Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 74.2% → 82.5%

Time: 27.8s

Alternatives: 16

Speedup: 0.5×

• 58.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 74.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.5% accurate, 0.5× speedup

Math

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

FPCore

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

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

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t * ((c * j) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = t * ((c * j) - (x * a))
	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(a * i) - Float64(z * c)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = t * ((c * j) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.5%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around -inf 64.8%

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

      1. mul-1-neg 64.8%

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

      2. *-commutative 64.8%

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

      3. distribute-rgt-neg-in 64.8%

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

      4. +-commutative 64.8%

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

      5. mul-1-neg 64.8%

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

      6. unsub-neg 64.8%

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

   5. Simplified 64.8%

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

   6. Taylor expanded in a around 0 47.1%

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

      1. +-commutative 47.1%

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

      2. *-commutative 47.1%

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

      3. *-commutative 47.1%

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

      4. associate-*l* 49.3%

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

      5. mul-1-neg 49.3%

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

      6. *-commutative 49.3%

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

      7. associate-*r* 51.5%

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

      8. distribute-rgt-neg-in 51.5%

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

      9. distribute-lft-in 64.8%

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

      10. unsub-neg 64.8%

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

   8. Simplified 64.8%

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

4. Final simplification 89.3%

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

Alternative 2: 50.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -4.2 \cdot 10^{+14}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-106}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.75 \cdot 10^{-150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -9.5 \cdot 10^{-166}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.55 \cdot 10^{-179}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 6.3 \cdot 10^{-280}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{-105}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 2.15 \cdot 10^{-54} \lor \neg \left(j \leq 9.2 \cdot 10^{+45}\right) \land j \leq 9.5 \cdot 10^{+86}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (* a (- (* b i) (* x t))))
        (t_3 (* j (- (* t c) (* y i)))))
   (if (<= j -4.2e+14)
     t_3
     (if (<= j -6e-106)
       t_2
       (if (<= j -1.75e-150)
         t_1
         (if (<= j -9.5e-166)
           t_2
           (if (<= j -1.55e-179)
             t_1
             (if (<= j 6.3e-280)
               t_2
               (if (<= j 1.45e-105)
                 (* z (- (* x y) (* b c)))
                 (if (or (<= j 2.15e-54)
                         (and (not (<= j 9.2e+45)) (<= j 9.5e+86)))
                   t_2
                   t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = a * ((b * i) - (x * t));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -4.2e+14) {
		tmp = t_3;
	} else if (j <= -6e-106) {
		tmp = t_2;
	} else if (j <= -1.75e-150) {
		tmp = t_1;
	} else if (j <= -9.5e-166) {
		tmp = t_2;
	} else if (j <= -1.55e-179) {
		tmp = t_1;
	} else if (j <= 6.3e-280) {
		tmp = t_2;
	} else if (j <= 1.45e-105) {
		tmp = z * ((x * y) - (b * c));
	} else if ((j <= 2.15e-54) || (!(j <= 9.2e+45) && (j <= 9.5e+86))) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    t_2 = a * ((b * i) - (x * t))
    t_3 = j * ((t * c) - (y * i))
    if (j <= (-4.2d+14)) then
        tmp = t_3
    else if (j <= (-6d-106)) then
        tmp = t_2
    else if (j <= (-1.75d-150)) then
        tmp = t_1
    else if (j <= (-9.5d-166)) then
        tmp = t_2
    else if (j <= (-1.55d-179)) then
        tmp = t_1
    else if (j <= 6.3d-280) then
        tmp = t_2
    else if (j <= 1.45d-105) then
        tmp = z * ((x * y) - (b * c))
    else if ((j <= 2.15d-54) .or. (.not. (j <= 9.2d+45)) .and. (j <= 9.5d+86)) then
        tmp = t_2
    else
        tmp = t_3
    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 = y * ((x * z) - (i * j));
	double t_2 = a * ((b * i) - (x * t));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -4.2e+14) {
		tmp = t_3;
	} else if (j <= -6e-106) {
		tmp = t_2;
	} else if (j <= -1.75e-150) {
		tmp = t_1;
	} else if (j <= -9.5e-166) {
		tmp = t_2;
	} else if (j <= -1.55e-179) {
		tmp = t_1;
	} else if (j <= 6.3e-280) {
		tmp = t_2;
	} else if (j <= 1.45e-105) {
		tmp = z * ((x * y) - (b * c));
	} else if ((j <= 2.15e-54) || (!(j <= 9.2e+45) && (j <= 9.5e+86))) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = a * ((b * i) - (x * t))
	t_3 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -4.2e+14:
		tmp = t_3
	elif j <= -6e-106:
		tmp = t_2
	elif j <= -1.75e-150:
		tmp = t_1
	elif j <= -9.5e-166:
		tmp = t_2
	elif j <= -1.55e-179:
		tmp = t_1
	elif j <= 6.3e-280:
		tmp = t_2
	elif j <= 1.45e-105:
		tmp = z * ((x * y) - (b * c))
	elif (j <= 2.15e-54) or (not (j <= 9.2e+45) and (j <= 9.5e+86)):
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -4.2e+14)
		tmp = t_3;
	elseif (j <= -6e-106)
		tmp = t_2;
	elseif (j <= -1.75e-150)
		tmp = t_1;
	elseif (j <= -9.5e-166)
		tmp = t_2;
	elseif (j <= -1.55e-179)
		tmp = t_1;
	elseif (j <= 6.3e-280)
		tmp = t_2;
	elseif (j <= 1.45e-105)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif ((j <= 2.15e-54) || (!(j <= 9.2e+45) && (j <= 9.5e+86)))
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = a * ((b * i) - (x * t));
	t_3 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -4.2e+14)
		tmp = t_3;
	elseif (j <= -6e-106)
		tmp = t_2;
	elseif (j <= -1.75e-150)
		tmp = t_1;
	elseif (j <= -9.5e-166)
		tmp = t_2;
	elseif (j <= -1.55e-179)
		tmp = t_1;
	elseif (j <= 6.3e-280)
		tmp = t_2;
	elseif (j <= 1.45e-105)
		tmp = z * ((x * y) - (b * c));
	elseif ((j <= 2.15e-54) || (~((j <= 9.2e+45)) && (j <= 9.5e+86)))
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4.2e+14], t$95$3, If[LessEqual[j, -6e-106], t$95$2, If[LessEqual[j, -1.75e-150], t$95$1, If[LessEqual[j, -9.5e-166], t$95$2, If[LessEqual[j, -1.55e-179], t$95$1, If[LessEqual[j, 6.3e-280], t$95$2, If[LessEqual[j, 1.45e-105], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[j, 2.15e-54], And[N[Not[LessEqual[j, 9.2e+45]], $MachinePrecision], LessEqual[j, 9.5e+86]]], t$95$2, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -4.2e14 or 2.15e-54 < j < 9.20000000000000049e45 or 9.50000000000000028e86 < j

   1. Initial program 79.8%

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

   3. Taylor expanded in b around 0 72.8%

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

   4. Taylor expanded in j around inf 71.5%

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

      1. *-commutative 71.5%

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

      2. *-commutative 71.5%

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

   6. Simplified 71.5%

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

   if -4.2e14 < j < -6.00000000000000037e-106 or -1.7499999999999999e-150 < j < -9.50000000000000046e-166 or -1.5500000000000001e-179 < j < 6.2999999999999998e-280 or 1.45000000000000002e-105 < j < 2.15e-54 or 9.20000000000000049e45 < j < 9.50000000000000028e86

   1. Initial program 72.7%

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

   3. Taylor expanded in a around inf 80.4%

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

      1. distribute-lft-out-- 80.4%

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

   5. Simplified 80.4%

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

   6. Taylor expanded in a around 0 80.4%

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

      1. mul-1-neg 80.4%

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

      2. cancel-sign-sub-inv 80.4%

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

      3. +-commutative 80.4%

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

      4. +-commutative 80.4%

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

      5. cancel-sign-sub-inv 80.4%

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

      6. *-commutative 80.4%

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

      7. distribute-rgt-neg-in 80.4%

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

   8. Simplified 80.4%

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

   if -6.00000000000000037e-106 < j < -1.7499999999999999e-150 or -9.50000000000000046e-166 < j < -1.5500000000000001e-179

   1. Initial program 68.9%

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

   3. Taylor expanded in y around inf 64.8%

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

   if 6.2999999999999998e-280 < j < 1.45000000000000002e-105

   1. Initial program 86.7%

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

   3. Taylor expanded in z around inf 59.1%

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

      1. *-commutative 59.1%

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

   5. Simplified 59.1%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.2 \cdot 10^{+14}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-106}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq -1.75 \cdot 10^{-150}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq -9.5 \cdot 10^{-166}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq -1.55 \cdot 10^{-179}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq 6.3 \cdot 10^{-280}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{-105}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 2.15 \cdot 10^{-54} \lor \neg \left(j \leq 9.2 \cdot 10^{+45}\right) \land j \leq 9.5 \cdot 10^{+86}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 30.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;j \leq -4.8 \cdot 10^{+54}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;j \leq -3.3 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq -3.9 \cdot 10^{-212}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq -4.3 \cdot 10^{-225}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{-284}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;j \leq 2.25 \cdot 10^{-278}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.95 \cdot 10^{-115}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 5.1 \cdot 10^{+178}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* b i))))
   (if (<= j -4.8e+54)
     (* j (* t c))
     (if (<= j -3.3e-178)
       (* x (* y z))
       (if (<= j -3.9e-212)
         (* b (* a i))
         (if (<= j -4.3e-225)
           (* b (* z (- c)))
           (if (<= j 2.5e-284)
             (* a (* x (- t)))
             (if (<= j 2.25e-278)
               t_1
               (if (<= j 2.95e-115)
                 (* y (* x z))
                 (if (<= j 2.8e-59)
                   t_1
                   (if (<= j 5.1e+178)
                     (* (* y i) (- j))
                     (* c (* t j)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double tmp;
	if (j <= -4.8e+54) {
		tmp = j * (t * c);
	} else if (j <= -3.3e-178) {
		tmp = x * (y * z);
	} else if (j <= -3.9e-212) {
		tmp = b * (a * i);
	} else if (j <= -4.3e-225) {
		tmp = b * (z * -c);
	} else if (j <= 2.5e-284) {
		tmp = a * (x * -t);
	} else if (j <= 2.25e-278) {
		tmp = t_1;
	} else if (j <= 2.95e-115) {
		tmp = y * (x * z);
	} else if (j <= 2.8e-59) {
		tmp = t_1;
	} else if (j <= 5.1e+178) {
		tmp = (y * i) * -j;
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * i)
    if (j <= (-4.8d+54)) then
        tmp = j * (t * c)
    else if (j <= (-3.3d-178)) then
        tmp = x * (y * z)
    else if (j <= (-3.9d-212)) then
        tmp = b * (a * i)
    else if (j <= (-4.3d-225)) then
        tmp = b * (z * -c)
    else if (j <= 2.5d-284) then
        tmp = a * (x * -t)
    else if (j <= 2.25d-278) then
        tmp = t_1
    else if (j <= 2.95d-115) then
        tmp = y * (x * z)
    else if (j <= 2.8d-59) then
        tmp = t_1
    else if (j <= 5.1d+178) then
        tmp = (y * i) * -j
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double tmp;
	if (j <= -4.8e+54) {
		tmp = j * (t * c);
	} else if (j <= -3.3e-178) {
		tmp = x * (y * z);
	} else if (j <= -3.9e-212) {
		tmp = b * (a * i);
	} else if (j <= -4.3e-225) {
		tmp = b * (z * -c);
	} else if (j <= 2.5e-284) {
		tmp = a * (x * -t);
	} else if (j <= 2.25e-278) {
		tmp = t_1;
	} else if (j <= 2.95e-115) {
		tmp = y * (x * z);
	} else if (j <= 2.8e-59) {
		tmp = t_1;
	} else if (j <= 5.1e+178) {
		tmp = (y * i) * -j;
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (b * i)
	tmp = 0
	if j <= -4.8e+54:
		tmp = j * (t * c)
	elif j <= -3.3e-178:
		tmp = x * (y * z)
	elif j <= -3.9e-212:
		tmp = b * (a * i)
	elif j <= -4.3e-225:
		tmp = b * (z * -c)
	elif j <= 2.5e-284:
		tmp = a * (x * -t)
	elif j <= 2.25e-278:
		tmp = t_1
	elif j <= 2.95e-115:
		tmp = y * (x * z)
	elif j <= 2.8e-59:
		tmp = t_1
	elif j <= 5.1e+178:
		tmp = (y * i) * -j
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (j <= -4.8e+54)
		tmp = Float64(j * Float64(t * c));
	elseif (j <= -3.3e-178)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= -3.9e-212)
		tmp = Float64(b * Float64(a * i));
	elseif (j <= -4.3e-225)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (j <= 2.5e-284)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (j <= 2.25e-278)
		tmp = t_1;
	elseif (j <= 2.95e-115)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 2.8e-59)
		tmp = t_1;
	elseif (j <= 5.1e+178)
		tmp = Float64(Float64(y * i) * Float64(-j));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (b * i);
	tmp = 0.0;
	if (j <= -4.8e+54)
		tmp = j * (t * c);
	elseif (j <= -3.3e-178)
		tmp = x * (y * z);
	elseif (j <= -3.9e-212)
		tmp = b * (a * i);
	elseif (j <= -4.3e-225)
		tmp = b * (z * -c);
	elseif (j <= 2.5e-284)
		tmp = a * (x * -t);
	elseif (j <= 2.25e-278)
		tmp = t_1;
	elseif (j <= 2.95e-115)
		tmp = y * (x * z);
	elseif (j <= 2.8e-59)
		tmp = t_1;
	elseif (j <= 5.1e+178)
		tmp = (y * i) * -j;
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4.8e+54], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.3e-178], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.9e-212], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.3e-225], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.5e-284], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.25e-278], t$95$1, If[LessEqual[j, 2.95e-115], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.8e-59], t$95$1, If[LessEqual[j, 5.1e+178], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if j < -4.79999999999999997e54

   1. Initial program 78.2%

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

   3. Taylor expanded in t around -inf 66.4%

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

      1. mul-1-neg 66.4%

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

      2. *-commutative 66.4%

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

      3. distribute-rgt-neg-in 66.4%

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

      4. +-commutative 66.4%

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

      5. mul-1-neg 66.4%

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

      6. unsub-neg 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in a around 0 57.3%

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

      1. *-commutative 57.3%

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

      2. associate-*l* 59.4%

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

   8. Simplified 59.4%

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

   if -4.79999999999999997e54 < j < -3.3000000000000002e-178

   1. Initial program 70.4%

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

   3. Taylor expanded in z around inf 43.3%

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

      1. *-commutative 43.3%

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

   5. Simplified 43.3%

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

   6. Taylor expanded in y around inf 35.7%

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

   if -3.3000000000000002e-178 < j < -3.9e-212

   1. Initial program 63.1%

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

   3. Taylor expanded in b around inf 75.6%

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

   4. Taylor expanded in a around inf 52.2%

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

      1. *-commutative 52.2%

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

   6. Simplified 52.2%

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

   if -3.9e-212 < j < -4.29999999999999979e-225

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 100.0%

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

   4. Taylor expanded in a around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

   6. Simplified 100.0%

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

   if -4.29999999999999979e-225 < j < 2.49999999999999987e-284

   1. Initial program 79.8%

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

   3. Taylor expanded in a around inf 87.2%

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

      1. distribute-lft-out-- 87.2%

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

   5. Simplified 87.2%

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

   6. Taylor expanded in t around inf 61.1%

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

      1. mul-1-neg 61.1%

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

      2. *-commutative 61.1%

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

      3. distribute-rgt-neg-in 61.1%

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

   8. Simplified 61.1%

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

   if 2.49999999999999987e-284 < j < 2.2499999999999999e-278 or 2.94999999999999997e-115 < j < 2.79999999999999981e-59

   1. Initial program 84.8%

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

   3. Taylor expanded in b around inf 51.6%

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

   4. Taylor expanded in a around inf 45.1%

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

      1. *-commutative 45.1%

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

   6. Simplified 45.1%

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

   if 2.2499999999999999e-278 < j < 2.94999999999999997e-115

   1. Initial program 84.3%

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

   3. Taylor expanded in z around inf 61.1%

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

      1. *-commutative 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in y around inf 45.1%

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

      1. *-commutative 45.1%

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

      2. associate-*r* 48.2%

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

   8. Simplified 48.2%

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

   if 2.79999999999999981e-59 < j < 5.0999999999999997e178

   1. Initial program 82.0%

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

   3. Taylor expanded in y around inf 49.4%

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

   4. Taylor expanded in i around inf 39.3%

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

      1. mul-1-neg 39.3%

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

      2. associate-*r* 35.7%

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

      3. *-commutative 35.7%

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

      4. associate-*l* 39.4%

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

      5. distribute-rgt-neg-in 39.4%

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

      6. distribute-lft-neg-out 39.4%

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

      7. *-commutative 39.4%

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

   6. Simplified 39.4%

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

   if 5.0999999999999997e178 < j

   1. Initial program 74.0%

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

   3. Taylor expanded in t around -inf 47.0%

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

      1. mul-1-neg 47.0%

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

      2. *-commutative 47.0%

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

      3. distribute-rgt-neg-in 47.0%

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

      4. +-commutative 47.0%

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

      5. mul-1-neg 47.0%

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

      6. unsub-neg 47.0%

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

   5. Simplified 47.0%

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

   6. Taylor expanded in a around 0 59.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.8 \cdot 10^{+54}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;j \leq -3.3 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq -3.9 \cdot 10^{-212}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq -4.3 \cdot 10^{-225}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{-284}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;j \leq 2.25 \cdot 10^{-278}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 2.95 \cdot 10^{-115}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 5.1 \cdot 10^{+178}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -4.5 \cdot 10^{+16}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -2.4 \cdot 10^{-165}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{-278}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 2.65 \cdot 10^{-105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.15 \cdot 10^{-54} \lor \neg \left(j \leq 1.75 \cdot 10^{+44}\right) \land j \leq 5.2 \cdot 10^{+88}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c))))
        (t_2 (* a (- (* b i) (* x t))))
        (t_3 (* j (- (* t c) (* y i)))))
   (if (<= j -4.5e+16)
     t_3
     (if (<= j -2.4e-165)
       t_2
       (if (<= j -3.5e-191)
         t_1
         (if (<= j 1.4e-278)
           t_2
           (if (<= j 2.65e-105)
             t_1
             (if (or (<= j 2.15e-54)
                     (and (not (<= j 1.75e+44)) (<= j 5.2e+88)))
               t_2
               t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = a * ((b * i) - (x * t));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -4.5e+16) {
		tmp = t_3;
	} else if (j <= -2.4e-165) {
		tmp = t_2;
	} else if (j <= -3.5e-191) {
		tmp = t_1;
	} else if (j <= 1.4e-278) {
		tmp = t_2;
	} else if (j <= 2.65e-105) {
		tmp = t_1;
	} else if ((j <= 2.15e-54) || (!(j <= 1.75e+44) && (j <= 5.2e+88))) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    t_2 = a * ((b * i) - (x * t))
    t_3 = j * ((t * c) - (y * i))
    if (j <= (-4.5d+16)) then
        tmp = t_3
    else if (j <= (-2.4d-165)) then
        tmp = t_2
    else if (j <= (-3.5d-191)) then
        tmp = t_1
    else if (j <= 1.4d-278) then
        tmp = t_2
    else if (j <= 2.65d-105) then
        tmp = t_1
    else if ((j <= 2.15d-54) .or. (.not. (j <= 1.75d+44)) .and. (j <= 5.2d+88)) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = a * ((b * i) - (x * t));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -4.5e+16) {
		tmp = t_3;
	} else if (j <= -2.4e-165) {
		tmp = t_2;
	} else if (j <= -3.5e-191) {
		tmp = t_1;
	} else if (j <= 1.4e-278) {
		tmp = t_2;
	} else if (j <= 2.65e-105) {
		tmp = t_1;
	} else if ((j <= 2.15e-54) || (!(j <= 1.75e+44) && (j <= 5.2e+88))) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = a * ((b * i) - (x * t))
	t_3 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -4.5e+16:
		tmp = t_3
	elif j <= -2.4e-165:
		tmp = t_2
	elif j <= -3.5e-191:
		tmp = t_1
	elif j <= 1.4e-278:
		tmp = t_2
	elif j <= 2.65e-105:
		tmp = t_1
	elif (j <= 2.15e-54) or (not (j <= 1.75e+44) and (j <= 5.2e+88)):
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -4.5e+16)
		tmp = t_3;
	elseif (j <= -2.4e-165)
		tmp = t_2;
	elseif (j <= -3.5e-191)
		tmp = t_1;
	elseif (j <= 1.4e-278)
		tmp = t_2;
	elseif (j <= 2.65e-105)
		tmp = t_1;
	elseif ((j <= 2.15e-54) || (!(j <= 1.75e+44) && (j <= 5.2e+88)))
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	t_2 = a * ((b * i) - (x * t));
	t_3 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -4.5e+16)
		tmp = t_3;
	elseif (j <= -2.4e-165)
		tmp = t_2;
	elseif (j <= -3.5e-191)
		tmp = t_1;
	elseif (j <= 1.4e-278)
		tmp = t_2;
	elseif (j <= 2.65e-105)
		tmp = t_1;
	elseif ((j <= 2.15e-54) || (~((j <= 1.75e+44)) && (j <= 5.2e+88)))
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4.5e+16], t$95$3, If[LessEqual[j, -2.4e-165], t$95$2, If[LessEqual[j, -3.5e-191], t$95$1, If[LessEqual[j, 1.4e-278], t$95$2, If[LessEqual[j, 2.65e-105], t$95$1, If[Or[LessEqual[j, 2.15e-54], And[N[Not[LessEqual[j, 1.75e+44]], $MachinePrecision], LessEqual[j, 5.2e+88]]], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -4.5e16 or 2.15e-54 < j < 1.75e44 or 5.2000000000000001e88 < j

   1. Initial program 79.8%

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

   3. Taylor expanded in b around 0 72.8%

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

   4. Taylor expanded in j around inf 71.5%

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

      1. *-commutative 71.5%

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

      2. *-commutative 71.5%

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

   6. Simplified 71.5%

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

   if -4.5e16 < j < -2.4000000000000002e-165 or -3.50000000000000007e-191 < j < 1.40000000000000004e-278 or 2.6500000000000001e-105 < j < 2.15e-54 or 1.75e44 < j < 5.2000000000000001e88

   1. Initial program 70.9%

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

   3. Taylor expanded in a around inf 71.8%

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

      1. distribute-lft-out-- 71.8%

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

   5. Simplified 71.8%

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

   6. Taylor expanded in a around 0 71.8%

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

      1. mul-1-neg 71.8%

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

      2. cancel-sign-sub-inv 71.8%

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

      3. +-commutative 71.8%

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

      4. +-commutative 71.8%

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

      5. cancel-sign-sub-inv 71.8%

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

      6. *-commutative 71.8%

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

      7. distribute-rgt-neg-in 71.8%

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

   8. Simplified 71.8%

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

   if -2.4000000000000002e-165 < j < -3.50000000000000007e-191 or 1.40000000000000004e-278 < j < 2.6500000000000001e-105

   1. Initial program 84.3%

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

   3. Taylor expanded in z around inf 61.8%

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

      1. *-commutative 61.8%

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

   5. Simplified 61.8%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.5 \cdot 10^{+16}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -2.4 \cdot 10^{-165}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-191}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{-278}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq 2.65 \cdot 10^{-105}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 2.15 \cdot 10^{-54} \lor \neg \left(j \leq 1.75 \cdot 10^{+44}\right) \land j \leq 5.2 \cdot 10^{+88}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -5.5 \cdot 10^{-11}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -1.02 \cdot 10^{-178}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{-277}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.8 \cdot 10^{-108}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{-50}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;j \leq 0.0072:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (* z (- (* x y) (* b c))))
        (t_3 (* j (- (* t c) (* y i)))))
   (if (<= j -5.5e-11)
     t_3
     (if (<= j -1.02e-178)
       t_2
       (if (<= j 6.5e-277)
         t_1
         (if (<= j 1.8e-108)
           t_2
           (if (<= j 6.2e-61)
             t_1
             (if (<= j 6.4e-50)
               (* a (* x (- t)))
               (if (<= j 0.0072) t_2 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -5.5e-11) {
		tmp = t_3;
	} else if (j <= -1.02e-178) {
		tmp = t_2;
	} else if (j <= 6.5e-277) {
		tmp = t_1;
	} else if (j <= 1.8e-108) {
		tmp = t_2;
	} else if (j <= 6.2e-61) {
		tmp = t_1;
	} else if (j <= 6.4e-50) {
		tmp = a * (x * -t);
	} else if (j <= 0.0072) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = z * ((x * y) - (b * c))
    t_3 = j * ((t * c) - (y * i))
    if (j <= (-5.5d-11)) then
        tmp = t_3
    else if (j <= (-1.02d-178)) then
        tmp = t_2
    else if (j <= 6.5d-277) then
        tmp = t_1
    else if (j <= 1.8d-108) then
        tmp = t_2
    else if (j <= 6.2d-61) then
        tmp = t_1
    else if (j <= 6.4d-50) then
        tmp = a * (x * -t)
    else if (j <= 0.0072d0) then
        tmp = t_2
    else
        tmp = t_3
    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 * ((a * i) - (z * c));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -5.5e-11) {
		tmp = t_3;
	} else if (j <= -1.02e-178) {
		tmp = t_2;
	} else if (j <= 6.5e-277) {
		tmp = t_1;
	} else if (j <= 1.8e-108) {
		tmp = t_2;
	} else if (j <= 6.2e-61) {
		tmp = t_1;
	} else if (j <= 6.4e-50) {
		tmp = a * (x * -t);
	} else if (j <= 0.0072) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = z * ((x * y) - (b * c))
	t_3 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -5.5e-11:
		tmp = t_3
	elif j <= -1.02e-178:
		tmp = t_2
	elif j <= 6.5e-277:
		tmp = t_1
	elif j <= 1.8e-108:
		tmp = t_2
	elif j <= 6.2e-61:
		tmp = t_1
	elif j <= 6.4e-50:
		tmp = a * (x * -t)
	elif j <= 0.0072:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -5.5e-11)
		tmp = t_3;
	elseif (j <= -1.02e-178)
		tmp = t_2;
	elseif (j <= 6.5e-277)
		tmp = t_1;
	elseif (j <= 1.8e-108)
		tmp = t_2;
	elseif (j <= 6.2e-61)
		tmp = t_1;
	elseif (j <= 6.4e-50)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (j <= 0.0072)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = z * ((x * y) - (b * c));
	t_3 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -5.5e-11)
		tmp = t_3;
	elseif (j <= -1.02e-178)
		tmp = t_2;
	elseif (j <= 6.5e-277)
		tmp = t_1;
	elseif (j <= 1.8e-108)
		tmp = t_2;
	elseif (j <= 6.2e-61)
		tmp = t_1;
	elseif (j <= 6.4e-50)
		tmp = a * (x * -t);
	elseif (j <= 0.0072)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5.5e-11], t$95$3, If[LessEqual[j, -1.02e-178], t$95$2, If[LessEqual[j, 6.5e-277], t$95$1, If[LessEqual[j, 1.8e-108], t$95$2, If[LessEqual[j, 6.2e-61], t$95$1, If[LessEqual[j, 6.4e-50], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 0.0072], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -5.49999999999999975e-11 or 0.0071999999999999998 < j

   1. Initial program 78.5%

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

   3. Taylor expanded in b around 0 73.7%

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

   4. Taylor expanded in j around inf 68.6%

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

      1. *-commutative 68.6%

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

      2. *-commutative 68.6%

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

   6. Simplified 68.6%

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

   if -5.49999999999999975e-11 < j < -1.02000000000000006e-178 or 6.49999999999999961e-277 < j < 1.8e-108 or 6.4e-50 < j < 0.0071999999999999998

   1. Initial program 76.9%

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

   3. Taylor expanded in z around inf 54.5%

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

      1. *-commutative 54.5%

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

   5. Simplified 54.5%

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

   if -1.02000000000000006e-178 < j < 6.49999999999999961e-277 or 1.8e-108 < j < 6.1999999999999999e-61

   1. Initial program 76.1%

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

   3. Taylor expanded in b around inf 59.8%

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

   if 6.1999999999999999e-61 < j < 6.4e-50

   1. Initial program 99.6%

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

   3. Taylor expanded in a around inf 75.0%

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

      1. distribute-lft-out-- 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in t around inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. *-commutative 62.2%

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

      3. distribute-rgt-neg-in 62.2%

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

   8. Simplified 62.2%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.5 \cdot 10^{-11}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.02 \cdot 10^{-178}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{-277}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.8 \cdot 10^{-108}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-61}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{-50}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;j \leq 0.0072:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 40.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;j \leq -1 \cdot 10^{+47}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -3.8 \cdot 10^{-178}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-276}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-245}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{+176}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* y (* x z))))
   (if (<= j -1e+47)
     (* j (* t c))
     (if (<= j -8.5e-166)
       t_1
       (if (<= j -3.8e-178)
         t_2
         (if (<= j 4.4e-276)
           t_1
           (if (<= j 1.5e-245)
             t_2
             (if (<= j 2.8e+98)
               t_1
               (if (<= j 2.6e+176) (* (* y i) (- j)) (* c (* t j)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = y * (x * z);
	double tmp;
	if (j <= -1e+47) {
		tmp = j * (t * c);
	} else if (j <= -8.5e-166) {
		tmp = t_1;
	} else if (j <= -3.8e-178) {
		tmp = t_2;
	} else if (j <= 4.4e-276) {
		tmp = t_1;
	} else if (j <= 1.5e-245) {
		tmp = t_2;
	} else if (j <= 2.8e+98) {
		tmp = t_1;
	} else if (j <= 2.6e+176) {
		tmp = (y * i) * -j;
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = y * (x * z)
    if (j <= (-1d+47)) then
        tmp = j * (t * c)
    else if (j <= (-8.5d-166)) then
        tmp = t_1
    else if (j <= (-3.8d-178)) then
        tmp = t_2
    else if (j <= 4.4d-276) then
        tmp = t_1
    else if (j <= 1.5d-245) then
        tmp = t_2
    else if (j <= 2.8d+98) then
        tmp = t_1
    else if (j <= 2.6d+176) then
        tmp = (y * i) * -j
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = y * (x * z);
	double tmp;
	if (j <= -1e+47) {
		tmp = j * (t * c);
	} else if (j <= -8.5e-166) {
		tmp = t_1;
	} else if (j <= -3.8e-178) {
		tmp = t_2;
	} else if (j <= 4.4e-276) {
		tmp = t_1;
	} else if (j <= 1.5e-245) {
		tmp = t_2;
	} else if (j <= 2.8e+98) {
		tmp = t_1;
	} else if (j <= 2.6e+176) {
		tmp = (y * i) * -j;
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = y * (x * z)
	tmp = 0
	if j <= -1e+47:
		tmp = j * (t * c)
	elif j <= -8.5e-166:
		tmp = t_1
	elif j <= -3.8e-178:
		tmp = t_2
	elif j <= 4.4e-276:
		tmp = t_1
	elif j <= 1.5e-245:
		tmp = t_2
	elif j <= 2.8e+98:
		tmp = t_1
	elif j <= 2.6e+176:
		tmp = (y * i) * -j
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (j <= -1e+47)
		tmp = Float64(j * Float64(t * c));
	elseif (j <= -8.5e-166)
		tmp = t_1;
	elseif (j <= -3.8e-178)
		tmp = t_2;
	elseif (j <= 4.4e-276)
		tmp = t_1;
	elseif (j <= 1.5e-245)
		tmp = t_2;
	elseif (j <= 2.8e+98)
		tmp = t_1;
	elseif (j <= 2.6e+176)
		tmp = Float64(Float64(y * i) * Float64(-j));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = y * (x * z);
	tmp = 0.0;
	if (j <= -1e+47)
		tmp = j * (t * c);
	elseif (j <= -8.5e-166)
		tmp = t_1;
	elseif (j <= -3.8e-178)
		tmp = t_2;
	elseif (j <= 4.4e-276)
		tmp = t_1;
	elseif (j <= 1.5e-245)
		tmp = t_2;
	elseif (j <= 2.8e+98)
		tmp = t_1;
	elseif (j <= 2.6e+176)
		tmp = (y * i) * -j;
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1e+47], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -8.5e-166], t$95$1, If[LessEqual[j, -3.8e-178], t$95$2, If[LessEqual[j, 4.4e-276], t$95$1, If[LessEqual[j, 1.5e-245], t$95$2, If[LessEqual[j, 2.8e+98], t$95$1, If[LessEqual[j, 2.6e+176], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1e47

   1. Initial program 79.6%

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

   3. Taylor expanded in t around -inf 62.5%

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

      1. mul-1-neg 62.5%

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

      2. *-commutative 62.5%

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

      3. distribute-rgt-neg-in 62.5%

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

      4. +-commutative 62.5%

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

      5. mul-1-neg 62.5%

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

      6. unsub-neg 62.5%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in a around 0 53.9%

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

      1. *-commutative 53.9%

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

      2. associate-*l* 55.9%

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

   8. Simplified 55.9%

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

   if -1e47 < j < -8.5e-166 or -3.80000000000000015e-178 < j < 4.39999999999999961e-276 or 1.5000000000000001e-245 < j < 2.8000000000000001e98

   1. Initial program 77.1%

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

   3. Taylor expanded in b around inf 48.0%

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

   if -8.5e-166 < j < -3.80000000000000015e-178 or 4.39999999999999961e-276 < j < 1.5000000000000001e-245

   1. Initial program 80.1%

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

   3. Taylor expanded in z around inf 80.3%

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

      1. *-commutative 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in y around inf 80.7%

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

      1. *-commutative 80.7%

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

      2. associate-*r* 80.9%

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

   8. Simplified 80.9%

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

   if 2.8000000000000001e98 < j < 2.59999999999999991e176

   1. Initial program 84.3%

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

   3. Taylor expanded in y around inf 64.5%

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

   4. Taylor expanded in i around inf 53.5%

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

      1. mul-1-neg 53.5%

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

      2. associate-*r* 43.8%

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

      3. *-commutative 43.8%

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

      4. associate-*l* 53.6%

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

      5. distribute-rgt-neg-in 53.6%

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

      6. distribute-lft-neg-out 53.6%

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

      7. *-commutative 53.6%

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

   6. Simplified 53.6%

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

   if 2.59999999999999991e176 < j

   1. Initial program 74.0%

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

   3. Taylor expanded in t around -inf 47.0%

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

      1. mul-1-neg 47.0%

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

      2. *-commutative 47.0%

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

      3. distribute-rgt-neg-in 47.0%

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

      4. +-commutative 47.0%

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

      5. mul-1-neg 47.0%

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

      6. unsub-neg 47.0%

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

   5. Simplified 47.0%

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

   6. Taylor expanded in a around 0 59.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1 \cdot 10^{+47}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-166}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -3.8 \cdot 10^{-178}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-276}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-245}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{+98}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{+176}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 43.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -6.4 \cdot 10^{+47}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-166}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -3.8 \cdot 10^{-178}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2 \cdot 10^{-276}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{-243}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{+95}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 4.7 \cdot 10^{+178}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= j -6.4e+47)
     (* c (- (* t j) (* z b)))
     (if (<= j -8.5e-166)
       t_2
       (if (<= j -3.8e-178)
         t_1
         (if (<= j 2e-276)
           t_2
           (if (<= j 1.45e-243)
             t_1
             (if (<= j 7.2e+95)
               t_2
               (if (<= j 4.7e+178) (* (* y i) (- j)) (* c (* t j)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (j <= -6.4e+47) {
		tmp = c * ((t * j) - (z * b));
	} else if (j <= -8.5e-166) {
		tmp = t_2;
	} else if (j <= -3.8e-178) {
		tmp = t_1;
	} else if (j <= 2e-276) {
		tmp = t_2;
	} else if (j <= 1.45e-243) {
		tmp = t_1;
	} else if (j <= 7.2e+95) {
		tmp = t_2;
	} else if (j <= 4.7e+178) {
		tmp = (y * i) * -j;
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (x * z)
    t_2 = b * ((a * i) - (z * c))
    if (j <= (-6.4d+47)) then
        tmp = c * ((t * j) - (z * b))
    else if (j <= (-8.5d-166)) then
        tmp = t_2
    else if (j <= (-3.8d-178)) then
        tmp = t_1
    else if (j <= 2d-276) then
        tmp = t_2
    else if (j <= 1.45d-243) then
        tmp = t_1
    else if (j <= 7.2d+95) then
        tmp = t_2
    else if (j <= 4.7d+178) then
        tmp = (y * i) * -j
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (j <= -6.4e+47) {
		tmp = c * ((t * j) - (z * b));
	} else if (j <= -8.5e-166) {
		tmp = t_2;
	} else if (j <= -3.8e-178) {
		tmp = t_1;
	} else if (j <= 2e-276) {
		tmp = t_2;
	} else if (j <= 1.45e-243) {
		tmp = t_1;
	} else if (j <= 7.2e+95) {
		tmp = t_2;
	} else if (j <= 4.7e+178) {
		tmp = (y * i) * -j;
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if j <= -6.4e+47:
		tmp = c * ((t * j) - (z * b))
	elif j <= -8.5e-166:
		tmp = t_2
	elif j <= -3.8e-178:
		tmp = t_1
	elif j <= 2e-276:
		tmp = t_2
	elif j <= 1.45e-243:
		tmp = t_1
	elif j <= 7.2e+95:
		tmp = t_2
	elif j <= 4.7e+178:
		tmp = (y * i) * -j
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (j <= -6.4e+47)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (j <= -8.5e-166)
		tmp = t_2;
	elseif (j <= -3.8e-178)
		tmp = t_1;
	elseif (j <= 2e-276)
		tmp = t_2;
	elseif (j <= 1.45e-243)
		tmp = t_1;
	elseif (j <= 7.2e+95)
		tmp = t_2;
	elseif (j <= 4.7e+178)
		tmp = Float64(Float64(y * i) * Float64(-j));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (x * z);
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (j <= -6.4e+47)
		tmp = c * ((t * j) - (z * b));
	elseif (j <= -8.5e-166)
		tmp = t_2;
	elseif (j <= -3.8e-178)
		tmp = t_1;
	elseif (j <= 2e-276)
		tmp = t_2;
	elseif (j <= 1.45e-243)
		tmp = t_1;
	elseif (j <= 7.2e+95)
		tmp = t_2;
	elseif (j <= 4.7e+178)
		tmp = (y * i) * -j;
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6.4e+47], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -8.5e-166], t$95$2, If[LessEqual[j, -3.8e-178], t$95$1, If[LessEqual[j, 2e-276], t$95$2, If[LessEqual[j, 1.45e-243], t$95$1, If[LessEqual[j, 7.2e+95], t$95$2, If[LessEqual[j, 4.7e+178], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -6.4e47

   1. Initial program 79.6%

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

   3. Taylor expanded in c around inf 59.6%

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

   if -6.4e47 < j < -8.5e-166 or -3.80000000000000015e-178 < j < 2e-276 or 1.44999999999999988e-243 < j < 7.19999999999999955e95

   1. Initial program 77.1%

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

   3. Taylor expanded in b around inf 48.0%

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

   if -8.5e-166 < j < -3.80000000000000015e-178 or 2e-276 < j < 1.44999999999999988e-243

   1. Initial program 80.1%

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

   3. Taylor expanded in z around inf 80.3%

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

      1. *-commutative 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in y around inf 80.7%

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

      1. *-commutative 80.7%

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

      2. associate-*r* 80.9%

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

   8. Simplified 80.9%

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

   if 7.19999999999999955e95 < j < 4.69999999999999992e178

   1. Initial program 84.3%

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

   3. Taylor expanded in y around inf 64.5%

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

   4. Taylor expanded in i around inf 53.5%

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

      1. mul-1-neg 53.5%

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

      2. associate-*r* 43.8%

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

      3. *-commutative 43.8%

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

      4. associate-*l* 53.6%

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

      5. distribute-rgt-neg-in 53.6%

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

      6. distribute-lft-neg-out 53.6%

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

      7. *-commutative 53.6%

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

   6. Simplified 53.6%

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

   if 4.69999999999999992e178 < j

   1. Initial program 74.0%

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

   3. Taylor expanded in t around -inf 47.0%

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

      1. mul-1-neg 47.0%

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

      2. *-commutative 47.0%

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

      3. distribute-rgt-neg-in 47.0%

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

      4. +-commutative 47.0%

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

      5. mul-1-neg 47.0%

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

      6. unsub-neg 47.0%

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

   5. Simplified 47.0%

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

   6. Taylor expanded in a around 0 59.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.4 \cdot 10^{+47}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-166}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -3.8 \cdot 10^{-178}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{-276}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{-243}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.7 \cdot 10^{+178}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -8.5 \cdot 10^{-14}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-166}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-178}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-275}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 7 \cdot 10^{-245}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.85 \cdot 10^{-61}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z)))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* j (- (* t c) (* y i)))))
   (if (<= j -8.5e-14)
     t_3
     (if (<= j -8.5e-166)
       t_2
       (if (<= j -3.5e-178)
         t_1
         (if (<= j 1.5e-275)
           t_2
           (if (<= j 7e-245) t_1 (if (<= j 2.85e-61) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -8.5e-14) {
		tmp = t_3;
	} else if (j <= -8.5e-166) {
		tmp = t_2;
	} else if (j <= -3.5e-178) {
		tmp = t_1;
	} else if (j <= 1.5e-275) {
		tmp = t_2;
	} else if (j <= 7e-245) {
		tmp = t_1;
	} else if (j <= 2.85e-61) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = y * (x * z)
    t_2 = b * ((a * i) - (z * c))
    t_3 = j * ((t * c) - (y * i))
    if (j <= (-8.5d-14)) then
        tmp = t_3
    else if (j <= (-8.5d-166)) then
        tmp = t_2
    else if (j <= (-3.5d-178)) then
        tmp = t_1
    else if (j <= 1.5d-275) then
        tmp = t_2
    else if (j <= 7d-245) then
        tmp = t_1
    else if (j <= 2.85d-61) then
        tmp = t_2
    else
        tmp = t_3
    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 = y * (x * z);
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -8.5e-14) {
		tmp = t_3;
	} else if (j <= -8.5e-166) {
		tmp = t_2;
	} else if (j <= -3.5e-178) {
		tmp = t_1;
	} else if (j <= 1.5e-275) {
		tmp = t_2;
	} else if (j <= 7e-245) {
		tmp = t_1;
	} else if (j <= 2.85e-61) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	t_2 = b * ((a * i) - (z * c))
	t_3 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -8.5e-14:
		tmp = t_3
	elif j <= -8.5e-166:
		tmp = t_2
	elif j <= -3.5e-178:
		tmp = t_1
	elif j <= 1.5e-275:
		tmp = t_2
	elif j <= 7e-245:
		tmp = t_1
	elif j <= 2.85e-61:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -8.5e-14)
		tmp = t_3;
	elseif (j <= -8.5e-166)
		tmp = t_2;
	elseif (j <= -3.5e-178)
		tmp = t_1;
	elseif (j <= 1.5e-275)
		tmp = t_2;
	elseif (j <= 7e-245)
		tmp = t_1;
	elseif (j <= 2.85e-61)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (x * z);
	t_2 = b * ((a * i) - (z * c));
	t_3 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -8.5e-14)
		tmp = t_3;
	elseif (j <= -8.5e-166)
		tmp = t_2;
	elseif (j <= -3.5e-178)
		tmp = t_1;
	elseif (j <= 1.5e-275)
		tmp = t_2;
	elseif (j <= 7e-245)
		tmp = t_1;
	elseif (j <= 2.85e-61)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -8.5e-14], t$95$3, If[LessEqual[j, -8.5e-166], t$95$2, If[LessEqual[j, -3.5e-178], t$95$1, If[LessEqual[j, 1.5e-275], t$95$2, If[LessEqual[j, 7e-245], t$95$1, If[LessEqual[j, 2.85e-61], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -8.50000000000000038e-14 or 2.85000000000000003e-61 < j

   1. Initial program 78.8%

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

   3. Taylor expanded in b around 0 72.8%

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

   4. Taylor expanded in j around inf 65.8%

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

      1. *-commutative 65.8%

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

      2. *-commutative 65.8%

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

   6. Simplified 65.8%

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

   if -8.50000000000000038e-14 < j < -8.5e-166 or -3.49999999999999983e-178 < j < 1.5e-275 or 7.00000000000000033e-245 < j < 2.85000000000000003e-61

   1. Initial program 76.4%

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

   3. Taylor expanded in b around inf 50.7%

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

   if -8.5e-166 < j < -3.49999999999999983e-178 or 1.5e-275 < j < 7.00000000000000033e-245

   1. Initial program 80.1%

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

   3. Taylor expanded in z around inf 80.3%

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

      1. *-commutative 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in y around inf 80.7%

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

      1. *-commutative 80.7%

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

      2. associate-*r* 80.9%

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

   8. Simplified 80.9%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8.5 \cdot 10^{-14}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-166}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-178}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-275}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{-245}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 2.85 \cdot 10^{-61}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{if}\;j \leq -6.6 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-109}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{-146}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* j (- (* t c) (* y i))) (* x (- (* t a) (* y z))))))
   (if (<= j -6.6e-18)
     t_1
     (if (<= j -8.5e-109)
       (* a (- (* b i) (* x t)))
       (if (<= j -4.2e-146)
         (* y (- (* x z) (* i j)))
         (if (<= j 2.5e-8)
           (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	double tmp;
	if (j <= -6.6e-18) {
		tmp = t_1;
	} else if (j <= -8.5e-109) {
		tmp = a * ((b * i) - (x * t));
	} else if (j <= -4.2e-146) {
		tmp = y * ((x * z) - (i * j));
	} else if (j <= 2.5e-8) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
    if (j <= (-6.6d-18)) then
        tmp = t_1
    else if (j <= (-8.5d-109)) then
        tmp = a * ((b * i) - (x * t))
    else if (j <= (-4.2d-146)) then
        tmp = y * ((x * z) - (i * j))
    else if (j <= 2.5d-8) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	double tmp;
	if (j <= -6.6e-18) {
		tmp = t_1;
	} else if (j <= -8.5e-109) {
		tmp = a * ((b * i) - (x * t));
	} else if (j <= -4.2e-146) {
		tmp = y * ((x * z) - (i * j));
	} else if (j <= 2.5e-8) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
	tmp = 0
	if j <= -6.6e-18:
		tmp = t_1
	elif j <= -8.5e-109:
		tmp = a * ((b * i) - (x * t))
	elif j <= -4.2e-146:
		tmp = y * ((x * z) - (i * j))
	elif j <= 2.5e-8:
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))))
	tmp = 0.0
	if (j <= -6.6e-18)
		tmp = t_1;
	elseif (j <= -8.5e-109)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (j <= -4.2e-146)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (j <= 2.5e-8)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	tmp = 0.0;
	if (j <= -6.6e-18)
		tmp = t_1;
	elseif (j <= -8.5e-109)
		tmp = a * ((b * i) - (x * t));
	elseif (j <= -4.2e-146)
		tmp = y * ((x * z) - (i * j));
	elseif (j <= 2.5e-8)
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6.6e-18], t$95$1, If[LessEqual[j, -8.5e-109], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.2e-146], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.5e-8], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -6.6000000000000003e-18 or 2.4999999999999999e-8 < j

   1. Initial program 77.8%

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

   3. Taylor expanded in b around 0 73.9%

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

   if -6.6000000000000003e-18 < j < -8.50000000000000005e-109

   1. Initial program 69.6%

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

   3. Taylor expanded in a around inf 84.6%

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

      1. distribute-lft-out-- 84.6%

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

   5. Simplified 84.6%

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

   6. Taylor expanded in a around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. cancel-sign-sub-inv 84.6%

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

      3. +-commutative 84.6%

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

      4. +-commutative 84.6%

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

      5. cancel-sign-sub-inv 84.6%

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

      6. *-commutative 84.6%

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

      7. distribute-rgt-neg-in 84.6%

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

   8. Simplified 84.6%

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

   if -8.50000000000000005e-109 < j < -4.1999999999999998e-146

   1. Initial program 61.2%

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

   3. Taylor expanded in y around inf 61.3%

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

   if -4.1999999999999998e-146 < j < 2.4999999999999999e-8

   1. Initial program 81.0%

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

   3. Taylor expanded in j around 0 80.0%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.6 \cdot 10^{-18}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-109}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{-146}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 30.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;j \leq -5.4 \cdot 10^{+54}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-277}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{-115}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.32 \cdot 10^{+174}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* b i))))
   (if (<= j -5.4e+54)
     (* j (* t c))
     (if (<= j -1.45e-178)
       (* x (* y z))
       (if (<= j 3.5e-277)
         t_1
         (if (<= j 9.5e-115)
           (* y (* x z))
           (if (<= j 1.4e-59)
             t_1
             (if (<= j 1.32e+174) (* (* y i) (- j)) (* c (* t j))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double tmp;
	if (j <= -5.4e+54) {
		tmp = j * (t * c);
	} else if (j <= -1.45e-178) {
		tmp = x * (y * z);
	} else if (j <= 3.5e-277) {
		tmp = t_1;
	} else if (j <= 9.5e-115) {
		tmp = y * (x * z);
	} else if (j <= 1.4e-59) {
		tmp = t_1;
	} else if (j <= 1.32e+174) {
		tmp = (y * i) * -j;
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * i)
    if (j <= (-5.4d+54)) then
        tmp = j * (t * c)
    else if (j <= (-1.45d-178)) then
        tmp = x * (y * z)
    else if (j <= 3.5d-277) then
        tmp = t_1
    else if (j <= 9.5d-115) then
        tmp = y * (x * z)
    else if (j <= 1.4d-59) then
        tmp = t_1
    else if (j <= 1.32d+174) then
        tmp = (y * i) * -j
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double tmp;
	if (j <= -5.4e+54) {
		tmp = j * (t * c);
	} else if (j <= -1.45e-178) {
		tmp = x * (y * z);
	} else if (j <= 3.5e-277) {
		tmp = t_1;
	} else if (j <= 9.5e-115) {
		tmp = y * (x * z);
	} else if (j <= 1.4e-59) {
		tmp = t_1;
	} else if (j <= 1.32e+174) {
		tmp = (y * i) * -j;
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (b * i)
	tmp = 0
	if j <= -5.4e+54:
		tmp = j * (t * c)
	elif j <= -1.45e-178:
		tmp = x * (y * z)
	elif j <= 3.5e-277:
		tmp = t_1
	elif j <= 9.5e-115:
		tmp = y * (x * z)
	elif j <= 1.4e-59:
		tmp = t_1
	elif j <= 1.32e+174:
		tmp = (y * i) * -j
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (j <= -5.4e+54)
		tmp = Float64(j * Float64(t * c));
	elseif (j <= -1.45e-178)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 3.5e-277)
		tmp = t_1;
	elseif (j <= 9.5e-115)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 1.4e-59)
		tmp = t_1;
	elseif (j <= 1.32e+174)
		tmp = Float64(Float64(y * i) * Float64(-j));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (b * i);
	tmp = 0.0;
	if (j <= -5.4e+54)
		tmp = j * (t * c);
	elseif (j <= -1.45e-178)
		tmp = x * (y * z);
	elseif (j <= 3.5e-277)
		tmp = t_1;
	elseif (j <= 9.5e-115)
		tmp = y * (x * z);
	elseif (j <= 1.4e-59)
		tmp = t_1;
	elseif (j <= 1.32e+174)
		tmp = (y * i) * -j;
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5.4e+54], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.45e-178], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.5e-277], t$95$1, If[LessEqual[j, 9.5e-115], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.4e-59], t$95$1, If[LessEqual[j, 1.32e+174], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -5.40000000000000022e54

   1. Initial program 78.2%

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

   3. Taylor expanded in t around -inf 66.4%

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

      1. mul-1-neg 66.4%

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

      2. *-commutative 66.4%

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

      3. distribute-rgt-neg-in 66.4%

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

      4. +-commutative 66.4%

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

      5. mul-1-neg 66.4%

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

      6. unsub-neg 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in a around 0 57.3%

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

      1. *-commutative 57.3%

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

      2. associate-*l* 59.4%

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

   8. Simplified 59.4%

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

   if -5.40000000000000022e54 < j < -1.4499999999999999e-178

   1. Initial program 70.4%

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

   3. Taylor expanded in z around inf 43.3%

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

      1. *-commutative 43.3%

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

   5. Simplified 43.3%

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

   6. Taylor expanded in y around inf 35.7%

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

   if -1.4499999999999999e-178 < j < 3.49999999999999983e-277 or 9.4999999999999996e-115 < j < 1.3999999999999999e-59

   1. Initial program 79.9%

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

   3. Taylor expanded in b around inf 54.6%

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

   4. Taylor expanded in a around inf 43.1%

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

      1. *-commutative 43.1%

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

   6. Simplified 43.1%

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

   if 3.49999999999999983e-277 < j < 9.4999999999999996e-115

   1. Initial program 84.3%

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

   3. Taylor expanded in z around inf 61.1%

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

      1. *-commutative 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in y around inf 45.1%

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

      1. *-commutative 45.1%

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

      2. associate-*r* 48.2%

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

   8. Simplified 48.2%

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

   if 1.3999999999999999e-59 < j < 1.31999999999999999e174

   1. Initial program 82.0%

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

   3. Taylor expanded in y around inf 49.4%

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

   4. Taylor expanded in i around inf 39.3%

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

      1. mul-1-neg 39.3%

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

      2. associate-*r* 35.7%

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

      3. *-commutative 35.7%

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

      4. associate-*l* 39.4%

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

      5. distribute-rgt-neg-in 39.4%

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

      6. distribute-lft-neg-out 39.4%

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

      7. *-commutative 39.4%

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

   6. Simplified 39.4%

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

   if 1.31999999999999999e174 < j

   1. Initial program 74.0%

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

   3. Taylor expanded in t around -inf 47.0%

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

      1. mul-1-neg 47.0%

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

      2. *-commutative 47.0%

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

      3. distribute-rgt-neg-in 47.0%

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

      4. +-commutative 47.0%

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

      5. mul-1-neg 47.0%

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

      6. unsub-neg 47.0%

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

   5. Simplified 47.0%

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

   6. Taylor expanded in a around 0 59.9%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.4 \cdot 10^{+54}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-277}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{-115}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 1.32 \cdot 10^{+174}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 30.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;j \leq -6.8 \cdot 10^{+54}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{-178}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{-276}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{-105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 8.5:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* a (* b i))))
   (if (<= j -6.8e+54)
     (* j (* t c))
     (if (<= j -1.45e-178)
       t_1
       (if (<= j 7.5e-276)
         t_2
         (if (<= j 2.2e-105) t_1 (if (<= j 8.5) t_2 (* c (* t j)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = a * (b * i);
	double tmp;
	if (j <= -6.8e+54) {
		tmp = j * (t * c);
	} else if (j <= -1.45e-178) {
		tmp = t_1;
	} else if (j <= 7.5e-276) {
		tmp = t_2;
	} else if (j <= 2.2e-105) {
		tmp = t_1;
	} else if (j <= 8.5) {
		tmp = t_2;
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = a * (b * i)
    if (j <= (-6.8d+54)) then
        tmp = j * (t * c)
    else if (j <= (-1.45d-178)) then
        tmp = t_1
    else if (j <= 7.5d-276) then
        tmp = t_2
    else if (j <= 2.2d-105) then
        tmp = t_1
    else if (j <= 8.5d0) then
        tmp = t_2
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = a * (b * i);
	double tmp;
	if (j <= -6.8e+54) {
		tmp = j * (t * c);
	} else if (j <= -1.45e-178) {
		tmp = t_1;
	} else if (j <= 7.5e-276) {
		tmp = t_2;
	} else if (j <= 2.2e-105) {
		tmp = t_1;
	} else if (j <= 8.5) {
		tmp = t_2;
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	t_2 = a * (b * i)
	tmp = 0
	if j <= -6.8e+54:
		tmp = j * (t * c)
	elif j <= -1.45e-178:
		tmp = t_1
	elif j <= 7.5e-276:
		tmp = t_2
	elif j <= 2.2e-105:
		tmp = t_1
	elif j <= 8.5:
		tmp = t_2
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (j <= -6.8e+54)
		tmp = Float64(j * Float64(t * c));
	elseif (j <= -1.45e-178)
		tmp = t_1;
	elseif (j <= 7.5e-276)
		tmp = t_2;
	elseif (j <= 2.2e-105)
		tmp = t_1;
	elseif (j <= 8.5)
		tmp = t_2;
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	t_2 = a * (b * i);
	tmp = 0.0;
	if (j <= -6.8e+54)
		tmp = j * (t * c);
	elseif (j <= -1.45e-178)
		tmp = t_1;
	elseif (j <= 7.5e-276)
		tmp = t_2;
	elseif (j <= 2.2e-105)
		tmp = t_1;
	elseif (j <= 8.5)
		tmp = t_2;
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6.8e+54], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.45e-178], t$95$1, If[LessEqual[j, 7.5e-276], t$95$2, If[LessEqual[j, 2.2e-105], t$95$1, If[LessEqual[j, 8.5], t$95$2, N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -6.8000000000000001e54

   1. Initial program 78.2%

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

   3. Taylor expanded in t around -inf 66.4%

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

      1. mul-1-neg 66.4%

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

      2. *-commutative 66.4%

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

      3. distribute-rgt-neg-in 66.4%

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

      4. +-commutative 66.4%

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

      5. mul-1-neg 66.4%

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

      6. unsub-neg 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in a around 0 57.3%

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

      1. *-commutative 57.3%

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

      2. associate-*l* 59.4%

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

   8. Simplified 59.4%

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

   if -6.8000000000000001e54 < j < -1.4499999999999999e-178 or 7.500000000000001e-276 < j < 2.20000000000000004e-105

   1. Initial program 77.2%

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

   3. Taylor expanded in z around inf 49.9%

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

      1. *-commutative 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in y around inf 37.9%

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

   if -1.4499999999999999e-178 < j < 7.500000000000001e-276 or 2.20000000000000004e-105 < j < 8.5

   1. Initial program 78.7%

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

   3. Taylor expanded in b around inf 55.4%

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

   4. Taylor expanded in a around inf 43.1%

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

      1. *-commutative 43.1%

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

   6. Simplified 43.1%

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

   if 8.5 < j

   1. Initial program 77.9%

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

   3. Taylor expanded in t around -inf 44.5%

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

      1. mul-1-neg 44.5%

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

      2. *-commutative 44.5%

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

      3. distribute-rgt-neg-in 44.5%

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

      4. +-commutative 44.5%

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

      5. mul-1-neg 44.5%

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

      6. unsub-neg 44.5%

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

   5. Simplified 44.5%

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

   6. Taylor expanded in a around 0 43.3%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.8 \cdot 10^{+54}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{-276}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{-105}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 8.5:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 30.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;j \leq -2.8 \cdot 10^{+54}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;j \leq -3.4 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.55 \cdot 10^{-279}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.95 \cdot 10^{-115}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 0.027:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* b i))))
   (if (<= j -2.8e+54)
     (* j (* t c))
     (if (<= j -3.4e-178)
       (* x (* y z))
       (if (<= j 1.55e-279)
         t_1
         (if (<= j 2.95e-115)
           (* y (* x z))
           (if (<= j 0.027) t_1 (* c (* t j)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double tmp;
	if (j <= -2.8e+54) {
		tmp = j * (t * c);
	} else if (j <= -3.4e-178) {
		tmp = x * (y * z);
	} else if (j <= 1.55e-279) {
		tmp = t_1;
	} else if (j <= 2.95e-115) {
		tmp = y * (x * z);
	} else if (j <= 0.027) {
		tmp = t_1;
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * i)
    if (j <= (-2.8d+54)) then
        tmp = j * (t * c)
    else if (j <= (-3.4d-178)) then
        tmp = x * (y * z)
    else if (j <= 1.55d-279) then
        tmp = t_1
    else if (j <= 2.95d-115) then
        tmp = y * (x * z)
    else if (j <= 0.027d0) then
        tmp = t_1
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double tmp;
	if (j <= -2.8e+54) {
		tmp = j * (t * c);
	} else if (j <= -3.4e-178) {
		tmp = x * (y * z);
	} else if (j <= 1.55e-279) {
		tmp = t_1;
	} else if (j <= 2.95e-115) {
		tmp = y * (x * z);
	} else if (j <= 0.027) {
		tmp = t_1;
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (b * i)
	tmp = 0
	if j <= -2.8e+54:
		tmp = j * (t * c)
	elif j <= -3.4e-178:
		tmp = x * (y * z)
	elif j <= 1.55e-279:
		tmp = t_1
	elif j <= 2.95e-115:
		tmp = y * (x * z)
	elif j <= 0.027:
		tmp = t_1
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (j <= -2.8e+54)
		tmp = Float64(j * Float64(t * c));
	elseif (j <= -3.4e-178)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 1.55e-279)
		tmp = t_1;
	elseif (j <= 2.95e-115)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 0.027)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (b * i);
	tmp = 0.0;
	if (j <= -2.8e+54)
		tmp = j * (t * c);
	elseif (j <= -3.4e-178)
		tmp = x * (y * z);
	elseif (j <= 1.55e-279)
		tmp = t_1;
	elseif (j <= 2.95e-115)
		tmp = y * (x * z);
	elseif (j <= 0.027)
		tmp = t_1;
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.8e+54], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.4e-178], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.55e-279], t$95$1, If[LessEqual[j, 2.95e-115], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 0.027], t$95$1, N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -2.80000000000000015e54

   1. Initial program 78.2%

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

   3. Taylor expanded in t around -inf 66.4%

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

      1. mul-1-neg 66.4%

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

      2. *-commutative 66.4%

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

      3. distribute-rgt-neg-in 66.4%

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

      4. +-commutative 66.4%

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

      5. mul-1-neg 66.4%

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

      6. unsub-neg 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in a around 0 57.3%

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

      1. *-commutative 57.3%

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

      2. associate-*l* 59.4%

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

   8. Simplified 59.4%

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

   if -2.80000000000000015e54 < j < -3.39999999999999973e-178

   1. Initial program 70.4%

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

   3. Taylor expanded in z around inf 43.3%

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

      1. *-commutative 43.3%

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

   5. Simplified 43.3%

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

   6. Taylor expanded in y around inf 35.7%

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

   if -3.39999999999999973e-178 < j < 1.55e-279 or 2.94999999999999997e-115 < j < 0.0269999999999999997

   1. Initial program 80.9%

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

   3. Taylor expanded in b around inf 54.6%

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

   4. Taylor expanded in a around inf 40.5%

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

      1. *-commutative 40.5%

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

   6. Simplified 40.5%

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

   if 1.55e-279 < j < 2.94999999999999997e-115

   1. Initial program 84.3%

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

   3. Taylor expanded in z around inf 61.1%

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

      1. *-commutative 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in y around inf 45.1%

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

      1. *-commutative 45.1%

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

      2. associate-*r* 48.2%

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

   8. Simplified 48.2%

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

   if 0.0269999999999999997 < j

   1. Initial program 77.9%

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

   3. Taylor expanded in t around -inf 44.5%

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

      1. mul-1-neg 44.5%

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

      2. *-commutative 44.5%

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

      3. distribute-rgt-neg-in 44.5%

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

      4. +-commutative 44.5%

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

      5. mul-1-neg 44.5%

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

      6. unsub-neg 44.5%

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

   5. Simplified 44.5%

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

   6. Taylor expanded in a around 0 43.3%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.8 \cdot 10^{+54}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;j \leq -3.4 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.55 \cdot 10^{-279}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 2.95 \cdot 10^{-115}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 0.027:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 67.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+37} \lor \neg \left(b \leq 3.8 \cdot 10^{+144}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -8.2e+37) (not (<= b 3.8e+144)))
   (* b (- (* a i) (* z c)))
   (- (* j (- (* t c) (* y i))) (* x (- (* t a) (* y z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -8.2e+37) || !(b <= 3.8e+144)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-8.2d+37)) .or. (.not. (b <= 3.8d+144))) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -8.2e+37) || !(b <= 3.8e+144)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -8.2e+37) or not (b <= 3.8e+144):
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -8.2e+37) || !(b <= 3.8e+144))
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -8.2e+37) || ~((b <= 3.8e+144)))
		tmp = b * ((a * i) - (z * c));
	else
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -8.2e+37], N[Not[LessEqual[b, 3.8e+144]], $MachinePrecision]], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.1999999999999996e37 or 3.80000000000000026e144 < b

   1. Initial program 75.8%

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

   3. Taylor expanded in b around inf 67.8%

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

   if -8.1999999999999996e37 < b < 3.80000000000000026e144

   1. Initial program 78.9%

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

   3. Taylor expanded in b around 0 71.6%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+37} \lor \neg \left(b \leq 3.8 \cdot 10^{+144}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 30.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -5.2 \cdot 10^{+48} \lor \neg \left(j \leq 25.5\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -5.2e+48) (not (<= j 25.5))) (* c (* t j)) (* a (* b 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 ((j <= -5.2e+48) || !(j <= 25.5)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * 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 ((j <= (-5.2d+48)) .or. (.not. (j <= 25.5d0))) then
        tmp = c * (t * j)
    else
        tmp = a * (b * 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 ((j <= -5.2e+48) || !(j <= 25.5)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -5.2e+48) or not (j <= 25.5):
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -5.2e+48) || !(j <= 25.5))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -5.2e+48) || ~((j <= 25.5)))
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -5.2e+48], N[Not[LessEqual[j, 25.5]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -5.1999999999999999e48 or 25.5 < j

   1. Initial program 78.6%

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

   3. Taylor expanded in t around -inf 52.0%

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

      1. mul-1-neg 52.0%

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

      2. *-commutative 52.0%

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

      3. distribute-rgt-neg-in 52.0%

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

      4. +-commutative 52.0%

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

      5. mul-1-neg 52.0%

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

      6. unsub-neg 52.0%

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

   5. Simplified 52.0%

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

   6. Taylor expanded in a around 0 47.7%

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

   if -5.1999999999999999e48 < j < 25.5

   1. Initial program 77.3%

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

   3. Taylor expanded in b around inf 45.6%

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

   4. Taylor expanded in a around inf 32.1%

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

      1. *-commutative 32.1%

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

   6. Simplified 32.1%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.2 \cdot 10^{+48} \lor \neg \left(j \leq 25.5\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -8 \cdot 10^{+44}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;j \leq 0.62:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -8e+44) (* j (* t c)) (if (<= j 0.62) (* a (* b i)) (* c (* t j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -8e+44) {
		tmp = j * (t * c);
	} else if (j <= 0.62) {
		tmp = a * (b * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-8d+44)) then
        tmp = j * (t * c)
    else if (j <= 0.62d0) then
        tmp = a * (b * i)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -8e+44) {
		tmp = j * (t * c);
	} else if (j <= 0.62) {
		tmp = a * (b * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -8e+44:
		tmp = j * (t * c)
	elif j <= 0.62:
		tmp = a * (b * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -8e+44)
		tmp = Float64(j * Float64(t * c));
	elseif (j <= 0.62)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -8e+44)
		tmp = j * (t * c);
	elseif (j <= 0.62)
		tmp = a * (b * i);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -8e+44], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 0.62], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -8.0000000000000007e44

   1. Initial program 79.6%

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

   3. Taylor expanded in t around -inf 62.5%

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

      1. mul-1-neg 62.5%

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

      2. *-commutative 62.5%

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

      3. distribute-rgt-neg-in 62.5%

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

      4. +-commutative 62.5%

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

      5. mul-1-neg 62.5%

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

      6. unsub-neg 62.5%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in a around 0 53.9%

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

      1. *-commutative 53.9%

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

      2. associate-*l* 55.9%

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

   8. Simplified 55.9%

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

   if -8.0000000000000007e44 < j < 0.619999999999999996

   1. Initial program 77.3%

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

   3. Taylor expanded in b around inf 45.6%

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

   4. Taylor expanded in a around inf 32.1%

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

      1. *-commutative 32.1%

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

   6. Simplified 32.1%

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

   if 0.619999999999999996 < j

   1. Initial program 77.9%

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

   3. Taylor expanded in t around -inf 44.5%

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

      1. mul-1-neg 44.5%

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

      2. *-commutative 44.5%

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

      3. distribute-rgt-neg-in 44.5%

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

      4. +-commutative 44.5%

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

      5. mul-1-neg 44.5%

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

      6. unsub-neg 44.5%

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

   5. Simplified 44.5%

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

   6. Taylor expanded in a around 0 43.3%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8 \cdot 10^{+44}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;j \leq 0.62:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 22.2% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.9%

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

3. Taylor expanded in b around inf 34.5%

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

4. Taylor expanded in a around inf 22.7%

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

   1. *-commutative 22.7%

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

6. Simplified 22.7%

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

7. Final simplification 22.7%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
8. Add Preprocessing

Developer target: 69.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024040 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))