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

Percentage Accurate: 74.0% → 83.0%

Time: 16.8s

Alternatives: 24

Speedup: 0.5×

• 58.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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) - (t * i)))) + (j * ((c * a) - (y * i)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 74.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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) - (t * i)))) + (j * ((c * a) - (y * i)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 83.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 59.8

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

   5. Applied rewrites 59.8%

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

Alternative 2: 68.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i\\ \mathbf{if}\;i \leq -4.2 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 7 \cdot 10^{-269}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(c \cdot b\right) \cdot z\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;i \leq 5.7 \cdot 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-x, t, j \cdot c\right), a, \mathsf{fma}\left(-z, c, i \cdot t\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- y) j (* b t)) i)))
   (if (<= i -4.2e+107)
     t_1
     (if (<= i 7e-269)
       (+
        (- (* x (- (* y z) (* t a))) (* (* c b) z))
        (* j (- (* c a) (* y i))))
       (if (<= i 5.7e+53)
         (fma (fma (- x) t (* j c)) a (* (fma (- z) c (* i t)) b))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-y, j, (b * t)) * i;
	double tmp;
	if (i <= -4.2e+107) {
		tmp = t_1;
	} else if (i <= 7e-269) {
		tmp = ((x * ((y * z) - (t * a))) - ((c * b) * z)) + (j * ((c * a) - (y * i)));
	} else if (i <= 5.7e+53) {
		tmp = fma(fma(-x, t, (j * c)), a, (fma(-z, c, (i * t)) * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-y), j, Float64(b * t)) * i)
	tmp = 0.0
	if (i <= -4.2e+107)
		tmp = t_1;
	elseif (i <= 7e-269)
		tmp = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(c * b) * z)) + Float64(j * Float64(Float64(c * a) - Float64(y * i))));
	elseif (i <= 5.7e+53)
		tmp = fma(fma(Float64(-x), t, Float64(j * c)), a, Float64(fma(Float64(-z), c, Float64(i * t)) * b));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-y) * j + N[(b * t), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[i, -4.2e+107], t$95$1, If[LessEqual[i, 7e-269], N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(c * b), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.7e+53], N[(N[((-x) * t + N[(j * c), $MachinePrecision]), $MachinePrecision] * a + N[(N[((-z) * c + N[(i * t), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -4.1999999999999999e107 or 5.70000000000000017e53 < i

   1. Initial program 53.4%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 71.5

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

   5. Applied rewrites 71.5%

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

   if -4.1999999999999999e107 < i < 7.00000000000000038e-269

   1. Initial program 86.2%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 85.1

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

   5. Applied rewrites 85.1%

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

   if 7.00000000000000038e-269 < i < 5.70000000000000017e53

   1. Initial program 82.8%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 80.5%

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

Alternative 3: 67.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i\\ \mathbf{if}\;i \leq -8.8 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 5.4 \cdot 10^{-241}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-b, c, y \cdot x\right), z, \mathsf{fma}\left(-x, t, c \cdot j\right) \cdot a\right)\\ \mathbf{elif}\;i \leq 5.7 \cdot 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-x, t, j \cdot c\right), a, \mathsf{fma}\left(-z, c, i \cdot t\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- y) j (* b t)) i)))
   (if (<= i -8.8e+105)
     t_1
     (if (<= i 5.4e-241)
       (fma (fma (- b) c (* y x)) z (* (fma (- x) t (* c j)) a))
       (if (<= i 5.7e+53)
         (fma (fma (- x) t (* j c)) a (* (fma (- z) c (* i t)) b))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-y, j, (b * t)) * i;
	double tmp;
	if (i <= -8.8e+105) {
		tmp = t_1;
	} else if (i <= 5.4e-241) {
		tmp = fma(fma(-b, c, (y * x)), z, (fma(-x, t, (c * j)) * a));
	} else if (i <= 5.7e+53) {
		tmp = fma(fma(-x, t, (j * c)), a, (fma(-z, c, (i * t)) * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-y), j, Float64(b * t)) * i)
	tmp = 0.0
	if (i <= -8.8e+105)
		tmp = t_1;
	elseif (i <= 5.4e-241)
		tmp = fma(fma(Float64(-b), c, Float64(y * x)), z, Float64(fma(Float64(-x), t, Float64(c * j)) * a));
	elseif (i <= 5.7e+53)
		tmp = fma(fma(Float64(-x), t, Float64(j * c)), a, Float64(fma(Float64(-z), c, Float64(i * t)) * b));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-y) * j + N[(b * t), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[i, -8.8e+105], t$95$1, If[LessEqual[i, 5.4e-241], N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z + N[(N[((-x) * t + N[(c * j), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.7e+53], N[(N[((-x) * t + N[(j * c), $MachinePrecision]), $MachinePrecision] * a + N[(N[((-z) * c + N[(i * t), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -8.80000000000000027e105 or 5.70000000000000017e53 < i

   1. Initial program 53.4%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 71.5

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

   5. Applied rewrites 71.5%

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

   if -8.80000000000000027e105 < i < 5.3999999999999998e-241

   1. Initial program 86.4%

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

   3. Taylor expanded in a around -inf

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

   5. Applied rewrites 79.1%

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

   6. Taylor expanded in i around 0

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

   8. Applied rewrites 78.5%

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

   if 5.3999999999999998e-241 < i < 5.70000000000000017e53

   1. Initial program 82.1%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 79.5%

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

Alternative 4: 68.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -8.8 \cdot 10^{+105} \lor \neg \left(i \leq 1.45 \cdot 10^{+28}\right):\\ \;\;\;\;\mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-b, c, y \cdot x\right), z, \mathsf{fma}\left(-x, t, c \cdot j\right) \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -8.8e+105) (not (<= i 1.45e+28)))
   (* (fma (- y) j (* b t)) i)
   (fma (fma (- b) c (* y x)) z (* (fma (- x) t (* c j)) 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 ((i <= -8.8e+105) || !(i <= 1.45e+28)) {
		tmp = fma(-y, j, (b * t)) * i;
	} else {
		tmp = fma(fma(-b, c, (y * x)), z, (fma(-x, t, (c * j)) * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -8.8e+105) || !(i <= 1.45e+28))
		tmp = Float64(fma(Float64(-y), j, Float64(b * t)) * i);
	else
		tmp = fma(fma(Float64(-b), c, Float64(y * x)), z, Float64(fma(Float64(-x), t, Float64(c * j)) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -8.8e+105], N[Not[LessEqual[i, 1.45e+28]], $MachinePrecision]], N[(N[((-y) * j + N[(b * t), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision], N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z + N[(N[((-x) * t + N[(c * j), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -8.80000000000000027e105 or 1.4500000000000001e28 < i

   1. Initial program 54.1%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 71.3

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

   5. Applied rewrites 71.3%

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

   if -8.80000000000000027e105 < i < 1.4500000000000001e28

   1. Initial program 85.4%

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

   3. Taylor expanded in a around -inf

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

   5. Applied rewrites 77.2%

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

   6. Taylor expanded in i around 0

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

   8. Applied rewrites 72.9%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8.8 \cdot 10^{+105} \lor \neg \left(i \leq 1.45 \cdot 10^{+28}\right):\\ \;\;\;\;\mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-b, c, y \cdot x\right), z, \mathsf{fma}\left(-x, t, c \cdot j\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot y - a \cdot t\right) \cdot x\\ t_2 := \mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i\\ \mathbf{if}\;i \leq -7.2 \cdot 10^{+105}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -2.8 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z\\ \mathbf{elif}\;i \leq -1.26 \cdot 10^{-250}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{-84}:\\ \;\;\;\;\mathsf{fma}\left(j, a, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;i \leq 7 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- (* z y) (* a t)) x)) (t_2 (* (fma (- y) j (* b t)) i)))
   (if (<= i -7.2e+105)
     t_2
     (if (<= i -2.8e+31)
       (* (fma (- c) b (* y x)) z)
       (if (<= i -1.26e-250)
         t_1
         (if (<= i 4.2e-84)
           (* (fma j a (* (- b) z)) c)
           (if (<= i 7e+27) 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 = ((z * y) - (a * t)) * x;
	double t_2 = fma(-y, j, (b * t)) * i;
	double tmp;
	if (i <= -7.2e+105) {
		tmp = t_2;
	} else if (i <= -2.8e+31) {
		tmp = fma(-c, b, (y * x)) * z;
	} else if (i <= -1.26e-250) {
		tmp = t_1;
	} else if (i <= 4.2e-84) {
		tmp = fma(j, a, (-b * z)) * c;
	} else if (i <= 7e+27) {
		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(z * y) - Float64(a * t)) * x)
	t_2 = Float64(fma(Float64(-y), j, Float64(b * t)) * i)
	tmp = 0.0
	if (i <= -7.2e+105)
		tmp = t_2;
	elseif (i <= -2.8e+31)
		tmp = Float64(fma(Float64(-c), b, Float64(y * x)) * z);
	elseif (i <= -1.26e-250)
		tmp = t_1;
	elseif (i <= 4.2e-84)
		tmp = Float64(fma(j, a, Float64(Float64(-b) * z)) * c);
	elseif (i <= 7e+27)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-y) * j + N[(b * t), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[i, -7.2e+105], t$95$2, If[LessEqual[i, -2.8e+31], N[(N[((-c) * b + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[i, -1.26e-250], t$95$1, If[LessEqual[i, 4.2e-84], N[(N[(j * a + N[((-b) * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[i, 7e+27], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -7.1999999999999998e105 or 7.0000000000000004e27 < i

   1. Initial program 54.1%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 71.3

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

   5. Applied rewrites 71.3%

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

   if -7.1999999999999998e105 < i < -2.80000000000000017e31

   1. Initial program 82.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

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

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

      10. lower-fma.f64 N/A

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

      11. lower-neg.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 65.0

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

   5. Applied rewrites 65.0%

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

   if -2.80000000000000017e31 < i < -1.26e-250 or 4.19999999999999996e-84 < i < 7.0000000000000004e27

   1. Initial program 88.2%

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

   3. Taylor expanded in a around -inf

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

   5. Applied rewrites 77.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 72.0%

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

   9. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 N/A

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

       4. *-commutative N/A

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

       5. lower-*.f64 N/A

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

       6. lower-*.f64 59.3

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

   11. Applied rewrites 59.3%

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

   if -1.26e-250 < i < 4.19999999999999996e-84

   1. Initial program 82.7%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 59.6

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

   5. Applied rewrites 59.6%

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

   7. Applied rewrites 59.6%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -7.2 \cdot 10^{+105}:\\ \;\;\;\;\mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i\\ \mathbf{elif}\;i \leq -2.8 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z\\ \mathbf{elif}\;i \leq -1.26 \cdot 10^{-250}:\\ \;\;\;\;\left(z \cdot y - a \cdot t\right) \cdot x\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{-84}:\\ \;\;\;\;\mathsf{fma}\left(j, a, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;i \leq 7 \cdot 10^{+27}:\\ \;\;\;\;\left(z \cdot y - a \cdot t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i\\ \mathbf{if}\;i \leq -8.2 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 6 \cdot 10^{-233}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-b, c, y \cdot x\right), z, \left(\left(-x\right) \cdot t\right) \cdot a\right)\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-x, t, c \cdot j\right), a, \left(y \cdot z\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- y) j (* b t)) i)))
   (if (<= i -8.2e+105)
     t_1
     (if (<= i 6e-233)
       (fma (fma (- b) c (* y x)) z (* (* (- x) t) a))
       (if (<= i 9.5e+27) (fma (fma (- x) t (* c j)) a (* (* y z) 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(-y, j, (b * t)) * i;
	double tmp;
	if (i <= -8.2e+105) {
		tmp = t_1;
	} else if (i <= 6e-233) {
		tmp = fma(fma(-b, c, (y * x)), z, ((-x * t) * a));
	} else if (i <= 9.5e+27) {
		tmp = fma(fma(-x, t, (c * j)), a, ((y * z) * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-y), j, Float64(b * t)) * i)
	tmp = 0.0
	if (i <= -8.2e+105)
		tmp = t_1;
	elseif (i <= 6e-233)
		tmp = fma(fma(Float64(-b), c, Float64(y * x)), z, Float64(Float64(Float64(-x) * t) * a));
	elseif (i <= 9.5e+27)
		tmp = fma(fma(Float64(-x), t, Float64(c * j)), a, Float64(Float64(y * z) * 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[((-y) * j + N[(b * t), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[i, -8.2e+105], t$95$1, If[LessEqual[i, 6e-233], N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z + N[(N[((-x) * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 9.5e+27], N[(N[((-x) * t + N[(c * j), $MachinePrecision]), $MachinePrecision] * a + N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -8.2000000000000005e105 or 9.4999999999999997e27 < i

   1. Initial program 54.1%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 71.3

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

   5. Applied rewrites 71.3%

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

   if -8.2000000000000005e105 < i < 5.99999999999999997e-233

   1. Initial program 85.8%

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

   3. Taylor expanded in a around -inf

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

   5. Applied rewrites 78.8%

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

   6. Taylor expanded in i around 0

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

   8. Applied rewrites 77.1%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 68.4%

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

   if 5.99999999999999997e-233 < i < 9.4999999999999997e27

   1. Initial program 84.8%

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

   3. Taylor expanded in i around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. distribute-rgt-in N/A

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

      11. mul-1-neg N/A

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

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

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

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

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

      14. +-commutative N/A

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

      15. *-commutative N/A

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

   5. Applied rewrites 62.5%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 62.8%

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

Alternative 7: 61.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i\\ \mathbf{if}\;i \leq -8.2 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.9 \cdot 10^{-234}:\\ \;\;\;\;\mathsf{fma}\left(\left(-b\right) \cdot z, c, \mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\right)\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-x, t, c \cdot j\right), a, \left(y \cdot z\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- y) j (* b t)) i)))
   (if (<= i -8.2e+105)
     t_1
     (if (<= i 1.9e-234)
       (fma (* (- b) z) c (* (fma (- a) t (* z y)) x))
       (if (<= i 9.5e+27) (fma (fma (- x) t (* c j)) a (* (* y z) 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(-y, j, (b * t)) * i;
	double tmp;
	if (i <= -8.2e+105) {
		tmp = t_1;
	} else if (i <= 1.9e-234) {
		tmp = fma((-b * z), c, (fma(-a, t, (z * y)) * x));
	} else if (i <= 9.5e+27) {
		tmp = fma(fma(-x, t, (c * j)), a, ((y * z) * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-y), j, Float64(b * t)) * i)
	tmp = 0.0
	if (i <= -8.2e+105)
		tmp = t_1;
	elseif (i <= 1.9e-234)
		tmp = fma(Float64(Float64(-b) * z), c, Float64(fma(Float64(-a), t, Float64(z * y)) * x));
	elseif (i <= 9.5e+27)
		tmp = fma(fma(Float64(-x), t, Float64(c * j)), a, Float64(Float64(y * z) * 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[((-y) * j + N[(b * t), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[i, -8.2e+105], t$95$1, If[LessEqual[i, 1.9e-234], N[(N[((-b) * z), $MachinePrecision] * c + N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 9.5e+27], N[(N[((-x) * t + N[(c * j), $MachinePrecision]), $MachinePrecision] * a + N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -8.2000000000000005e105 or 9.4999999999999997e27 < i

   1. Initial program 54.1%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 71.3

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

   5. Applied rewrites 71.3%

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

   if -8.2000000000000005e105 < i < 1.89999999999999992e-234

   1. Initial program 86.6%

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

   3. Taylor expanded in i around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. distribute-rgt-in N/A

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

      11. mul-1-neg N/A

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

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

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

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

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

      14. +-commutative N/A

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

      15. *-commutative N/A

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

   5. Applied rewrites 77.7%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 67.4%

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

   if 1.89999999999999992e-234 < i < 9.4999999999999997e27

   1. Initial program 83.2%

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

   3. Taylor expanded in i around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. distribute-rgt-in N/A

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

      11. mul-1-neg N/A

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

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

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

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

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

      14. +-commutative N/A

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

      15. *-commutative N/A

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

   5. Applied rewrites 61.4%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 61.6%

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

Alternative 8: 61.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i\\ \mathbf{if}\;i \leq -7.2 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -3.5 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-x, t, c \cdot j\right), a, \left(y \cdot z\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- y) j (* b t)) i)))
   (if (<= i -7.2e+105)
     t_1
     (if (<= i -3.5e+31)
       (* (fma (- c) b (* y x)) z)
       (if (<= i 9.5e+27) (fma (fma (- x) t (* c j)) a (* (* y z) 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(-y, j, (b * t)) * i;
	double tmp;
	if (i <= -7.2e+105) {
		tmp = t_1;
	} else if (i <= -3.5e+31) {
		tmp = fma(-c, b, (y * x)) * z;
	} else if (i <= 9.5e+27) {
		tmp = fma(fma(-x, t, (c * j)), a, ((y * z) * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-y), j, Float64(b * t)) * i)
	tmp = 0.0
	if (i <= -7.2e+105)
		tmp = t_1;
	elseif (i <= -3.5e+31)
		tmp = Float64(fma(Float64(-c), b, Float64(y * x)) * z);
	elseif (i <= 9.5e+27)
		tmp = fma(fma(Float64(-x), t, Float64(c * j)), a, Float64(Float64(y * z) * 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[((-y) * j + N[(b * t), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[i, -7.2e+105], t$95$1, If[LessEqual[i, -3.5e+31], N[(N[((-c) * b + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[i, 9.5e+27], N[(N[((-x) * t + N[(c * j), $MachinePrecision]), $MachinePrecision] * a + N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -7.1999999999999998e105 or 9.4999999999999997e27 < i

   1. Initial program 54.1%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 71.3

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

   5. Applied rewrites 71.3%

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

   if -7.1999999999999998e105 < i < -3.5e31

   1. Initial program 82.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

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

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

      10. lower-fma.f64 N/A

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

      11. lower-neg.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 65.0

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

   5. Applied rewrites 65.0%

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

   if -3.5e31 < i < 9.4999999999999997e27

   1. Initial program 85.8%

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

   3. Taylor expanded in i around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. distribute-rgt-in N/A

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

      11. mul-1-neg N/A

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

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

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

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

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

      14. +-commutative N/A

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

      15. *-commutative N/A

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

   5. Applied rewrites 72.1%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 61.2%

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

Alternative 9: 29.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot i\right) \cdot t\\ t_2 := \left(\left(-y\right) \cdot i\right) \cdot j\\ \mathbf{if}\;b \leq -1.65 \cdot 10^{+100}:\\ \;\;\;\;\left(\left(-b\right) \cdot c\right) \cdot z\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-300}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-142}:\\ \;\;\;\;a \cdot \left(\left(-x\right) \cdot t\right)\\ \mathbf{elif}\;b \leq 2.95 \cdot 10^{+128}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* b i) t)) (t_2 (* (* (- y) i) j)))
   (if (<= b -1.65e+100)
     (* (* (- b) c) z)
     (if (<= b -1.75e-25)
       t_1
       (if (<= b 6e-300)
         t_2
         (if (<= b 6.8e-142)
           (* a (* (- x) t))
           (if (<= b 2.95e+128) t_2 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 = (b * i) * t;
	double t_2 = (-y * i) * j;
	double tmp;
	if (b <= -1.65e+100) {
		tmp = (-b * c) * z;
	} else if (b <= -1.75e-25) {
		tmp = t_1;
	} else if (b <= 6e-300) {
		tmp = t_2;
	} else if (b <= 6.8e-142) {
		tmp = a * (-x * t);
	} else if (b <= 2.95e+128) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (b * i) * t
    t_2 = (-y * i) * j
    if (b <= (-1.65d+100)) then
        tmp = (-b * c) * z
    else if (b <= (-1.75d-25)) then
        tmp = t_1
    else if (b <= 6d-300) then
        tmp = t_2
    else if (b <= 6.8d-142) then
        tmp = a * (-x * t)
    else if (b <= 2.95d+128) then
        tmp = t_2
    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 = (b * i) * t;
	double t_2 = (-y * i) * j;
	double tmp;
	if (b <= -1.65e+100) {
		tmp = (-b * c) * z;
	} else if (b <= -1.75e-25) {
		tmp = t_1;
	} else if (b <= 6e-300) {
		tmp = t_2;
	} else if (b <= 6.8e-142) {
		tmp = a * (-x * t);
	} else if (b <= 2.95e+128) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (b * i) * t
	t_2 = (-y * i) * j
	tmp = 0
	if b <= -1.65e+100:
		tmp = (-b * c) * z
	elif b <= -1.75e-25:
		tmp = t_1
	elif b <= 6e-300:
		tmp = t_2
	elif b <= 6.8e-142:
		tmp = a * (-x * t)
	elif b <= 2.95e+128:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(b * i) * t)
	t_2 = Float64(Float64(Float64(-y) * i) * j)
	tmp = 0.0
	if (b <= -1.65e+100)
		tmp = Float64(Float64(Float64(-b) * c) * z);
	elseif (b <= -1.75e-25)
		tmp = t_1;
	elseif (b <= 6e-300)
		tmp = t_2;
	elseif (b <= 6.8e-142)
		tmp = Float64(a * Float64(Float64(-x) * t));
	elseif (b <= 2.95e+128)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (b * i) * t;
	t_2 = (-y * i) * j;
	tmp = 0.0;
	if (b <= -1.65e+100)
		tmp = (-b * c) * z;
	elseif (b <= -1.75e-25)
		tmp = t_1;
	elseif (b <= 6e-300)
		tmp = t_2;
	elseif (b <= 6.8e-142)
		tmp = a * (-x * t);
	elseif (b <= 2.95e+128)
		tmp = t_2;
	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[(b * i), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-y) * i), $MachinePrecision] * j), $MachinePrecision]}, If[LessEqual[b, -1.65e+100], N[(N[((-b) * c), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[b, -1.75e-25], t$95$1, If[LessEqual[b, 6e-300], t$95$2, If[LessEqual[b, 6.8e-142], N[(a * N[((-x) * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.95e+128], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.6500000000000001e100

   1. Initial program 79.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

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

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

      10. lower-fma.f64 N/A

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

      11. lower-neg.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 65.6

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

   5. Applied rewrites 65.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 62.9%

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

   if -1.6500000000000001e100 < b < -1.7500000000000001e-25 or 2.94999999999999993e128 < b

   1. Initial program 68.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

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

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

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

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

      6. associate-*r* N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 56.9

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

   5. Applied rewrites 56.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 43.7%

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

   if -1.7500000000000001e-25 < b < 6.00000000000000048e-300 or 6.80000000000000057e-142 < b < 2.94999999999999993e128

   1. Initial program 76.7%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 50.8

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

   5. Applied rewrites 50.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 38.1%

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

   if 6.00000000000000048e-300 < b < 6.80000000000000057e-142

   1. Initial program 59.7%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

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

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

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

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

      6. associate-*r* N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 44.3

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

   5. Applied rewrites 44.3%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 42.1%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+100}:\\ \;\;\;\;\left(\left(-b\right) \cdot c\right) \cdot z\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-25}:\\ \;\;\;\;\left(b \cdot i\right) \cdot t\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-300}:\\ \;\;\;\;\left(\left(-y\right) \cdot i\right) \cdot j\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-142}:\\ \;\;\;\;a \cdot \left(\left(-x\right) \cdot t\right)\\ \mathbf{elif}\;b \leq 2.95 \cdot 10^{+128}:\\ \;\;\;\;\left(\left(-y\right) \cdot i\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot i\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 29.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{+102}:\\ \;\;\;\;\left(j \cdot a\right) \cdot c\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{+41}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-142}:\\ \;\;\;\;\left(b \cdot i\right) \cdot t\\ \mathbf{elif}\;a \leq 4.15 \cdot 10^{-206}:\\ \;\;\;\;\left(-b\right) \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+47}:\\ \;\;\;\;\left(b \cdot t\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(-x\right) \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.46e+102)
   (* (* j a) c)
   (if (<= a -1.15e+41)
     (* (* x y) z)
     (if (<= a -4.7e-142)
       (* (* b i) t)
       (if (<= a 4.15e-206)
         (* (- b) (* z c))
         (if (<= a 1.2e+47) (* (* b t) i) (* a (* (- x) t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.46e+102) {
		tmp = (j * a) * c;
	} else if (a <= -1.15e+41) {
		tmp = (x * y) * z;
	} else if (a <= -4.7e-142) {
		tmp = (b * i) * t;
	} else if (a <= 4.15e-206) {
		tmp = -b * (z * c);
	} else if (a <= 1.2e+47) {
		tmp = (b * t) * i;
	} else {
		tmp = a * (-x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-1.46d+102)) then
        tmp = (j * a) * c
    else if (a <= (-1.15d+41)) then
        tmp = (x * y) * z
    else if (a <= (-4.7d-142)) then
        tmp = (b * i) * t
    else if (a <= 4.15d-206) then
        tmp = -b * (z * c)
    else if (a <= 1.2d+47) then
        tmp = (b * t) * i
    else
        tmp = a * (-x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.46e+102) {
		tmp = (j * a) * c;
	} else if (a <= -1.15e+41) {
		tmp = (x * y) * z;
	} else if (a <= -4.7e-142) {
		tmp = (b * i) * t;
	} else if (a <= 4.15e-206) {
		tmp = -b * (z * c);
	} else if (a <= 1.2e+47) {
		tmp = (b * t) * i;
	} else {
		tmp = a * (-x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.46e+102:
		tmp = (j * a) * c
	elif a <= -1.15e+41:
		tmp = (x * y) * z
	elif a <= -4.7e-142:
		tmp = (b * i) * t
	elif a <= 4.15e-206:
		tmp = -b * (z * c)
	elif a <= 1.2e+47:
		tmp = (b * t) * i
	else:
		tmp = a * (-x * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.46e+102)
		tmp = Float64(Float64(j * a) * c);
	elseif (a <= -1.15e+41)
		tmp = Float64(Float64(x * y) * z);
	elseif (a <= -4.7e-142)
		tmp = Float64(Float64(b * i) * t);
	elseif (a <= 4.15e-206)
		tmp = Float64(Float64(-b) * Float64(z * c));
	elseif (a <= 1.2e+47)
		tmp = Float64(Float64(b * t) * i);
	else
		tmp = Float64(a * Float64(Float64(-x) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.46e+102)
		tmp = (j * a) * c;
	elseif (a <= -1.15e+41)
		tmp = (x * y) * z;
	elseif (a <= -4.7e-142)
		tmp = (b * i) * t;
	elseif (a <= 4.15e-206)
		tmp = -b * (z * c);
	elseif (a <= 1.2e+47)
		tmp = (b * t) * i;
	else
		tmp = a * (-x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.46e+102], N[(N[(j * a), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[a, -1.15e+41], N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[a, -4.7e-142], N[(N[(b * i), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[a, 4.15e-206], N[((-b) * N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e+47], N[(N[(b * t), $MachinePrecision] * i), $MachinePrecision], N[(a * N[((-x) * t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.4599999999999999e102

   1. Initial program 52.4%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 46.3

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

   5. Applied rewrites 46.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 40.2%

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

   if -1.4599999999999999e102 < a < -1.1499999999999999e41

   1. Initial program 88.1%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

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

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

      10. lower-fma.f64 N/A

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

      11. lower-neg.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 65.8

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

   5. Applied rewrites 65.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 59.8%

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

   if -1.1499999999999999e41 < a < -4.6999999999999999e-142

   1. Initial program 67.6%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

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

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

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

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

      6. associate-*r* N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 44.1

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

   5. Applied rewrites 44.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 38.3%

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

   if -4.6999999999999999e-142 < a < 4.1500000000000002e-206

   1. Initial program 83.6%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 42.1

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

   5. Applied rewrites 42.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 40.6%

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

   if 4.1500000000000002e-206 < a < 1.20000000000000009e47

   1. Initial program 76.1%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

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

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

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

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

      6. associate-*r* N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 37.9

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

   5. Applied rewrites 37.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 29.7%

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

   10. Applied rewrites 31.5%

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

   if 1.20000000000000009e47 < a

   1. Initial program 68.7%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

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

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

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

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

      6. associate-*r* N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 58.1

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

   5. Applied rewrites 58.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 51.9%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{+102}:\\ \;\;\;\;\left(j \cdot a\right) \cdot c\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{+41}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-142}:\\ \;\;\;\;\left(b \cdot i\right) \cdot t\\ \mathbf{elif}\;a \leq 4.15 \cdot 10^{-206}:\\ \;\;\;\;\left(-b\right) \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+47}:\\ \;\;\;\;\left(b \cdot t\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(-x\right) \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+131}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot a\right) \cdot j\\ \mathbf{elif}\;y \leq -1.62 \cdot 10^{-19}:\\ \;\;\;\;\left(z \cdot y - a \cdot t\right) \cdot x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-237}:\\ \;\;\;\;\mathsf{fma}\left(j, a, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(i, b, \left(-x\right) \cdot a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -5.1e+131)
   (* (fma (- i) y (* c a)) j)
   (if (<= y -1.62e-19)
     (* (- (* z y) (* a t)) x)
     (if (<= y 9e-237)
       (* (fma j a (* (- b) z)) c)
       (if (<= y 5e+88)
         (* (fma i b (* (- x) a)) 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 (y <= -5.1e+131) {
		tmp = fma(-i, y, (c * a)) * j;
	} else if (y <= -1.62e-19) {
		tmp = ((z * y) - (a * t)) * x;
	} else if (y <= 9e-237) {
		tmp = fma(j, a, (-b * z)) * c;
	} else if (y <= 5e+88) {
		tmp = fma(i, b, (-x * a)) * 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 (y <= -5.1e+131)
		tmp = Float64(fma(Float64(-i), y, Float64(c * a)) * j);
	elseif (y <= -1.62e-19)
		tmp = Float64(Float64(Float64(z * y) - Float64(a * t)) * x);
	elseif (y <= 9e-237)
		tmp = Float64(fma(j, a, Float64(Float64(-b) * z)) * c);
	elseif (y <= 5e+88)
		tmp = Float64(fma(i, b, Float64(Float64(-x) * a)) * 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[LessEqual[y, -5.1e+131], N[(N[((-i) * y + N[(c * a), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[y, -1.62e-19], N[(N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 9e-237], N[(N[(j * a + N[((-b) * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[y, 5e+88], N[(N[(i * b + N[((-x) * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.1000000000000004e131

   1. Initial program 67.5%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 68.4

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

   5. Applied rewrites 68.4%

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

   if -5.1000000000000004e131 < y < -1.62000000000000009e-19

   1. Initial program 78.9%

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

   3. Taylor expanded in a around -inf

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

   5. Applied rewrites 82.3%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 69.4%

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

   9. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 N/A

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

       4. *-commutative N/A

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

       5. lower-*.f64 N/A

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

       6. lower-*.f64 55.4

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

   11. Applied rewrites 55.4%

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

   if -1.62000000000000009e-19 < y < 9.00000000000000019e-237

   1. Initial program 73.9%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 55.4

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

   5. Applied rewrites 55.4%

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

   7. Applied rewrites 53.6%

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

   if 9.00000000000000019e-237 < y < 4.99999999999999997e88

   1. Initial program 82.2%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

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

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

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

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

      6. associate-*r* N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 55.4

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

   5. Applied rewrites 55.4%

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

   7. Applied rewrites 56.8%

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

   if 4.99999999999999997e88 < y

   1. Initial program 54.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 79.8

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

   5. Applied rewrites 79.8%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+131}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot a\right) \cdot j\\ \mathbf{elif}\;y \leq -1.62 \cdot 10^{-19}:\\ \;\;\;\;\left(z \cdot y - a \cdot t\right) \cdot x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-237}:\\ \;\;\;\;\mathsf{fma}\left(j, a, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(i, b, \left(-x\right) \cdot a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, b, \left(-x\right) \cdot a\right) \cdot t\\ t_2 := \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{if}\;y \leq -7.7 \cdot 10^{+71}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-237}:\\ \;\;\;\;\mathsf{fma}\left(j, a, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma i b (* (- x) a)) t)) (t_2 (* (fma (- i) j (* z x)) y)))
   (if (<= y -7.7e+71)
     t_2
     (if (<= y -9e-304)
       t_1
       (if (<= y 9e-237)
         (* (fma j a (* (- b) z)) c)
         (if (<= y 5e+88) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(i, b, (-x * a)) * t;
	double t_2 = fma(-i, j, (z * x)) * y;
	double tmp;
	if (y <= -7.7e+71) {
		tmp = t_2;
	} else if (y <= -9e-304) {
		tmp = t_1;
	} else if (y <= 9e-237) {
		tmp = fma(j, a, (-b * z)) * c;
	} else if (y <= 5e+88) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(i, b, Float64(Float64(-x) * a)) * t)
	t_2 = Float64(fma(Float64(-i), j, Float64(z * x)) * y)
	tmp = 0.0
	if (y <= -7.7e+71)
		tmp = t_2;
	elseif (y <= -9e-304)
		tmp = t_1;
	elseif (y <= 9e-237)
		tmp = Float64(fma(j, a, Float64(Float64(-b) * z)) * c);
	elseif (y <= 5e+88)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * b + N[((-x) * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -7.7e+71], t$95$2, If[LessEqual[y, -9e-304], t$95$1, If[LessEqual[y, 9e-237], N[(N[(j * a + N[((-b) * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[y, 5e+88], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.70000000000000018e71 or 4.99999999999999997e88 < y

   1. Initial program 59.8%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 67.5

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

   5. Applied rewrites 67.5%

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

   if -7.70000000000000018e71 < y < -8.9999999999999995e-304 or 9.00000000000000019e-237 < y < 4.99999999999999997e88

   1. Initial program 82.3%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

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

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

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

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

      6. associate-*r* N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 52.2

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

   5. Applied rewrites 52.2%

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

   7. Applied rewrites 53.6%

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

   if -8.9999999999999995e-304 < y < 9.00000000000000019e-237

   1. Initial program 65.1%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 76.6

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

   5. Applied rewrites 76.6%

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

   7. Applied rewrites 76.6%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.7 \cdot 10^{+71}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-304}:\\ \;\;\;\;\mathsf{fma}\left(i, b, \left(-x\right) \cdot a\right) \cdot t\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-237}:\\ \;\;\;\;\mathsf{fma}\left(j, a, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(i, b, \left(-x\right) \cdot a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(j, a, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{if}\;c \leq -4.2 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -6800000:\\ \;\;\;\;\mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(i, b, \left(-x\right) \cdot a\right) \cdot t\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{+94}:\\ \;\;\;\;\left(z \cdot y - a \cdot t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma j a (* (- b) z)) c)))
   (if (<= c -4.2e+119)
     t_1
     (if (<= c -6800000.0)
       (* (fma (- c) b (* y x)) z)
       (if (<= c 1.3e+31)
         (* (fma i b (* (- x) a)) t)
         (if (<= c 4.7e+94) (* (- (* z y) (* a t)) x) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(j, a, (-b * z)) * c;
	double tmp;
	if (c <= -4.2e+119) {
		tmp = t_1;
	} else if (c <= -6800000.0) {
		tmp = fma(-c, b, (y * x)) * z;
	} else if (c <= 1.3e+31) {
		tmp = fma(i, b, (-x * a)) * t;
	} else if (c <= 4.7e+94) {
		tmp = ((z * y) - (a * t)) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(j, a, Float64(Float64(-b) * z)) * c)
	tmp = 0.0
	if (c <= -4.2e+119)
		tmp = t_1;
	elseif (c <= -6800000.0)
		tmp = Float64(fma(Float64(-c), b, Float64(y * x)) * z);
	elseif (c <= 1.3e+31)
		tmp = Float64(fma(i, b, Float64(Float64(-x) * a)) * t);
	elseif (c <= 4.7e+94)
		tmp = Float64(Float64(Float64(z * y) - Float64(a * t)) * x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * a + N[((-b) * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]}, If[LessEqual[c, -4.2e+119], t$95$1, If[LessEqual[c, -6800000.0], N[(N[((-c) * b + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[c, 1.3e+31], N[(N[(i * b + N[((-x) * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[c, 4.7e+94], N[(N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -4.19999999999999966e119 or 4.70000000000000017e94 < c

   1. Initial program 65.6%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 63.4

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

   5. Applied rewrites 63.4%

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

   7. Applied rewrites 63.4%

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

   if -4.19999999999999966e119 < c < -6.8e6

   1. Initial program 62.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

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

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

      10. lower-fma.f64 N/A

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

      11. lower-neg.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 56.8

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

   5. Applied rewrites 56.8%

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

   if -6.8e6 < c < 1.3e31

   1. Initial program 80.9%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

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

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

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

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

      6. associate-*r* N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 49.9

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

   5. Applied rewrites 49.9%

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

   7. Applied rewrites 51.6%

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

   if 1.3e31 < c < 4.70000000000000017e94

   1. Initial program 66.7%

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

   3. Taylor expanded in a around -inf

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

   5. Applied rewrites 66.5%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 74.9%

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

   9. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 N/A

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

       4. *-commutative N/A

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

       5. lower-*.f64 N/A

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

       6. lower-*.f64 75.1

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

   11. Applied rewrites 75.1%

       \[\leadsto \color{blue}{\left(z \cdot y - a \cdot t\right) \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.2 \cdot 10^{+119}:\\ \;\;\;\;\mathsf{fma}\left(j, a, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;c \leq -6800000:\\ \;\;\;\;\mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(i, b, \left(-x\right) \cdot a\right) \cdot t\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{+94}:\\ \;\;\;\;\left(z \cdot y - a \cdot t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, a, \left(-b\right) \cdot z\right) \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot y - a \cdot t\right) \cdot x\\ t_2 := \mathsf{fma}\left(j, a, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{if}\;c \leq -6.5 \cdot 10^{+120}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -6800000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(i, b, \left(-x\right) \cdot a\right) \cdot t\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- (* z y) (* a t)) x)) (t_2 (* (fma j a (* (- b) z)) c)))
   (if (<= c -6.5e+120)
     t_2
     (if (<= c -6800000.0)
       t_1
       (if (<= c 1.3e+31)
         (* (fma i b (* (- x) a)) t)
         (if (<= c 4.7e+94) 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 = ((z * y) - (a * t)) * x;
	double t_2 = fma(j, a, (-b * z)) * c;
	double tmp;
	if (c <= -6.5e+120) {
		tmp = t_2;
	} else if (c <= -6800000.0) {
		tmp = t_1;
	} else if (c <= 1.3e+31) {
		tmp = fma(i, b, (-x * a)) * t;
	} else if (c <= 4.7e+94) {
		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(z * y) - Float64(a * t)) * x)
	t_2 = Float64(fma(j, a, Float64(Float64(-b) * z)) * c)
	tmp = 0.0
	if (c <= -6.5e+120)
		tmp = t_2;
	elseif (c <= -6800000.0)
		tmp = t_1;
	elseif (c <= 1.3e+31)
		tmp = Float64(fma(i, b, Float64(Float64(-x) * a)) * t);
	elseif (c <= 4.7e+94)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * a + N[((-b) * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]}, If[LessEqual[c, -6.5e+120], t$95$2, If[LessEqual[c, -6800000.0], t$95$1, If[LessEqual[c, 1.3e+31], N[(N[(i * b + N[((-x) * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[c, 4.7e+94], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -6.4999999999999997e120 or 4.70000000000000017e94 < c

   1. Initial program 65.6%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 63.4

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

   5. Applied rewrites 63.4%

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

   7. Applied rewrites 63.4%

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

   if -6.4999999999999997e120 < c < -6.8e6 or 1.3e31 < c < 4.70000000000000017e94

   1. Initial program 64.0%

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

   3. Taylor expanded in a around -inf

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

   5. Applied rewrites 71.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 64.1%

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

   9. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 N/A

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

       4. *-commutative N/A

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

       5. lower-*.f64 N/A

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

       6. lower-*.f64 59.7

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

   11. Applied rewrites 59.7%

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

   if -6.8e6 < c < 1.3e31

   1. Initial program 80.9%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

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

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

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

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

      6. associate-*r* N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 49.9

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

   5. Applied rewrites 49.9%

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

   7. Applied rewrites 51.6%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.5 \cdot 10^{+120}:\\ \;\;\;\;\mathsf{fma}\left(j, a, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;c \leq -6800000:\\ \;\;\;\;\left(z \cdot y - a \cdot t\right) \cdot x\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(i, b, \left(-x\right) \cdot a\right) \cdot t\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{+94}:\\ \;\;\;\;\left(z \cdot y - a \cdot t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, a, \left(-b\right) \cdot z\right) \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{+102}:\\ \;\;\;\;\left(j \cdot a\right) \cdot c\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{+41}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-142}:\\ \;\;\;\;\left(b \cdot i\right) \cdot t\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+105}:\\ \;\;\;\;\left(\left(-b\right) \cdot c\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(-x\right) \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.46e+102)
   (* (* j a) c)
   (if (<= a -1.15e+41)
     (* (* x y) z)
     (if (<= a -5.2e-142)
       (* (* b i) t)
       (if (<= a 9e+105) (* (* (- b) c) z) (* a (* (- x) t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.46e+102) {
		tmp = (j * a) * c;
	} else if (a <= -1.15e+41) {
		tmp = (x * y) * z;
	} else if (a <= -5.2e-142) {
		tmp = (b * i) * t;
	} else if (a <= 9e+105) {
		tmp = (-b * c) * z;
	} else {
		tmp = a * (-x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-1.46d+102)) then
        tmp = (j * a) * c
    else if (a <= (-1.15d+41)) then
        tmp = (x * y) * z
    else if (a <= (-5.2d-142)) then
        tmp = (b * i) * t
    else if (a <= 9d+105) then
        tmp = (-b * c) * z
    else
        tmp = a * (-x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.46e+102) {
		tmp = (j * a) * c;
	} else if (a <= -1.15e+41) {
		tmp = (x * y) * z;
	} else if (a <= -5.2e-142) {
		tmp = (b * i) * t;
	} else if (a <= 9e+105) {
		tmp = (-b * c) * z;
	} else {
		tmp = a * (-x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.46e+102:
		tmp = (j * a) * c
	elif a <= -1.15e+41:
		tmp = (x * y) * z
	elif a <= -5.2e-142:
		tmp = (b * i) * t
	elif a <= 9e+105:
		tmp = (-b * c) * z
	else:
		tmp = a * (-x * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.46e+102)
		tmp = Float64(Float64(j * a) * c);
	elseif (a <= -1.15e+41)
		tmp = Float64(Float64(x * y) * z);
	elseif (a <= -5.2e-142)
		tmp = Float64(Float64(b * i) * t);
	elseif (a <= 9e+105)
		tmp = Float64(Float64(Float64(-b) * c) * z);
	else
		tmp = Float64(a * Float64(Float64(-x) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.46e+102)
		tmp = (j * a) * c;
	elseif (a <= -1.15e+41)
		tmp = (x * y) * z;
	elseif (a <= -5.2e-142)
		tmp = (b * i) * t;
	elseif (a <= 9e+105)
		tmp = (-b * c) * z;
	else
		tmp = a * (-x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.46e+102], N[(N[(j * a), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[a, -1.15e+41], N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[a, -5.2e-142], N[(N[(b * i), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[a, 9e+105], N[(N[((-b) * c), $MachinePrecision] * z), $MachinePrecision], N[(a * N[((-x) * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.4599999999999999e102

   1. Initial program 52.4%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 46.3

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

   5. Applied rewrites 46.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 40.2%

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

   if -1.4599999999999999e102 < a < -1.1499999999999999e41

   1. Initial program 88.1%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

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

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

      10. lower-fma.f64 N/A

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

      11. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-c}, b, x \cdot y\right) \cdot z \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-c, b, \color{blue}{y \cdot x}\right) \cdot z \]

      13. lower-*.f64 65.8

          \[\leadsto \mathsf{fma}\left(-c, b, \color{blue}{y \cdot x}\right) \cdot z \]

   5. Applied rewrites 65.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z} \]

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot y\right) \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 59.8%

      \[\leadsto \left(x \cdot y\right) \cdot z \]

   if -1.1499999999999999e41 < a < -5.1999999999999999e-142

   1. Initial program 67.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot t} \]

      3. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(\mathsf{neg}\left(b \cdot i\right)\right)}\right) \cdot t \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(\mathsf{neg}\left(b\right)\right) \cdot i}\right) \cdot t \]

      5. fp-cancel-sign-sub N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)} \cdot t \]

      6. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + b \cdot i\right) \cdot t \]

      7. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + b \cdot i\right) \cdot t \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, b \cdot i\right)} \cdot t \]

      9. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, b \cdot i\right) \cdot t \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \cdot t \]

      11. lower-*.f64 44.1

          \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \cdot t \]

   5. Applied rewrites 44.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t} \]

   6. Taylor expanded in x around 0

      \[\leadsto \left(b \cdot i\right) \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 38.3%

      \[\leadsto \left(b \cdot i\right) \cdot t \]

   if -5.1999999999999999e-142 < a < 9.0000000000000002e105

   1. Initial program 79.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot y - b \cdot c\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot y - b \cdot c\right) \cdot z} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(x \cdot y + \left(\mathsf{neg}\left(b\right)\right) \cdot c\right)} \cdot z \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \left(x \cdot y + \color{blue}{\left(\mathsf{neg}\left(b \cdot c\right)\right)}\right) \cdot z \]

      5. mul-1-neg N/A

         \[\leadsto \left(x \cdot y + \color{blue}{-1 \cdot \left(b \cdot c\right)}\right) \cdot z \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot c\right) + x \cdot y\right)} \cdot z \]

      7. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(b \cdot c\right)\right)} + x \cdot y\right) \cdot z \]

      8. *-commutative N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\color{blue}{c \cdot b}\right)\right) + x \cdot y\right) \cdot z \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(c\right)\right) \cdot b} + x \cdot y\right) \cdot z \]

      10. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(c\right), b, x \cdot y\right)} \cdot z \]

      11. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-c}, b, x \cdot y\right) \cdot z \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-c, b, \color{blue}{y \cdot x}\right) \cdot z \]

      13. lower-*.f64 49.7

          \[\leadsto \mathsf{fma}\left(-c, b, \color{blue}{y \cdot x}\right) \cdot z \]

   5. Applied rewrites 49.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z} \]

   6. Taylor expanded in x around 0

      \[\leadsto \left(-1 \cdot \left(b \cdot c\right)\right) \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 32.7%

      \[\leadsto \left(\left(-b\right) \cdot c\right) \cdot z \]

   if 9.0000000000000002e105 < a

   1. Initial program 66.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot t} \]

      3. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(\mathsf{neg}\left(b \cdot i\right)\right)}\right) \cdot t \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(\mathsf{neg}\left(b\right)\right) \cdot i}\right) \cdot t \]

      5. fp-cancel-sign-sub N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)} \cdot t \]

      6. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + b \cdot i\right) \cdot t \]

      7. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + b \cdot i\right) \cdot t \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, b \cdot i\right)} \cdot t \]

      9. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, b \cdot i\right) \cdot t \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \cdot t \]

      11. lower-*.f64 65.5

          \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \cdot t \]

   5. Applied rewrites 65.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t} \]

   6. Taylor expanded in x around inf

      \[\leadsto -1 \cdot \color{blue}{\left(a \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 57.9%

      \[\leadsto \left(-a\right) \cdot \color{blue}{\left(x \cdot t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{+102}:\\ \;\;\;\;\left(j \cdot a\right) \cdot c\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{+41}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-142}:\\ \;\;\;\;\left(b \cdot i\right) \cdot t\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+105}:\\ \;\;\;\;\left(\left(-b\right) \cdot c\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(-x\right) \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 42.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(-y\right) \cdot i\right) \cdot j\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+60}:\\ \;\;\;\;\left(z \cdot y - a \cdot t\right) \cdot x\\ \mathbf{elif}\;y \leq 1.76 \cdot 10^{+89}:\\ \;\;\;\;\mathsf{fma}\left(i, b, \left(-x\right) \cdot a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* (- y) i) j)))
   (if (<= y -1.25e+116)
     t_1
     (if (<= y -3.5e+60)
       (* (- (* z y) (* a t)) x)
       (if (<= y 1.76e+89) (* (fma i b (* (- x) a)) t) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (-y * i) * j;
	double tmp;
	if (y <= -1.25e+116) {
		tmp = t_1;
	} else if (y <= -3.5e+60) {
		tmp = ((z * y) - (a * t)) * x;
	} else if (y <= 1.76e+89) {
		tmp = fma(i, b, (-x * a)) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(-y) * i) * j)
	tmp = 0.0
	if (y <= -1.25e+116)
		tmp = t_1;
	elseif (y <= -3.5e+60)
		tmp = Float64(Float64(Float64(z * y) - Float64(a * t)) * x);
	elseif (y <= 1.76e+89)
		tmp = Float64(fma(i, b, Float64(Float64(-x) * a)) * t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-y) * i), $MachinePrecision] * j), $MachinePrecision]}, If[LessEqual[y, -1.25e+116], t$95$1, If[LessEqual[y, -3.5e+60], N[(N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 1.76e+89], N[(N[(i * b + N[((-x) * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25000000000000006e116 or 1.76000000000000007e89 < y

   1. Initial program 58.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot c - i \cdot y\right) \cdot j} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot c - i \cdot y\right) \cdot j} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(a \cdot c + \left(\mathsf{neg}\left(i\right)\right) \cdot y\right)} \cdot j \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(i\right)\right) \cdot y + a \cdot c\right)} \cdot j \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(i\right), y, a \cdot c\right)} \cdot j \]

      6. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-i}, y, a \cdot c\right) \cdot j \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-i, y, \color{blue}{c \cdot a}\right) \cdot j \]

      8. lower-*.f64 62.6

         \[\leadsto \mathsf{fma}\left(-i, y, \color{blue}{c \cdot a}\right) \cdot j \]

   5. Applied rewrites 62.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-i, y, c \cdot a\right) \cdot j} \]

   6. Taylor expanded in y around inf

      \[\leadsto \left(-1 \cdot \left(i \cdot y\right)\right) \cdot j \]
   7. Step-by-step derivation

   8. Applied rewrites 53.8%

      \[\leadsto \left(\left(-y\right) \cdot i\right) \cdot j \]

   if -1.25000000000000006e116 < y < -3.5000000000000002e60

   1. Initial program 78.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(-1 \cdot \left(c \cdot j\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{a} + t \cdot x\right)\right)\right)} \]

   5. Applied rewrites 85.9%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \mathsf{fma}\left(t, x, -\mathsf{fma}\left(j, c, \frac{\mathsf{fma}\left(\mathsf{fma}\left(-z, c, i \cdot t\right), b, \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\right)}{a}\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(t - \frac{y \cdot z}{a}\right)\right) + \frac{a \cdot \left(-1 \cdot \frac{i \cdot \left(j \cdot y\right)}{a} + \left(c \cdot j + \frac{b \cdot \left(-1 \cdot \left(c \cdot z\right) + i \cdot t\right)}{a}\right)\right)}{x}\right)} \]

   8. Applied rewrites 58.5%

      \[\leadsto \left(a \cdot \mathsf{fma}\left(-1, t - \frac{y \cdot z}{a}, \frac{\frac{\mathsf{fma}\left(\left(-j\right) \cdot y, i, \mathsf{fma}\left(-c, z, i \cdot t\right) \cdot b\right)}{a} + c \cdot j}{x}\right)\right) \cdot \color{blue}{x} \]

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

       2. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

       3. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right)} \cdot x \]

       4. *-commutative N/A

          \[\leadsto \left(\color{blue}{z \cdot y} - a \cdot t\right) \cdot x \]

       5. lower-*.f64 N/A

          \[\leadsto \left(\color{blue}{z \cdot y} - a \cdot t\right) \cdot x \]

       6. lower-*.f64 57.7

          \[\leadsto \left(z \cdot y - \color{blue}{a \cdot t}\right) \cdot x \]

   11. Applied rewrites 57.7%

       \[\leadsto \color{blue}{\left(z \cdot y - a \cdot t\right) \cdot x} \]

   if -3.5000000000000002e60 < y < 1.76000000000000007e89

   1. Initial program 79.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot t} \]

      3. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(\mathsf{neg}\left(b \cdot i\right)\right)}\right) \cdot t \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(\mathsf{neg}\left(b\right)\right) \cdot i}\right) \cdot t \]

      5. fp-cancel-sign-sub N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)} \cdot t \]

      6. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + b \cdot i\right) \cdot t \]

      7. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + b \cdot i\right) \cdot t \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, b \cdot i\right)} \cdot t \]

      9. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, b \cdot i\right) \cdot t \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \cdot t \]

      11. lower-*.f64 48.8

          \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \cdot t \]

   5. Applied rewrites 48.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t} \]
   6. Step-by-step derivation

   7. Applied rewrites 50.2%

      \[\leadsto \mathsf{fma}\left(i, b, x \cdot \left(-a\right)\right) \cdot t \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+116}:\\ \;\;\;\;\left(\left(-y\right) \cdot i\right) \cdot j\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+60}:\\ \;\;\;\;\left(z \cdot y - a \cdot t\right) \cdot x\\ \mathbf{elif}\;y \leq 1.76 \cdot 10^{+89}:\\ \;\;\;\;\mathsf{fma}\left(i, b, \left(-x\right) \cdot a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-y\right) \cdot i\right) \cdot j\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot a\right) \cdot c\\ \mathbf{if}\;c \leq -1.4 \cdot 10^{+122}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -250:\\ \;\;\;\;\left(x \cdot y\right) \cdot z\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{-25}:\\ \;\;\;\;\left(i \cdot t\right) \cdot b\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{+94}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* j a) c)))
   (if (<= c -1.4e+122)
     t_1
     (if (<= c -250.0)
       (* (* x y) z)
       (if (<= c 3.4e-25)
         (* (* i t) b)
         (if (<= c 4.5e+94) (* (* 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 = (j * a) * c;
	double tmp;
	if (c <= -1.4e+122) {
		tmp = t_1;
	} else if (c <= -250.0) {
		tmp = (x * y) * z;
	} else if (c <= 3.4e-25) {
		tmp = (i * t) * b;
	} else if (c <= 4.5e+94) {
		tmp = (z * y) * x;
	} 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 * a) * c
    if (c <= (-1.4d+122)) then
        tmp = t_1
    else if (c <= (-250.0d0)) then
        tmp = (x * y) * z
    else if (c <= 3.4d-25) then
        tmp = (i * t) * b
    else if (c <= 4.5d+94) then
        tmp = (z * y) * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * a) * c;
	double tmp;
	if (c <= -1.4e+122) {
		tmp = t_1;
	} else if (c <= -250.0) {
		tmp = (x * y) * z;
	} else if (c <= 3.4e-25) {
		tmp = (i * t) * b;
	} else if (c <= 4.5e+94) {
		tmp = (z * y) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * a) * c
	tmp = 0
	if c <= -1.4e+122:
		tmp = t_1
	elif c <= -250.0:
		tmp = (x * y) * z
	elif c <= 3.4e-25:
		tmp = (i * t) * b
	elif c <= 4.5e+94:
		tmp = (z * y) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * a) * c)
	tmp = 0.0
	if (c <= -1.4e+122)
		tmp = t_1;
	elseif (c <= -250.0)
		tmp = Float64(Float64(x * y) * z);
	elseif (c <= 3.4e-25)
		tmp = Float64(Float64(i * t) * b);
	elseif (c <= 4.5e+94)
		tmp = Float64(Float64(z * y) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * a) * c;
	tmp = 0.0;
	if (c <= -1.4e+122)
		tmp = t_1;
	elseif (c <= -250.0)
		tmp = (x * y) * z;
	elseif (c <= 3.4e-25)
		tmp = (i * t) * b;
	elseif (c <= 4.5e+94)
		tmp = (z * y) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * a), $MachinePrecision] * c), $MachinePrecision]}, If[LessEqual[c, -1.4e+122], t$95$1, If[LessEqual[c, -250.0], N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[c, 3.4e-25], N[(N[(i * t), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[c, 4.5e+94], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.4e122 or 4.49999999999999972e94 < c

   1. Initial program 65.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot j - b \cdot z\right) \cdot c} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot j - b \cdot z\right) \cdot c} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(a \cdot j + \left(\mathsf{neg}\left(b\right)\right) \cdot z\right)} \cdot c \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \left(a \cdot j + \color{blue}{\left(\mathsf{neg}\left(b \cdot z\right)\right)}\right) \cdot c \]

      5. mul-1-neg N/A

         \[\leadsto \left(a \cdot j + \color{blue}{-1 \cdot \left(b \cdot z\right)}\right) \cdot c \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot z\right) + a \cdot j\right)} \cdot c \]

      7. *-commutative N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(z \cdot b\right)} + a \cdot j\right) \cdot c \]

      8. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot z\right) \cdot b} + a \cdot j\right) \cdot c \]

      9. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot z, b, a \cdot j\right)} \cdot c \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(z\right)}, b, a \cdot j\right) \cdot c \]

      11. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-z}, b, a \cdot j\right) \cdot c \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-z, b, \color{blue}{j \cdot a}\right) \cdot c \]

      13. lower-*.f64 63.4

          \[\leadsto \mathsf{fma}\left(-z, b, \color{blue}{j \cdot a}\right) \cdot c \]

   5. Applied rewrites 63.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-z, b, j \cdot a\right) \cdot c} \]

   6. Taylor expanded in z around 0

      \[\leadsto \left(a \cdot j\right) \cdot c \]
   7. Step-by-step derivation

   8. Applied rewrites 36.1%

      \[\leadsto \left(j \cdot a\right) \cdot c \]

   if -1.4e122 < c < -250

   1. Initial program 60.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot y - b \cdot c\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot y - b \cdot c\right) \cdot z} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(x \cdot y + \left(\mathsf{neg}\left(b\right)\right) \cdot c\right)} \cdot z \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \left(x \cdot y + \color{blue}{\left(\mathsf{neg}\left(b \cdot c\right)\right)}\right) \cdot z \]

      5. mul-1-neg N/A

         \[\leadsto \left(x \cdot y + \color{blue}{-1 \cdot \left(b \cdot c\right)}\right) \cdot z \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot c\right) + x \cdot y\right)} \cdot z \]

      7. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(b \cdot c\right)\right)} + x \cdot y\right) \cdot z \]

      8. *-commutative N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\color{blue}{c \cdot b}\right)\right) + x \cdot y\right) \cdot z \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(c\right)\right) \cdot b} + x \cdot y\right) \cdot z \]

      10. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(c\right), b, x \cdot y\right)} \cdot z \]

      11. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-c}, b, x \cdot y\right) \cdot z \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-c, b, \color{blue}{y \cdot x}\right) \cdot z \]

      13. lower-*.f64 54.7

          \[\leadsto \mathsf{fma}\left(-c, b, \color{blue}{y \cdot x}\right) \cdot z \]

   5. Applied rewrites 54.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z} \]

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot y\right) \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 34.0%

      \[\leadsto \left(x \cdot y\right) \cdot z \]

   if -250 < c < 3.40000000000000002e-25

   1. Initial program 80.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot t} \]

      3. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(\mathsf{neg}\left(b \cdot i\right)\right)}\right) \cdot t \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(\mathsf{neg}\left(b\right)\right) \cdot i}\right) \cdot t \]

      5. fp-cancel-sign-sub N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)} \cdot t \]

      6. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + b \cdot i\right) \cdot t \]

      7. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + b \cdot i\right) \cdot t \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, b \cdot i\right)} \cdot t \]

      9. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, b \cdot i\right) \cdot t \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \cdot t \]

      11. lower-*.f64 50.3

          \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \cdot t \]

   5. Applied rewrites 50.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t} \]

   6. Taylor expanded in x around 0

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 30.7%

      \[\leadsto \left(i \cdot t\right) \cdot \color{blue}{b} \]

   if 3.40000000000000002e-25 < c < 4.49999999999999972e94

   1. Initial program 79.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot y - b \cdot c\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot y - b \cdot c\right) \cdot z} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(x \cdot y + \left(\mathsf{neg}\left(b\right)\right) \cdot c\right)} \cdot z \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \left(x \cdot y + \color{blue}{\left(\mathsf{neg}\left(b \cdot c\right)\right)}\right) \cdot z \]

      5. mul-1-neg N/A

         \[\leadsto \left(x \cdot y + \color{blue}{-1 \cdot \left(b \cdot c\right)}\right) \cdot z \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot c\right) + x \cdot y\right)} \cdot z \]

      7. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(b \cdot c\right)\right)} + x \cdot y\right) \cdot z \]

      8. *-commutative N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\color{blue}{c \cdot b}\right)\right) + x \cdot y\right) \cdot z \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(c\right)\right) \cdot b} + x \cdot y\right) \cdot z \]

      10. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(c\right), b, x \cdot y\right)} \cdot z \]

      11. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-c}, b, x \cdot y\right) \cdot z \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-c, b, \color{blue}{y \cdot x}\right) \cdot z \]

      13. lower-*.f64 54.4

          \[\leadsto \mathsf{fma}\left(-c, b, \color{blue}{y \cdot x}\right) \cdot z \]

   5. Applied rewrites 54.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z} \]

   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 46.5%

      \[\leadsto \left(z \cdot y\right) \cdot \color{blue}{x} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 18: 30.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{+102}:\\ \;\;\;\;\left(j \cdot a\right) \cdot c\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{+41}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+46}:\\ \;\;\;\;\left(b \cdot i\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(-x\right) \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.46e+102)
   (* (* j a) c)
   (if (<= a -1.15e+41)
     (* (* x y) z)
     (if (<= a 2.8e+46) (* (* b i) t) (* a (* (- x) t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.46e+102) {
		tmp = (j * a) * c;
	} else if (a <= -1.15e+41) {
		tmp = (x * y) * z;
	} else if (a <= 2.8e+46) {
		tmp = (b * i) * t;
	} else {
		tmp = a * (-x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-1.46d+102)) then
        tmp = (j * a) * c
    else if (a <= (-1.15d+41)) then
        tmp = (x * y) * z
    else if (a <= 2.8d+46) then
        tmp = (b * i) * t
    else
        tmp = a * (-x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.46e+102) {
		tmp = (j * a) * c;
	} else if (a <= -1.15e+41) {
		tmp = (x * y) * z;
	} else if (a <= 2.8e+46) {
		tmp = (b * i) * t;
	} else {
		tmp = a * (-x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.46e+102:
		tmp = (j * a) * c
	elif a <= -1.15e+41:
		tmp = (x * y) * z
	elif a <= 2.8e+46:
		tmp = (b * i) * t
	else:
		tmp = a * (-x * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.46e+102)
		tmp = Float64(Float64(j * a) * c);
	elseif (a <= -1.15e+41)
		tmp = Float64(Float64(x * y) * z);
	elseif (a <= 2.8e+46)
		tmp = Float64(Float64(b * i) * t);
	else
		tmp = Float64(a * Float64(Float64(-x) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.46e+102)
		tmp = (j * a) * c;
	elseif (a <= -1.15e+41)
		tmp = (x * y) * z;
	elseif (a <= 2.8e+46)
		tmp = (b * i) * t;
	else
		tmp = a * (-x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.46e+102], N[(N[(j * a), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[a, -1.15e+41], N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[a, 2.8e+46], N[(N[(b * i), $MachinePrecision] * t), $MachinePrecision], N[(a * N[((-x) * t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.4599999999999999e102

   1. Initial program 52.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot j - b \cdot z\right) \cdot c} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot j - b \cdot z\right) \cdot c} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(a \cdot j + \left(\mathsf{neg}\left(b\right)\right) \cdot z\right)} \cdot c \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \left(a \cdot j + \color{blue}{\left(\mathsf{neg}\left(b \cdot z\right)\right)}\right) \cdot c \]

      5. mul-1-neg N/A

         \[\leadsto \left(a \cdot j + \color{blue}{-1 \cdot \left(b \cdot z\right)}\right) \cdot c \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot z\right) + a \cdot j\right)} \cdot c \]

      7. *-commutative N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(z \cdot b\right)} + a \cdot j\right) \cdot c \]

      8. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot z\right) \cdot b} + a \cdot j\right) \cdot c \]

      9. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot z, b, a \cdot j\right)} \cdot c \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(z\right)}, b, a \cdot j\right) \cdot c \]

      11. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-z}, b, a \cdot j\right) \cdot c \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-z, b, \color{blue}{j \cdot a}\right) \cdot c \]

      13. lower-*.f64 46.3

          \[\leadsto \mathsf{fma}\left(-z, b, \color{blue}{j \cdot a}\right) \cdot c \]

   5. Applied rewrites 46.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-z, b, j \cdot a\right) \cdot c} \]

   6. Taylor expanded in z around 0

      \[\leadsto \left(a \cdot j\right) \cdot c \]
   7. Step-by-step derivation

   8. Applied rewrites 40.2%

      \[\leadsto \left(j \cdot a\right) \cdot c \]

   if -1.4599999999999999e102 < a < -1.1499999999999999e41

   1. Initial program 88.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot y - b \cdot c\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot y - b \cdot c\right) \cdot z} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(x \cdot y + \left(\mathsf{neg}\left(b\right)\right) \cdot c\right)} \cdot z \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \left(x \cdot y + \color{blue}{\left(\mathsf{neg}\left(b \cdot c\right)\right)}\right) \cdot z \]

      5. mul-1-neg N/A

         \[\leadsto \left(x \cdot y + \color{blue}{-1 \cdot \left(b \cdot c\right)}\right) \cdot z \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot c\right) + x \cdot y\right)} \cdot z \]

      7. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(b \cdot c\right)\right)} + x \cdot y\right) \cdot z \]

      8. *-commutative N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\color{blue}{c \cdot b}\right)\right) + x \cdot y\right) \cdot z \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(c\right)\right) \cdot b} + x \cdot y\right) \cdot z \]

      10. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(c\right), b, x \cdot y\right)} \cdot z \]

      11. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-c}, b, x \cdot y\right) \cdot z \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-c, b, \color{blue}{y \cdot x}\right) \cdot z \]

      13. lower-*.f64 65.8

          \[\leadsto \mathsf{fma}\left(-c, b, \color{blue}{y \cdot x}\right) \cdot z \]

   5. Applied rewrites 65.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z} \]

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot y\right) \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 59.8%

      \[\leadsto \left(x \cdot y\right) \cdot z \]

   if -1.1499999999999999e41 < a < 2.80000000000000018e46

   1. Initial program 76.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot t} \]

      3. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(\mathsf{neg}\left(b \cdot i\right)\right)}\right) \cdot t \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(\mathsf{neg}\left(b\right)\right) \cdot i}\right) \cdot t \]

      5. fp-cancel-sign-sub N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)} \cdot t \]

      6. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + b \cdot i\right) \cdot t \]

      7. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + b \cdot i\right) \cdot t \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, b \cdot i\right)} \cdot t \]

      9. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, b \cdot i\right) \cdot t \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \cdot t \]

      11. lower-*.f64 32.9

          \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \cdot t \]

   5. Applied rewrites 32.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t} \]

   6. Taylor expanded in x around 0

      \[\leadsto \left(b \cdot i\right) \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 27.7%

      \[\leadsto \left(b \cdot i\right) \cdot t \]

   if 2.80000000000000018e46 < a

   1. Initial program 68.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot t} \]

      3. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(\mathsf{neg}\left(b \cdot i\right)\right)}\right) \cdot t \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(\mathsf{neg}\left(b\right)\right) \cdot i}\right) \cdot t \]

      5. fp-cancel-sign-sub N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)} \cdot t \]

      6. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + b \cdot i\right) \cdot t \]

      7. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + b \cdot i\right) \cdot t \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, b \cdot i\right)} \cdot t \]

      9. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, b \cdot i\right) \cdot t \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \cdot t \]

      11. lower-*.f64 58.1

          \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \cdot t \]

   5. Applied rewrites 58.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t} \]

   6. Taylor expanded in x around inf

      \[\leadsto -1 \cdot \color{blue}{\left(a \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 51.9%

      \[\leadsto \left(-a\right) \cdot \color{blue}{\left(x \cdot t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{+102}:\\ \;\;\;\;\left(j \cdot a\right) \cdot c\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{+41}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+46}:\\ \;\;\;\;\left(b \cdot i\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(-x\right) \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 42.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -6 \cdot 10^{+105}:\\ \;\;\;\;\left(b \cdot i\right) \cdot t\\ \mathbf{elif}\;i \leq 1.55 \cdot 10^{+29}:\\ \;\;\;\;\left(z \cdot y - a \cdot t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-y\right) \cdot i\right) \cdot j\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -6e+105)
   (* (* b i) t)
   (if (<= i 1.55e+29) (* (- (* z y) (* a t)) x) (* (* (- y) i) j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -6e+105) {
		tmp = (b * i) * t;
	} else if (i <= 1.55e+29) {
		tmp = ((z * y) - (a * t)) * x;
	} else {
		tmp = (-y * i) * j;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-6d+105)) then
        tmp = (b * i) * t
    else if (i <= 1.55d+29) then
        tmp = ((z * y) - (a * t)) * x
    else
        tmp = (-y * i) * j
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -6e+105) {
		tmp = (b * i) * t;
	} else if (i <= 1.55e+29) {
		tmp = ((z * y) - (a * t)) * x;
	} else {
		tmp = (-y * i) * j;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -6e+105:
		tmp = (b * i) * t
	elif i <= 1.55e+29:
		tmp = ((z * y) - (a * t)) * x
	else:
		tmp = (-y * i) * j
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -6e+105)
		tmp = Float64(Float64(b * i) * t);
	elseif (i <= 1.55e+29)
		tmp = Float64(Float64(Float64(z * y) - Float64(a * t)) * x);
	else
		tmp = Float64(Float64(Float64(-y) * i) * j);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -6e+105)
		tmp = (b * i) * t;
	elseif (i <= 1.55e+29)
		tmp = ((z * y) - (a * t)) * x;
	else
		tmp = (-y * i) * j;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -6e+105], N[(N[(b * i), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[i, 1.55e+29], N[(N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[((-y) * i), $MachinePrecision] * j), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -6.0000000000000001e105

   1. Initial program 47.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot t} \]

      3. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(\mathsf{neg}\left(b \cdot i\right)\right)}\right) \cdot t \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(\mathsf{neg}\left(b\right)\right) \cdot i}\right) \cdot t \]

      5. fp-cancel-sign-sub N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)} \cdot t \]

      6. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + b \cdot i\right) \cdot t \]

      7. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + b \cdot i\right) \cdot t \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, b \cdot i\right)} \cdot t \]

      9. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, b \cdot i\right) \cdot t \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \cdot t \]

      11. lower-*.f64 52.4

          \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \cdot t \]

   5. Applied rewrites 52.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t} \]

   6. Taylor expanded in x around 0

      \[\leadsto \left(b \cdot i\right) \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 47.9%

      \[\leadsto \left(b \cdot i\right) \cdot t \]

   if -6.0000000000000001e105 < i < 1.5499999999999999e29

   1. Initial program 85.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(-1 \cdot \left(c \cdot j\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{a} + t \cdot x\right)\right)\right)} \]

   5. Applied rewrites 77.6%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \mathsf{fma}\left(t, x, -\mathsf{fma}\left(j, c, \frac{\mathsf{fma}\left(\mathsf{fma}\left(-z, c, i \cdot t\right), b, \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\right)}{a}\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(t - \frac{y \cdot z}{a}\right)\right) + \frac{a \cdot \left(-1 \cdot \frac{i \cdot \left(j \cdot y\right)}{a} + \left(c \cdot j + \frac{b \cdot \left(-1 \cdot \left(c \cdot z\right) + i \cdot t\right)}{a}\right)\right)}{x}\right)} \]

   8. Applied rewrites 68.2%

      \[\leadsto \left(a \cdot \mathsf{fma}\left(-1, t - \frac{y \cdot z}{a}, \frac{\frac{\mathsf{fma}\left(\left(-j\right) \cdot y, i, \mathsf{fma}\left(-c, z, i \cdot t\right) \cdot b\right)}{a} + c \cdot j}{x}\right)\right) \cdot \color{blue}{x} \]

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

       2. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

       3. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right)} \cdot x \]

       4. *-commutative N/A

          \[\leadsto \left(\color{blue}{z \cdot y} - a \cdot t\right) \cdot x \]

       5. lower-*.f64 N/A

          \[\leadsto \left(\color{blue}{z \cdot y} - a \cdot t\right) \cdot x \]

       6. lower-*.f64 43.9

          \[\leadsto \left(z \cdot y - \color{blue}{a \cdot t}\right) \cdot x \]

   11. Applied rewrites 43.9%

       \[\leadsto \color{blue}{\left(z \cdot y - a \cdot t\right) \cdot x} \]

   if 1.5499999999999999e29 < i

   1. Initial program 60.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot c - i \cdot y\right) \cdot j} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot c - i \cdot y\right) \cdot j} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(a \cdot c + \left(\mathsf{neg}\left(i\right)\right) \cdot y\right)} \cdot j \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(i\right)\right) \cdot y + a \cdot c\right)} \cdot j \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(i\right), y, a \cdot c\right)} \cdot j \]

      6. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-i}, y, a \cdot c\right) \cdot j \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-i, y, \color{blue}{c \cdot a}\right) \cdot j \]

      8. lower-*.f64 57.0

         \[\leadsto \mathsf{fma}\left(-i, y, \color{blue}{c \cdot a}\right) \cdot j \]

   5. Applied rewrites 57.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-i, y, c \cdot a\right) \cdot j} \]

   6. Taylor expanded in y around inf

      \[\leadsto \left(-1 \cdot \left(i \cdot y\right)\right) \cdot j \]
   7. Step-by-step derivation

   8. Applied rewrites 48.1%

      \[\leadsto \left(\left(-y\right) \cdot i\right) \cdot j \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 20: 29.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot i\right) \cdot t\\ \mathbf{if}\;i \leq -2.6 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -6.1 \cdot 10^{-74}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{-78}:\\ \;\;\;\;\left(c \cdot a\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* b i) t)))
   (if (<= i -2.6e+105)
     t_1
     (if (<= i -6.1e-74)
       (* (* x y) z)
       (if (<= i 3.6e-78) (* (* c a) j) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * i) * t;
	double tmp;
	if (i <= -2.6e+105) {
		tmp = t_1;
	} else if (i <= -6.1e-74) {
		tmp = (x * y) * z;
	} else if (i <= 3.6e-78) {
		tmp = (c * a) * j;
	} 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 = (b * i) * t
    if (i <= (-2.6d+105)) then
        tmp = t_1
    else if (i <= (-6.1d-74)) then
        tmp = (x * y) * z
    else if (i <= 3.6d-78) then
        tmp = (c * a) * j
    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 = (b * i) * t;
	double tmp;
	if (i <= -2.6e+105) {
		tmp = t_1;
	} else if (i <= -6.1e-74) {
		tmp = (x * y) * z;
	} else if (i <= 3.6e-78) {
		tmp = (c * a) * j;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (b * i) * t
	tmp = 0
	if i <= -2.6e+105:
		tmp = t_1
	elif i <= -6.1e-74:
		tmp = (x * y) * z
	elif i <= 3.6e-78:
		tmp = (c * a) * j
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(b * i) * t)
	tmp = 0.0
	if (i <= -2.6e+105)
		tmp = t_1;
	elseif (i <= -6.1e-74)
		tmp = Float64(Float64(x * y) * z);
	elseif (i <= 3.6e-78)
		tmp = Float64(Float64(c * a) * j);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (b * i) * t;
	tmp = 0.0;
	if (i <= -2.6e+105)
		tmp = t_1;
	elseif (i <= -6.1e-74)
		tmp = (x * y) * z;
	elseif (i <= 3.6e-78)
		tmp = (c * a) * j;
	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[(b * i), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[i, -2.6e+105], t$95$1, If[LessEqual[i, -6.1e-74], N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[i, 3.6e-78], N[(N[(c * a), $MachinePrecision] * j), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -2.6000000000000002e105 or 3.6000000000000002e-78 < i

   1. Initial program 61.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot t} \]

      3. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(\mathsf{neg}\left(b \cdot i\right)\right)}\right) \cdot t \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(\mathsf{neg}\left(b\right)\right) \cdot i}\right) \cdot t \]

      5. fp-cancel-sign-sub N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)} \cdot t \]

      6. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + b \cdot i\right) \cdot t \]

      7. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + b \cdot i\right) \cdot t \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, b \cdot i\right)} \cdot t \]

      9. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, b \cdot i\right) \cdot t \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \cdot t \]

      11. lower-*.f64 46.5

          \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \cdot t \]

   5. Applied rewrites 46.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t} \]

   6. Taylor expanded in x around 0

      \[\leadsto \left(b \cdot i\right) \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 35.3%

      \[\leadsto \left(b \cdot i\right) \cdot t \]

   if -2.6000000000000002e105 < i < -6.0999999999999998e-74

   1. Initial program 82.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot y - b \cdot c\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot y - b \cdot c\right) \cdot z} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(x \cdot y + \left(\mathsf{neg}\left(b\right)\right) \cdot c\right)} \cdot z \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \left(x \cdot y + \color{blue}{\left(\mathsf{neg}\left(b \cdot c\right)\right)}\right) \cdot z \]

      5. mul-1-neg N/A

         \[\leadsto \left(x \cdot y + \color{blue}{-1 \cdot \left(b \cdot c\right)}\right) \cdot z \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot c\right) + x \cdot y\right)} \cdot z \]

      7. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(b \cdot c\right)\right)} + x \cdot y\right) \cdot z \]

      8. *-commutative N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\color{blue}{c \cdot b}\right)\right) + x \cdot y\right) \cdot z \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(c\right)\right) \cdot b} + x \cdot y\right) \cdot z \]

      10. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(c\right), b, x \cdot y\right)} \cdot z \]

      11. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-c}, b, x \cdot y\right) \cdot z \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-c, b, \color{blue}{y \cdot x}\right) \cdot z \]

      13. lower-*.f64 52.4

          \[\leadsto \mathsf{fma}\left(-c, b, \color{blue}{y \cdot x}\right) \cdot z \]

   5. Applied rewrites 52.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z} \]

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot y\right) \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 30.2%

      \[\leadsto \left(x \cdot y\right) \cdot z \]

   if -6.0999999999999998e-74 < i < 3.6000000000000002e-78

   1. Initial program 84.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot c - i \cdot y\right) \cdot j} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot c - i \cdot y\right) \cdot j} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(a \cdot c + \left(\mathsf{neg}\left(i\right)\right) \cdot y\right)} \cdot j \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(i\right)\right) \cdot y + a \cdot c\right)} \cdot j \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(i\right), y, a \cdot c\right)} \cdot j \]

      6. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-i}, y, a \cdot c\right) \cdot j \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-i, y, \color{blue}{c \cdot a}\right) \cdot j \]

      8. lower-*.f64 36.3

         \[\leadsto \mathsf{fma}\left(-i, y, \color{blue}{c \cdot a}\right) \cdot j \]

   5. Applied rewrites 36.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-i, y, c \cdot a\right) \cdot j} \]

   6. Taylor expanded in y around 0

      \[\leadsto \left(a \cdot c\right) \cdot j \]
   7. Step-by-step derivation

   8. Applied rewrites 29.7%

      \[\leadsto \left(c \cdot a\right) \cdot j \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 21: 30.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+30} \lor \neg \left(y \leq 2.35 \cdot 10^{+88}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot t\right) \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -2.6e+30) (not (<= y 2.35e+88))) (* (* x y) z) (* (* b t) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -2.6e+30) || !(y <= 2.35e+88)) {
		tmp = (x * y) * z;
	} else {
		tmp = (b * t) * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((y <= (-2.6d+30)) .or. (.not. (y <= 2.35d+88))) then
        tmp = (x * y) * z
    else
        tmp = (b * t) * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -2.6e+30) || !(y <= 2.35e+88)) {
		tmp = (x * y) * z;
	} else {
		tmp = (b * t) * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (y <= -2.6e+30) or not (y <= 2.35e+88):
		tmp = (x * y) * z
	else:
		tmp = (b * t) * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -2.6e+30) || !(y <= 2.35e+88))
		tmp = Float64(Float64(x * y) * z);
	else
		tmp = Float64(Float64(b * t) * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((y <= -2.6e+30) || ~((y <= 2.35e+88)))
		tmp = (x * y) * z;
	else
		tmp = (b * t) * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[y, -2.6e+30], N[Not[LessEqual[y, 2.35e+88]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision], N[(N[(b * t), $MachinePrecision] * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.59999999999999988e30 or 2.35000000000000004e88 < y

   1. Initial program 64.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot y - b \cdot c\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot y - b \cdot c\right) \cdot z} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(x \cdot y + \left(\mathsf{neg}\left(b\right)\right) \cdot c\right)} \cdot z \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \left(x \cdot y + \color{blue}{\left(\mathsf{neg}\left(b \cdot c\right)\right)}\right) \cdot z \]

      5. mul-1-neg N/A

         \[\leadsto \left(x \cdot y + \color{blue}{-1 \cdot \left(b \cdot c\right)}\right) \cdot z \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot c\right) + x \cdot y\right)} \cdot z \]

      7. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(b \cdot c\right)\right)} + x \cdot y\right) \cdot z \]

      8. *-commutative N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\color{blue}{c \cdot b}\right)\right) + x \cdot y\right) \cdot z \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(c\right)\right) \cdot b} + x \cdot y\right) \cdot z \]

      10. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(c\right), b, x \cdot y\right)} \cdot z \]

      11. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-c}, b, x \cdot y\right) \cdot z \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-c, b, \color{blue}{y \cdot x}\right) \cdot z \]

      13. lower-*.f64 41.1

          \[\leadsto \mathsf{fma}\left(-c, b, \color{blue}{y \cdot x}\right) \cdot z \]

   5. Applied rewrites 41.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z} \]

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot y\right) \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 31.8%

      \[\leadsto \left(x \cdot y\right) \cdot z \]

   if -2.59999999999999988e30 < y < 2.35000000000000004e88

   1. Initial program 78.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot t} \]

      3. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(\mathsf{neg}\left(b \cdot i\right)\right)}\right) \cdot t \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(\mathsf{neg}\left(b\right)\right) \cdot i}\right) \cdot t \]

      5. fp-cancel-sign-sub N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)} \cdot t \]

      6. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + b \cdot i\right) \cdot t \]

      7. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + b \cdot i\right) \cdot t \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, b \cdot i\right)} \cdot t \]

      9. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, b \cdot i\right) \cdot t \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \cdot t \]

      11. lower-*.f64 48.1

          \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \cdot t \]

   5. Applied rewrites 48.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t} \]

   6. Taylor expanded in x around 0

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 28.4%

      \[\leadsto \left(i \cdot t\right) \cdot \color{blue}{b} \]
   9. Step-by-step derivation

   10. Applied rewrites 29.7%

       \[\leadsto \left(b \cdot t\right) \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+30} \lor \neg \left(y \leq 2.35 \cdot 10^{+88}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot t\right) \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 30.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+15} \lor \neg \left(t \leq 1.26 \cdot 10^{+49}\right):\\ \;\;\;\;\left(b \cdot t\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -1.2e+15) (not (<= t 1.26e+49))) (* (* b t) i) (* (* 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 ((t <= -1.2e+15) || !(t <= 1.26e+49)) {
		tmp = (b * t) * i;
	} else {
		tmp = (z * y) * x;
	}
	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 <= (-1.2d+15)) .or. (.not. (t <= 1.26d+49))) then
        tmp = (b * t) * i
    else
        tmp = (z * y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -1.2e+15) || !(t <= 1.26e+49)) {
		tmp = (b * t) * i;
	} else {
		tmp = (z * y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -1.2e+15) or not (t <= 1.26e+49):
		tmp = (b * t) * i
	else:
		tmp = (z * y) * x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -1.2e+15) || !(t <= 1.26e+49))
		tmp = Float64(Float64(b * t) * i);
	else
		tmp = Float64(Float64(z * y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -1.2e+15) || ~((t <= 1.26e+49)))
		tmp = (b * t) * i;
	else
		tmp = (z * y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -1.2e+15], N[Not[LessEqual[t, 1.26e+49]], $MachinePrecision]], N[(N[(b * t), $MachinePrecision] * i), $MachinePrecision], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2e15 or 1.2599999999999999e49 < t

   1. Initial program 61.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot t} \]

      3. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(\mathsf{neg}\left(b \cdot i\right)\right)}\right) \cdot t \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(\mathsf{neg}\left(b\right)\right) \cdot i}\right) \cdot t \]

      5. fp-cancel-sign-sub N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)} \cdot t \]

      6. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + b \cdot i\right) \cdot t \]

      7. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + b \cdot i\right) \cdot t \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, b \cdot i\right)} \cdot t \]

      9. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, b \cdot i\right) \cdot t \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \cdot t \]

      11. lower-*.f64 58.9

          \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \cdot t \]

   5. Applied rewrites 58.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t} \]

   6. Taylor expanded in x around 0

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 33.7%

      \[\leadsto \left(i \cdot t\right) \cdot \color{blue}{b} \]
   9. Step-by-step derivation

   10. Applied rewrites 33.7%

       \[\leadsto \left(b \cdot t\right) \cdot i \]

   if -1.2e15 < t < 1.2599999999999999e49

   1. Initial program 82.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot y - b \cdot c\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot y - b \cdot c\right) \cdot z} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(x \cdot y + \left(\mathsf{neg}\left(b\right)\right) \cdot c\right)} \cdot z \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \left(x \cdot y + \color{blue}{\left(\mathsf{neg}\left(b \cdot c\right)\right)}\right) \cdot z \]

      5. mul-1-neg N/A

         \[\leadsto \left(x \cdot y + \color{blue}{-1 \cdot \left(b \cdot c\right)}\right) \cdot z \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot c\right) + x \cdot y\right)} \cdot z \]

      7. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(b \cdot c\right)\right)} + x \cdot y\right) \cdot z \]

      8. *-commutative N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\color{blue}{c \cdot b}\right)\right) + x \cdot y\right) \cdot z \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(c\right)\right) \cdot b} + x \cdot y\right) \cdot z \]

      10. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(c\right), b, x \cdot y\right)} \cdot z \]

      11. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-c}, b, x \cdot y\right) \cdot z \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-c, b, \color{blue}{y \cdot x}\right) \cdot z \]

      13. lower-*.f64 49.0

          \[\leadsto \mathsf{fma}\left(-c, b, \color{blue}{y \cdot x}\right) \cdot z \]

   5. Applied rewrites 49.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z} \]

   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 25.5%

      \[\leadsto \left(z \cdot y\right) \cdot \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+15} \lor \neg \left(t \leq 1.26 \cdot 10^{+49}\right):\\ \;\;\;\;\left(b \cdot t\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 22.7% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \left(i \cdot t\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* (* i t) b))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return (i * t) * b;
}

Fortran

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 = (i * t) * b
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return (i * t) * b;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return (i * t) * b

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(i * t) * b)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = (i * t) * b;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(i * t), $MachinePrecision] * b), $MachinePrecision]

Derivation

1. Initial program 72.5%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Add Preprocessing

3. Taylor expanded in t around inf

   \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot t} \]

   2. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot t} \]

   3. mul-1-neg N/A

      \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(\mathsf{neg}\left(b \cdot i\right)\right)}\right) \cdot t \]

   4. distribute-lft-neg-in N/A

      \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(\mathsf{neg}\left(b\right)\right) \cdot i}\right) \cdot t \]

   5. fp-cancel-sign-sub N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)} \cdot t \]

   6. associate-*r* N/A

      \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + b \cdot i\right) \cdot t \]

   7. mul-1-neg N/A

      \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + b \cdot i\right) \cdot t \]

   8. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, b \cdot i\right)} \cdot t \]

   9. lower-neg.f64 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, b \cdot i\right) \cdot t \]

   10. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \cdot t \]

   11. lower-*.f64 38.8

       \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \cdot t \]

5. Applied rewrites 38.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t} \]

6. Taylor expanded in x around 0

   \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
7. Step-by-step derivation

8. Applied rewrites 21.2%

   \[\leadsto \left(i \cdot t\right) \cdot \color{blue}{b} \]
9. Add Preprocessing

Alternative 24: 23.1% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \left(b \cdot t\right) \cdot i \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* (* b t) i))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return (b * t) * i;
}

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 = (b * t) * i
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return (b * t) * i;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return (b * t) * i

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(b * t) * i)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = (b * t) * i;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(b * t), $MachinePrecision] * i), $MachinePrecision]

Derivation

1. Initial program 72.5%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Add Preprocessing

3. Taylor expanded in t around inf

   \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot t} \]

   2. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \cdot t} \]

   3. mul-1-neg N/A

      \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(\mathsf{neg}\left(b \cdot i\right)\right)}\right) \cdot t \]

   4. distribute-lft-neg-in N/A

      \[\leadsto \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(\mathsf{neg}\left(b\right)\right) \cdot i}\right) \cdot t \]

   5. fp-cancel-sign-sub N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)} \cdot t \]

   6. associate-*r* N/A

      \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + b \cdot i\right) \cdot t \]

   7. mul-1-neg N/A

      \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + b \cdot i\right) \cdot t \]

   8. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, b \cdot i\right)} \cdot t \]

   9. lower-neg.f64 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, b \cdot i\right) \cdot t \]

   10. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \cdot t \]

   11. lower-*.f64 38.8

       \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \cdot t \]

5. Applied rewrites 38.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t} \]

6. Taylor expanded in x around 0

   \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
7. Step-by-step derivation

8. Applied rewrites 21.2%

   \[\leadsto \left(i \cdot t\right) \cdot \color{blue}{b} \]
9. Step-by-step derivation

10. Applied rewrites 20.9%

    \[\leadsto \left(b \cdot t\right) \cdot i \]
11. Add Preprocessing

Developer Target 1: 59.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

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 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024329 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -293938859355541/2000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 32113527362226803/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))