Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.6% → 83.0%

Time: 14.1s

Alternatives: 26

Speedup: 0.9×

• 57.9% 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

real(8) function code(x, y, z, t, a, b, c, i, j)
    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: 73.6% 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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 83.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{if}\;t\_1 \leq 10^{+303}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot \mathsf{fma}\left(a, x, -\mathsf{fma}\left(j, c, \frac{\mathsf{fma}\left(\mathsf{fma}\left(-z, c, i \cdot a\right), b, \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\right)}{t}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (* j (- (* c t) (* i y))))))
   (if (<= t_1 1e+303)
     t_1
     (*
      (- t)
      (fma
       a
       x
       (-
        (fma
         j
         c
         (/ (fma (fma (- z) c (* i a)) b (* (fma (- i) j (* z x)) y)) t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
	double tmp;
	if (t_1 <= 1e+303) {
		tmp = t_1;
	} else {
		tmp = -t * fma(a, x, -fma(j, c, (fma(fma(-z, c, (i * a)), b, (fma(-i, j, (z * x)) * y)) / t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
	tmp = 0.0
	if (t_1 <= 1e+303)
		tmp = t_1;
	else
		tmp = Float64(Float64(-t) * fma(a, x, Float64(-fma(j, c, Float64(fma(fma(Float64(-z), c, Float64(i * a)), b, Float64(fma(Float64(-i), j, Float64(z * x)) * y)) / t)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(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, 1e+303], t$95$1, N[((-t) * N[(a * x + (-N[(j * c + N[(N[(N[((-z) * c + N[(i * a), $MachinePrecision]), $MachinePrecision] * b + N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < 1e303

   1. Initial program 92.6%

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

   if 1e303 < (+.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 46.8%

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

   3. Taylor expanded in t around -inf

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

   5. Applied rewrites 80.3%

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

Alternative 2: 78.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+91} \lor \neg \left(t \leq 1.9 \cdot 10^{+48}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-z, c, i \cdot a\right), b, \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-x, t, i \cdot b\right), a, \mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -5e+91) (not (<= t 1.9e+48)))
   (fma (fma (- z) c (* i a)) b (* (fma (- a) x (* j c)) t))
   (fma
    (fma (- x) t (* i b))
    a
    (fma (fma (- i) y (* c t)) j (* (fma (- b) c (* 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 ((t <= -5e+91) || !(t <= 1.9e+48)) {
		tmp = fma(fma(-z, c, (i * a)), b, (fma(-a, x, (j * c)) * t));
	} else {
		tmp = fma(fma(-x, t, (i * b)), a, fma(fma(-i, y, (c * t)), j, (fma(-b, c, (y * x)) * z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -5e+91) || !(t <= 1.9e+48))
		tmp = fma(fma(Float64(-z), c, Float64(i * a)), b, Float64(fma(Float64(-a), x, Float64(j * c)) * t));
	else
		tmp = fma(fma(Float64(-x), t, Float64(i * b)), a, fma(fma(Float64(-i), y, Float64(c * t)), j, Float64(fma(Float64(-b), c, Float64(y * x)) * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -5e+91], N[Not[LessEqual[t, 1.9e+48]], $MachinePrecision]], N[(N[((-z) * c + N[(i * a), $MachinePrecision]), $MachinePrecision] * b + N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a + N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j + N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.0000000000000002e91 or 1.9e48 < t

   1. Initial program 61.9%

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

   3. Taylor expanded in 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. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

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

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

   5. Applied rewrites 78.8%

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

   if -5.0000000000000002e91 < t < 1.9e48

   1. Initial program 81.6%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 87.5%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+91} \lor \neg \left(t \leq 1.9 \cdot 10^{+48}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-z, c, i \cdot a\right), b, \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-x, t, i \cdot b\right), a, \mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, x, j \cdot c\right)\\ t_2 := \mathsf{fma}\left(-z, c, i \cdot a\right)\\ \mathbf{if}\;t \leq -5 \cdot 10^{+91}:\\ \;\;\;\;\mathsf{fma}\left(t\_2, b, t\_1 \cdot t\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+30}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-x, t, i \cdot b\right), a, \mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_2, b, \mathsf{fma}\left(t\_1, t, \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (fma (- a) x (* j c))) (t_2 (fma (- z) c (* i a))))
   (if (<= t -5e+91)
     (fma t_2 b (* t_1 t))
     (if (<= t 4e+30)
       (fma
        (fma (- x) t (* i b))
        a
        (fma (fma (- i) y (* c t)) j (* (fma (- b) c (* y x)) z)))
       (fma t_2 b (fma t_1 t (* (fma (- i) j (* z x)) y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-a, x, (j * c));
	double t_2 = fma(-z, c, (i * a));
	double tmp;
	if (t <= -5e+91) {
		tmp = fma(t_2, b, (t_1 * t));
	} else if (t <= 4e+30) {
		tmp = fma(fma(-x, t, (i * b)), a, fma(fma(-i, y, (c * t)), j, (fma(-b, c, (y * x)) * z)));
	} else {
		tmp = fma(t_2, b, fma(t_1, t, (fma(-i, j, (z * x)) * y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = fma(Float64(-a), x, Float64(j * c))
	t_2 = fma(Float64(-z), c, Float64(i * a))
	tmp = 0.0
	if (t <= -5e+91)
		tmp = fma(t_2, b, Float64(t_1 * t));
	elseif (t <= 4e+30)
		tmp = fma(fma(Float64(-x), t, Float64(i * b)), a, fma(fma(Float64(-i), y, Float64(c * t)), j, Float64(fma(Float64(-b), c, Float64(y * x)) * z)));
	else
		tmp = fma(t_2, b, fma(t_1, t, Float64(fma(Float64(-i), j, Float64(z * x)) * y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-z) * c + N[(i * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e+91], N[(t$95$2 * b + N[(t$95$1 * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+30], N[(N[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a + N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j + N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 * b + N[(t$95$1 * t + N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.0000000000000002e91

   1. Initial program 60.2%

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

   3. Taylor expanded in 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. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

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

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

   5. Applied rewrites 81.0%

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

   if -5.0000000000000002e91 < t < 4.0000000000000001e30

   1. Initial program 81.4%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 87.3%

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

   if 4.0000000000000001e30 < t

   1. Initial program 64.5%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 88.5%

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

Alternative 4: 73.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.14 \cdot 10^{+58} \lor \neg \left(z \leq 1.25 \cdot 10^{+65}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-b, c, y \cdot x\right), z, \mathsf{fma}\left(-t, x, i \cdot b\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, t \cdot x, \mathsf{fma}\left(-z, c, i \cdot a\right) \cdot b\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -1.14e+58) (not (<= z 1.25e+65)))
   (fma (fma (- b) c (* y x)) z (* (fma (- t) x (* i b)) a))
   (+
    (fma (- a) (* t x) (* (fma (- z) c (* i a)) b))
    (* 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 ((z <= -1.14e+58) || !(z <= 1.25e+65)) {
		tmp = fma(fma(-b, c, (y * x)), z, (fma(-t, x, (i * b)) * a));
	} else {
		tmp = fma(-a, (t * x), (fma(-z, c, (i * a)) * b)) + (j * ((c * t) - (i * y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -1.14e+58) || !(z <= 1.25e+65))
		tmp = fma(fma(Float64(-b), c, Float64(y * x)), z, Float64(fma(Float64(-t), x, Float64(i * b)) * a));
	else
		tmp = Float64(fma(Float64(-a), Float64(t * x), Float64(fma(Float64(-z), c, Float64(i * a)) * b)) + 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[z, -1.14e+58], N[Not[LessEqual[z, 1.25e+65]], $MachinePrecision]], N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z + N[(N[((-t) * x + N[(i * b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[((-a) * N[(t * x), $MachinePrecision] + N[(N[((-z) * c + N[(i * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.14e58 or 1.24999999999999993e65 < z

   1. Initial program 61.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 74.1%

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

   6. Taylor expanded in j around 0

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

   8. Applied rewrites 81.5%

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

   if -1.14e58 < z < 1.24999999999999993e65

   1. Initial program 83.0%

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

   3. Taylor expanded in y around 0

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

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

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-*.f64 N/A

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

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

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

      8. *-commutative N/A

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

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

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

   5. Applied rewrites 80.6%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.14 \cdot 10^{+58} \lor \neg \left(z \leq 1.25 \cdot 10^{+65}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-b, c, y \cdot x\right), z, \mathsf{fma}\left(-t, x, i \cdot b\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, t \cdot x, \mathsf{fma}\left(-z, c, i \cdot a\right) \cdot b\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-b, c, y \cdot x\right)\\ t_2 := \mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-z, c, i \cdot a\right) \cdot b\right)\\ \mathbf{if}\;j \leq -7.5 \cdot 10^{+66}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-124}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, z, \mathsf{fma}\left(-t, x, i \cdot b\right) \cdot a\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(-a, t \cdot x, \mathsf{fma}\left(t\_1, z, \left(j \cdot t\right) \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (fma (- b) c (* y x)))
        (t_2 (fma (fma (- i) y (* c t)) j (* (fma (- z) c (* i a)) b))))
   (if (<= j -7.5e+66)
     t_2
     (if (<= j 3.5e-124)
       (fma t_1 z (* (fma (- t) x (* i b)) a))
       (if (<= j 8e-8) (fma (- a) (* t x) (fma t_1 z (* (* j t) c))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-b, c, (y * x));
	double t_2 = fma(fma(-i, y, (c * t)), j, (fma(-z, c, (i * a)) * b));
	double tmp;
	if (j <= -7.5e+66) {
		tmp = t_2;
	} else if (j <= 3.5e-124) {
		tmp = fma(t_1, z, (fma(-t, x, (i * b)) * a));
	} else if (j <= 8e-8) {
		tmp = fma(-a, (t * x), fma(t_1, z, ((j * t) * c)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = fma(Float64(-b), c, Float64(y * x))
	t_2 = fma(fma(Float64(-i), y, Float64(c * t)), j, Float64(fma(Float64(-z), c, Float64(i * a)) * b))
	tmp = 0.0
	if (j <= -7.5e+66)
		tmp = t_2;
	elseif (j <= 3.5e-124)
		tmp = fma(t_1, z, Float64(fma(Float64(-t), x, Float64(i * b)) * a));
	elseif (j <= 8e-8)
		tmp = fma(Float64(-a), Float64(t * x), fma(t_1, z, Float64(Float64(j * t) * c)));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j + N[(N[((-z) * c + N[(i * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7.5e+66], t$95$2, If[LessEqual[j, 3.5e-124], N[(t$95$1 * z + N[(N[((-t) * x + N[(i * b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8e-8], N[((-a) * N[(t * x), $MachinePrecision] + N[(t$95$1 * z + N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -7.50000000000000024e66 or 8.0000000000000002e-8 < j

   1. Initial program 77.8%

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

   3. Taylor expanded in x around 0

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

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

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

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

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 N/A

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

      8. lower-*.f64 N/A

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

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

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

      10. *-commutative N/A

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

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

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

      12. mul-1-neg N/A

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

      13. lower-*.f64 N/A

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

   5. Applied rewrites 79.0%

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

   if -7.50000000000000024e66 < j < 3.4999999999999999e-124

   1. Initial program 69.8%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 75.7%

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

   6. Taylor expanded in j around 0

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

   8. Applied rewrites 77.4%

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

   if 3.4999999999999999e-124 < j < 8.0000000000000002e-8

   1. Initial program 71.8%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 88.0%

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

   6. Taylor expanded in i around 0

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

   8. Applied rewrites 94.1%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.5 \cdot 10^{+66}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-z, c, i \cdot a\right) \cdot b\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-124}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-b, c, y \cdot x\right), z, \mathsf{fma}\left(-t, x, i \cdot b\right) \cdot a\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(-a, t \cdot x, \mathsf{fma}\left(\mathsf{fma}\left(-b, c, y \cdot x\right), z, \left(j \cdot t\right) \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-z, c, i \cdot a\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -7.5 \cdot 10^{+66} \lor \neg \left(j \leq 5 \cdot 10^{-7}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-z, c, i \cdot a\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-b, c, y \cdot x\right), z, \mathsf{fma}\left(-t, x, i \cdot b\right) \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -7.5e+66) (not (<= j 5e-7)))
   (fma (fma (- i) y (* c t)) j (* (fma (- z) c (* i a)) b))
   (fma (fma (- b) c (* y x)) z (* (fma (- t) x (* i b)) a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -7.5e+66) || !(j <= 5e-7)) {
		tmp = fma(fma(-i, y, (c * t)), j, (fma(-z, c, (i * a)) * b));
	} else {
		tmp = fma(fma(-b, c, (y * x)), z, (fma(-t, x, (i * b)) * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -7.5e+66) || !(j <= 5e-7))
		tmp = fma(fma(Float64(-i), y, Float64(c * t)), j, Float64(fma(Float64(-z), c, Float64(i * a)) * b));
	else
		tmp = fma(fma(Float64(-b), c, Float64(y * x)), z, Float64(fma(Float64(-t), x, Float64(i * b)) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -7.5e+66], N[Not[LessEqual[j, 5e-7]], $MachinePrecision]], N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j + N[(N[((-z) * c + N[(i * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z + N[(N[((-t) * x + N[(i * b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -7.50000000000000024e66 or 4.99999999999999977e-7 < j

   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 x around 0

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

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

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

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

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 N/A

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

      8. lower-*.f64 N/A

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

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

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

      10. *-commutative N/A

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

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

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

      12. mul-1-neg N/A

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

      13. lower-*.f64 N/A

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

   5. Applied rewrites 78.9%

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

   if -7.50000000000000024e66 < j < 4.99999999999999977e-7

   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 z around 0

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

   5. Applied rewrites 78.0%

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

   6. Taylor expanded in j around 0

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

   8. Applied rewrites 77.5%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.5 \cdot 10^{+66} \lor \neg \left(j \leq 5 \cdot 10^{-7}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-z, c, i \cdot a\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-b, c, y \cdot x\right), z, \mathsf{fma}\left(-t, x, i \cdot b\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-x, t, i \cdot b\right) \cdot a\\ \mathbf{if}\;a \leq -1 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7 \cdot 10^{+34}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+127}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-y, i, c \cdot t\right), j, \left(\left(-z\right) \cdot c\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- x) t (* i b)) a)))
   (if (<= a -1e+117)
     t_1
     (if (<= a -7e+34)
       (+ (* (* z x) y) (* j (- (* c t) (* i y))))
       (if (<= a 1.95e+127)
         (fma (fma (- y) i (* c t)) j (* (* (- z) c) 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(-x, t, (i * b)) * a;
	double tmp;
	if (a <= -1e+117) {
		tmp = t_1;
	} else if (a <= -7e+34) {
		tmp = ((z * x) * y) + (j * ((c * t) - (i * y)));
	} else if (a <= 1.95e+127) {
		tmp = fma(fma(-y, i, (c * t)), j, ((-z * c) * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-x), t, Float64(i * b)) * a)
	tmp = 0.0
	if (a <= -1e+117)
		tmp = t_1;
	elseif (a <= -7e+34)
		tmp = Float64(Float64(Float64(z * x) * y) + Float64(j * Float64(Float64(c * t) - Float64(i * y))));
	elseif (a <= 1.95e+127)
		tmp = fma(fma(Float64(-y), i, Float64(c * t)), j, Float64(Float64(Float64(-z) * c) * 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[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -1e+117], t$95$1, If[LessEqual[a, -7e+34], N[(N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.95e+127], N[(N[((-y) * i + N[(c * t), $MachinePrecision]), $MachinePrecision] * j + N[(N[((-z) * c), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.00000000000000005e117 or 1.94999999999999991e127 < a

   1. Initial program 62.6%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. mul-1-neg N/A

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

      7. *-commutative N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 81.9

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

   5. Applied rewrites 81.9%

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

   if -1.00000000000000005e117 < a < -6.99999999999999996e34

   1. Initial program 83.2%

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

   3. Taylor expanded in 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

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 73.1

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

   5. Applied rewrites 73.1%

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

   if -6.99999999999999996e34 < a < 1.94999999999999991e127

   1. Initial program 77.8%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 62.3

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

   5. Applied rewrites 62.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 63.6

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

   7. Applied rewrites 63.2%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+117}:\\ \;\;\;\;\mathsf{fma}\left(-x, t, i \cdot b\right) \cdot a\\ \mathbf{elif}\;a \leq -7 \cdot 10^{+34}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+127}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-y, i, c \cdot t\right), j, \left(\left(-z\right) \cdot c\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-x, t, i \cdot b\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(\left(-c\right) \cdot z, b, \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\right)\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-44}:\\ \;\;\;\;\mathsf{fma}\left(\left(-t\right) \cdot a, x, \mathsf{fma}\left(-z, c, a \cdot i\right) \cdot b\right)\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+95}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(c, \frac{j}{x}, -a\right) \cdot x\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -3.1e-9)
   (fma (* (- c) z) b (* (fma (- a) x (* j c)) t))
   (if (<= t 8.8e-44)
     (fma (* (- t) a) x (* (fma (- z) c (* a i)) b))
     (if (<= t 2.15e+95)
       (+ (* (* z x) y) (* j (- (* c t) (* i y))))
       (* (* (fma c (/ j x) (- a)) x) t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -3.1e-9) {
		tmp = fma((-c * z), b, (fma(-a, x, (j * c)) * t));
	} else if (t <= 8.8e-44) {
		tmp = fma((-t * a), x, (fma(-z, c, (a * i)) * b));
	} else if (t <= 2.15e+95) {
		tmp = ((z * x) * y) + (j * ((c * t) - (i * y)));
	} else {
		tmp = (fma(c, (j / x), -a) * x) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -3.1e-9)
		tmp = fma(Float64(Float64(-c) * z), b, Float64(fma(Float64(-a), x, Float64(j * c)) * t));
	elseif (t <= 8.8e-44)
		tmp = fma(Float64(Float64(-t) * a), x, Float64(fma(Float64(-z), c, Float64(a * i)) * b));
	elseif (t <= 2.15e+95)
		tmp = Float64(Float64(Float64(z * x) * y) + Float64(j * Float64(Float64(c * t) - Float64(i * y))));
	else
		tmp = Float64(Float64(fma(c, Float64(j / x), Float64(-a)) * x) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -3.1e-9], N[(N[((-c) * z), $MachinePrecision] * b + N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.8e-44], N[(N[((-t) * a), $MachinePrecision] * x + N[(N[((-z) * c + N[(a * i), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.15e+95], N[(N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(c * N[(j / x), $MachinePrecision] + (-a)), $MachinePrecision] * x), $MachinePrecision] * t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.10000000000000005e-9

   1. Initial program 64.0%

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

   3. Taylor expanded in y around 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. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

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

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

   5. Applied rewrites 70.7%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 69.5%

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

   if -3.10000000000000005e-9 < t < 8.80000000000000048e-44

   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 0

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

   5. Applied rewrites 89.1%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 73.2%

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

   9. Taylor expanded in j around 0

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

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

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

       2. *-commutative N/A

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

       3. lower-fma.f64 N/A

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

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

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

       5. mul-1-neg N/A

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

       6. associate-*r* N/A

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

       7. +-commutative N/A

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

       8. associate-*r* N/A

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

       9. lower-fma.f64 N/A

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

       10. mul-1-neg N/A

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

       11. lower-neg.f64 N/A

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

       12. *-commutative N/A

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

       13. lower-*.f64 N/A

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

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

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

       15. *-commutative N/A

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

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

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

       17. mul-1-neg N/A

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

       18. lower-*.f64 N/A

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

   11. Applied rewrites 75.6%

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

   12. Taylor expanded in y around 0

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

   14. Applied rewrites 65.8%

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

   if 8.80000000000000048e-44 < t < 2.15e95

   1. Initial program 73.9%

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

   3. Taylor expanded in 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

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 70.3

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

   5. Applied rewrites 70.3%

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

   if 2.15e95 < t

   1. Initial program 63.1%

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

   3. Taylor expanded in 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

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 70.3

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

   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 inf

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

   8. Applied rewrites 74.4%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(\left(-c\right) \cdot z, b, \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\right)\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-44}:\\ \;\;\;\;\mathsf{fma}\left(\left(-t\right) \cdot a, x, \mathsf{fma}\left(-z, c, a \cdot i\right) \cdot b\right)\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+95}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(c, \frac{j}{x}, -a\right) \cdot x\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -4.7 \cdot 10^{+134}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-y, i, c \cdot t\right), j, \left(\left(-z\right) \cdot c\right) \cdot b\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-b, c, y \cdot x\right), z, \mathsf{fma}\left(-t, x, i \cdot b\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -4.7e+134)
   (fma (fma (- y) i (* c t)) j (* (* (- z) c) b))
   (if (<= j 2.6e+14)
     (fma (fma (- b) c (* y x)) z (* (fma (- t) x (* i b)) a))
     (+ (* (* z x) y) (* 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 (j <= -4.7e+134) {
		tmp = fma(fma(-y, i, (c * t)), j, ((-z * c) * b));
	} else if (j <= 2.6e+14) {
		tmp = fma(fma(-b, c, (y * x)), z, (fma(-t, x, (i * b)) * a));
	} else {
		tmp = ((z * x) * y) + (j * ((c * t) - (i * y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -4.7e+134)
		tmp = fma(fma(Float64(-y), i, Float64(c * t)), j, Float64(Float64(Float64(-z) * c) * b));
	elseif (j <= 2.6e+14)
		tmp = fma(fma(Float64(-b), c, Float64(y * x)), z, Float64(fma(Float64(-t), x, Float64(i * b)) * a));
	else
		tmp = Float64(Float64(Float64(z * x) * y) + 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[LessEqual[j, -4.7e+134], N[(N[((-y) * i + N[(c * t), $MachinePrecision]), $MachinePrecision] * j + N[(N[((-z) * c), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.6e+14], N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z + N[(N[((-t) * x + N[(i * b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -4.70000000000000026e134

   1. Initial program 73.5%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 76.6

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

   5. Applied rewrites 76.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 82.4

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

   7. Applied rewrites 82.4%

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

   if -4.70000000000000026e134 < j < 2.6e14

   1. Initial program 71.8%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 79.2%

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

   6. Taylor expanded in j around 0

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

   8. Applied rewrites 77.6%

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

   if 2.6e14 < j

   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 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

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 72.5

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

   5. Applied rewrites 72.5%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.7 \cdot 10^{+134}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-y, i, c \cdot t\right), j, \left(\left(-z\right) \cdot c\right) \cdot b\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-b, c, y \cdot x\right), z, \mathsf{fma}\left(-t, x, i \cdot b\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 55.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(\left(-c\right) \cdot z, b, \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-43}:\\ \;\;\;\;\mathsf{fma}\left(\left(-t\right) \cdot a, x, \mathsf{fma}\left(-z, c, a \cdot i\right) \cdot b\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(c, \frac{j}{x}, -a\right) \cdot x\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -3.1e-9)
   (fma (* (- c) z) b (* (fma (- a) x (* j c)) t))
   (if (<= t 2.7e-43)
     (fma (* (- t) a) x (* (fma (- z) c (* a i)) b))
     (if (<= t 3.7e+64)
       (* (fma (- i) j (* z x)) y)
       (* (* (fma c (/ j x) (- a)) x) t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -3.1e-9) {
		tmp = fma((-c * z), b, (fma(-a, x, (j * c)) * t));
	} else if (t <= 2.7e-43) {
		tmp = fma((-t * a), x, (fma(-z, c, (a * i)) * b));
	} else if (t <= 3.7e+64) {
		tmp = fma(-i, j, (z * x)) * y;
	} else {
		tmp = (fma(c, (j / x), -a) * x) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -3.1e-9)
		tmp = fma(Float64(Float64(-c) * z), b, Float64(fma(Float64(-a), x, Float64(j * c)) * t));
	elseif (t <= 2.7e-43)
		tmp = fma(Float64(Float64(-t) * a), x, Float64(fma(Float64(-z), c, Float64(a * i)) * b));
	elseif (t <= 3.7e+64)
		tmp = Float64(fma(Float64(-i), j, Float64(z * x)) * y);
	else
		tmp = Float64(Float64(fma(c, Float64(j / x), Float64(-a)) * x) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -3.1e-9], N[(N[((-c) * z), $MachinePrecision] * b + N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e-43], N[(N[((-t) * a), $MachinePrecision] * x + N[(N[((-z) * c + N[(a * i), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.7e+64], N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[(N[(N[(c * N[(j / x), $MachinePrecision] + (-a)), $MachinePrecision] * x), $MachinePrecision] * t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.10000000000000005e-9

   1. Initial program 64.0%

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

   3. Taylor expanded in y around 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. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

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

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

   5. Applied rewrites 70.7%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 69.5%

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

   if -3.10000000000000005e-9 < t < 2.69999999999999991e-43

   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 0

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

   5. Applied rewrites 89.1%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 73.2%

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

   9. Taylor expanded in j around 0

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

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

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

       2. *-commutative N/A

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

       3. lower-fma.f64 N/A

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

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

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

       5. mul-1-neg N/A

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

       6. associate-*r* N/A

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

       7. +-commutative N/A

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

       8. associate-*r* N/A

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

       9. lower-fma.f64 N/A

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

       10. mul-1-neg N/A

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

       11. lower-neg.f64 N/A

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

       12. *-commutative N/A

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

       13. lower-*.f64 N/A

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

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

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

       15. *-commutative N/A

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

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

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

       17. mul-1-neg N/A

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

       18. lower-*.f64 N/A

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

   11. Applied rewrites 75.6%

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

   12. Taylor expanded in y around 0

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

   14. Applied rewrites 65.8%

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

   if 2.69999999999999991e-43 < t < 3.69999999999999983e64

   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 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

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 65.5

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

   5. Applied rewrites 65.5%

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

   if 3.69999999999999983e64 < t

   1. Initial program 63.8%

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

   3. Taylor expanded in 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

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 66.3

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

   5. Applied rewrites 66.3%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 69.7%

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

Alternative 11: 55.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-43}:\\ \;\;\;\;\mathsf{fma}\left(\left(-t\right) \cdot a, x, \mathsf{fma}\left(-z, c, a \cdot i\right) \cdot b\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(c, \frac{j}{x}, -a\right) \cdot x\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -1.25e+75)
   (* (fma (- a) x (* j c)) t)
   (if (<= t 2.7e-43)
     (fma (* (- t) a) x (* (fma (- z) c (* a i)) b))
     (if (<= t 3.7e+64)
       (* (fma (- i) j (* z x)) y)
       (* (* (fma c (/ j x) (- a)) x) t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -1.25e+75) {
		tmp = fma(-a, x, (j * c)) * t;
	} else if (t <= 2.7e-43) {
		tmp = fma((-t * a), x, (fma(-z, c, (a * i)) * b));
	} else if (t <= 3.7e+64) {
		tmp = fma(-i, j, (z * x)) * y;
	} else {
		tmp = (fma(c, (j / x), -a) * x) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -1.25e+75)
		tmp = Float64(fma(Float64(-a), x, Float64(j * c)) * t);
	elseif (t <= 2.7e-43)
		tmp = fma(Float64(Float64(-t) * a), x, Float64(fma(Float64(-z), c, Float64(a * i)) * b));
	elseif (t <= 3.7e+64)
		tmp = Float64(fma(Float64(-i), j, Float64(z * x)) * y);
	else
		tmp = Float64(Float64(fma(c, Float64(j / x), Float64(-a)) * x) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -1.25e+75], N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, 2.7e-43], N[(N[((-t) * a), $MachinePrecision] * x + N[(N[((-z) * c + N[(a * i), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.7e+64], N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[(N[(N[(c * N[(j / x), $MachinePrecision] + (-a)), $MachinePrecision] * x), $MachinePrecision] * t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.2500000000000001e75

   1. Initial program 58.6%

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

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 75.9

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

   5. Applied rewrites 75.9%

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

   if -1.2500000000000001e75 < t < 2.69999999999999991e-43

   1. Initial program 82.8%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 87.3%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 74.3%

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

   9. Taylor expanded in j around 0

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

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

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

       2. *-commutative N/A

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

       3. lower-fma.f64 N/A

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

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

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

       5. mul-1-neg N/A

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

       6. associate-*r* N/A

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

       7. +-commutative N/A

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

       8. associate-*r* N/A

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

       9. lower-fma.f64 N/A

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

       10. mul-1-neg N/A

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

       11. lower-neg.f64 N/A

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

       12. *-commutative N/A

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

       13. lower-*.f64 N/A

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

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

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

       15. *-commutative N/A

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

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

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

       17. mul-1-neg N/A

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

       18. lower-*.f64 N/A

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

   11. Applied rewrites 73.4%

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

   12. Taylor expanded in y around 0

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

   14. Applied rewrites 62.5%

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

   if 2.69999999999999991e-43 < t < 3.69999999999999983e64

   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 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

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 65.5

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

   5. Applied rewrites 65.5%

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

   if 3.69999999999999983e64 < t

   1. Initial program 63.8%

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

   3. Taylor expanded in 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

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 66.3

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

   5. Applied rewrites 66.3%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 69.7%

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

Alternative 12: 28.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+261}:\\ \;\;\;\;\left(b \cdot a\right) \cdot i\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{+77}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-261}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+149}:\\ \;\;\;\;\left(j \cdot c\right) \cdot t\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{+196}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(a \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.7e+261)
   (* (* b a) i)
   (if (<= a -3.1e+77)
     (* (- a) (* t x))
     (if (<= a -1.95e-261)
       (* (* z y) x)
       (if (<= a 7.2e+149)
         (* (* j c) t)
         (if (<= a 2.75e+196) (* (* i b) a) (* (- x) (* 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 (a <= -1.7e+261) {
		tmp = (b * a) * i;
	} else if (a <= -3.1e+77) {
		tmp = -a * (t * x);
	} else if (a <= -1.95e-261) {
		tmp = (z * y) * x;
	} else if (a <= 7.2e+149) {
		tmp = (j * c) * t;
	} else if (a <= 2.75e+196) {
		tmp = (i * b) * a;
	} else {
		tmp = -x * (a * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-1.7d+261)) then
        tmp = (b * a) * i
    else if (a <= (-3.1d+77)) then
        tmp = -a * (t * x)
    else if (a <= (-1.95d-261)) then
        tmp = (z * y) * x
    else if (a <= 7.2d+149) then
        tmp = (j * c) * t
    else if (a <= 2.75d+196) then
        tmp = (i * b) * a
    else
        tmp = -x * (a * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.7e+261) {
		tmp = (b * a) * i;
	} else if (a <= -3.1e+77) {
		tmp = -a * (t * x);
	} else if (a <= -1.95e-261) {
		tmp = (z * y) * x;
	} else if (a <= 7.2e+149) {
		tmp = (j * c) * t;
	} else if (a <= 2.75e+196) {
		tmp = (i * b) * a;
	} else {
		tmp = -x * (a * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.7e+261:
		tmp = (b * a) * i
	elif a <= -3.1e+77:
		tmp = -a * (t * x)
	elif a <= -1.95e-261:
		tmp = (z * y) * x
	elif a <= 7.2e+149:
		tmp = (j * c) * t
	elif a <= 2.75e+196:
		tmp = (i * b) * a
	else:
		tmp = -x * (a * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.7e+261)
		tmp = Float64(Float64(b * a) * i);
	elseif (a <= -3.1e+77)
		tmp = Float64(Float64(-a) * Float64(t * x));
	elseif (a <= -1.95e-261)
		tmp = Float64(Float64(z * y) * x);
	elseif (a <= 7.2e+149)
		tmp = Float64(Float64(j * c) * t);
	elseif (a <= 2.75e+196)
		tmp = Float64(Float64(i * b) * a);
	else
		tmp = Float64(Float64(-x) * Float64(a * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.7e+261)
		tmp = (b * a) * i;
	elseif (a <= -3.1e+77)
		tmp = -a * (t * x);
	elseif (a <= -1.95e-261)
		tmp = (z * y) * x;
	elseif (a <= 7.2e+149)
		tmp = (j * c) * t;
	elseif (a <= 2.75e+196)
		tmp = (i * b) * a;
	else
		tmp = -x * (a * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.7e+261], N[(N[(b * a), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[a, -3.1e+77], N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.95e-261], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[a, 7.2e+149], N[(N[(j * c), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[a, 2.75e+196], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], N[((-x) * N[(a * t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.7e261

   1. Initial program 33.9%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 68.1

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

   5. Applied rewrites 68.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 68.1%

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

   if -1.7e261 < a < -3.09999999999999999e77

   1. Initial program 62.5%

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

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 62.5

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

   5. Applied rewrites 62.5%

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

   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

   8. Applied rewrites 54.0%

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

   if -3.09999999999999999e77 < a < -1.95000000000000009e-261

   1. Initial program 78.1%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 76.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 76.3%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 31.4%

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

   if -1.95000000000000009e-261 < a < 7.1999999999999999e149

   1. Initial program 79.9%

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

   3. Taylor expanded in 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

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 52.9

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

   5. Applied rewrites 52.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 41.0%

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

   if 7.1999999999999999e149 < a < 2.74999999999999987e196

   1. Initial program 78.1%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 73.1

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

   5. Applied rewrites 73.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 73.2%

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

   if 2.74999999999999987e196 < a

   1. Initial program 68.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

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

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

   5. Applied rewrites 69.0%

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

   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

   8. Applied rewrites 59.9%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+261}:\\ \;\;\;\;\left(b \cdot a\right) \cdot i\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{+77}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-261}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+149}:\\ \;\;\;\;\left(j \cdot c\right) \cdot t\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{+196}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(a \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 28.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{+261}:\\ \;\;\;\;\left(b \cdot a\right) \cdot i\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-261}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+149}:\\ \;\;\;\;\left(j \cdot c\right) \cdot t\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{+196}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- a) (* t x))))
   (if (<= a -1.7e+261)
     (* (* b a) i)
     (if (<= a -3.1e+77)
       t_1
       (if (<= a -1.95e-261)
         (* (* z y) x)
         (if (<= a 7.2e+149)
           (* (* j c) t)
           (if (<= a 2.75e+196) (* (* 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 = -a * (t * x);
	double tmp;
	if (a <= -1.7e+261) {
		tmp = (b * a) * i;
	} else if (a <= -3.1e+77) {
		tmp = t_1;
	} else if (a <= -1.95e-261) {
		tmp = (z * y) * x;
	} else if (a <= 7.2e+149) {
		tmp = (j * c) * t;
	} else if (a <= 2.75e+196) {
		tmp = (i * b) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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 = -a * (t * x)
    if (a <= (-1.7d+261)) then
        tmp = (b * a) * i
    else if (a <= (-3.1d+77)) then
        tmp = t_1
    else if (a <= (-1.95d-261)) then
        tmp = (z * y) * x
    else if (a <= 7.2d+149) then
        tmp = (j * c) * t
    else if (a <= 2.75d+196) 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 = -a * (t * x);
	double tmp;
	if (a <= -1.7e+261) {
		tmp = (b * a) * i;
	} else if (a <= -3.1e+77) {
		tmp = t_1;
	} else if (a <= -1.95e-261) {
		tmp = (z * y) * x;
	} else if (a <= 7.2e+149) {
		tmp = (j * c) * t;
	} else if (a <= 2.75e+196) {
		tmp = (i * b) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = -a * (t * x)
	tmp = 0
	if a <= -1.7e+261:
		tmp = (b * a) * i
	elif a <= -3.1e+77:
		tmp = t_1
	elif a <= -1.95e-261:
		tmp = (z * y) * x
	elif a <= 7.2e+149:
		tmp = (j * c) * t
	elif a <= 2.75e+196:
		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(-a) * Float64(t * x))
	tmp = 0.0
	if (a <= -1.7e+261)
		tmp = Float64(Float64(b * a) * i);
	elseif (a <= -3.1e+77)
		tmp = t_1;
	elseif (a <= -1.95e-261)
		tmp = Float64(Float64(z * y) * x);
	elseif (a <= 7.2e+149)
		tmp = Float64(Float64(j * c) * t);
	elseif (a <= 2.75e+196)
		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 = -a * (t * x);
	tmp = 0.0;
	if (a <= -1.7e+261)
		tmp = (b * a) * i;
	elseif (a <= -3.1e+77)
		tmp = t_1;
	elseif (a <= -1.95e-261)
		tmp = (z * y) * x;
	elseif (a <= 7.2e+149)
		tmp = (j * c) * t;
	elseif (a <= 2.75e+196)
		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[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.7e+261], N[(N[(b * a), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[a, -3.1e+77], t$95$1, If[LessEqual[a, -1.95e-261], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[a, 7.2e+149], N[(N[(j * c), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[a, 2.75e+196], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.7e261

   1. Initial program 33.9%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 68.1

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

   5. Applied rewrites 68.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 68.1%

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

   if -1.7e261 < a < -3.09999999999999999e77 or 2.74999999999999987e196 < a

   1. Initial program 64.6%

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

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 61.7

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

   5. Applied rewrites 61.7%

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

   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

   8. Applied rewrites 56.2%

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

   if -3.09999999999999999e77 < a < -1.95000000000000009e-261

   1. Initial program 78.1%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 76.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 76.3%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 31.4%

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

   if -1.95000000000000009e-261 < a < 7.1999999999999999e149

   1. Initial program 79.9%

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

   3. Taylor expanded in 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

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 52.9

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

   5. Applied rewrites 52.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 41.0%

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

   if 7.1999999999999999e149 < a < 2.74999999999999987e196

   1. Initial program 78.1%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 73.1

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

   5. Applied rewrites 73.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 73.2%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+261}:\\ \;\;\;\;\left(b \cdot a\right) \cdot i\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{+77}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-261}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+149}:\\ \;\;\;\;\left(j \cdot c\right) \cdot t\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{+196}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-x, t, i \cdot b\right) \cdot a\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-273}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-20}:\\ \;\;\;\;\mathsf{fma}\left(-z, b, j \cdot t\right) \cdot c\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+147}:\\ \;\;\;\;\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- x) t (* i b)) a)))
   (if (<= a -1.9e+70)
     t_1
     (if (<= a -3.1e-273)
       (* (fma (- b) c (* y x)) z)
       (if (<= a 1.12e-20)
         (* (fma (- z) b (* j t)) c)
         (if (<= a 2.5e+147) (* (fma (- a) x (* j c)) t) 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(-x, t, (i * b)) * a;
	double tmp;
	if (a <= -1.9e+70) {
		tmp = t_1;
	} else if (a <= -3.1e-273) {
		tmp = fma(-b, c, (y * x)) * z;
	} else if (a <= 1.12e-20) {
		tmp = fma(-z, b, (j * t)) * c;
	} else if (a <= 2.5e+147) {
		tmp = fma(-a, x, (j * c)) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-x), t, Float64(i * b)) * a)
	tmp = 0.0
	if (a <= -1.9e+70)
		tmp = t_1;
	elseif (a <= -3.1e-273)
		tmp = Float64(fma(Float64(-b), c, Float64(y * x)) * z);
	elseif (a <= 1.12e-20)
		tmp = Float64(fma(Float64(-z), b, Float64(j * t)) * c);
	elseif (a <= 2.5e+147)
		tmp = Float64(fma(Float64(-a), x, Float64(j * c)) * t);
	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[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -1.9e+70], t$95$1, If[LessEqual[a, -3.1e-273], N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[a, 1.12e-20], N[(N[((-z) * b + N[(j * t), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[a, 2.5e+147], N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.8999999999999999e70 or 2.5000000000000001e147 < a

   1. Initial program 62.4%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. mul-1-neg N/A

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

      7. *-commutative N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 78.9

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

   5. Applied rewrites 78.9%

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

   if -1.8999999999999999e70 < a < -3.09999999999999988e-273

   1. Initial program 77.1%

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

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

      2. lower-*.f64 N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 54.2

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

   5. Applied rewrites 54.2%

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

   if -3.09999999999999988e-273 < a < 1.12000000000000002e-20

   1. Initial program 83.5%

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

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

      2. lower-*.f64 N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 N/A

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

      12. lower-*.f64 60.0

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

   5. Applied rewrites 60.0%

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

   if 1.12000000000000002e-20 < a < 2.5000000000000001e147

   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 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

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 68.7

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

   5. Applied rewrites 68.7%

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

Alternative 15: 51.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{-65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-111}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-141}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-z\right) \cdot c\right) \cdot b\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- a) x (* j c)) t)))
   (if (<= t -2.1e-65)
     t_1
     (if (<= t -2.2e-111)
       (* (fma (- i) j (* z x)) y)
       (if (<= t 6.5e-141)
         (* (fma i a (* (- z) c)) b)
         (if (<= t 5.8e+64) (* (fma (- b) c (* y x)) z) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-a, x, (j * c)) * t;
	double tmp;
	if (t <= -2.1e-65) {
		tmp = t_1;
	} else if (t <= -2.2e-111) {
		tmp = fma(-i, j, (z * x)) * y;
	} else if (t <= 6.5e-141) {
		tmp = fma(i, a, (-z * c)) * b;
	} else if (t <= 5.8e+64) {
		tmp = fma(-b, c, (y * x)) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-a), x, Float64(j * c)) * t)
	tmp = 0.0
	if (t <= -2.1e-65)
		tmp = t_1;
	elseif (t <= -2.2e-111)
		tmp = Float64(fma(Float64(-i), j, Float64(z * x)) * y);
	elseif (t <= 6.5e-141)
		tmp = Float64(fma(i, a, Float64(Float64(-z) * c)) * b);
	elseif (t <= 5.8e+64)
		tmp = Float64(fma(Float64(-b), c, Float64(y * x)) * z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -2.1e-65], t$95$1, If[LessEqual[t, -2.2e-111], N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 6.5e-141], N[(N[(i * a + N[((-z) * c), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t, 5.8e+64], N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.10000000000000003e-65 or 5.79999999999999986e64 < t

   1. Initial program 65.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 66.7

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

   5. Applied rewrites 66.7%

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

   if -2.10000000000000003e-65 < t < -2.2e-111

   1. Initial program 85.7%

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

   3. Taylor expanded in 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

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 86.5

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

   5. Applied rewrites 86.5%

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

   if -2.2e-111 < t < 6.4999999999999995e-141

   1. Initial program 83.7%

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

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

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

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

      3. +-commutative N/A

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

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

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

      5. *-lft-identity N/A

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

      6. metadata-eval N/A

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

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

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

      8. mul-1-neg N/A

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

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

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

      10. distribute-neg-in N/A

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

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

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

      12. mul-1-neg N/A

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

      13. lower-*.f64 N/A

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

   5. Applied rewrites 60.0%

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

   7. Applied rewrites 60.1%

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

   if 6.4999999999999995e-141 < t < 5.79999999999999986e64

   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

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

      2. lower-*.f64 N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 56.3

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

   5. Applied rewrites 56.3%

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

Alternative 16: 51.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-x, t, i \cdot b\right) \cdot a\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-268}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+127}:\\ \;\;\;\;\mathsf{fma}\left(-y, i, c \cdot t\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- x) t (* i b)) a)))
   (if (<= a -1.9e+70)
     t_1
     (if (<= a 1.05e-268)
       (* (fma (- b) c (* y x)) z)
       (if (<= a 2.7e+127) (* (fma (- y) i (* c t)) j) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-x, t, (i * b)) * a;
	double tmp;
	if (a <= -1.9e+70) {
		tmp = t_1;
	} else if (a <= 1.05e-268) {
		tmp = fma(-b, c, (y * x)) * z;
	} else if (a <= 2.7e+127) {
		tmp = fma(-y, i, (c * t)) * j;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-x), t, Float64(i * b)) * a)
	tmp = 0.0
	if (a <= -1.9e+70)
		tmp = t_1;
	elseif (a <= 1.05e-268)
		tmp = Float64(fma(Float64(-b), c, Float64(y * x)) * z);
	elseif (a <= 2.7e+127)
		tmp = Float64(fma(Float64(-y), i, Float64(c * t)) * j);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -1.9e+70], t$95$1, If[LessEqual[a, 1.05e-268], N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[a, 2.7e+127], N[(N[((-y) * i + N[(c * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.8999999999999999e70 or 2.7000000000000002e127 < a

   1. Initial program 62.6%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. mul-1-neg N/A

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

      7. *-commutative N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 78.5

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

   5. Applied rewrites 78.5%

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

   if -1.8999999999999999e70 < a < 1.04999999999999999e-268

   1. Initial program 78.5%

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

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

      2. lower-*.f64 N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 53.8

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

   5. Applied rewrites 53.8%

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

   if 1.04999999999999999e-268 < a < 2.7000000000000002e127

   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 z around 0

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

   5. Applied rewrites 81.0%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 74.1%

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

   9. Taylor expanded in j around inf

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

       1. *-commutative N/A

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

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

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

       3. mul-1-neg N/A

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

       4. associate-*r* N/A

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

       5. +-commutative N/A

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

       6. lower-*.f64 N/A

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

       7. mul-1-neg N/A

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

       8. *-commutative N/A

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

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

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

       10. mul-1-neg N/A

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

       11. lower-fma.f64 N/A

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

       12. mul-1-neg N/A

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

       13. lower-neg.f64 N/A

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

       14. lower-*.f64 54.9

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

   11. Applied rewrites 54.9%

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

Alternative 17: 51.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-141}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-z\right) \cdot c\right) \cdot b\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- a) x (* j c)) t)))
   (if (<= t -3.5e-60)
     t_1
     (if (<= t 6.5e-141)
       (* (fma i a (* (- z) c)) b)
       (if (<= t 5.8e+64) (* (fma (- b) c (* y x)) z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-a, x, (j * c)) * t;
	double tmp;
	if (t <= -3.5e-60) {
		tmp = t_1;
	} else if (t <= 6.5e-141) {
		tmp = fma(i, a, (-z * c)) * b;
	} else if (t <= 5.8e+64) {
		tmp = fma(-b, c, (y * x)) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-a), x, Float64(j * c)) * t)
	tmp = 0.0
	if (t <= -3.5e-60)
		tmp = t_1;
	elseif (t <= 6.5e-141)
		tmp = Float64(fma(i, a, Float64(Float64(-z) * c)) * b);
	elseif (t <= 5.8e+64)
		tmp = Float64(fma(Float64(-b), c, Float64(y * x)) * z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -3.5e-60], t$95$1, If[LessEqual[t, 6.5e-141], N[(N[(i * a + N[((-z) * c), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t, 5.8e+64], N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.49999999999999976e-60 or 5.79999999999999986e64 < t

   1. Initial program 65.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 66.7

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

   5. Applied rewrites 66.7%

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

   if -3.49999999999999976e-60 < t < 6.4999999999999995e-141

   1. Initial program 83.9%

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

   3. Taylor expanded in 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

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

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

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

      3. +-commutative N/A

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

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

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

      5. *-lft-identity N/A

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

      6. metadata-eval N/A

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

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

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

      8. mul-1-neg N/A

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

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

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

      10. distribute-neg-in N/A

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

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

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

      12. mul-1-neg N/A

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

      13. lower-*.f64 N/A

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

   5. Applied rewrites 57.5%

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

   7. Applied rewrites 56.3%

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

   if 6.4999999999999995e-141 < t < 5.79999999999999986e64

   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

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

      2. lower-*.f64 N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 56.3

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

   5. Applied rewrites 56.3%

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

Alternative 18: 51.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-77}:\\ \;\;\;\;\left(c \cdot t\right) \cdot j\\ \mathbf{elif}\;x \leq 0.6:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-z\right) \cdot c\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- a) t (* z y)) x)))
   (if (<= x -6.5e+63)
     t_1
     (if (<= x -4.2e-77)
       (* (* c t) j)
       (if (<= x 0.6) (* (fma i a (* (- z) c)) 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 <= -6.5e+63) {
		tmp = t_1;
	} else if (x <= -4.2e-77) {
		tmp = (c * t) * j;
	} else if (x <= 0.6) {
		tmp = fma(i, a, (-z * c)) * 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 <= -6.5e+63)
		tmp = t_1;
	elseif (x <= -4.2e-77)
		tmp = Float64(Float64(c * t) * j);
	elseif (x <= 0.6)
		tmp = Float64(fma(i, a, Float64(Float64(-z) * c)) * 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, -6.5e+63], t$95$1, If[LessEqual[x, -4.2e-77], N[(N[(c * t), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[x, 0.6], N[(N[(i * a + N[((-z) * c), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.49999999999999992e63 or 0.599999999999999978 < x

   1. Initial program 74.5%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 73.7%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. +-commutative N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 63.1

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

   8. Applied rewrites 63.1%

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

   if -6.49999999999999992e63 < x < -4.20000000000000031e-77

   1. Initial program 73.3%

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

   3. Taylor expanded in t around 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

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 57.1

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

   5. Applied rewrites 57.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 44.8%

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

   10. Applied rewrites 47.9%

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

   if -4.20000000000000031e-77 < x < 0.599999999999999978

   1. Initial program 72.8%

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

   3. Taylor expanded in 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

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

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

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

      3. +-commutative N/A

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

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

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

      5. *-lft-identity N/A

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

      6. metadata-eval N/A

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

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

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

      8. mul-1-neg N/A

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

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

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

      10. distribute-neg-in N/A

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

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

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

      12. mul-1-neg N/A

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

      13. lower-*.f64 N/A

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

   5. Applied rewrites 52.9%

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

   7. Applied rewrites 51.1%

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

Alternative 19: 51.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-60} \lor \neg \left(t \leq 9.8 \cdot 10^{+113}\right):\\ \;\;\;\;\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-z\right) \cdot c\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -3.5e-60) (not (<= t 9.8e+113)))
   (* (fma (- a) x (* j c)) t)
   (* (fma i a (* (- z) c)) 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 ((t <= -3.5e-60) || !(t <= 9.8e+113)) {
		tmp = fma(-a, x, (j * c)) * t;
	} else {
		tmp = fma(i, a, (-z * c)) * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -3.5e-60) || !(t <= 9.8e+113))
		tmp = Float64(fma(Float64(-a), x, Float64(j * c)) * t);
	else
		tmp = Float64(fma(i, a, Float64(Float64(-z) * c)) * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -3.5e-60], N[Not[LessEqual[t, 9.8e+113]], $MachinePrecision]], N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(i * a + N[((-z) * c), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.49999999999999976e-60 or 9.80000000000000043e113 < t

   1. Initial program 64.9%

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

   3. Taylor expanded in 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

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

      8. lower-*.f64 69.0

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

   5. Applied rewrites 69.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]

   if -3.49999999999999976e-60 < t < 9.80000000000000043e113

   1. Initial program 82.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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

         \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

      2. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(a \cdot i + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right)} \cdot b \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(c\right)\right) \cdot z + a \cdot i\right)} \cdot b \]

      4. distribute-lft-neg-out N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(c \cdot z\right)\right)} + a \cdot i\right) \cdot b \]

      5. *-lft-identity N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \color{blue}{\left(1 \cdot a\right)} \cdot i\right) \cdot b \]

      6. metadata-eval N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \left(\color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot a\right) \cdot i\right) \cdot b \]

      7. distribute-lft-neg-in N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1 \cdot a\right)\right)} \cdot i\right) \cdot b \]

      8. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)}\right)\right) \cdot i\right) \cdot b \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right) \cdot i\right)\right)}\right) \cdot b \]

      10. distribute-neg-in N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z + \left(\mathsf{neg}\left(a\right)\right) \cdot i\right)\right)\right)} \cdot b \]

      11. fp-cancel-sub-sign-inv N/A

          \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z - a \cdot i\right)}\right)\right) \cdot b \]

      12. mul-1-neg N/A

          \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)} \cdot b \]

      13. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right) \cdot b} \]

   5. Applied rewrites 50.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-z, c, i \cdot a\right) \cdot b} \]
   6. Step-by-step derivation

   7. Applied rewrites 49.2%

      \[\leadsto \mathsf{fma}\left(i, a, \left(-z\right) \cdot c\right) \cdot b \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-60} \lor \neg \left(t \leq 9.8 \cdot 10^{+113}\right):\\ \;\;\;\;\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-z\right) \cdot c\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 42.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{+75}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+129}:\\ \;\;\;\;\mathsf{fma}\left(i, a, \left(-z\right) \cdot c\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -1.16e+75)
   (* (* j t) c)
   (if (<= t 1.05e+129) (* (fma i a (* (- z) c)) b) (* (- a) (* t 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 (t <= -1.16e+75) {
		tmp = (j * t) * c;
	} else if (t <= 1.05e+129) {
		tmp = fma(i, a, (-z * c)) * b;
	} else {
		tmp = -a * (t * x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -1.16e+75)
		tmp = Float64(Float64(j * t) * c);
	elseif (t <= 1.05e+129)
		tmp = Float64(fma(i, a, Float64(Float64(-z) * c)) * b);
	else
		tmp = Float64(Float64(-a) * Float64(t * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -1.16e+75], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[t, 1.05e+129], N[(N[(i * a + N[((-z) * c), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1600000000000001e75

   1. Initial program 58.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

      3. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + c \cdot j\right) \cdot t \]

      4. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + c \cdot j\right) \cdot t \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, c \cdot j\right)} \cdot t \]

      6. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, c \cdot j\right) \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

      8. lower-*.f64 75.9

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

   5. Applied rewrites 75.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]

   6. Taylor expanded in x around 0

      \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 49.4%

      \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{c} \]

   if -1.1600000000000001e75 < t < 1.04999999999999998e129

   1. Initial program 80.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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

         \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

      2. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(a \cdot i + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right)} \cdot b \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(c\right)\right) \cdot z + a \cdot i\right)} \cdot b \]

      4. distribute-lft-neg-out N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(c \cdot z\right)\right)} + a \cdot i\right) \cdot b \]

      5. *-lft-identity N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \color{blue}{\left(1 \cdot a\right)} \cdot i\right) \cdot b \]

      6. metadata-eval N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \left(\color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot a\right) \cdot i\right) \cdot b \]

      7. distribute-lft-neg-in N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1 \cdot a\right)\right)} \cdot i\right) \cdot b \]

      8. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)}\right)\right) \cdot i\right) \cdot b \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right) \cdot i\right)\right)}\right) \cdot b \]

      10. distribute-neg-in N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z + \left(\mathsf{neg}\left(a\right)\right) \cdot i\right)\right)\right)} \cdot b \]

      11. fp-cancel-sub-sign-inv N/A

          \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z - a \cdot i\right)}\right)\right) \cdot b \]

      12. mul-1-neg N/A

          \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)} \cdot b \]

      13. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right) \cdot b} \]

   5. Applied rewrites 46.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-z, c, i \cdot a\right) \cdot b} \]
   6. Step-by-step derivation

   7. Applied rewrites 45.9%

      \[\leadsto \mathsf{fma}\left(i, a, \left(-z\right) \cdot c\right) \cdot b \]

   if 1.04999999999999998e129 < t

   1. Initial program 63.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

      3. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + c \cdot j\right) \cdot t \]

      4. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + c \cdot j\right) \cdot t \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, c \cdot j\right)} \cdot t \]

      6. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, c \cdot j\right) \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

      8. lower-*.f64 74.1

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

   5. Applied rewrites 74.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]

   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

   8. Applied rewrites 60.7%

      \[\leadsto \left(-a\right) \cdot \color{blue}{\left(t \cdot x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 21: 30.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -3.5 \cdot 10^{+98}:\\ \;\;\;\;\left(a \cdot i\right) \cdot b\\ \mathbf{elif}\;i \leq -1.95 \cdot 10^{-240}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+31}:\\ \;\;\;\;\left(j \cdot c\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -3.5e+98)
   (* (* a i) b)
   (if (<= i -1.95e-240)
     (* (* z x) y)
     (if (<= i 2.5e+31) (* (* j c) t) (* (* b a) i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -3.5e+98) {
		tmp = (a * i) * b;
	} else if (i <= -1.95e-240) {
		tmp = (z * x) * y;
	} else if (i <= 2.5e+31) {
		tmp = (j * c) * t;
	} else {
		tmp = (b * a) * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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 <= (-3.5d+98)) then
        tmp = (a * i) * b
    else if (i <= (-1.95d-240)) then
        tmp = (z * x) * y
    else if (i <= 2.5d+31) then
        tmp = (j * c) * t
    else
        tmp = (b * a) * i
    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 <= -3.5e+98) {
		tmp = (a * i) * b;
	} else if (i <= -1.95e-240) {
		tmp = (z * x) * y;
	} else if (i <= 2.5e+31) {
		tmp = (j * c) * t;
	} else {
		tmp = (b * a) * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -3.5e+98:
		tmp = (a * i) * b
	elif i <= -1.95e-240:
		tmp = (z * x) * y
	elif i <= 2.5e+31:
		tmp = (j * c) * t
	else:
		tmp = (b * a) * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -3.5e+98)
		tmp = Float64(Float64(a * i) * b);
	elseif (i <= -1.95e-240)
		tmp = Float64(Float64(z * x) * y);
	elseif (i <= 2.5e+31)
		tmp = Float64(Float64(j * c) * t);
	else
		tmp = Float64(Float64(b * a) * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -3.5e+98)
		tmp = (a * i) * b;
	elseif (i <= -1.95e-240)
		tmp = (z * x) * y;
	elseif (i <= 2.5e+31)
		tmp = (j * c) * t;
	else
		tmp = (b * a) * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -3.5e+98], N[(N[(a * i), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[i, -1.95e-240], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[i, 2.5e+31], N[(N[(j * c), $MachinePrecision] * t), $MachinePrecision], N[(N[(b * a), $MachinePrecision] * i), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if i < -3.5e98

   1. Initial program 64.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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

         \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

      2. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(a \cdot i + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right)} \cdot b \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(c\right)\right) \cdot z + a \cdot i\right)} \cdot b \]

      4. distribute-lft-neg-out N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(c \cdot z\right)\right)} + a \cdot i\right) \cdot b \]

      5. *-lft-identity N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \color{blue}{\left(1 \cdot a\right)} \cdot i\right) \cdot b \]

      6. metadata-eval N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \left(\color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot a\right) \cdot i\right) \cdot b \]

      7. distribute-lft-neg-in N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1 \cdot a\right)\right)} \cdot i\right) \cdot b \]

      8. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)}\right)\right) \cdot i\right) \cdot b \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right) \cdot i\right)\right)}\right) \cdot b \]

      10. distribute-neg-in N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z + \left(\mathsf{neg}\left(a\right)\right) \cdot i\right)\right)\right)} \cdot b \]

      11. fp-cancel-sub-sign-inv N/A

          \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z - a \cdot i\right)}\right)\right) \cdot b \]

      12. mul-1-neg N/A

          \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)} \cdot b \]

      13. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right) \cdot b} \]

   5. Applied rewrites 60.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-z, c, i \cdot a\right) \cdot b} \]

   6. Taylor expanded in z around 0

      \[\leadsto \left(a \cdot i\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 50.0%

      \[\leadsto \left(a \cdot i\right) \cdot b \]

   if -3.5e98 < i < -1.95000000000000007e-240

   1. Initial program 80.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(j \cdot \left(c \cdot t - i \cdot y\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)} \]

   5. Applied rewrites 78.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-x, t, i \cdot b\right), a, \mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(t \cdot \left(-1 \cdot x + \frac{b \cdot i}{t}\right), a, \mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 77.1%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(b, \frac{i}{t}, -x\right) \cdot t, a, \mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\right) \]

   9. Taylor expanded in j around 0

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   10. Step-by-step derivation

       1. fp-cancel-sub-sign-inv N/A

          \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) + \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)} \]

       2. *-commutative N/A

          \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} + \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right) \]

       3. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot z - a \cdot t, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

       4. fp-cancel-sub-sign-inv N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot z + \left(\mathsf{neg}\left(a\right)\right) \cdot t}, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(y \cdot z + \color{blue}{\left(-1 \cdot a\right)} \cdot t, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       6. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(y \cdot z + \color{blue}{-1 \cdot \left(a \cdot t\right)}, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       7. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot \left(a \cdot t\right) + y \cdot z}, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       8. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(-1 \cdot a\right) \cdot t} + y \cdot z, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       9. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(-1 \cdot a, t, y \cdot z\right)}, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       10. mul-1-neg N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(a\right)}, t, y \cdot z\right), x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       11. lower-neg.f64 N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{-a}, t, y \cdot z\right), x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, \color{blue}{z \cdot y}\right), x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       13. lower-*.f64 N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, \color{blue}{z \cdot y}\right), x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       14. distribute-lft-neg-in N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \color{blue}{\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)}\right) \]

       15. *-commutative N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \mathsf{neg}\left(\color{blue}{\left(c \cdot z - a \cdot i\right) \cdot b}\right)\right) \]

       16. distribute-lft-neg-in N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right) \cdot b}\right) \]

       17. mul-1-neg N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)} \cdot b\right) \]

       18. lower-*.f64 N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right) \cdot b}\right) \]

   11. Applied rewrites 64.7%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \mathsf{fma}\left(-z, c, a \cdot i\right) \cdot b\right)} \]

   12. Taylor expanded in y around inf

       \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   13. Step-by-step derivation

   14. Applied rewrites 32.5%

       \[\leadsto \left(z \cdot x\right) \cdot \color{blue}{y} \]

   if -1.95000000000000007e-240 < i < 2.50000000000000013e31

   1. Initial program 76.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

      3. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + c \cdot j\right) \cdot t \]

      4. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + c \cdot j\right) \cdot t \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, c \cdot j\right)} \cdot t \]

      6. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, c \cdot j\right) \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

      8. lower-*.f64 55.3

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

   5. Applied rewrites 55.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]

   6. Taylor expanded in x around 0

      \[\leadsto \left(c \cdot j\right) \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 38.5%

      \[\leadsto \left(j \cdot c\right) \cdot t \]

   if 2.50000000000000013e31 < i

   1. Initial program 66.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(a \cdot b\right)\right)} \cdot i \]

      4. metadata-eval N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) + \color{blue}{1} \cdot \left(a \cdot b\right)\right) \cdot i \]

      5. *-lft-identity N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) + \color{blue}{a \cdot b}\right) \cdot i \]

      6. *-commutative N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(y \cdot j\right)} + a \cdot b\right) \cdot i \]

      7. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot y\right) \cdot j} + a \cdot b\right) \cdot i \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot y, j, a \cdot b\right)} \cdot i \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y\right)}, j, a \cdot b\right) \cdot i \]

      10. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-y}, j, a \cdot b\right) \cdot i \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-y, j, \color{blue}{b \cdot a}\right) \cdot i \]

      12. lower-*.f64 53.5

          \[\leadsto \mathsf{fma}\left(-y, j, \color{blue}{b \cdot a}\right) \cdot i \]

   5. Applied rewrites 53.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, j, b \cdot a\right) \cdot i} \]

   6. Taylor expanded in y around 0

      \[\leadsto \left(a \cdot b\right) \cdot i \]
   7. Step-by-step derivation

   8. Applied rewrites 37.9%

      \[\leadsto \left(b \cdot a\right) \cdot i \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 22: 30.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -3.5 \cdot 10^{+98}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{elif}\;i \leq -1.95 \cdot 10^{-240}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+31}:\\ \;\;\;\;\left(j \cdot c\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -3.5e+98)
   (* (* i b) a)
   (if (<= i -1.95e-240)
     (* (* z x) y)
     (if (<= i 2.5e+31) (* (* j c) t) (* (* b a) i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -3.5e+98) {
		tmp = (i * b) * a;
	} else if (i <= -1.95e-240) {
		tmp = (z * x) * y;
	} else if (i <= 2.5e+31) {
		tmp = (j * c) * t;
	} else {
		tmp = (b * a) * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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 <= (-3.5d+98)) then
        tmp = (i * b) * a
    else if (i <= (-1.95d-240)) then
        tmp = (z * x) * y
    else if (i <= 2.5d+31) then
        tmp = (j * c) * t
    else
        tmp = (b * a) * i
    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 <= -3.5e+98) {
		tmp = (i * b) * a;
	} else if (i <= -1.95e-240) {
		tmp = (z * x) * y;
	} else if (i <= 2.5e+31) {
		tmp = (j * c) * t;
	} else {
		tmp = (b * a) * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -3.5e+98:
		tmp = (i * b) * a
	elif i <= -1.95e-240:
		tmp = (z * x) * y
	elif i <= 2.5e+31:
		tmp = (j * c) * t
	else:
		tmp = (b * a) * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -3.5e+98)
		tmp = Float64(Float64(i * b) * a);
	elseif (i <= -1.95e-240)
		tmp = Float64(Float64(z * x) * y);
	elseif (i <= 2.5e+31)
		tmp = Float64(Float64(j * c) * t);
	else
		tmp = Float64(Float64(b * a) * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -3.5e+98)
		tmp = (i * b) * a;
	elseif (i <= -1.95e-240)
		tmp = (z * x) * y;
	elseif (i <= 2.5e+31)
		tmp = (j * c) * t;
	else
		tmp = (b * a) * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -3.5e+98], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[i, -1.95e-240], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[i, 2.5e+31], N[(N[(j * c), $MachinePrecision] * t), $MachinePrecision], N[(N[(b * a), $MachinePrecision] * i), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if i < -3.5e98

   1. Initial program 64.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(a \cdot b\right)\right)} \cdot i \]

      4. metadata-eval N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) + \color{blue}{1} \cdot \left(a \cdot b\right)\right) \cdot i \]

      5. *-lft-identity N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) + \color{blue}{a \cdot b}\right) \cdot i \]

      6. *-commutative N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(y \cdot j\right)} + a \cdot b\right) \cdot i \]

      7. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot y\right) \cdot j} + a \cdot b\right) \cdot i \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot y, j, a \cdot b\right)} \cdot i \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y\right)}, j, a \cdot b\right) \cdot i \]

      10. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-y}, j, a \cdot b\right) \cdot i \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-y, j, \color{blue}{b \cdot a}\right) \cdot i \]

      12. lower-*.f64 67.6

          \[\leadsto \mathsf{fma}\left(-y, j, \color{blue}{b \cdot a}\right) \cdot i \]

   5. Applied rewrites 67.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, j, b \cdot a\right) \cdot i} \]

   6. Taylor expanded in y around 0

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 47.9%

      \[\leadsto \left(i \cdot b\right) \cdot \color{blue}{a} \]

   if -3.5e98 < i < -1.95000000000000007e-240

   1. Initial program 80.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(j \cdot \left(c \cdot t - i \cdot y\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)} \]

   5. Applied rewrites 78.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-x, t, i \cdot b\right), a, \mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(t \cdot \left(-1 \cdot x + \frac{b \cdot i}{t}\right), a, \mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 77.1%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(b, \frac{i}{t}, -x\right) \cdot t, a, \mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\right) \]

   9. Taylor expanded in j around 0

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   10. Step-by-step derivation

       1. fp-cancel-sub-sign-inv N/A

          \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) + \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)} \]

       2. *-commutative N/A

          \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} + \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right) \]

       3. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot z - a \cdot t, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

       4. fp-cancel-sub-sign-inv N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot z + \left(\mathsf{neg}\left(a\right)\right) \cdot t}, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(y \cdot z + \color{blue}{\left(-1 \cdot a\right)} \cdot t, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       6. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(y \cdot z + \color{blue}{-1 \cdot \left(a \cdot t\right)}, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       7. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot \left(a \cdot t\right) + y \cdot z}, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       8. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(-1 \cdot a\right) \cdot t} + y \cdot z, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       9. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(-1 \cdot a, t, y \cdot z\right)}, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       10. mul-1-neg N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(a\right)}, t, y \cdot z\right), x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       11. lower-neg.f64 N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{-a}, t, y \cdot z\right), x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, \color{blue}{z \cdot y}\right), x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       13. lower-*.f64 N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, \color{blue}{z \cdot y}\right), x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       14. distribute-lft-neg-in N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \color{blue}{\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)}\right) \]

       15. *-commutative N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \mathsf{neg}\left(\color{blue}{\left(c \cdot z - a \cdot i\right) \cdot b}\right)\right) \]

       16. distribute-lft-neg-in N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right) \cdot b}\right) \]

       17. mul-1-neg N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)} \cdot b\right) \]

       18. lower-*.f64 N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right) \cdot b}\right) \]

   11. Applied rewrites 64.7%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \mathsf{fma}\left(-z, c, a \cdot i\right) \cdot b\right)} \]

   12. Taylor expanded in y around inf

       \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   13. Step-by-step derivation

   14. Applied rewrites 32.5%

       \[\leadsto \left(z \cdot x\right) \cdot \color{blue}{y} \]

   if -1.95000000000000007e-240 < i < 2.50000000000000013e31

   1. Initial program 76.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

      3. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + c \cdot j\right) \cdot t \]

      4. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + c \cdot j\right) \cdot t \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, c \cdot j\right)} \cdot t \]

      6. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, c \cdot j\right) \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

      8. lower-*.f64 55.3

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

   5. Applied rewrites 55.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]

   6. Taylor expanded in x around 0

      \[\leadsto \left(c \cdot j\right) \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 38.5%

      \[\leadsto \left(j \cdot c\right) \cdot t \]

   if 2.50000000000000013e31 < i

   1. Initial program 66.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(a \cdot b\right)\right)} \cdot i \]

      4. metadata-eval N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) + \color{blue}{1} \cdot \left(a \cdot b\right)\right) \cdot i \]

      5. *-lft-identity N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) + \color{blue}{a \cdot b}\right) \cdot i \]

      6. *-commutative N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(y \cdot j\right)} + a \cdot b\right) \cdot i \]

      7. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot y\right) \cdot j} + a \cdot b\right) \cdot i \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot y, j, a \cdot b\right)} \cdot i \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y\right)}, j, a \cdot b\right) \cdot i \]

      10. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-y}, j, a \cdot b\right) \cdot i \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-y, j, \color{blue}{b \cdot a}\right) \cdot i \]

      12. lower-*.f64 53.5

          \[\leadsto \mathsf{fma}\left(-y, j, \color{blue}{b \cdot a}\right) \cdot i \]

   5. Applied rewrites 53.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, j, b \cdot a\right) \cdot i} \]

   6. Taylor expanded in y around 0

      \[\leadsto \left(a \cdot b\right) \cdot i \]
   7. Step-by-step derivation

   8. Applied rewrites 37.9%

      \[\leadsto \left(b \cdot a\right) \cdot i \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 23: 30.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(i \cdot b\right) \cdot a\\ \mathbf{if}\;i \leq -3.5 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -1.95 \cdot 10^{-240}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+31}:\\ \;\;\;\;\left(j \cdot c\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* i b) a)))
   (if (<= i -3.5e+98)
     t_1
     (if (<= i -1.95e-240)
       (* (* z x) y)
       (if (<= i 2.5e+31) (* (* j c) t) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * b) * a;
	double tmp;
	if (i <= -3.5e+98) {
		tmp = t_1;
	} else if (i <= -1.95e-240) {
		tmp = (z * x) * y;
	} else if (i <= 2.5e+31) {
		tmp = (j * c) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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 * b) * a
    if (i <= (-3.5d+98)) then
        tmp = t_1
    else if (i <= (-1.95d-240)) then
        tmp = (z * x) * y
    else if (i <= 2.5d+31) then
        tmp = (j * c) * t
    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 = (i * b) * a;
	double tmp;
	if (i <= -3.5e+98) {
		tmp = t_1;
	} else if (i <= -1.95e-240) {
		tmp = (z * x) * y;
	} else if (i <= 2.5e+31) {
		tmp = (j * c) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (i * b) * a
	tmp = 0
	if i <= -3.5e+98:
		tmp = t_1
	elif i <= -1.95e-240:
		tmp = (z * x) * y
	elif i <= 2.5e+31:
		tmp = (j * c) * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * b) * a)
	tmp = 0.0
	if (i <= -3.5e+98)
		tmp = t_1;
	elseif (i <= -1.95e-240)
		tmp = Float64(Float64(z * x) * y);
	elseif (i <= 2.5e+31)
		tmp = Float64(Float64(j * c) * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (i * b) * a;
	tmp = 0.0;
	if (i <= -3.5e+98)
		tmp = t_1;
	elseif (i <= -1.95e-240)
		tmp = (z * x) * y;
	elseif (i <= 2.5e+31)
		tmp = (j * c) * t;
	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[(i * b), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[i, -3.5e+98], t$95$1, If[LessEqual[i, -1.95e-240], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[i, 2.5e+31], N[(N[(j * c), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -3.5e98 or 2.50000000000000013e31 < i

   1. Initial program 66.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(a \cdot b\right)\right)} \cdot i \]

      4. metadata-eval N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) + \color{blue}{1} \cdot \left(a \cdot b\right)\right) \cdot i \]

      5. *-lft-identity N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) + \color{blue}{a \cdot b}\right) \cdot i \]

      6. *-commutative N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(y \cdot j\right)} + a \cdot b\right) \cdot i \]

      7. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot y\right) \cdot j} + a \cdot b\right) \cdot i \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot y, j, a \cdot b\right)} \cdot i \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y\right)}, j, a \cdot b\right) \cdot i \]

      10. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-y}, j, a \cdot b\right) \cdot i \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-y, j, \color{blue}{b \cdot a}\right) \cdot i \]

      12. lower-*.f64 59.7

          \[\leadsto \mathsf{fma}\left(-y, j, \color{blue}{b \cdot a}\right) \cdot i \]

   5. Applied rewrites 59.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, j, b \cdot a\right) \cdot i} \]

   6. Taylor expanded in y around 0

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 41.8%

      \[\leadsto \left(i \cdot b\right) \cdot \color{blue}{a} \]

   if -3.5e98 < i < -1.95000000000000007e-240

   1. Initial program 80.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(j \cdot \left(c \cdot t - i \cdot y\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)} \]

   5. Applied rewrites 78.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-x, t, i \cdot b\right), a, \mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(t \cdot \left(-1 \cdot x + \frac{b \cdot i}{t}\right), a, \mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 77.1%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(b, \frac{i}{t}, -x\right) \cdot t, a, \mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\right) \]

   9. Taylor expanded in j around 0

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   10. Step-by-step derivation

       1. fp-cancel-sub-sign-inv N/A

          \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) + \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)} \]

       2. *-commutative N/A

          \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} + \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right) \]

       3. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot z - a \cdot t, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

       4. fp-cancel-sub-sign-inv N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot z + \left(\mathsf{neg}\left(a\right)\right) \cdot t}, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(y \cdot z + \color{blue}{\left(-1 \cdot a\right)} \cdot t, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       6. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(y \cdot z + \color{blue}{-1 \cdot \left(a \cdot t\right)}, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       7. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot \left(a \cdot t\right) + y \cdot z}, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       8. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(-1 \cdot a\right) \cdot t} + y \cdot z, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       9. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(-1 \cdot a, t, y \cdot z\right)}, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       10. mul-1-neg N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(a\right)}, t, y \cdot z\right), x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       11. lower-neg.f64 N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{-a}, t, y \cdot z\right), x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, \color{blue}{z \cdot y}\right), x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       13. lower-*.f64 N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, \color{blue}{z \cdot y}\right), x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       14. distribute-lft-neg-in N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \color{blue}{\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)}\right) \]

       15. *-commutative N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \mathsf{neg}\left(\color{blue}{\left(c \cdot z - a \cdot i\right) \cdot b}\right)\right) \]

       16. distribute-lft-neg-in N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right) \cdot b}\right) \]

       17. mul-1-neg N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)} \cdot b\right) \]

       18. lower-*.f64 N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right) \cdot b}\right) \]

   11. Applied rewrites 64.7%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \mathsf{fma}\left(-z, c, a \cdot i\right) \cdot b\right)} \]

   12. Taylor expanded in y around inf

       \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   13. Step-by-step derivation

   14. Applied rewrites 32.5%

       \[\leadsto \left(z \cdot x\right) \cdot \color{blue}{y} \]

   if -1.95000000000000007e-240 < i < 2.50000000000000013e31

   1. Initial program 76.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

      3. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + c \cdot j\right) \cdot t \]

      4. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + c \cdot j\right) \cdot t \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, c \cdot j\right)} \cdot t \]

      6. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, c \cdot j\right) \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

      8. lower-*.f64 55.3

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

   5. Applied rewrites 55.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]

   6. Taylor expanded in x around 0

      \[\leadsto \left(c \cdot j\right) \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 38.5%

      \[\leadsto \left(j \cdot c\right) \cdot t \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 24: 30.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(i \cdot b\right) \cdot a\\ \mathbf{if}\;i \leq -3.5 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -1.95 \cdot 10^{-240}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+31}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* i b) a)))
   (if (<= i -3.5e+98)
     t_1
     (if (<= i -1.95e-240)
       (* (* z x) y)
       (if (<= i 2.5e+31) (* (* j t) c) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * b) * a;
	double tmp;
	if (i <= -3.5e+98) {
		tmp = t_1;
	} else if (i <= -1.95e-240) {
		tmp = (z * x) * y;
	} else if (i <= 2.5e+31) {
		tmp = (j * t) * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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 * b) * a
    if (i <= (-3.5d+98)) then
        tmp = t_1
    else if (i <= (-1.95d-240)) then
        tmp = (z * x) * y
    else if (i <= 2.5d+31) then
        tmp = (j * t) * c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * b) * a;
	double tmp;
	if (i <= -3.5e+98) {
		tmp = t_1;
	} else if (i <= -1.95e-240) {
		tmp = (z * x) * y;
	} else if (i <= 2.5e+31) {
		tmp = (j * t) * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (i * b) * a
	tmp = 0
	if i <= -3.5e+98:
		tmp = t_1
	elif i <= -1.95e-240:
		tmp = (z * x) * y
	elif i <= 2.5e+31:
		tmp = (j * t) * c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * b) * a)
	tmp = 0.0
	if (i <= -3.5e+98)
		tmp = t_1;
	elseif (i <= -1.95e-240)
		tmp = Float64(Float64(z * x) * y);
	elseif (i <= 2.5e+31)
		tmp = Float64(Float64(j * t) * c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (i * b) * a;
	tmp = 0.0;
	if (i <= -3.5e+98)
		tmp = t_1;
	elseif (i <= -1.95e-240)
		tmp = (z * x) * y;
	elseif (i <= 2.5e+31)
		tmp = (j * t) * c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[i, -3.5e+98], t$95$1, If[LessEqual[i, -1.95e-240], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[i, 2.5e+31], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -3.5e98 or 2.50000000000000013e31 < i

   1. Initial program 66.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(a \cdot b\right)\right)} \cdot i \]

      4. metadata-eval N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) + \color{blue}{1} \cdot \left(a \cdot b\right)\right) \cdot i \]

      5. *-lft-identity N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) + \color{blue}{a \cdot b}\right) \cdot i \]

      6. *-commutative N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(y \cdot j\right)} + a \cdot b\right) \cdot i \]

      7. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot y\right) \cdot j} + a \cdot b\right) \cdot i \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot y, j, a \cdot b\right)} \cdot i \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y\right)}, j, a \cdot b\right) \cdot i \]

      10. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-y}, j, a \cdot b\right) \cdot i \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-y, j, \color{blue}{b \cdot a}\right) \cdot i \]

      12. lower-*.f64 59.7

          \[\leadsto \mathsf{fma}\left(-y, j, \color{blue}{b \cdot a}\right) \cdot i \]

   5. Applied rewrites 59.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, j, b \cdot a\right) \cdot i} \]

   6. Taylor expanded in y around 0

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 41.8%

      \[\leadsto \left(i \cdot b\right) \cdot \color{blue}{a} \]

   if -3.5e98 < i < -1.95000000000000007e-240

   1. Initial program 80.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(j \cdot \left(c \cdot t - i \cdot y\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)} \]

   5. Applied rewrites 78.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-x, t, i \cdot b\right), a, \mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(t \cdot \left(-1 \cdot x + \frac{b \cdot i}{t}\right), a, \mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 77.1%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(b, \frac{i}{t}, -x\right) \cdot t, a, \mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\right) \]

   9. Taylor expanded in j around 0

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   10. Step-by-step derivation

       1. fp-cancel-sub-sign-inv N/A

          \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) + \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)} \]

       2. *-commutative N/A

          \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} + \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right) \]

       3. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot z - a \cdot t, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

       4. fp-cancel-sub-sign-inv N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot z + \left(\mathsf{neg}\left(a\right)\right) \cdot t}, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(y \cdot z + \color{blue}{\left(-1 \cdot a\right)} \cdot t, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       6. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(y \cdot z + \color{blue}{-1 \cdot \left(a \cdot t\right)}, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       7. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot \left(a \cdot t\right) + y \cdot z}, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       8. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(-1 \cdot a\right) \cdot t} + y \cdot z, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       9. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(-1 \cdot a, t, y \cdot z\right)}, x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       10. mul-1-neg N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(a\right)}, t, y \cdot z\right), x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       11. lower-neg.f64 N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{-a}, t, y \cdot z\right), x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, \color{blue}{z \cdot y}\right), x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       13. lower-*.f64 N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, \color{blue}{z \cdot y}\right), x, \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - a \cdot i\right)\right) \]

       14. distribute-lft-neg-in N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \color{blue}{\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)}\right) \]

       15. *-commutative N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \mathsf{neg}\left(\color{blue}{\left(c \cdot z - a \cdot i\right) \cdot b}\right)\right) \]

       16. distribute-lft-neg-in N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right) \cdot b}\right) \]

       17. mul-1-neg N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)} \cdot b\right) \]

       18. lower-*.f64 N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right) \cdot b}\right) \]

   11. Applied rewrites 64.7%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-a, t, z \cdot y\right), x, \mathsf{fma}\left(-z, c, a \cdot i\right) \cdot b\right)} \]

   12. Taylor expanded in y around inf

       \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   13. Step-by-step derivation

   14. Applied rewrites 32.5%

       \[\leadsto \left(z \cdot x\right) \cdot \color{blue}{y} \]

   if -1.95000000000000007e-240 < i < 2.50000000000000013e31

   1. Initial program 76.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

      3. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + c \cdot j\right) \cdot t \]

      4. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + c \cdot j\right) \cdot t \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, c \cdot j\right)} \cdot t \]

      6. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, c \cdot j\right) \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

      8. lower-*.f64 55.3

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

   5. Applied rewrites 55.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]

   6. Taylor expanded in x around 0

      \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 37.4%

      \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{c} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 25: 30.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -6.4 \cdot 10^{+142} \lor \neg \left(i \leq 2.5 \cdot 10^{+31}\right):\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot t\right) \cdot j\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -6.4e+142) (not (<= i 2.5e+31))) (* (* i b) a) (* (* 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 ((i <= -6.4e+142) || !(i <= 2.5e+31)) {
		tmp = (i * b) * a;
	} else {
		tmp = (c * t) * j;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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 <= (-6.4d+142)) .or. (.not. (i <= 2.5d+31))) then
        tmp = (i * b) * a
    else
        tmp = (c * t) * j
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -6.4e+142) || !(i <= 2.5e+31)) {
		tmp = (i * b) * a;
	} else {
		tmp = (c * t) * j;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -6.4e+142) or not (i <= 2.5e+31):
		tmp = (i * b) * a
	else:
		tmp = (c * t) * j
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -6.4e+142) || !(i <= 2.5e+31))
		tmp = Float64(Float64(i * b) * a);
	else
		tmp = Float64(Float64(c * t) * j);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -6.4e+142) || ~((i <= 2.5e+31)))
		tmp = (i * b) * a;
	else
		tmp = (c * t) * j;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -6.4e+142], N[Not[LessEqual[i, 2.5e+31]], $MachinePrecision]], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], N[(N[(c * t), $MachinePrecision] * j), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -6.40000000000000011e142 or 2.50000000000000013e31 < i

   1. Initial program 66.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(a \cdot b\right)\right)} \cdot i \]

      4. metadata-eval N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) + \color{blue}{1} \cdot \left(a \cdot b\right)\right) \cdot i \]

      5. *-lft-identity N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) + \color{blue}{a \cdot b}\right) \cdot i \]

      6. *-commutative N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(y \cdot j\right)} + a \cdot b\right) \cdot i \]

      7. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot y\right) \cdot j} + a \cdot b\right) \cdot i \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot y, j, a \cdot b\right)} \cdot i \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y\right)}, j, a \cdot b\right) \cdot i \]

      10. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-y}, j, a \cdot b\right) \cdot i \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-y, j, \color{blue}{b \cdot a}\right) \cdot i \]

      12. lower-*.f64 60.4

          \[\leadsto \mathsf{fma}\left(-y, j, \color{blue}{b \cdot a}\right) \cdot i \]

   5. Applied rewrites 60.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, j, b \cdot a\right) \cdot i} \]

   6. Taylor expanded in y around 0

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 42.1%

      \[\leadsto \left(i \cdot b\right) \cdot \color{blue}{a} \]

   if -6.40000000000000011e142 < i < 2.50000000000000013e31

   1. Initial program 77.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

      3. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + c \cdot j\right) \cdot t \]

      4. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + c \cdot j\right) \cdot t \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, c \cdot j\right)} \cdot t \]

      6. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, c \cdot j\right) \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

      8. lower-*.f64 51.3

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

   5. Applied rewrites 51.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]

   6. Taylor expanded in x around 0

      \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 29.9%

      \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{c} \]
   9. Step-by-step derivation

   10. Applied rewrites 31.7%

       \[\leadsto \left(c \cdot t\right) \cdot j \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6.4 \cdot 10^{+142} \lor \neg \left(i \leq 2.5 \cdot 10^{+31}\right):\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot t\right) \cdot j\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 22.1% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \left(c \cdot t\right) \cdot j \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* (* c t) j))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return (c * t) * j;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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 = (c * t) * j
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return (c * t) * j;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return (c * t) * j

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(c * t) * j)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = (c * t) * j;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(c * t), $MachinePrecision] * j), $MachinePrecision]

Derivation

1. Initial program 73.6%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
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

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

   2. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

   3. associate-*r* N/A

      \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + c \cdot j\right) \cdot t \]

   4. mul-1-neg N/A

      \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + c \cdot j\right) \cdot t \]

   5. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, c \cdot j\right)} \cdot t \]

   6. lower-neg.f64 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, c \cdot j\right) \cdot t \]

   7. *-commutative N/A

      \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

   8. lower-*.f64 43.5

      \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

5. Applied rewrites 43.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]

6. Taylor expanded in x around 0

   \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
7. Step-by-step derivation

8. Applied rewrites 24.9%

   \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{c} \]
9. Step-by-step derivation

10. Applied rewrites 26.0%

    \[\leadsto \left(c \cdot t\right) \cdot j \]
11. Add Preprocessing

Developer Target 1: 68.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024320 
(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)))))