * fma(Float64(-a), i, Float64(c * z))));
	else
		tmp = Float64(fma(Float64(-i), y, Float64(c * t)) * j);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -2.1e+101], N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4e+89], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x + N[((-b) * N[((-a) * i + N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.1e101

   1. Initial program 71.1%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 62.6

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

   5. Applied rewrites 62.6%

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

   if -2.1e101 < j < 3.99999999999999998e89

   1. Initial program 78.2%

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

   3. Taylor expanded in j around 0

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

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

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. associate-*r* N/A

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

      9. +-commutative N/A

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

      10. associate-*r* N/A

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

      11. mul-1-neg N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-neg.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

   5. Applied rewrites 75.4%

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

   if 3.99999999999999998e89 < j

   1. Initial program 79.7%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. +-commutative N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lift-*.f64 79.1

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

   5. Applied rewrites 79.1%

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

Alternative 8: 52.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-13}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-274}:\\ \;\;\;\;\mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-237}:\\ \;\;\;\;\left(-i\right) \cdot \mathsf{fma}\left(j, y, \left(-a\right) \cdot b\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-83}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{elif}\;x \leq 5600000000:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \mathsf{fma}\left(-y, z, a \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -7.2e-13)
   (* (fma (- a) t (* z y)) x)
   (if (<= x -1.15e-274)
     (* (fma j t (* (- b) z)) c)
     (if (<= x 1.9e-237)
       (* (- i) (fma j y (* (- a) b)))
       (if (<= x 1.85e-83)
         (* (fma i a (* (- c) z)) b)
         (if (<= x 5600000000.0)
           (* (fma (- i) j (* z x)) y)
           (* (- x) (fma (- y) z (* a 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 (x <= -7.2e-13) {
		tmp = fma(-a, t, (z * y)) * x;
	} else if (x <= -1.15e-274) {
		tmp = fma(j, t, (-b * z)) * c;
	} else if (x <= 1.9e-237) {
		tmp = -i * fma(j, y, (-a * b));
	} else if (x <= 1.85e-83) {
		tmp = fma(i, a, (-c * z)) * b;
	} else if (x <= 5600000000.0) {
		tmp = fma(-i, j, (z * x)) * y;
	} else {
		tmp = -x * fma(-y, z, (a * t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -7.2e-13)
		tmp = Float64(fma(Float64(-a), t, Float64(z * y)) * x);
	elseif (x <= -1.15e-274)
		tmp = Float64(fma(j, t, Float64(Float64(-b) * z)) * c);
	elseif (x <= 1.9e-237)
		tmp = Float64(Float64(-i) * fma(j, y, Float64(Float64(-a) * b)));
	elseif (x <= 1.85e-83)
		tmp = Float64(fma(i, a, Float64(Float64(-c) * z)) * b);
	elseif (x <= 5600000000.0)
		tmp = Float64(fma(Float64(-i), j, Float64(z * x)) * y);
	else
		tmp = Float64(Float64(-x) * fma(Float64(-y), z, Float64(a * t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -7.2e-13], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, -1.15e-274], N[(N[(j * t + N[((-b) * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[x, 1.9e-237], N[((-i) * N[(j * y + N[((-a) * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.85e-83], N[(N[(i * a + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[x, 5600000000.0], N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[((-x) * N[((-y) * z + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -7.1999999999999996e-13

   1. Initial program 76.4%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. +-commutative N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-neg.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 62.1

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

   5. Applied rewrites 62.1%

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

   if -7.1999999999999996e-13 < x < -1.14999999999999998e-274

   1. Initial program 88.0%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 60.1

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

   5. Applied rewrites 60.1%

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

   if -1.14999999999999998e-274 < x < 1.90000000000000012e-237

   1. Initial program 70.7%

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

   3. Taylor expanded in i around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

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

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 71.0

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

   5. Applied rewrites 71.0%

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

   if 1.90000000000000012e-237 < x < 1.84999999999999997e-83

   1. Initial program 70.3%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 74.4

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

   5. Applied rewrites 74.4%

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

   if 1.84999999999999997e-83 < x < 5.6e9

   1. Initial program 78.8%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 66.2

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

   5. Applied rewrites 66.2%

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

   if 5.6e9 < x

   1. Initial program 74.3%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 67.1%

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

   6. Taylor expanded in x around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-*.f64 69.6

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

   8. Applied rewrites 69.6%

      \[\leadsto \left(-x\right) \cdot \color{blue}{\mathsf{fma}\left(-y, z, a \cdot t\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-13}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-274}:\\ \;\;\;\;\mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-237}:\\ \;\;\;\;\left(-i\right) \cdot \mathsf{fma}\left(j, y, \left(-a\right) \cdot b\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-83}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{elif}\;x \leq 5600000000:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \mathsf{fma}\left(-y, z, a \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+87} \lor \neg \left(a \leq 4 \cdot 10^{+29}\right):\\ \;\;\;\;\mathsf{fma}\left(-t, x, i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -6.8e+87) (not (<= a 4e+29)))
   (* (fma (- t) x (* i b)) a)
   (+ (* (* z y) x) (* j (- (* c t) (* i y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -6.8e+87) || !(a <= 4e+29)) {
		tmp = fma(-t, x, (i * b)) * a;
	} else {
		tmp = ((z * y) * x) + (j * ((c * t) - (i * y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -6.8e+87) || !(a <= 4e+29))
		tmp = Float64(fma(Float64(-t), x, Float64(i * b)) * a);
	else
		tmp = Float64(Float64(Float64(z * y) * x) + Float64(j * Float64(Float64(c * t) - Float64(i * y))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -6.8e+87], N[Not[LessEqual[a, 4e+29]], $MachinePrecision]], N[(N[((-t) * x + N[(i * b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.8000000000000004e87 or 3.99999999999999966e29 < a

   1. Initial program 64.3%

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

   3. Taylor expanded in i around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 66.2%

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

   6. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 68.7

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

   8. Applied rewrites 68.7%

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

   if -6.8000000000000004e87 < a < 3.99999999999999966e29

   1. Initial program 86.6%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 66.0

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

   5. Applied rewrites 66.0%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+87} \lor \neg \left(a \leq 4 \cdot 10^{+29}\right):\\ \;\;\;\;\mathsf{fma}\left(-t, x, i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -7.8 \cdot 10^{-19}:\\ \;\;\;\;\mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-80}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{elif}\;j \leq 1.16 \cdot 10^{-299}:\\ \;\;\;\;\mathsf{fma}\left(-t, x, i \cdot b\right) \cdot a\\ \mathbf{elif}\;j \leq 6 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -7.8e-19)
   (* (fma j t (* (- b) z)) c)
   (if (<= j -8.5e-80)
     (* (fma (- i) j (* z x)) y)
     (if (<= j 1.16e-299)
       (* (fma (- t) x (* i b)) a)
       (if (<= j 6e+33)
         (* (fma y x (* (- b) c)) z)
         (* (fma (- i) y (* c t)) j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -7.8e-19) {
		tmp = fma(j, t, (-b * z)) * c;
	} else if (j <= -8.5e-80) {
		tmp = fma(-i, j, (z * x)) * y;
	} else if (j <= 1.16e-299) {
		tmp = fma(-t, x, (i * b)) * a;
	} else if (j <= 6e+33) {
		tmp = fma(y, x, (-b * c)) * z;
	} else {
		tmp = fma(-i, y, (c * t)) * j;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -7.8e-19)
		tmp = Float64(fma(j, t, Float64(Float64(-b) * z)) * c);
	elseif (j <= -8.5e-80)
		tmp = Float64(fma(Float64(-i), j, Float64(z * x)) * y);
	elseif (j <= 1.16e-299)
		tmp = Float64(fma(Float64(-t), x, Float64(i * b)) * a);
	elseif (j <= 6e+33)
		tmp = Float64(fma(y, x, Float64(Float64(-b) * c)) * z);
	else
		tmp = Float64(fma(Float64(-i), y, Float64(c * t)) * j);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -7.8e-19], N[(N[(j * t + N[((-b) * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[j, -8.5e-80], N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[j, 1.16e-299], N[(N[((-t) * x + N[(i * b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[j, 6e+33], N[(N[(y * x + N[((-b) * c), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -7.7999999999999999e-19

   1. Initial program 70.9%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 58.3

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

   5. Applied rewrites 58.3%

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

   if -7.7999999999999999e-19 < j < -8.49999999999999939e-80

   1. Initial program 79.8%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 70.2

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

   5. Applied rewrites 70.2%

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

   if -8.49999999999999939e-80 < j < 1.15999999999999997e-299

   1. Initial program 74.9%

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

   3. Taylor expanded in i around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 71.6%

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

   6. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 62.7

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

   8. Applied rewrites 62.7%

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

   if 1.15999999999999997e-299 < j < 5.99999999999999967e33

   1. Initial program 83.6%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-neg.f64 60.1

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

   5. Applied rewrites 60.1%

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

   if 5.99999999999999967e33 < j

   1. Initial program 79.4%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. +-commutative N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lift-*.f64 75.7

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

   5. Applied rewrites 75.7%

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

Alternative 11: 52.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-222}:\\ \;\;\;\;\mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-83}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{elif}\;x \leq 5600000000:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- a) t (* z y)) x)))
   (if (<= x -7.2e-13)
     t_1
     (if (<= x -5e-222)
       (* (fma j t (* (- b) z)) c)
       (if (<= x 1.85e-83)
         (* (fma i a (* (- c) z)) b)
         (if (<= x 5600000000.0) (* (fma (- i) j (* z x)) y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-a, t, (z * y)) * x;
	double tmp;
	if (x <= -7.2e-13) {
		tmp = t_1;
	} else if (x <= -5e-222) {
		tmp = fma(j, t, (-b * z)) * c;
	} else if (x <= 1.85e-83) {
		tmp = fma(i, a, (-c * z)) * b;
	} else if (x <= 5600000000.0) {
		tmp = fma(-i, j, (z * x)) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-a), t, Float64(z * y)) * x)
	tmp = 0.0
	if (x <= -7.2e-13)
		tmp = t_1;
	elseif (x <= -5e-222)
		tmp = Float64(fma(j, t, Float64(Float64(-b) * z)) * c);
	elseif (x <= 1.85e-83)
		tmp = Float64(fma(i, a, Float64(Float64(-c) * z)) * b);
	elseif (x <= 5600000000.0)
		tmp = Float64(fma(Float64(-i), j, Float64(z * x)) * y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -7.2e-13], t$95$1, If[LessEqual[x, -5e-222], N[(N[(j * t + N[((-b) * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[x, 1.85e-83], N[(N[(i * a + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[x, 5600000000.0], N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.1999999999999996e-13 or 5.6e9 < x

   1. Initial program 75.4%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. +-commutative N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-neg.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 65.1

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

   5. Applied rewrites 65.1%

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

   if -7.1999999999999996e-13 < x < -5.00000000000000008e-222

   1. Initial program 91.2%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 62.3

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

   5. Applied rewrites 62.3%

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

   if -5.00000000000000008e-222 < x < 1.84999999999999997e-83

   1. Initial program 71.6%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 61.0

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

   5. Applied rewrites 61.0%

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

   if 1.84999999999999997e-83 < x < 5.6e9

   1. Initial program 78.8%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 66.2

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

   5. Applied rewrites 66.2%

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

Alternative 12: 29.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(i \cdot a\right) \cdot b\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+212}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{+102}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{-221}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-83}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* i a) b)))
   (if (<= x -4.8e+212)
     (* (- a) (* t x))
     (if (<= x -7.2e+102)
       (* (* z y) x)
       (if (<= x -1.45e-114)
         t_1
         (if (<= x -2.35e-221)
           (* (* j t) c)
           (if (<= x 3.4e-83) t_1 (* (* y x) z))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * a) * b;
	double tmp;
	if (x <= -4.8e+212) {
		tmp = -a * (t * x);
	} else if (x <= -7.2e+102) {
		tmp = (z * y) * x;
	} else if (x <= -1.45e-114) {
		tmp = t_1;
	} else if (x <= -2.35e-221) {
		tmp = (j * t) * c;
	} else if (x <= 3.4e-83) {
		tmp = t_1;
	} else {
		tmp = (y * x) * z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (i * a) * b
    if (x <= (-4.8d+212)) then
        tmp = -a * (t * x)
    else if (x <= (-7.2d+102)) then
        tmp = (z * y) * x
    else if (x <= (-1.45d-114)) then
        tmp = t_1
    else if (x <= (-2.35d-221)) then
        tmp = (j * t) * c
    else if (x <= 3.4d-83) then
        tmp = t_1
    else
        tmp = (y * x) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * a) * b;
	double tmp;
	if (x <= -4.8e+212) {
		tmp = -a * (t * x);
	} else if (x <= -7.2e+102) {
		tmp = (z * y) * x;
	} else if (x <= -1.45e-114) {
		tmp = t_1;
	} else if (x <= -2.35e-221) {
		tmp = (j * t) * c;
	} else if (x <= 3.4e-83) {
		tmp = t_1;
	} else {
		tmp = (y * x) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (i * a) * b
	tmp = 0
	if x <= -4.8e+212:
		tmp = -a * (t * x)
	elif x <= -7.2e+102:
		tmp = (z * y) * x
	elif x <= -1.45e-114:
		tmp = t_1
	elif x <= -2.35e-221:
		tmp = (j * t) * c
	elif x <= 3.4e-83:
		tmp = t_1
	else:
		tmp = (y * x) * z
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * a) * b)
	tmp = 0.0
	if (x <= -4.8e+212)
		tmp = Float64(Float64(-a) * Float64(t * x));
	elseif (x <= -7.2e+102)
		tmp = Float64(Float64(z * y) * x);
	elseif (x <= -1.45e-114)
		tmp = t_1;
	elseif (x <= -2.35e-221)
		tmp = Float64(Float64(j * t) * c);
	elseif (x <= 3.4e-83)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * x) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (i * a) * b;
	tmp = 0.0;
	if (x <= -4.8e+212)
		tmp = -a * (t * x);
	elseif (x <= -7.2e+102)
		tmp = (z * y) * x;
	elseif (x <= -1.45e-114)
		tmp = t_1;
	elseif (x <= -2.35e-221)
		tmp = (j * t) * c;
	elseif (x <= 3.4e-83)
		tmp = t_1;
	else
		tmp = (y * x) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * a), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[x, -4.8e+212], N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.2e+102], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, -1.45e-114], t$95$1, If[LessEqual[x, -2.35e-221], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[x, 3.4e-83], t$95$1, N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.8e212

   1. Initial program 82.4%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 63.9

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

   5. Applied rewrites 63.9%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lift-neg.f64 N/A

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

      5. lower-*.f64 46.7

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

   8. Applied rewrites 46.7%

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

   if -4.8e212 < x < -7.2000000000000003e102

   1. Initial program 71.6%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-neg.f64 59.8

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

   5. Applied rewrites 59.8%

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

   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

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 59.7

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

   8. Applied rewrites 59.7%

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

   if -7.2000000000000003e102 < x < -1.44999999999999998e-114 or -2.34999999999999987e-221 < x < 3.3999999999999998e-83

   1. Initial program 77.4%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 58.8

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

   5. Applied rewrites 58.8%

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

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lift-*.f64 38.9

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

   8. Applied rewrites 38.9%

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

   if -1.44999999999999998e-114 < x < -2.34999999999999987e-221

   1. Initial program 88.5%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 57.3

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

   5. Applied rewrites 57.3%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 49.1

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

   8. Applied rewrites 49.1%

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

   if 3.3999999999999998e-83 < x

   1. Initial program 75.5%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-neg.f64 44.9

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

   5. Applied rewrites 44.9%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 40.6

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

   8. Applied rewrites 40.6%

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

Alternative 13: 51.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-222}:\\ \;\;\;\;\mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-83}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- a) t (* z y)) x)))
   (if (<= x -7.2e-13)
     t_1
     (if (<= x -5e-222)
       (* (fma j t (* (- b) z)) c)
       (if (<= x 1.85e-83) (* (fma i a (* (- c) z)) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-a, t, (z * y)) * x;
	double tmp;
	if (x <= -7.2e-13) {
		tmp = t_1;
	} else if (x <= -5e-222) {
		tmp = fma(j, t, (-b * z)) * c;
	} else if (x <= 1.85e-83) {
		tmp = fma(i, a, (-c * z)) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-a), t, Float64(z * y)) * x)
	tmp = 0.0
	if (x <= -7.2e-13)
		tmp = t_1;
	elseif (x <= -5e-222)
		tmp = Float64(fma(j, t, Float64(Float64(-b) * z)) * c);
	elseif (x <= 1.85e-83)
		tmp = Float64(fma(i, a, Float64(Float64(-c) * z)) * b);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -7.2e-13], t$95$1, If[LessEqual[x, -5e-222], N[(N[(j * t + N[((-b) * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[x, 1.85e-83], N[(N[(i * a + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.1999999999999996e-13 or 1.84999999999999997e-83 < x

   1. Initial program 75.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. +-commutative N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-neg.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 62.2

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

   5. Applied rewrites 62.2%

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

   if -7.1999999999999996e-13 < x < -5.00000000000000008e-222

   1. Initial program 91.2%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 62.3

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

   5. Applied rewrites 62.3%

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

   if -5.00000000000000008e-222 < x < 1.84999999999999997e-83

   1. Initial program 71.6%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 61.0

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

   5. Applied rewrites 61.0%

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

Alternative 14: 45.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{if}\;j \leq -2.2 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-253}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{elif}\;j \leq 10^{+50}:\\ \;\;\;\;\mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma j t (* (- b) z)) c)))
   (if (<= j -2.2e-66)
     t_1
     (if (<= j 5.5e-253)
       (* (fma i a (* (- c) z)) b)
       (if (<= j 1e+50) (* (fma y x (* (- b) c)) z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(j, t, (-b * z)) * c;
	double tmp;
	if (j <= -2.2e-66) {
		tmp = t_1;
	} else if (j <= 5.5e-253) {
		tmp = fma(i, a, (-c * z)) * b;
	} else if (j <= 1e+50) {
		tmp = fma(y, x, (-b * c)) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(j, t, Float64(Float64(-b) * z)) * c)
	tmp = 0.0
	if (j <= -2.2e-66)
		tmp = t_1;
	elseif (j <= 5.5e-253)
		tmp = Float64(fma(i, a, Float64(Float64(-c) * z)) * b);
	elseif (j <= 1e+50)
		tmp = Float64(fma(y, x, Float64(Float64(-b) * c)) * z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * t + N[((-b) * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]}, If[LessEqual[j, -2.2e-66], t$95$1, If[LessEqual[j, 5.5e-253], N[(N[(i * a + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[j, 1e+50], N[(N[(y * x + N[((-b) * c), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.2000000000000001e-66 or 1.0000000000000001e50 < j

   1. Initial program 76.7%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 53.8

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

   5. Applied rewrites 53.8%

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

   if -2.2000000000000001e-66 < j < 5.49999999999999974e-253

   1. Initial program 72.1%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 49.3

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

   5. Applied rewrites 49.3%

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

   if 5.49999999999999974e-253 < j < 1.0000000000000001e50

   1. Initial program 84.4%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-neg.f64 60.6

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

   5. Applied rewrites 60.6%

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

Alternative 15: 41.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+212}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{+103}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -4.8e+212)
   (* (- a) (* t x))
   (if (<= x -1.55e+103)
     (* (* z y) x)
     (if (<= x 2.3e+72) (* (fma i a (* (- c) z)) b) (* (* y x) z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -4.8e+212) {
		tmp = -a * (t * x);
	} else if (x <= -1.55e+103) {
		tmp = (z * y) * x;
	} else if (x <= 2.3e+72) {
		tmp = fma(i, a, (-c * z)) * b;
	} else {
		tmp = (y * x) * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -4.8e+212)
		tmp = Float64(Float64(-a) * Float64(t * x));
	elseif (x <= -1.55e+103)
		tmp = Float64(Float64(z * y) * x);
	elseif (x <= 2.3e+72)
		tmp = Float64(fma(i, a, Float64(Float64(-c) * z)) * b);
	else
		tmp = Float64(Float64(y * x) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -4.8e+212], N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.55e+103], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 2.3e+72], N[(N[(i * a + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.8e212

   1. Initial program 82.4%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(a\right)\right) \cdot x + c \cdot j\right) \cdot t \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(a\right), x, c \cdot j\right) \cdot t \]

      6. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-a, x, c \cdot j\right) \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t \]

      8. lower-*.f64 63.9

         \[\leadsto \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t \]

   5. Applied rewrites 63.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]

   6. Taylor expanded in x around inf

      \[\leadsto -1 \cdot \color{blue}{\left(a \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \left(t \cdot \color{blue}{x}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \left(t \cdot \color{blue}{x}\right) \]

      3. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t \cdot x\right) \]

      4. lift-neg.f64 N/A

         \[\leadsto \left(-a\right) \cdot \left(t \cdot x\right) \]

      5. lower-*.f64 46.7

         \[\leadsto \left(-a\right) \cdot \left(t \cdot x\right) \]

   8. Applied rewrites 46.7%

      \[\leadsto \left(-a\right) \cdot \color{blue}{\left(t \cdot x\right)} \]

   if -4.8e212 < x < -1.5500000000000001e103

   1. Initial program 71.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(x \cdot y - b \cdot c\right) \cdot \color{blue}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x \cdot y - b \cdot c\right) \cdot \color{blue}{z} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(x \cdot y + \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      4. *-commutative N/A

         \[\leadsto \left(y \cdot x + \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      7. lower-neg.f64 59.8

         \[\leadsto \mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z \]

   5. Applied rewrites 59.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z} \]

   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

         \[\leadsto x \cdot \left(z \cdot y\right) \]

      2. *-commutative N/A

         \[\leadsto \left(z \cdot y\right) \cdot x \]

      3. lift-*.f64 N/A

         \[\leadsto \left(z \cdot y\right) \cdot x \]

      4. lift-*.f64 59.7

         \[\leadsto \left(z \cdot y\right) \cdot x \]

   8. Applied rewrites 59.7%

      \[\leadsto \left(z \cdot y\right) \cdot \color{blue}{x} \]

   if -1.5500000000000001e103 < x < 2.3e72

   1. Initial program 80.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(a \cdot i + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      4. *-commutative N/A

         \[\leadsto \left(i \cdot a + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      9. lower-neg.f64 50.5

         \[\leadsto \mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b \]

   5. Applied rewrites 50.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b} \]

   if 2.3e72 < x

   1. Initial program 68.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(x \cdot y - b \cdot c\right) \cdot \color{blue}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x \cdot y - b \cdot c\right) \cdot \color{blue}{z} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(x \cdot y + \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      4. *-commutative N/A

         \[\leadsto \left(y \cdot x + \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      7. lower-neg.f64 47.8

         \[\leadsto \mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z \]

   5. Applied rewrites 47.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z} \]

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot y\right) \cdot z \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(y \cdot x\right) \cdot z \]

      2. lower-*.f64 47.9

         \[\leadsto \left(y \cdot x\right) \cdot z \]

   8. Applied rewrites 47.9%

      \[\leadsto \left(y \cdot x\right) \cdot z \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 16: 29.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+212}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{+81}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-237}:\\ \;\;\;\;\left(\left(-c\right) \cdot z\right) \cdot b\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-83}:\\ \;\;\;\;\left(i \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -4.8e+212)
   (* (- a) (* t x))
   (if (<= x -4.5e+81)
     (* (* z y) x)
     (if (<= x -5.8e-237)
       (* (* (- c) z) b)
       (if (<= x 3.4e-83) (* (* i a) b) (* (* y x) z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -4.8e+212) {
		tmp = -a * (t * x);
	} else if (x <= -4.5e+81) {
		tmp = (z * y) * x;
	} else if (x <= -5.8e-237) {
		tmp = (-c * z) * b;
	} else if (x <= 3.4e-83) {
		tmp = (i * a) * b;
	} else {
		tmp = (y * x) * z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (x <= (-4.8d+212)) then
        tmp = -a * (t * x)
    else if (x <= (-4.5d+81)) then
        tmp = (z * y) * x
    else if (x <= (-5.8d-237)) then
        tmp = (-c * z) * b
    else if (x <= 3.4d-83) then
        tmp = (i * a) * b
    else
        tmp = (y * x) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -4.8e+212) {
		tmp = -a * (t * x);
	} else if (x <= -4.5e+81) {
		tmp = (z * y) * x;
	} else if (x <= -5.8e-237) {
		tmp = (-c * z) * b;
	} else if (x <= 3.4e-83) {
		tmp = (i * a) * b;
	} else {
		tmp = (y * x) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -4.8e+212:
		tmp = -a * (t * x)
	elif x <= -4.5e+81:
		tmp = (z * y) * x
	elif x <= -5.8e-237:
		tmp = (-c * z) * b
	elif x <= 3.4e-83:
		tmp = (i * a) * b
	else:
		tmp = (y * x) * z
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -4.8e+212)
		tmp = Float64(Float64(-a) * Float64(t * x));
	elseif (x <= -4.5e+81)
		tmp = Float64(Float64(z * y) * x);
	elseif (x <= -5.8e-237)
		tmp = Float64(Float64(Float64(-c) * z) * b);
	elseif (x <= 3.4e-83)
		tmp = Float64(Float64(i * a) * b);
	else
		tmp = Float64(Float64(y * x) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -4.8e+212)
		tmp = -a * (t * x);
	elseif (x <= -4.5e+81)
		tmp = (z * y) * x;
	elseif (x <= -5.8e-237)
		tmp = (-c * z) * b;
	elseif (x <= 3.4e-83)
		tmp = (i * a) * b;
	else
		tmp = (y * x) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -4.8e+212], N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.5e+81], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, -5.8e-237], N[(N[((-c) * z), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[x, 3.4e-83], N[(N[(i * a), $MachinePrecision] * b), $MachinePrecision], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.8e212

   1. Initial program 82.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot \color{blue}{t} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot \color{blue}{t} \]

      3. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot a\right) \cdot x + c \cdot j\right) \cdot t \]

      4. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(a\right)\right) \cdot x + c \cdot j\right) \cdot t \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(a\right), x, c \cdot j\right) \cdot t \]

      6. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-a, x, c \cdot j\right) \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t \]

      8. lower-*.f64 63.9

         \[\leadsto \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t \]

   5. Applied rewrites 63.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]

   6. Taylor expanded in x around inf

      \[\leadsto -1 \cdot \color{blue}{\left(a \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \left(t \cdot \color{blue}{x}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \left(t \cdot \color{blue}{x}\right) \]

      3. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t \cdot x\right) \]

      4. lift-neg.f64 N/A

         \[\leadsto \left(-a\right) \cdot \left(t \cdot x\right) \]

      5. lower-*.f64 46.7

         \[\leadsto \left(-a\right) \cdot \left(t \cdot x\right) \]

   8. Applied rewrites 46.7%

      \[\leadsto \left(-a\right) \cdot \color{blue}{\left(t \cdot x\right)} \]

   if -4.8e212 < x < -4.50000000000000017e81

   1. Initial program 72.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(x \cdot y - b \cdot c\right) \cdot \color{blue}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x \cdot y - b \cdot c\right) \cdot \color{blue}{z} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(x \cdot y + \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      4. *-commutative N/A

         \[\leadsto \left(y \cdot x + \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      7. lower-neg.f64 53.8

         \[\leadsto \mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z \]

   5. Applied rewrites 53.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z} \]

   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

         \[\leadsto x \cdot \left(z \cdot y\right) \]

      2. *-commutative N/A

         \[\leadsto \left(z \cdot y\right) \cdot x \]

      3. lift-*.f64 N/A

         \[\leadsto \left(z \cdot y\right) \cdot x \]

      4. lift-*.f64 53.8

         \[\leadsto \left(z \cdot y\right) \cdot x \]

   8. Applied rewrites 53.8%

      \[\leadsto \left(z \cdot y\right) \cdot \color{blue}{x} \]

   if -4.50000000000000017e81 < x < -5.80000000000000022e-237

   1. Initial program 86.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(a \cdot i + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      4. *-commutative N/A

         \[\leadsto \left(i \cdot a + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      9. lower-neg.f64 51.6

         \[\leadsto \mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b \]

   5. Applied rewrites 51.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b} \]

   6. Taylor expanded in z around inf

      \[\leadsto \left(-1 \cdot \left(c \cdot z\right)\right) \cdot b \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(c \cdot z\right)\right) \cdot b \]

      2. distribute-lft-neg-out N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      3. lift-*.f64 N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      4. lift-neg.f64 34.3

         \[\leadsto \left(\left(-c\right) \cdot z\right) \cdot b \]

   8. Applied rewrites 34.3%

      \[\leadsto \left(\left(-c\right) \cdot z\right) \cdot b \]

   if -5.80000000000000022e-237 < x < 3.3999999999999998e-83

   1. Initial program 70.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(a \cdot i + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      4. *-commutative N/A

         \[\leadsto \left(i \cdot a + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      9. lower-neg.f64 59.2

         \[\leadsto \mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b \]

   5. Applied rewrites 59.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b} \]

   6. Taylor expanded in z around 0

      \[\leadsto \left(a \cdot i\right) \cdot b \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(i \cdot a\right) \cdot b \]

      2. lift-*.f64 44.8

         \[\leadsto \left(i \cdot a\right) \cdot b \]

   8. Applied rewrites 44.8%

      \[\leadsto \left(i \cdot a\right) \cdot b \]

   if 3.3999999999999998e-83 < x

   1. Initial program 75.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(x \cdot y - b \cdot c\right) \cdot \color{blue}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x \cdot y - b \cdot c\right) \cdot \color{blue}{z} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(x \cdot y + \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      4. *-commutative N/A

         \[\leadsto \left(y \cdot x + \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      7. lower-neg.f64 44.9

         \[\leadsto \mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z \]

   5. Applied rewrites 44.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z} \]

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot y\right) \cdot z \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(y \cdot x\right) \cdot z \]

      2. lower-*.f64 40.6

         \[\leadsto \left(y \cdot x\right) \cdot z \]

   8. Applied rewrites 40.6%

      \[\leadsto \left(y \cdot x\right) \cdot z \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 17: 29.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(i \cdot a\right) \cdot b\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{+102}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{-221}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-83}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* i a) b)))
   (if (<= x -7.2e+102)
     (* (* z y) x)
     (if (<= x -1.45e-114)
       t_1
       (if (<= x -2.35e-221)
         (* (* j t) c)
         (if (<= x 3.4e-83) t_1 (* (* y x) z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * a) * b;
	double tmp;
	if (x <= -7.2e+102) {
		tmp = (z * y) * x;
	} else if (x <= -1.45e-114) {
		tmp = t_1;
	} else if (x <= -2.35e-221) {
		tmp = (j * t) * c;
	} else if (x <= 3.4e-83) {
		tmp = t_1;
	} else {
		tmp = (y * x) * z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (i * a) * b
    if (x <= (-7.2d+102)) then
        tmp = (z * y) * x
    else if (x <= (-1.45d-114)) then
        tmp = t_1
    else if (x <= (-2.35d-221)) then
        tmp = (j * t) * c
    else if (x <= 3.4d-83) then
        tmp = t_1
    else
        tmp = (y * x) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * a) * b;
	double tmp;
	if (x <= -7.2e+102) {
		tmp = (z * y) * x;
	} else if (x <= -1.45e-114) {
		tmp = t_1;
	} else if (x <= -2.35e-221) {
		tmp = (j * t) * c;
	} else if (x <= 3.4e-83) {
		tmp = t_1;
	} else {
		tmp = (y * x) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (i * a) * b
	tmp = 0
	if x <= -7.2e+102:
		tmp = (z * y) * x
	elif x <= -1.45e-114:
		tmp = t_1
	elif x <= -2.35e-221:
		tmp = (j * t) * c
	elif x <= 3.4e-83:
		tmp = t_1
	else:
		tmp = (y * x) * z
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * a) * b)
	tmp = 0.0
	if (x <= -7.2e+102)
		tmp = Float64(Float64(z * y) * x);
	elseif (x <= -1.45e-114)
		tmp = t_1;
	elseif (x <= -2.35e-221)
		tmp = Float64(Float64(j * t) * c);
	elseif (x <= 3.4e-83)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * x) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (i * a) * b;
	tmp = 0.0;
	if (x <= -7.2e+102)
		tmp = (z * y) * x;
	elseif (x <= -1.45e-114)
		tmp = t_1;
	elseif (x <= -2.35e-221)
		tmp = (j * t) * c;
	elseif (x <= 3.4e-83)
		tmp = t_1;
	else
		tmp = (y * x) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * a), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[x, -7.2e+102], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, -1.45e-114], t$95$1, If[LessEqual[x, -2.35e-221], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[x, 3.4e-83], t$95$1, N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.2000000000000003e102

   1. Initial program 76.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(x \cdot y - b \cdot c\right) \cdot \color{blue}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x \cdot y - b \cdot c\right) \cdot \color{blue}{z} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(x \cdot y + \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      4. *-commutative N/A

         \[\leadsto \left(y \cdot x + \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      7. lower-neg.f64 50.2

         \[\leadsto \mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z \]

   5. Applied rewrites 50.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z} \]

   6. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x \cdot \left(z \cdot y\right) \]

      2. *-commutative N/A

         \[\leadsto \left(z \cdot y\right) \cdot x \]

      3. lift-*.f64 N/A

         \[\leadsto \left(z \cdot y\right) \cdot x \]

      4. lift-*.f64 43.3

         \[\leadsto \left(z \cdot y\right) \cdot x \]

   8. Applied rewrites 43.3%

      \[\leadsto \left(z \cdot y\right) \cdot \color{blue}{x} \]

   if -7.2000000000000003e102 < x < -1.44999999999999998e-114 or -2.34999999999999987e-221 < x < 3.3999999999999998e-83

   1. Initial program 77.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(a \cdot i + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      4. *-commutative N/A

         \[\leadsto \left(i \cdot a + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      9. lower-neg.f64 58.8

         \[\leadsto \mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b \]

   5. Applied rewrites 58.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b} \]

   6. Taylor expanded in z around 0

      \[\leadsto \left(a \cdot i\right) \cdot b \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(i \cdot a\right) \cdot b \]

      2. lift-*.f64 38.9

         \[\leadsto \left(i \cdot a\right) \cdot b \]

   8. Applied rewrites 38.9%

      \[\leadsto \left(i \cdot a\right) \cdot b \]

   if -1.44999999999999998e-114 < x < -2.34999999999999987e-221

   1. Initial program 88.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot \color{blue}{t} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot \color{blue}{t} \]

      3. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot a\right) \cdot x + c \cdot j\right) \cdot t \]

      4. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(a\right)\right) \cdot x + c \cdot j\right) \cdot t \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(a\right), x, c \cdot j\right) \cdot t \]

      6. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-a, x, c \cdot j\right) \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t \]

      8. lower-*.f64 57.3

         \[\leadsto \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t \]

   5. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]

   6. Taylor expanded in x around 0

      \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(j \cdot t\right) \cdot c \]

      2. lower-*.f64 N/A

         \[\leadsto \left(j \cdot t\right) \cdot c \]

      3. lower-*.f64 49.1

         \[\leadsto \left(j \cdot t\right) \cdot c \]

   8. Applied rewrites 49.1%

      \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{c} \]

   if 3.3999999999999998e-83 < x

   1. Initial program 75.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(x \cdot y - b \cdot c\right) \cdot \color{blue}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x \cdot y - b \cdot c\right) \cdot \color{blue}{z} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(x \cdot y + \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      4. *-commutative N/A

         \[\leadsto \left(y \cdot x + \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      7. lower-neg.f64 44.9

         \[\leadsto \mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z \]

   5. Applied rewrites 44.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z} \]

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot y\right) \cdot z \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(y \cdot x\right) \cdot z \]

      2. lower-*.f64 40.6

         \[\leadsto \left(y \cdot x\right) \cdot z \]

   8. Applied rewrites 40.6%

      \[\leadsto \left(y \cdot x\right) \cdot z \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 18: 28.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot x\\ \mathbf{if}\;z \leq -1.32 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-134}:\\ \;\;\;\;\left(i \cdot a\right) \cdot b\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-242}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-140}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z y) x)))
   (if (<= z -1.32e+68)
     t_1
     (if (<= z -5.5e-134)
       (* (* i a) b)
       (if (<= z -2.8e-242)
         (* (* j t) c)
         (if (<= z 6.5e-140) (* (* i b) a) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * y) * x;
	double tmp;
	if (z <= -1.32e+68) {
		tmp = t_1;
	} else if (z <= -5.5e-134) {
		tmp = (i * a) * b;
	} else if (z <= -2.8e-242) {
		tmp = (j * t) * c;
	} else if (z <= 6.5e-140) {
		tmp = (i * b) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * y) * x
    if (z <= (-1.32d+68)) then
        tmp = t_1
    else if (z <= (-5.5d-134)) then
        tmp = (i * a) * b
    else if (z <= (-2.8d-242)) then
        tmp = (j * t) * c
    else if (z <= 6.5d-140) then
        tmp = (i * b) * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * y) * x;
	double tmp;
	if (z <= -1.32e+68) {
		tmp = t_1;
	} else if (z <= -5.5e-134) {
		tmp = (i * a) * b;
	} else if (z <= -2.8e-242) {
		tmp = (j * t) * c;
	} else if (z <= 6.5e-140) {
		tmp = (i * b) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * y) * x
	tmp = 0
	if z <= -1.32e+68:
		tmp = t_1
	elif z <= -5.5e-134:
		tmp = (i * a) * b
	elif z <= -2.8e-242:
		tmp = (j * t) * c
	elif z <= 6.5e-140:
		tmp = (i * b) * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * y) * x)
	tmp = 0.0
	if (z <= -1.32e+68)
		tmp = t_1;
	elseif (z <= -5.5e-134)
		tmp = Float64(Float64(i * a) * b);
	elseif (z <= -2.8e-242)
		tmp = Float64(Float64(j * t) * c);
	elseif (z <= 6.5e-140)
		tmp = Float64(Float64(i * b) * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (z * y) * x;
	tmp = 0.0;
	if (z <= -1.32e+68)
		tmp = t_1;
	elseif (z <= -5.5e-134)
		tmp = (i * a) * b;
	elseif (z <= -2.8e-242)
		tmp = (j * t) * c;
	elseif (z <= 6.5e-140)
		tmp = (i * b) * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -1.32e+68], t$95$1, If[LessEqual[z, -5.5e-134], N[(N[(i * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[z, -2.8e-242], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[z, 6.5e-140], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.3200000000000001e68 or 6.4999999999999995e-140 < z

   1. Initial program 73.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(x \cdot y - b \cdot c\right) \cdot \color{blue}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x \cdot y - b \cdot c\right) \cdot \color{blue}{z} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(x \cdot y + \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      4. *-commutative N/A

         \[\leadsto \left(y \cdot x + \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      7. lower-neg.f64 58.6

         \[\leadsto \mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z \]

   5. Applied rewrites 58.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z} \]

   6. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x \cdot \left(z \cdot y\right) \]

      2. *-commutative N/A

         \[\leadsto \left(z \cdot y\right) \cdot x \]

      3. lift-*.f64 N/A

         \[\leadsto \left(z \cdot y\right) \cdot x \]

      4. lift-*.f64 38.0

         \[\leadsto \left(z \cdot y\right) \cdot x \]

   8. Applied rewrites 38.0%

      \[\leadsto \left(z \cdot y\right) \cdot \color{blue}{x} \]

   if -1.3200000000000001e68 < z < -5.5000000000000002e-134

   1. Initial program 89.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(a \cdot i + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      4. *-commutative N/A

         \[\leadsto \left(i \cdot a + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      9. lower-neg.f64 47.9

         \[\leadsto \mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b \]

   5. Applied rewrites 47.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b} \]

   6. Taylor expanded in z around 0

      \[\leadsto \left(a \cdot i\right) \cdot b \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(i \cdot a\right) \cdot b \]

      2. lift-*.f64 36.4

         \[\leadsto \left(i \cdot a\right) \cdot b \]

   8. Applied rewrites 36.4%

      \[\leadsto \left(i \cdot a\right) \cdot b \]

   if -5.5000000000000002e-134 < z < -2.79999999999999983e-242

   1. Initial program 76.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot \color{blue}{t} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot \color{blue}{t} \]

      3. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot a\right) \cdot x + c \cdot j\right) \cdot t \]

      4. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(a\right)\right) \cdot x + c \cdot j\right) \cdot t \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(a\right), x, c \cdot j\right) \cdot t \]

      6. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-a, x, c \cdot j\right) \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t \]

      8. lower-*.f64 70.3

         \[\leadsto \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t \]

   5. Applied rewrites 70.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]

   6. Taylor expanded in x around 0

      \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(j \cdot t\right) \cdot c \]

      2. lower-*.f64 N/A

         \[\leadsto \left(j \cdot t\right) \cdot c \]

      3. lower-*.f64 51.4

         \[\leadsto \left(j \cdot t\right) \cdot c \]

   8. Applied rewrites 51.4%

      \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{c} \]

   if -2.79999999999999983e-242 < z < 6.4999999999999995e-140

   1. Initial program 79.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(a \cdot i + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      4. *-commutative N/A

         \[\leadsto \left(i \cdot a + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      9. lower-neg.f64 41.6

         \[\leadsto \mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b \]

   5. Applied rewrites 41.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b} \]

   6. Taylor expanded in z around 0

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto a \cdot \left(i \cdot b\right) \]

      2. lift-*.f64 N/A

         \[\leadsto a \cdot \left(i \cdot b\right) \]

      3. *-commutative N/A

         \[\leadsto \left(i \cdot b\right) \cdot a \]

      4. lift-*.f64 39.1

         \[\leadsto \left(i \cdot b\right) \cdot a \]

   8. Applied rewrites 39.1%

      \[\leadsto \left(i \cdot b\right) \cdot \color{blue}{a} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 19: 28.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(i \cdot b\right) \cdot a\\ t_2 := \left(z \cdot y\right) \cdot x\\ \mathbf{if}\;z \leq -5.1 \cdot 10^{+23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-134}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-242}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-140}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* i b) a)) (t_2 (* (* z y) x)))
   (if (<= z -5.1e+23)
     t_2
     (if (<= z -5.5e-134)
       t_1
       (if (<= z -2.8e-242) (* (* j t) c) (if (<= z 6.5e-140) 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 = (i * b) * a;
	double t_2 = (z * y) * x;
	double tmp;
	if (z <= -5.1e+23) {
		tmp = t_2;
	} else if (z <= -5.5e-134) {
		tmp = t_1;
	} else if (z <= -2.8e-242) {
		tmp = (j * t) * c;
	} else if (z <= 6.5e-140) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (i * b) * a
    t_2 = (z * y) * x
    if (z <= (-5.1d+23)) then
        tmp = t_2
    else if (z <= (-5.5d-134)) then
        tmp = t_1
    else if (z <= (-2.8d-242)) then
        tmp = (j * t) * c
    else if (z <= 6.5d-140) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * b) * a;
	double t_2 = (z * y) * x;
	double tmp;
	if (z <= -5.1e+23) {
		tmp = t_2;
	} else if (z <= -5.5e-134) {
		tmp = t_1;
	} else if (z <= -2.8e-242) {
		tmp = (j * t) * c;
	} else if (z <= 6.5e-140) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (i * b) * a
	t_2 = (z * y) * x
	tmp = 0
	if z <= -5.1e+23:
		tmp = t_2
	elif z <= -5.5e-134:
		tmp = t_1
	elif z <= -2.8e-242:
		tmp = (j * t) * c
	elif z <= 6.5e-140:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * b) * a)
	t_2 = Float64(Float64(z * y) * x)
	tmp = 0.0
	if (z <= -5.1e+23)
		tmp = t_2;
	elseif (z <= -5.5e-134)
		tmp = t_1;
	elseif (z <= -2.8e-242)
		tmp = Float64(Float64(j * t) * c);
	elseif (z <= 6.5e-140)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (i * b) * a;
	t_2 = (z * y) * x;
	tmp = 0.0;
	if (z <= -5.1e+23)
		tmp = t_2;
	elseif (z <= -5.5e-134)
		tmp = t_1;
	elseif (z <= -2.8e-242)
		tmp = (j * t) * c;
	elseif (z <= 6.5e-140)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -5.1e+23], t$95$2, If[LessEqual[z, -5.5e-134], t$95$1, If[LessEqual[z, -2.8e-242], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[z, 6.5e-140], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.10000000000000021e23 or 6.4999999999999995e-140 < z

   1. Initial program 74.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(x \cdot y - b \cdot c\right) \cdot \color{blue}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x \cdot y - b \cdot c\right) \cdot \color{blue}{z} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(x \cdot y + \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      4. *-commutative N/A

         \[\leadsto \left(y \cdot x + \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      7. lower-neg.f64 58.5

         \[\leadsto \mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z \]

   5. Applied rewrites 58.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z} \]

   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

         \[\leadsto x \cdot \left(z \cdot y\right) \]

      2. *-commutative N/A

         \[\leadsto \left(z \cdot y\right) \cdot x \]

      3. lift-*.f64 N/A

         \[\leadsto \left(z \cdot y\right) \cdot x \]

      4. lift-*.f64 37.8

         \[\leadsto \left(z \cdot y\right) \cdot x \]

   8. Applied rewrites 37.8%

      \[\leadsto \left(z \cdot y\right) \cdot \color{blue}{x} \]

   if -5.10000000000000021e23 < z < -5.5000000000000002e-134 or -2.79999999999999983e-242 < z < 6.4999999999999995e-140

   1. Initial program 84.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(a \cdot i + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      4. *-commutative N/A

         \[\leadsto \left(i \cdot a + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      9. lower-neg.f64 43.9

         \[\leadsto \mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b \]

   5. Applied rewrites 43.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b} \]

   6. Taylor expanded in z around 0

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto a \cdot \left(i \cdot b\right) \]

      2. lift-*.f64 N/A

         \[\leadsto a \cdot \left(i \cdot b\right) \]

      3. *-commutative N/A

         \[\leadsto \left(i \cdot b\right) \cdot a \]

      4. lift-*.f64 36.5

         \[\leadsto \left(i \cdot b\right) \cdot a \]

   8. Applied rewrites 36.5%

      \[\leadsto \left(i \cdot b\right) \cdot \color{blue}{a} \]

   if -5.5000000000000002e-134 < z < -2.79999999999999983e-242

   1. Initial program 76.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot \color{blue}{t} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot \color{blue}{t} \]

      3. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot a\right) \cdot x + c \cdot j\right) \cdot t \]

      4. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(a\right)\right) \cdot x + c \cdot j\right) \cdot t \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(a\right), x, c \cdot j\right) \cdot t \]

      6. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-a, x, c \cdot j\right) \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t \]

      8. lower-*.f64 70.3

         \[\leadsto \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t \]

   5. Applied rewrites 70.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]

   6. Taylor expanded in x around 0

      \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(j \cdot t\right) \cdot c \]

      2. lower-*.f64 N/A

         \[\leadsto \left(j \cdot t\right) \cdot c \]

      3. lower-*.f64 51.4

         \[\leadsto \left(j \cdot t\right) \cdot c \]

   8. Applied rewrites 51.4%

      \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{c} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 20: 45.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.2 \cdot 10^{-66} \lor \neg \left(j \leq 2.5 \cdot 10^{+38}\right):\\ \;\;\;\;\mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -2.2e-66) (not (<= j 2.5e+38)))
   (* (fma j t (* (- b) z)) c)
   (* (fma i a (* (- c) z)) b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -2.2e-66) || !(j <= 2.5e+38)) {
		tmp = fma(j, t, (-b * z)) * c;
	} else {
		tmp = fma(i, a, (-c * z)) * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -2.2e-66) || !(j <= 2.5e+38))
		tmp = Float64(fma(j, t, Float64(Float64(-b) * z)) * c);
	else
		tmp = Float64(fma(i, a, Float64(Float64(-c) * z)) * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -2.2e-66], N[Not[LessEqual[j, 2.5e+38]], $MachinePrecision]], N[(N[(j * t + N[((-b) * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], N[(N[(i * a + N[((-c) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -2.2000000000000001e-66 or 2.49999999999999985e38 < j

   1. Initial program 76.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(j \cdot t - b \cdot z\right) \cdot \color{blue}{c} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(j \cdot t - b \cdot z\right) \cdot \color{blue}{c} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(j \cdot t + \left(\mathsf{neg}\left(b\right)\right) \cdot z\right) \cdot c \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(j, t, \left(\mathsf{neg}\left(b\right)\right) \cdot z\right) \cdot c \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(j, t, \left(\mathsf{neg}\left(b\right)\right) \cdot z\right) \cdot c \]

      6. lower-neg.f64 53.7

         \[\leadsto \mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c \]

   5. Applied rewrites 53.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c} \]

   if -2.2000000000000001e-66 < j < 2.49999999999999985e38

   1. Initial program 78.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(a \cdot i + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      4. *-commutative N/A

         \[\leadsto \left(i \cdot a + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      9. lower-neg.f64 47.2

         \[\leadsto \mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b \]

   5. Applied rewrites 47.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.2 \cdot 10^{-66} \lor \neg \left(j \leq 2.5 \cdot 10^{+38}\right):\\ \;\;\;\;\mathsf{fma}\left(j, t, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -5.8 \cdot 10^{+68} \lor \neg \left(i \leq 0.00062\right):\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -5.8e+68) (not (<= i 0.00062))) (* (* i b) a) (* (* z y) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -5.8e+68) || !(i <= 0.00062)) {
		tmp = (i * b) * a;
	} else {
		tmp = (z * y) * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-5.8d+68)) .or. (.not. (i <= 0.00062d0))) then
        tmp = (i * b) * a
    else
        tmp = (z * y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -5.8e+68) || !(i <= 0.00062)) {
		tmp = (i * b) * a;
	} else {
		tmp = (z * y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -5.8e+68) or not (i <= 0.00062):
		tmp = (i * b) * a
	else:
		tmp = (z * y) * x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -5.8e+68) || !(i <= 0.00062))
		tmp = Float64(Float64(i * b) * a);
	else
		tmp = Float64(Float64(z * y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -5.8e+68) || ~((i <= 0.00062)))
		tmp = (i * b) * a;
	else
		tmp = (z * y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -5.8e+68], N[Not[LessEqual[i, 0.00062]], $MachinePrecision]], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -5.80000000000000023e68 or 6.2e-4 < i

   1. Initial program 65.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(a \cdot i + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      4. *-commutative N/A

         \[\leadsto \left(i \cdot a + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

      9. lower-neg.f64 49.7

         \[\leadsto \mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b \]

   5. Applied rewrites 49.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b} \]

   6. Taylor expanded in z around 0

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto a \cdot \left(i \cdot b\right) \]

      2. lift-*.f64 N/A

         \[\leadsto a \cdot \left(i \cdot b\right) \]

      3. *-commutative N/A

         \[\leadsto \left(i \cdot b\right) \cdot a \]

      4. lift-*.f64 38.3

         \[\leadsto \left(i \cdot b\right) \cdot a \]

   8. Applied rewrites 38.3%

      \[\leadsto \left(i \cdot b\right) \cdot \color{blue}{a} \]

   if -5.80000000000000023e68 < i < 6.2e-4

   1. Initial program 87.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(x \cdot y - b \cdot c\right) \cdot \color{blue}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x \cdot y - b \cdot c\right) \cdot \color{blue}{z} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(x \cdot y + \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      4. *-commutative N/A

         \[\leadsto \left(y \cdot x + \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \left(\mathsf{neg}\left(b\right)\right) \cdot c\right) \cdot z \]

      7. lower-neg.f64 49.7

         \[\leadsto \mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z \]

   5. Applied rewrites 49.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, \left(-b\right) \cdot c\right) \cdot z} \]

   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

         \[\leadsto x \cdot \left(z \cdot y\right) \]

      2. *-commutative N/A

         \[\leadsto \left(z \cdot y\right) \cdot x \]

      3. lift-*.f64 N/A

         \[\leadsto \left(z \cdot y\right) \cdot x \]

      4. lift-*.f64 33.3

         \[\leadsto \left(z \cdot y\right) \cdot x \]

   8. Applied rewrites 33.3%

      \[\leadsto \left(z \cdot y\right) \cdot \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.8 \cdot 10^{+68} \lor \neg \left(i \leq 0.00062\right):\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 22.3% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \left(i \cdot b\right) \cdot a \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* (* i b) a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return (i * b) * a;
}

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 * b) * a
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 * b) * a;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return (i * b) * a

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(i * b) * a)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = (i * b) * a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision]

Derivation

1. Initial program 77.6%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Add Preprocessing

3. Taylor expanded in b around inf

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

   2. lower-*.f64 N/A

      \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

   3. fp-cancel-sub-sign-inv N/A

      \[\leadsto \left(a \cdot i + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

   4. *-commutative N/A

      \[\leadsto \left(i \cdot a + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

   5. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

   6. mul-1-neg N/A

      \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

   7. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

   8. mul-1-neg N/A

      \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

   9. lower-neg.f64 38.8

      \[\leadsto \mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b \]

5. Applied rewrites 38.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b} \]

6. Taylor expanded in z around 0

   \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
7. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto a \cdot \left(i \cdot b\right) \]

   2. lift-*.f64 N/A

      \[\leadsto a \cdot \left(i \cdot b\right) \]

   3. *-commutative N/A

      \[\leadsto \left(i \cdot b\right) \cdot a \]

   4. lift-*.f64 23.2

      \[\leadsto \left(i \cdot b\right) \cdot a \]

8. Applied rewrites 23.2%

   \[\leadsto \left(i \cdot b\right) \cdot \color{blue}{a} \]
9. Add Preprocessing

Alternative 23: 22.2% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \left(b \cdot a\right) \cdot i \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* (* b a) i))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return (b * a) * i;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = (b * a) * i
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return (b * a) * i;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return (b * a) * i

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(b * a) * i)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = (b * a) * i;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(b * a), $MachinePrecision] * i), $MachinePrecision]

Derivation

1. Initial program 77.6%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Add Preprocessing

3. Taylor expanded in b around inf

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

   2. lower-*.f64 N/A

      \[\leadsto \left(a \cdot i - c \cdot z\right) \cdot \color{blue}{b} \]

   3. fp-cancel-sub-sign-inv N/A

      \[\leadsto \left(a \cdot i + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

   4. *-commutative N/A

      \[\leadsto \left(i \cdot a + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

   5. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

   6. mul-1-neg N/A

      \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

   7. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(i, a, \left(-1 \cdot c\right) \cdot z\right) \cdot b \]

   8. mul-1-neg N/A

      \[\leadsto \mathsf{fma}\left(i, a, \left(\mathsf{neg}\left(c\right)\right) \cdot z\right) \cdot b \]

   9. lower-neg.f64 38.8

      \[\leadsto \mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b \]

5. Applied rewrites 38.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(i, a, \left(-c\right) \cdot z\right) \cdot b} \]

6. Taylor expanded in z around 0

   \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
7. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto a \cdot \left(i \cdot b\right) \]

   2. lift-*.f64 N/A

      \[\leadsto a \cdot \left(i \cdot b\right) \]

   3. *-commutative N/A

      \[\leadsto \left(i \cdot b\right) \cdot a \]

   4. lift-*.f64 23.2

      \[\leadsto \left(i \cdot b\right) \cdot a \]

8. Applied rewrites 23.2%

   \[\leadsto \left(i \cdot b\right) \cdot \color{blue}{a} \]
9. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(i \cdot b\right) \cdot a \]

   2. lift-*.f64 N/A

      \[\leadsto \left(i \cdot b\right) \cdot a \]

   3. *-commutative N/A

      \[\leadsto \left(b \cdot i\right) \cdot a \]

   4. *-commutative N/A

      \[\leadsto a \cdot \left(b \cdot \color{blue}{i}\right) \]

   5. associate-*r* N/A

      \[\leadsto \left(a \cdot b\right) \cdot i \]

   6. lower-*.f64 N/A

      \[\leadsto \left(a \cdot b\right) \cdot i \]

   7. *-commutative N/A

      \[\leadsto \left(b \cdot a\right) \cdot i \]

   8. lower-*.f64 21.8

      \[\leadsto \left(b \cdot a\right) \cdot i \]

10. Applied rewrites 21.8%

    \[\leadsto \left(b \cdot a\right) \cdot i \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2025085 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -1015122364899489/125000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -942510763643697/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (if (< t -238547917063487/3125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 10535888557455487/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))