Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.6% → 73.5%

Time: 13.1s

Alternatives: 24

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: 73.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+113}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, x, j \cdot c\right), t, t\_1\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-115}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-z, c, i \cdot a\right), b, \mathsf{fma}\left(-x, a, j \cdot c\right) \cdot t\right)\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+206}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-x, t, i \cdot b\right), a, \mathsf{fma}\left(\mathsf{fma}\left(-b, c, y \cdot x\right), z, \mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- i) j (* z x)) y)))
   (if (<= y -8.5e+113)
     (fma (fma (- a) x (* j c)) t t_1)
     (if (<= y 9e-115)
       (fma (fma (- z) c (* i a)) b (* (fma (- x) a (* j c)) t))
       (if (<= y 5.7e+206)
         (fma
          (fma (- x) t (* i b))
          a
          (fma (fma (- b) c (* y x)) z (* (fma (- i) y (* 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(-i, j, (z * x)) * y;
	double tmp;
	if (y <= -8.5e+113) {
		tmp = fma(fma(-a, x, (j * c)), t, t_1);
	} else if (y <= 9e-115) {
		tmp = fma(fma(-z, c, (i * a)), b, (fma(-x, a, (j * c)) * t));
	} else if (y <= 5.7e+206) {
		tmp = fma(fma(-x, t, (i * b)), a, fma(fma(-b, c, (y * x)), z, (fma(-i, y, (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(-i), j, Float64(z * x)) * y)
	tmp = 0.0
	if (y <= -8.5e+113)
		tmp = fma(fma(Float64(-a), x, Float64(j * c)), t, t_1);
	elseif (y <= 9e-115)
		tmp = fma(fma(Float64(-z), c, Float64(i * a)), b, Float64(fma(Float64(-x), a, Float64(j * c)) * t));
	elseif (y <= 5.7e+206)
		tmp = fma(fma(Float64(-x), t, Float64(i * b)), a, fma(fma(Float64(-b), c, Float64(y * x)), z, Float64(fma(Float64(-i), y, 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[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -8.5e+113], N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t + t$95$1), $MachinePrecision], If[LessEqual[y, 9e-115], N[(N[((-z) * c + N[(i * a), $MachinePrecision]), $MachinePrecision] * b + N[(N[((-x) * a + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.7e+206], N[(N[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a + N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z + N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.5000000000000001e113

   1. Initial program 56.1%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 78.9%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 83.8%

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

   if -8.5000000000000001e113 < y < 9.00000000000000046e-115

   1. Initial program 76.4%

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

   3. Taylor expanded in 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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. 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 80.7%

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

   if 9.00000000000000046e-115 < y < 5.6999999999999998e206

   1. Initial program 71.4%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

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

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

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

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

   5. Applied rewrites 87.1%

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

   if 5.6999999999999998e206 < y

   1. Initial program 45.3%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. neg-mul-1 N/A

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

      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 90.0

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

   5. Applied rewrites 90.0%

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

Alternative 2: 84.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(c \cdot z - i \cdot a\right)\\ t_2 := j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - t\_1\right) + t\_2 \leq \infty:\\ \;\;\;\;\left(\frac{x}{{\left(\mathsf{fma}\left(-a, t, z \cdot y\right)\right)}^{-1}} - t\_1\right) + t\_2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, x, j \cdot c\right), t, \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* c z) (* i a)))) (t_2 (* j (- (* c t) (* i y)))))
   (if (<= (+ (- (* x (- (* y z) (* t a))) t_1) t_2) INFINITY)
     (+ (- (/ x (pow (fma (- a) t (* z y)) -1.0)) t_1) t_2)
     (fma (fma (- a) x (* j c)) 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 = b * ((c * z) - (i * a));
	double t_2 = j * ((c * t) - (i * y));
	double tmp;
	if ((((x * ((y * z) - (t * a))) - t_1) + t_2) <= ((double) INFINITY)) {
		tmp = ((x / pow(fma(-a, t, (z * y)), -1.0)) - t_1) + t_2;
	} else {
		tmp = fma(fma(-a, x, (j * c)), t, (fma(-i, j, (z * x)) * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(c * z) - Float64(i * a)))
	t_2 = Float64(j * Float64(Float64(c * t) - Float64(i * y)))
	tmp = 0.0
	if (Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - t_1) + t_2) <= Inf)
		tmp = Float64(Float64(Float64(x / (fma(Float64(-a), t, Float64(z * y)) ^ -1.0)) - t_1) + t_2);
	else
		tmp = fma(fma(Float64(-a), x, Float64(j * c)), 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[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision], Infinity], N[(N[(N[(x / N[Power[N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision], N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t + N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 89.6%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. flip-- N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

      9. lift--.f64 N/A

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

      10. lower-/.f64 89.7

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

      11. lift--.f64 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

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

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

      17. lower-fma.f64 N/A

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

      18. lower-neg.f64 89.7

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 89.7

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

   4. Applied rewrites 89.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in 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 44.8%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 60.4%

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

4. Final simplification 83.0%

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

Alternative 3: 84.6% accurate, 0.5× speedup

Math

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

FPCore

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

Julia

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 89.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in 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 44.8%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 60.4%

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

Alternative 4: 77.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \mathbf{if}\;j \leq 4.5 \cdot 10^{-78}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-z, c, i \cdot a\right), b, \mathsf{fma}\left(\mathsf{fma}\left(-x, a, j \cdot c\right), t, \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\right)\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{+186}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-x, t, i \cdot b\right), a, \mathsf{fma}\left(\mathsf{fma}\left(-b, c, y \cdot x\right), z, t\_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- i) y (* c t)) j)))
   (if (<= j 4.5e-78)
     (fma
      (fma (- z) c (* i a))
      b
      (fma (fma (- x) a (* j c)) t (* (fma (- i) j (* z x)) y)))
     (if (<= j 4.4e+186)
       (fma (fma (- x) t (* i b)) a (fma (fma (- b) c (* y x)) z t_1))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-i, y, (c * t)) * j;
	double tmp;
	if (j <= 4.5e-78) {
		tmp = fma(fma(-z, c, (i * a)), b, fma(fma(-x, a, (j * c)), t, (fma(-i, j, (z * x)) * y)));
	} else if (j <= 4.4e+186) {
		tmp = fma(fma(-x, t, (i * b)), a, fma(fma(-b, c, (y * x)), z, t_1));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-i), y, Float64(c * t)) * j)
	tmp = 0.0
	if (j <= 4.5e-78)
		tmp = fma(fma(Float64(-z), c, Float64(i * a)), b, fma(fma(Float64(-x), a, Float64(j * c)), t, Float64(fma(Float64(-i), j, Float64(z * x)) * y)));
	elseif (j <= 4.4e+186)
		tmp = fma(fma(Float64(-x), t, Float64(i * b)), a, fma(fma(Float64(-b), c, Float64(y * x)), z, t_1));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]}, If[LessEqual[j, 4.5e-78], N[(N[((-z) * c + N[(i * a), $MachinePrecision]), $MachinePrecision] * b + N[(N[((-x) * a + N[(j * c), $MachinePrecision]), $MachinePrecision] * t + N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.4e+186], N[(N[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a + N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z + t$95$1), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if j < 4.5e-78

   1. Initial program 70.6%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 83.2%

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

   if 4.5e-78 < j < 4.3999999999999997e186

   1. Initial program 66.7%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

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

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

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

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

   5. Applied rewrites 83.5%

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

   if 4.3999999999999997e186 < j

   1. Initial program 67.7%

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

   3. Taylor expanded in y around 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 64.6%

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

   6. Taylor expanded in j around inf

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

   8. Applied rewrites 82.2%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq 4.5 \cdot 10^{-78}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-z, c, i \cdot a\right), b, \mathsf{fma}\left(\mathsf{fma}\left(-x, a, j \cdot c\right), t, \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\right)\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{+186}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-x, t, i \cdot b\right), a, \mathsf{fma}\left(\mathsf{fma}\left(-b, c, y \cdot x\right), z, \mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(-a, x, j \cdot c\right), t, \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\right)\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-82}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-z, c, i \cdot a\right), b, \mathsf{fma}\left(-x, a, j \cdot c\right) \cdot t\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+34}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-b, c, x \cdot y\right), z, \mathsf{fma}\left(-i, y, t \cdot c\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (fma (fma (- a) x (* j c)) t (* (fma (- i) j (* z x)) y))))
   (if (<= y -8.5e+113)
     t_1
     (if (<= y 1.5e-82)
       (fma (fma (- z) c (* i a)) b (* (fma (- x) a (* j c)) t))
       (if (<= y 4.1e+34)
         (fma (fma (- b) c (* x y)) z (* (fma (- i) y (* t c)) 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(fma(-a, x, (j * c)), t, (fma(-i, j, (z * x)) * y));
	double tmp;
	if (y <= -8.5e+113) {
		tmp = t_1;
	} else if (y <= 1.5e-82) {
		tmp = fma(fma(-z, c, (i * a)), b, (fma(-x, a, (j * c)) * t));
	} else if (y <= 4.1e+34) {
		tmp = fma(fma(-b, c, (x * y)), z, (fma(-i, y, (t * c)) * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = fma(fma(Float64(-a), x, Float64(j * c)), t, Float64(fma(Float64(-i), j, Float64(z * x)) * y))
	tmp = 0.0
	if (y <= -8.5e+113)
		tmp = t_1;
	elseif (y <= 1.5e-82)
		tmp = fma(fma(Float64(-z), c, Float64(i * a)), b, Float64(fma(Float64(-x), a, Float64(j * c)) * t));
	elseif (y <= 4.1e+34)
		tmp = fma(fma(Float64(-b), c, Float64(x * y)), z, Float64(fma(Float64(-i), y, Float64(t * c)) * 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[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t + N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.5e+113], t$95$1, If[LessEqual[y, 1.5e-82], N[(N[((-z) * c + N[(i * a), $MachinePrecision]), $MachinePrecision] * b + N[(N[((-x) * a + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+34], N[(N[((-b) * c + N[(x * y), $MachinePrecision]), $MachinePrecision] * z + N[(N[((-i) * y + N[(t * c), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.5000000000000001e113 or 4.0999999999999998e34 < y

   1. Initial program 59.7%

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

   3. Taylor expanded in y around 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 77.5%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 84.3%

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

   if -8.5000000000000001e113 < y < 1.4999999999999999e-82

   1. Initial program 75.3%

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

   3. Taylor expanded in y around 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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. 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 80.0%

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

   if 1.4999999999999999e-82 < y < 4.0999999999999998e34

   1. Initial program 69.9%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. flip-- N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

      9. lift--.f64 N/A

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

      10. lower-/.f64 70.0

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

      11. lift--.f64 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

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

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

      17. lower-fma.f64 N/A

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

      18. lower-neg.f64 70.0

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

   4. Applied rewrites 70.0%

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

   5. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. associate-*r* N/A

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

      4. distribute-rgt-out-- N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. +-commutative N/A

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

      11. associate-*r* N/A

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

      12. lower-fma.f64 N/A

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

      13. mul-1-neg N/A

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

      14. lower-neg.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

   7. Applied rewrites 81.4%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+113}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, x, j \cdot c\right), t, \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-82}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-z, c, i \cdot a\right), b, \mathsf{fma}\left(-x, a, j \cdot c\right) \cdot t\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+34}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-b, c, x \cdot y\right), z, \mathsf{fma}\left(-i, y, t \cdot c\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, x, j \cdot c\right), t, \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+113} \lor \neg \left(y \leq 1.75 \cdot 10^{-78}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, x, j \cdot c\right), t, \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-z, c, i \cdot a\right), b, \mathsf{fma}\left(-x, a, j \cdot c\right) \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -8.5e+113) (not (<= y 1.75e-78)))
   (fma (fma (- a) x (* j c)) t (* (fma (- i) j (* z x)) y))
   (fma (fma (- z) c (* i a)) b (* (fma (- x) a (* j c)) 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 ((y <= -8.5e+113) || !(y <= 1.75e-78)) {
		tmp = fma(fma(-a, x, (j * c)), t, (fma(-i, j, (z * x)) * y));
	} else {
		tmp = fma(fma(-z, c, (i * a)), b, (fma(-x, a, (j * c)) * t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -8.5e+113) || !(y <= 1.75e-78))
		tmp = fma(fma(Float64(-a), x, Float64(j * c)), t, Float64(fma(Float64(-i), j, Float64(z * x)) * y));
	else
		tmp = fma(fma(Float64(-z), c, Float64(i * a)), b, Float64(fma(Float64(-x), a, Float64(j * c)) * t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[y, -8.5e+113], N[Not[LessEqual[y, 1.75e-78]], $MachinePrecision]], N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t + N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(N[((-z) * c + N[(i * a), $MachinePrecision]), $MachinePrecision] * b + N[(N[((-x) * a + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.5000000000000001e113 or 1.75e-78 < y

   1. Initial program 61.7%

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

   3. Taylor expanded in y around 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 77.3%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 79.3%

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

   if -8.5000000000000001e113 < y < 1.75e-78

   1. Initial program 75.5%

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

   3. Taylor expanded in 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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. 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 80.2%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+113} \lor \neg \left(y \leq 1.75 \cdot 10^{-78}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, x, j \cdot c\right), t, \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-z, c, i \cdot a\right), b, \mathsf{fma}\left(-x, a, j \cdot c\right) \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+19} \lor \neg \left(b \leq 2.6 \cdot 10^{+134}\right):\\ \;\;\;\;\mathsf{fma}\left(-z, c, i \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, x, j \cdot c\right), t, \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1e+19) (not (<= b 2.6e+134)))
   (* (fma (- z) c (* i a)) b)
   (fma (fma (- a) x (* j c)) 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 tmp;
	if ((b <= -1e+19) || !(b <= 2.6e+134)) {
		tmp = fma(-z, c, (i * a)) * b;
	} else {
		tmp = fma(fma(-a, x, (j * c)), t, (fma(-i, j, (z * x)) * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1e+19) || !(b <= 2.6e+134))
		tmp = Float64(fma(Float64(-z), c, Float64(i * a)) * b);
	else
		tmp = fma(fma(Float64(-a), x, Float64(j * c)), 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_] := If[Or[LessEqual[b, -1e+19], N[Not[LessEqual[b, 2.6e+134]], $MachinePrecision]], N[(N[((-z) * c + N[(i * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t + N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1e19 or 2.6000000000000002e134 < b

   1. Initial program 69.3%

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

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

      3. +-commutative N/A

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

      4. remove-double-neg N/A

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

      5. distribute-neg-in N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. distribute-neg-in N/A

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

      12. remove-double-neg N/A

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

      13. *-commutative N/A

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

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

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

      15. mul-1-neg N/A

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

      16. lower-fma.f64 N/A

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

      17. mul-1-neg N/A

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

      18. lower-neg.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-*.f64 70.0

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

   5. Applied rewrites 70.0%

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

   if -1e19 < b < 2.6000000000000002e134

   1. Initial program 69.4%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 78.3%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 78.5%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+19} \lor \neg \left(b \leq 2.6 \cdot 10^{+134}\right):\\ \;\;\;\;\mathsf{fma}\left(-z, c, i \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-a, x, j \cdot c\right), t, \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-x, a, j \cdot c\right) \cdot t\\ t_2 := \mathsf{fma}\left(-z, c, i \cdot a\right) \cdot b\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+114}:\\ \;\;\;\;\mathsf{fma}\left(-z, x, j \cdot i\right) \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-163}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-202}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-134}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- x) a (* j c)) t)) (t_2 (* (fma (- z) c (* i a)) b)))
   (if (<= y -4.4e+114)
     (* (fma (- z) x (* j i)) (- y))
     (if (<= y -3.6e-163)
       t_2
       (if (<= y 3.1e-202)
         t_1
         (if (<= y 2.8e-134)
           t_2
           (if (<= y 9e+69) t_1 (* (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(-x, a, (j * c)) * t;
	double t_2 = fma(-z, c, (i * a)) * b;
	double tmp;
	if (y <= -4.4e+114) {
		tmp = fma(-z, x, (j * i)) * -y;
	} else if (y <= -3.6e-163) {
		tmp = t_2;
	} else if (y <= 3.1e-202) {
		tmp = t_1;
	} else if (y <= 2.8e-134) {
		tmp = t_2;
	} else if (y <= 9e+69) {
		tmp = t_1;
	} else {
		tmp = fma(-i, j, (z * x)) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-x), a, Float64(j * c)) * t)
	t_2 = Float64(fma(Float64(-z), c, Float64(i * a)) * b)
	tmp = 0.0
	if (y <= -4.4e+114)
		tmp = Float64(fma(Float64(-z), x, Float64(j * i)) * Float64(-y));
	elseif (y <= -3.6e-163)
		tmp = t_2;
	elseif (y <= 3.1e-202)
		tmp = t_1;
	elseif (y <= 2.8e-134)
		tmp = t_2;
	elseif (y <= 9e+69)
		tmp = t_1;
	else
		tmp = 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[(N[((-x) * a + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-z) * c + N[(i * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[y, -4.4e+114], N[(N[((-z) * x + N[(j * i), $MachinePrecision]), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[y, -3.6e-163], t$95$2, If[LessEqual[y, 3.1e-202], t$95$1, If[LessEqual[y, 2.8e-134], t$95$2, If[LessEqual[y, 9e+69], t$95$1, N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.4000000000000001e114

   1. Initial program 56.1%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 78.9%

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

   6. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. mul-1-neg N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. mul-1-neg N/A

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

      14. lower-neg.f64 80.1

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

   8. Applied rewrites 80.1%

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

   if -4.4000000000000001e114 < y < -3.5999999999999998e-163 or 3.1e-202 < y < 2.7999999999999999e-134

   1. Initial program 73.8%

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

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

      3. +-commutative N/A

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

      4. remove-double-neg N/A

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

      5. distribute-neg-in N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. distribute-neg-in N/A

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

      12. remove-double-neg N/A

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

      13. *-commutative N/A

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

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

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

      15. mul-1-neg N/A

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

      16. lower-fma.f64 N/A

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

      17. mul-1-neg N/A

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

      18. lower-neg.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-*.f64 62.1

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

   5. Applied rewrites 62.1%

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

   if -3.5999999999999998e-163 < y < 3.1e-202 or 2.7999999999999999e-134 < y < 8.9999999999999999e69

   1. Initial program 73.2%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 60.3

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

   5. Applied rewrites 60.3%

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

   if 8.9999999999999999e69 < y

   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 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. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. neg-mul-1 N/A

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

      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 83.9

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

   5. Applied rewrites 83.9%

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

Alternative 9: 52.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-x, a, j \cdot c\right) \cdot t\\ t_2 := \mathsf{fma}\left(-z, c, i \cdot a\right) \cdot b\\ t_3 := \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+114}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-163}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-202}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-134}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- x) a (* j c)) t))
        (t_2 (* (fma (- z) c (* i a)) b))
        (t_3 (* (fma (- i) j (* z x)) y)))
   (if (<= y -4.4e+114)
     t_3
     (if (<= y -3.6e-163)
       t_2
       (if (<= y 3.1e-202)
         t_1
         (if (<= y 2.8e-134) t_2 (if (<= y 9e+69) t_1 t_3)))))))

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, a, (j * c)) * t;
	double t_2 = fma(-z, c, (i * a)) * b;
	double t_3 = fma(-i, j, (z * x)) * y;
	double tmp;
	if (y <= -4.4e+114) {
		tmp = t_3;
	} else if (y <= -3.6e-163) {
		tmp = t_2;
	} else if (y <= 3.1e-202) {
		tmp = t_1;
	} else if (y <= 2.8e-134) {
		tmp = t_2;
	} else if (y <= 9e+69) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-x), a, Float64(j * c)) * t)
	t_2 = Float64(fma(Float64(-z), c, Float64(i * a)) * b)
	t_3 = Float64(fma(Float64(-i), j, Float64(z * x)) * y)
	tmp = 0.0
	if (y <= -4.4e+114)
		tmp = t_3;
	elseif (y <= -3.6e-163)
		tmp = t_2;
	elseif (y <= 3.1e-202)
		tmp = t_1;
	elseif (y <= 2.8e-134)
		tmp = t_2;
	elseif (y <= 9e+69)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-x) * a + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-z) * c + N[(i * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$3 = N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -4.4e+114], t$95$3, If[LessEqual[y, -3.6e-163], t$95$2, If[LessEqual[y, 3.1e-202], t$95$1, If[LessEqual[y, 2.8e-134], t$95$2, If[LessEqual[y, 9e+69], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.4000000000000001e114 or 8.9999999999999999e69 < y

   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 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. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. neg-mul-1 N/A

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

      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 80.6

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

   5. Applied rewrites 80.6%

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

   if -4.4000000000000001e114 < y < -3.5999999999999998e-163 or 3.1e-202 < y < 2.7999999999999999e-134

   1. Initial program 73.8%

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

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

      3. +-commutative N/A

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

      4. remove-double-neg N/A

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

      5. distribute-neg-in N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. distribute-neg-in N/A

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

      12. remove-double-neg N/A

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

      13. *-commutative N/A

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

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

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

      15. mul-1-neg N/A

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

      16. lower-fma.f64 N/A

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

      17. mul-1-neg N/A

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

      18. lower-neg.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-*.f64 62.1

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

   5. Applied rewrites 62.1%

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

   if -3.5999999999999998e-163 < y < 3.1e-202 or 2.7999999999999999e-134 < y < 8.9999999999999999e69

   1. Initial program 73.2%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 60.3

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

   5. Applied rewrites 60.3%

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

Alternative 10: 60.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.15 \cdot 10^{-128}:\\ \;\;\;\;\mathsf{fma}\left(c \cdot j, t, \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\right)\\ \mathbf{elif}\;j \leq 1.52 \cdot 10^{-62}:\\ \;\;\;\;\mathsf{fma}\left(-t, a \cdot x, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -2.15e-128)
   (fma (* c j) t (* (fma (- i) j (* z x)) y))
   (if (<= j 1.52e-62)
     (fma (- t) (* a x) (* (fma (- b) c (* y x)) z))
     (+ (* (* 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 <= -2.15e-128) {
		tmp = fma((c * j), t, (fma(-i, j, (z * x)) * y));
	} else if (j <= 1.52e-62) {
		tmp = fma(-t, (a * x), (fma(-b, c, (y * x)) * z));
	} 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 <= -2.15e-128)
		tmp = fma(Float64(c * j), t, Float64(fma(Float64(-i), j, Float64(z * x)) * y));
	elseif (j <= 1.52e-62)
		tmp = fma(Float64(-t), Float64(a * x), Float64(fma(Float64(-b), c, Float64(y * x)) * z));
	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, -2.15e-128], N[(N[(c * j), $MachinePrecision] * t + N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.52e-62], N[((-t) * N[(a * x), $MachinePrecision] + N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $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 < -2.14999999999999997e-128

   1. Initial program 67.8%

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

   3. Taylor expanded in y around 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 80.3%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 68.1%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 61.2%

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

   if -2.14999999999999997e-128 < j < 1.52000000000000007e-62

   1. Initial program 72.1%

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

   3. Taylor expanded in i around 0

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

      1. associate--l+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r+ N/A

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

      5. sub-neg N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

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

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 67.3%

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

   6. Taylor expanded in j around 0

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

   8. Applied rewrites 67.6%

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

   if 1.52000000000000007e-62 < j

   1. Initial program 67.4%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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 71.2

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

   5. Applied rewrites 71.2%

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

Alternative 11: 57.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(-x, t, i \cdot b\right) \cdot a\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-71}:\\ \;\;\;\;\mathsf{fma}\left(c \cdot j, t, \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, a \cdot x, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -3.2e+80)
   (* (fma (- x) t (* i b)) a)
   (if (<= a 7e-71)
     (fma (* c j) t (* (fma (- i) j (* z x)) y))
     (fma (- t) (* a x) (* (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 (a <= -3.2e+80) {
		tmp = fma(-x, t, (i * b)) * a;
	} else if (a <= 7e-71) {
		tmp = fma((c * j), t, (fma(-i, j, (z * x)) * y));
	} else {
		tmp = fma(-t, (a * x), (fma(-b, c, (y * x)) * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -3.2e+80)
		tmp = Float64(fma(Float64(-x), t, Float64(i * b)) * a);
	elseif (a <= 7e-71)
		tmp = fma(Float64(c * j), t, Float64(fma(Float64(-i), j, Float64(z * x)) * y));
	else
		tmp = fma(Float64(-t), Float64(a * x), 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[LessEqual[a, -3.2e+80], N[(N[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[a, 7e-71], N[(N[(c * j), $MachinePrecision] * t + N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[((-t) * N[(a * x), $MachinePrecision] + N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.1999999999999999e80

   1. Initial program 57.5%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   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. sub-neg N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      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 69.3

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

   5. Applied rewrites 69.3%

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

   if -3.1999999999999999e80 < a < 6.9999999999999998e-71

   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 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 79.4%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 71.9%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 69.3%

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

   if 6.9999999999999998e-71 < a

   1. Initial program 71.5%

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

   3. Taylor expanded in i around 0

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

      1. associate--l+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r+ N/A

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

      5. sub-neg N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

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

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 66.1%

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

   6. Taylor expanded in j around 0

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

   8. Applied rewrites 60.3%

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

Alternative 12: 60.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -440 \lor \neg \left(b \leq 2.5 \cdot 10^{+134}\right):\\ \;\;\;\;\mathsf{fma}\left(-z, c, i \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c \cdot j, t, \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -440.0) (not (<= b 2.5e+134)))
   (* (fma (- z) c (* i a)) b)
   (fma (* c j) 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 tmp;
	if ((b <= -440.0) || !(b <= 2.5e+134)) {
		tmp = fma(-z, c, (i * a)) * b;
	} else {
		tmp = fma((c * j), t, (fma(-i, j, (z * x)) * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -440.0) || !(b <= 2.5e+134))
		tmp = Float64(fma(Float64(-z), c, Float64(i * a)) * b);
	else
		tmp = fma(Float64(c * j), 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_] := If[Or[LessEqual[b, -440.0], N[Not[LessEqual[b, 2.5e+134]], $MachinePrecision]], N[(N[((-z) * c + N[(i * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], N[(N[(c * j), $MachinePrecision] * t + N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -440 or 2.4999999999999999e134 < b

   1. Initial program 69.2%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. remove-double-neg N/A

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

      5. distribute-neg-in N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. distribute-neg-in N/A

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

      12. remove-double-neg N/A

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

      13. *-commutative N/A

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

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

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

      15. mul-1-neg N/A

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

      16. lower-fma.f64 N/A

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

      17. mul-1-neg N/A

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

      18. lower-neg.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-*.f64 68.8

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

   5. Applied rewrites 68.8%

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

   if -440 < b < 2.4999999999999999e134

   1. Initial program 69.4%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 78.5%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 78.7%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 64.1%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -440 \lor \neg \left(b \leq 2.5 \cdot 10^{+134}\right):\\ \;\;\;\;\mathsf{fma}\left(-z, c, i \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c \cdot j, t, \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-58}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+103}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- b) c (* y x)) z)))
   (if (<= z -2.7e+126)
     t_1
     (if (<= z 7.2e-58)
       (* (fma (- i) y (* c t)) j)
       (if (<= z 3.15e+103) (* (fma (- t) a (* z y)) x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-b, c, (y * x)) * z;
	double tmp;
	if (z <= -2.7e+126) {
		tmp = t_1;
	} else if (z <= 7.2e-58) {
		tmp = fma(-i, y, (c * t)) * j;
	} else if (z <= 3.15e+103) {
		tmp = fma(-t, a, (z * y)) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-b), c, Float64(y * x)) * z)
	tmp = 0.0
	if (z <= -2.7e+126)
		tmp = t_1;
	elseif (z <= 7.2e-58)
		tmp = Float64(fma(Float64(-i), y, Float64(c * t)) * j);
	elseif (z <= 3.15e+103)
		tmp = Float64(fma(Float64(-t), a, Float64(z * y)) * x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -2.7e+126], t$95$1, If[LessEqual[z, 7.2e-58], N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[z, 3.15e+103], N[(N[((-t) * a + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.70000000000000002e126 or 3.14999999999999985e103 < z

   1. Initial program 63.9%

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

   3. Taylor expanded in 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. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. neg-mul-1 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 73.7

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

   5. Applied rewrites 73.7%

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

   if -2.70000000000000002e126 < z < 7.20000000000000019e-58

   1. Initial program 74.1%

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

   3. Taylor expanded in 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 83.1%

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

   6. Taylor expanded in j around inf

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

   8. Applied rewrites 46.9%

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

   if 7.20000000000000019e-58 < z < 3.14999999999999985e103

   1. Initial program 65.9%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 78.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 69.1%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 51.8%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+126}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-58}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+103}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 31.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot t\right) \cdot c\\ \mathbf{if}\;j \leq -580000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -2.3 \cdot 10^{-294}:\\ \;\;\;\;\left(\left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;j \leq 8 \cdot 10^{-208}:\\ \;\;\;\;\left(b \cdot a\right) \cdot i\\ \mathbf{elif}\;j \leq 1.04 \cdot 10^{+58}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* j t) c)))
   (if (<= j -580000.0)
     t_1
     (if (<= j -2.3e-294)
       (* (* (- b) z) c)
       (if (<= j 8e-208)
         (* (* b a) i)
         (if (<= j 1.04e+58) (* (* z x) y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * t) * c;
	double tmp;
	if (j <= -580000.0) {
		tmp = t_1;
	} else if (j <= -2.3e-294) {
		tmp = (-b * z) * c;
	} else if (j <= 8e-208) {
		tmp = (b * a) * i;
	} else if (j <= 1.04e+58) {
		tmp = (z * x) * y;
	} 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 = (j * t) * c
    if (j <= (-580000.0d0)) then
        tmp = t_1
    else if (j <= (-2.3d-294)) then
        tmp = (-b * z) * c
    else if (j <= 8d-208) then
        tmp = (b * a) * i
    else if (j <= 1.04d+58) then
        tmp = (z * x) * y
    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 = (j * t) * c;
	double tmp;
	if (j <= -580000.0) {
		tmp = t_1;
	} else if (j <= -2.3e-294) {
		tmp = (-b * z) * c;
	} else if (j <= 8e-208) {
		tmp = (b * a) * i;
	} else if (j <= 1.04e+58) {
		tmp = (z * x) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * t) * c
	tmp = 0
	if j <= -580000.0:
		tmp = t_1
	elif j <= -2.3e-294:
		tmp = (-b * z) * c
	elif j <= 8e-208:
		tmp = (b * a) * i
	elif j <= 1.04e+58:
		tmp = (z * x) * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * t) * c)
	tmp = 0.0
	if (j <= -580000.0)
		tmp = t_1;
	elseif (j <= -2.3e-294)
		tmp = Float64(Float64(Float64(-b) * z) * c);
	elseif (j <= 8e-208)
		tmp = Float64(Float64(b * a) * i);
	elseif (j <= 1.04e+58)
		tmp = Float64(Float64(z * x) * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * t) * c;
	tmp = 0.0;
	if (j <= -580000.0)
		tmp = t_1;
	elseif (j <= -2.3e-294)
		tmp = (-b * z) * c;
	elseif (j <= 8e-208)
		tmp = (b * a) * i;
	elseif (j <= 1.04e+58)
		tmp = (z * x) * y;
	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[(j * t), $MachinePrecision] * c), $MachinePrecision]}, If[LessEqual[j, -580000.0], t$95$1, If[LessEqual[j, -2.3e-294], N[(N[((-b) * z), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[j, 8e-208], N[(N[(b * a), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[j, 1.04e+58], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -5.8e5 or 1.04e58 < j

   1. Initial program 65.5%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. flip-- N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

      9. lift--.f64 N/A

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

      10. lower-/.f64 65.5

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

      11. lift--.f64 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

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

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

      17. lower-fma.f64 N/A

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

      18. lower-neg.f64 65.5

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

   4. Applied rewrites 65.5%

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

   5. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. 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. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 49.0

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

   7. Applied rewrites 49.0%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 40.5%

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

   if -5.8e5 < j < -2.30000000000000016e-294

   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 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. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. neg-mul-1 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 46.1

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

   5. Applied rewrites 46.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 22.4%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 32.4%

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

   if -2.30000000000000016e-294 < j < 8.0000000000000008e-208

   1. Initial program 67.3%

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

   3. Taylor expanded in i around 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. sub-neg N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      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 50.9

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

   5. Applied rewrites 50.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 51.1%

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

   if 8.0000000000000008e-208 < j < 1.04e58

   1. Initial program 74.4%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. neg-mul-1 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 47.7

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

   5. Applied rewrites 47.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 37.4%

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

   10. Applied rewrites 38.9%

       \[\leadsto \left(z \cdot x\right) \cdot y \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -580000:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;j \leq -2.3 \cdot 10^{-294}:\\ \;\;\;\;\left(\left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;j \leq 8 \cdot 10^{-208}:\\ \;\;\;\;\left(b \cdot a\right) \cdot i\\ \mathbf{elif}\;j \leq 1.04 \cdot 10^{+58}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-51} \lor \neg \left(t \leq 3.1 \cdot 10^{+132}\right):\\ \;\;\;\;\mathsf{fma}\left(-x, a, j \cdot c\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -4.7e-51) (not (<= t 3.1e+132)))
   (* (fma (- x) a (* j c)) 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 tmp;
	if ((t <= -4.7e-51) || !(t <= 3.1e+132)) {
		tmp = fma(-x, a, (j * c)) * t;
	} else {
		tmp = fma(-i, j, (z * x)) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -4.7e-51) || !(t <= 3.1e+132))
		tmp = Float64(fma(Float64(-x), a, Float64(j * c)) * t);
	else
		tmp = Float64(fma(Float64(-i), j, Float64(z * x)) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -4.7e-51], N[Not[LessEqual[t, 3.1e+132]], $MachinePrecision]], N[(N[((-x) * a + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.6999999999999997e-51 or 3.0999999999999998e132 < t

   1. Initial program 59.4%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 67.4

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

   5. Applied rewrites 67.4%

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

   if -4.6999999999999997e-51 < t < 3.0999999999999998e132

   1. Initial program 76.8%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. neg-mul-1 N/A

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

      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 56.6

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

   5. Applied rewrites 56.6%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-51} \lor \neg \left(t \leq 3.1 \cdot 10^{+132}\right):\\ \;\;\;\;\mathsf{fma}\left(-x, a, j \cdot c\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 52.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -5.5 \cdot 10^{-67} \lor \neg \left(j \leq 3.4 \cdot 10^{+61}\right):\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -5.5e-67) (not (<= j 3.4e+61)))
   (* (fma (- i) y (* c t)) j)
   (* (fma (- t) a (* z y)) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -5.5e-67) || !(j <= 3.4e+61)) {
		tmp = fma(-i, y, (c * t)) * j;
	} else {
		tmp = fma(-t, a, (z * y)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -5.5e-67) || !(j <= 3.4e+61))
		tmp = Float64(fma(Float64(-i), y, Float64(c * t)) * j);
	else
		tmp = Float64(fma(Float64(-t), a, Float64(z * y)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -5.5e-67], N[Not[LessEqual[j, 3.4e+61]], $MachinePrecision]], N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], N[(N[((-t) * a + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -5.5000000000000003e-67 or 3.40000000000000026e61 < j

   1. Initial program 66.9%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 70.9%

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

   6. Taylor expanded in j around inf

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

   8. Applied rewrites 59.0%

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

   if -5.5000000000000003e-67 < j < 3.40000000000000026e61

   1. Initial program 71.7%

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

   3. Taylor expanded in y around 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 82.4%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 61.3%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 52.3%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.5 \cdot 10^{-67} \lor \neg \left(j \leq 3.4 \cdot 10^{+61}\right):\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 42.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.32 \cdot 10^{+188} \lor \neg \left(j \leq 3.5 \cdot 10^{+134}\right):\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1.32e+188) (not (<= j 3.5e+134)))
   (* (* j t) c)
   (* (fma (- t) a (* z y)) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.32e+188) || !(j <= 3.5e+134)) {
		tmp = (j * t) * c;
	} else {
		tmp = fma(-t, a, (z * y)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -1.32e+188) || !(j <= 3.5e+134))
		tmp = Float64(Float64(j * t) * c);
	else
		tmp = Float64(fma(Float64(-t), a, Float64(z * y)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -1.32e+188], N[Not[LessEqual[j, 3.5e+134]], $MachinePrecision]], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], N[(N[((-t) * a + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.3200000000000001e188 or 3.50000000000000003e134 < j

   1. Initial program 58.8%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. flip-- N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

      9. lift--.f64 N/A

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

      10. lower-/.f64 58.9

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

      11. lift--.f64 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

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

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

      17. lower-fma.f64 N/A

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

      18. lower-neg.f64 58.9

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

   4. Applied rewrites 58.9%

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

   5. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. 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. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 55.6

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

   7. Applied rewrites 55.6%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 51.3%

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

   if -1.3200000000000001e188 < j < 3.50000000000000003e134

   1. Initial program 73.2%

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

   3. Taylor expanded in 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 82.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 63.5%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 46.2%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.32 \cdot 10^{+188} \lor \neg \left(j \leq 3.5 \cdot 10^{+134}\right):\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+38}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+43}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+120}:\\ \;\;\;\;\left(\left(-y\right) \cdot j\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-t\right) \cdot x\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -4.8e+38)
   (* (* j t) c)
   (if (<= t 1.02e+43)
     (* (* z x) y)
     (if (<= t 1.75e+120) (* (* (- y) j) i) (* (* (- t) x) 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 (t <= -4.8e+38) {
		tmp = (j * t) * c;
	} else if (t <= 1.02e+43) {
		tmp = (z * x) * y;
	} else if (t <= 1.75e+120) {
		tmp = (-y * j) * i;
	} else {
		tmp = (-t * x) * a;
	}
	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 (t <= (-4.8d+38)) then
        tmp = (j * t) * c
    else if (t <= 1.02d+43) then
        tmp = (z * x) * y
    else if (t <= 1.75d+120) then
        tmp = (-y * j) * i
    else
        tmp = (-t * x) * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -4.8e+38) {
		tmp = (j * t) * c;
	} else if (t <= 1.02e+43) {
		tmp = (z * x) * y;
	} else if (t <= 1.75e+120) {
		tmp = (-y * j) * i;
	} else {
		tmp = (-t * x) * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -4.8e+38:
		tmp = (j * t) * c
	elif t <= 1.02e+43:
		tmp = (z * x) * y
	elif t <= 1.75e+120:
		tmp = (-y * j) * i
	else:
		tmp = (-t * x) * a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -4.8e+38)
		tmp = Float64(Float64(j * t) * c);
	elseif (t <= 1.02e+43)
		tmp = Float64(Float64(z * x) * y);
	elseif (t <= 1.75e+120)
		tmp = Float64(Float64(Float64(-y) * j) * i);
	else
		tmp = Float64(Float64(Float64(-t) * x) * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -4.8e+38)
		tmp = (j * t) * c;
	elseif (t <= 1.02e+43)
		tmp = (z * x) * y;
	elseif (t <= 1.75e+120)
		tmp = (-y * j) * i;
	else
		tmp = (-t * x) * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -4.8e+38], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[t, 1.02e+43], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 1.75e+120], N[(N[((-y) * j), $MachinePrecision] * i), $MachinePrecision], N[(N[((-t) * x), $MachinePrecision] * a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.80000000000000035e38

   1. Initial program 47.6%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. flip-- N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

      9. lift--.f64 N/A

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

      10. lower-/.f64 47.6

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

      11. lift--.f64 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

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

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

      17. lower-fma.f64 N/A

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

      18. lower-neg.f64 47.6

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

   4. Applied rewrites 47.6%

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

   5. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. 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. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 54.2

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

   7. Applied rewrites 54.2%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 46.3%

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

   if -4.80000000000000035e38 < t < 1.02e43

   1. Initial program 79.1%

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

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. neg-mul-1 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 44.9

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

   5. Applied rewrites 44.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 30.7%

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

   10. Applied rewrites 30.7%

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

   if 1.02e43 < t < 1.75000000000000004e120

   1. Initial program 69.3%

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

   3. Taylor expanded in i around 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. sub-neg N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      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 57.6

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

   5. Applied rewrites 57.6%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 44.9%

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

   if 1.75000000000000004e120 < t

   1. Initial program 62.0%

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

   3. Taylor expanded in i around 0

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

      1. associate--l+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r+ N/A

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

      5. sub-neg N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

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

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 72.2%

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

   6. Taylor expanded in j around 0

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

   8. Applied rewrites 64.8%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 55.1%

       \[\leadsto \left(\left(-t\right) \cdot x\right) \cdot a \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+38}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+43}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+120}:\\ \;\;\;\;\left(\left(-y\right) \cdot j\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-t\right) \cdot x\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+38}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-63}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+132}:\\ \;\;\;\;\left(-b\right) \cdot \left(c \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-t\right) \cdot x\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -4.8e+38)
   (* (* j t) c)
   (if (<= t 1.2e-63)
     (* (* z x) y)
     (if (<= t 1.05e+132) (* (- b) (* c z)) (* (* (- t) x) 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 (t <= -4.8e+38) {
		tmp = (j * t) * c;
	} else if (t <= 1.2e-63) {
		tmp = (z * x) * y;
	} else if (t <= 1.05e+132) {
		tmp = -b * (c * z);
	} else {
		tmp = (-t * x) * a;
	}
	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 (t <= (-4.8d+38)) then
        tmp = (j * t) * c
    else if (t <= 1.2d-63) then
        tmp = (z * x) * y
    else if (t <= 1.05d+132) then
        tmp = -b * (c * z)
    else
        tmp = (-t * x) * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -4.8e+38) {
		tmp = (j * t) * c;
	} else if (t <= 1.2e-63) {
		tmp = (z * x) * y;
	} else if (t <= 1.05e+132) {
		tmp = -b * (c * z);
	} else {
		tmp = (-t * x) * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -4.8e+38:
		tmp = (j * t) * c
	elif t <= 1.2e-63:
		tmp = (z * x) * y
	elif t <= 1.05e+132:
		tmp = -b * (c * z)
	else:
		tmp = (-t * x) * a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -4.8e+38)
		tmp = Float64(Float64(j * t) * c);
	elseif (t <= 1.2e-63)
		tmp = Float64(Float64(z * x) * y);
	elseif (t <= 1.05e+132)
		tmp = Float64(Float64(-b) * Float64(c * z));
	else
		tmp = Float64(Float64(Float64(-t) * x) * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -4.8e+38)
		tmp = (j * t) * c;
	elseif (t <= 1.2e-63)
		tmp = (z * x) * y;
	elseif (t <= 1.05e+132)
		tmp = -b * (c * z);
	else
		tmp = (-t * x) * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -4.8e+38], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[t, 1.2e-63], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 1.05e+132], N[((-b) * N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[((-t) * x), $MachinePrecision] * a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.80000000000000035e38

   1. Initial program 47.6%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. flip-- N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

      9. lift--.f64 N/A

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

      10. lower-/.f64 47.6

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

      11. lift--.f64 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

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

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

      17. lower-fma.f64 N/A

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

      18. lower-neg.f64 47.6

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

   4. Applied rewrites 47.6%

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

   5. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. 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. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 54.2

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

   7. Applied rewrites 54.2%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 46.3%

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

   if -4.80000000000000035e38 < t < 1.2e-63

   1. Initial program 77.2%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. neg-mul-1 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 45.0

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

   5. Applied rewrites 45.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 32.4%

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

   10. Applied rewrites 32.4%

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

   if 1.2e-63 < t < 1.04999999999999997e132

   1. Initial program 78.0%

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

   3. Taylor expanded in z around 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. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. neg-mul-1 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 43.5

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

   5. Applied rewrites 43.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 33.6%

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

   if 1.04999999999999997e132 < t

   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 i around 0

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

      1. associate--l+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r+ N/A

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

      5. sub-neg N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

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

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 70.7%

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

   6. Taylor expanded in j around 0

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

   8. Applied rewrites 62.9%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 55.4%

       \[\leadsto \left(\left(-t\right) \cdot x\right) \cdot a \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+38}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-63}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+132}:\\ \;\;\;\;\left(-b\right) \cdot \left(c \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-t\right) \cdot x\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 30.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+38} \lor \neg \left(t \leq 4.45 \cdot 10^{+42}\right):\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -4.8e+38) (not (<= t 4.45e+42))) (* (* j t) c) (* (* z x) y)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -4.8e+38) || !(t <= 4.45e+42)) {
		tmp = (j * t) * c;
	} else {
		tmp = (z * x) * y;
	}
	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 ((t <= (-4.8d+38)) .or. (.not. (t <= 4.45d+42))) then
        tmp = (j * t) * c
    else
        tmp = (z * x) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -4.8e+38) || !(t <= 4.45e+42)) {
		tmp = (j * t) * c;
	} else {
		tmp = (z * x) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -4.8e+38) or not (t <= 4.45e+42):
		tmp = (j * t) * c
	else:
		tmp = (z * x) * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -4.8e+38) || !(t <= 4.45e+42))
		tmp = Float64(Float64(j * t) * c);
	else
		tmp = Float64(Float64(z * x) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -4.8e+38) || ~((t <= 4.45e+42)))
		tmp = (j * t) * c;
	else
		tmp = (z * x) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -4.8e+38], N[Not[LessEqual[t, 4.45e+42]], $MachinePrecision]], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.80000000000000035e38 or 4.44999999999999988e42 < t

   1. Initial program 57.0%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. flip-- N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

      9. lift--.f64 N/A

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

      10. lower-/.f64 57.0

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

      11. lift--.f64 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

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

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

      17. lower-fma.f64 N/A

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

      18. lower-neg.f64 57.0

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

   4. Applied rewrites 57.0%

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

   5. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. 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. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 55.1

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

   7. Applied rewrites 55.1%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 42.9%

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

   if -4.80000000000000035e38 < t < 4.44999999999999988e42

   1. Initial program 79.1%

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

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. neg-mul-1 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 44.9

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

   5. Applied rewrites 44.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 30.7%

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

   10. Applied rewrites 30.7%

       \[\leadsto \left(z \cdot x\right) \cdot y \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+38} \lor \neg \left(t \leq 4.45 \cdot 10^{+42}\right):\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{-5} \lor \neg \left(a \leq 1.55 \cdot 10^{+128}\right):\\ \;\;\;\;\left(b \cdot a\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -1.55e-5) (not (<= a 1.55e+128))) (* (* b a) i) (* (* z x) y)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.55e-5) || !(a <= 1.55e+128)) {
		tmp = (b * a) * i;
	} else {
		tmp = (z * x) * y;
	}
	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 <= (-1.55d-5)) .or. (.not. (a <= 1.55d+128))) then
        tmp = (b * a) * i
    else
        tmp = (z * x) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.55e-5) || !(a <= 1.55e+128)) {
		tmp = (b * a) * i;
	} else {
		tmp = (z * x) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -1.55e-5) or not (a <= 1.55e+128):
		tmp = (b * a) * i
	else:
		tmp = (z * x) * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -1.55e-5) || !(a <= 1.55e+128))
		tmp = Float64(Float64(b * a) * i);
	else
		tmp = Float64(Float64(z * x) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -1.55e-5) || ~((a <= 1.55e+128)))
		tmp = (b * a) * i;
	else
		tmp = (z * x) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -1.55e-5], N[Not[LessEqual[a, 1.55e+128]], $MachinePrecision]], N[(N[(b * a), $MachinePrecision] * i), $MachinePrecision], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.55000000000000007e-5 or 1.55000000000000002e128 < a

   1. Initial program 56.0%

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

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      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 52.3

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

   5. Applied rewrites 52.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 41.1%

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

   if -1.55000000000000007e-5 < a < 1.55000000000000002e128

   1. Initial program 78.8%

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

   3. Taylor expanded in 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. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. neg-mul-1 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 46.2

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

   5. Applied rewrites 46.2%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 26.0%

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

   10. Applied rewrites 29.2%

       \[\leadsto \left(z \cdot x\right) \cdot y \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{-5} \lor \neg \left(a \leq 1.55 \cdot 10^{+128}\right):\\ \;\;\;\;\left(b \cdot a\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 28.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+115}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;y \leq 7.9 \cdot 10^{-134}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -3.3e+115)
   (* (* z y) x)
   (if (<= y 7.9e-134) (* (* i b) a) (* (* 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 (y <= -3.3e+115) {
		tmp = (z * y) * x;
	} else if (y <= 7.9e-134) {
		tmp = (i * b) * a;
	} else {
		tmp = (y * x) * z;
	}
	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 (y <= (-3.3d+115)) then
        tmp = (z * y) * x
    else if (y <= 7.9d-134) then
        tmp = (i * b) * a
    else
        tmp = (y * x) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -3.3e+115) {
		tmp = (z * y) * x;
	} else if (y <= 7.9e-134) {
		tmp = (i * b) * a;
	} else {
		tmp = (y * x) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -3.3e+115:
		tmp = (z * y) * x
	elif y <= 7.9e-134:
		tmp = (i * b) * a
	else:
		tmp = (y * x) * z
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -3.3e+115)
		tmp = Float64(Float64(z * y) * x);
	elseif (y <= 7.9e-134)
		tmp = Float64(Float64(i * b) * a);
	else
		tmp = Float64(Float64(y * x) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -3.3e+115)
		tmp = (z * y) * x;
	elseif (y <= 7.9e-134)
		tmp = (i * b) * a;
	else
		tmp = (y * x) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -3.3e+115], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 7.9e-134], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.30000000000000005e115

   1. Initial program 55.1%

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

   3. Taylor expanded in 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. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. neg-mul-1 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 39.9

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

   5. Applied rewrites 39.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 42.1%

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

   if -3.30000000000000005e115 < y < 7.8999999999999998e-134

   1. Initial program 76.6%

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

   3. Taylor expanded in 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. sub-neg N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      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 35.8

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

   5. Applied rewrites 35.8%

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

   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 28.3%

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

   if 7.8999999999999998e-134 < y

   1. Initial program 65.4%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. neg-mul-1 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 46.4

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

   5. Applied rewrites 46.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 36.1%

      \[\leadsto \left(y \cdot x\right) \cdot z \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 23: 28.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+115}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-134}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -3.3e+115)
   (* (* z y) x)
   (if (<= y 7.8e-134) (* (* i b) a) (* (* z x) y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -3.3e+115) {
		tmp = (z * y) * x;
	} else if (y <= 7.8e-134) {
		tmp = (i * b) * a;
	} else {
		tmp = (z * x) * y;
	}
	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 (y <= (-3.3d+115)) then
        tmp = (z * y) * x
    else if (y <= 7.8d-134) then
        tmp = (i * b) * a
    else
        tmp = (z * x) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -3.3e+115) {
		tmp = (z * y) * x;
	} else if (y <= 7.8e-134) {
		tmp = (i * b) * a;
	} else {
		tmp = (z * x) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -3.3e+115:
		tmp = (z * y) * x
	elif y <= 7.8e-134:
		tmp = (i * b) * a
	else:
		tmp = (z * x) * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -3.3e+115)
		tmp = Float64(Float64(z * y) * x);
	elseif (y <= 7.8e-134)
		tmp = Float64(Float64(i * b) * a);
	else
		tmp = Float64(Float64(z * x) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -3.3e+115)
		tmp = (z * y) * x;
	elseif (y <= 7.8e-134)
		tmp = (i * b) * a;
	else
		tmp = (z * x) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -3.3e+115], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 7.8e-134], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.30000000000000005e115

   1. Initial program 55.1%

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

   3. Taylor expanded in 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. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. neg-mul-1 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(b\right)}, c, x \cdot y\right) \cdot z \]

      9. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-b}, c, x \cdot y\right) \cdot z \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-b, c, \color{blue}{y \cdot x}\right) \cdot z \]

      11. lower-*.f64 39.9

          \[\leadsto \mathsf{fma}\left(-b, c, \color{blue}{y \cdot x}\right) \cdot z \]

   5. Applied rewrites 39.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z} \]

   6. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 42.1%

      \[\leadsto \left(z \cdot y\right) \cdot \color{blue}{x} \]

   if -3.30000000000000005e115 < y < 7.8000000000000002e-134

   1. Initial program 76.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. sub-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot b\right)\right)\right)\right)} \cdot i \]

      4. *-commutative N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(y \cdot j\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot b\right)\right)\right)\right) \cdot i \]

      5. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot y\right) \cdot j} + \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot b\right)\right)\right)\right) \cdot i \]

      6. mul-1-neg N/A

         \[\leadsto \left(\left(-1 \cdot y\right) \cdot j + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(a \cdot b\right)\right)}\right)\right)\right) \cdot i \]

      7. remove-double-neg N/A

         \[\leadsto \left(\left(-1 \cdot y\right) \cdot j + \color{blue}{a \cdot b}\right) \cdot i \]

      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 35.8

          \[\leadsto \mathsf{fma}\left(-y, j, \color{blue}{b \cdot a}\right) \cdot i \]

   5. Applied rewrites 35.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, j, b \cdot a\right) \cdot i} \]

   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 28.3%

      \[\leadsto \left(i \cdot b\right) \cdot \color{blue}{a} \]

   if 7.8000000000000002e-134 < y

   1. Initial program 65.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot y - b \cdot c\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot y - b \cdot c\right) \cdot z} \]

      3. sub-neg N/A

         \[\leadsto \color{blue}{\left(x \cdot y + \left(\mathsf{neg}\left(b \cdot c\right)\right)\right)} \cdot z \]

      4. mul-1-neg N/A

         \[\leadsto \left(x \cdot y + \color{blue}{-1 \cdot \left(b \cdot c\right)}\right) \cdot z \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot c\right) + x \cdot y\right)} \cdot z \]

      6. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot b\right) \cdot c} + x \cdot y\right) \cdot z \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot b, c, x \cdot y\right)} \cdot z \]

      8. neg-mul-1 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(b\right)}, c, x \cdot y\right) \cdot z \]

      9. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-b}, c, x \cdot y\right) \cdot z \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-b, c, \color{blue}{y \cdot x}\right) \cdot z \]

      11. lower-*.f64 46.4

          \[\leadsto \mathsf{fma}\left(-b, c, \color{blue}{y \cdot x}\right) \cdot z \]

   5. Applied rewrites 46.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z} \]

   6. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 35.0%

      \[\leadsto \left(z \cdot y\right) \cdot \color{blue}{x} \]
   9. Step-by-step derivation

   10. Applied rewrites 35.0%

       \[\leadsto \left(z \cdot x\right) \cdot y \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 24: 22.2% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \left(z \cdot x\right) \cdot y \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* (* z x) y))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return (z * x) * 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 = (z * x) * 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 (z * x) * y;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return (z * x) * y

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(z * x) * y)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = (z * x) * y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision]

Derivation

1. Initial program 69.3%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Add Preprocessing

3. Taylor expanded in z around 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. sub-neg N/A

      \[\leadsto \color{blue}{\left(x \cdot y + \left(\mathsf{neg}\left(b \cdot c\right)\right)\right)} \cdot z \]

   4. mul-1-neg N/A

      \[\leadsto \left(x \cdot y + \color{blue}{-1 \cdot \left(b \cdot c\right)}\right) \cdot z \]

   5. +-commutative N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot c\right) + x \cdot y\right)} \cdot z \]

   6. associate-*r* N/A

      \[\leadsto \left(\color{blue}{\left(-1 \cdot b\right) \cdot c} + x \cdot y\right) \cdot z \]

   7. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot b, c, x \cdot y\right)} \cdot z \]

   8. neg-mul-1 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(b\right)}, c, x \cdot y\right) \cdot z \]

   9. lower-neg.f64 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{-b}, c, x \cdot y\right) \cdot z \]

   10. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(-b, c, \color{blue}{y \cdot x}\right) \cdot z \]

   11. lower-*.f64 37.7

       \[\leadsto \mathsf{fma}\left(-b, c, \color{blue}{y \cdot x}\right) \cdot z \]

5. Applied rewrites 37.7%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z} \]

6. Taylor expanded in x around inf

   \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
7. Step-by-step derivation

8. Applied rewrites 22.1%

   \[\leadsto \left(z \cdot y\right) \cdot \color{blue}{x} \]
9. Step-by-step derivation

10. Applied rewrites 22.9%

    \[\leadsto \left(z \cdot x\right) \cdot y \]
11. Add Preprocessing

Developer Target 1: 68.9% 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 2024324 
(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)))))