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

Percentage Accurate: 73.0% → 81.5%

Time: 17.5s

Alternatives: 15

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((a * c) - (y * i))) - ((b * ((z * c) - (t * i))) + (x * ((t * a) - (y * z))));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = c * ((a * j) - (z * b));
	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[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $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 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 93.6%

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

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

   1. Initial program 0.0%

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

      1. cancel-sign-sub 0.0%

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

      2. cancel-sign-sub-inv 0.0%

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

      3. *-commutative 0.0%

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

      4. remove-double-neg 0.0%

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

      5. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in c around inf 54.1%

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

4. Final simplification 85.0%

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

Alternative 2: 67.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-46}:\\ \;\;\;\;\left(c \cdot \left(a \cdot j\right) - a \cdot \left(x \cdot t\right)\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+140}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= y -8.2e+149)
     t_1
     (if (<= y 2.6e-46)
       (- (- (* c (* a j)) (* a (* x t))) (* b (- (* z c) (* t i))))
       (if (<= y 3.9e+140)
         (+ (* x (- (* y z) (* t a))) (* j (- (* a c) (* y i))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -8.2e+149) {
		tmp = t_1;
	} else if (y <= 2.6e-46) {
		tmp = ((c * (a * j)) - (a * (x * t))) - (b * ((z * c) - (t * i)));
	} else if (y <= 3.9e+140) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	} 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 = y * ((x * z) - (i * j))
    if (y <= (-8.2d+149)) then
        tmp = t_1
    else if (y <= 2.6d-46) then
        tmp = ((c * (a * j)) - (a * (x * t))) - (b * ((z * c) - (t * i)))
    else if (y <= 3.9d+140) then
        tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
    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 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -8.2e+149) {
		tmp = t_1;
	} else if (y <= 2.6e-46) {
		tmp = ((c * (a * j)) - (a * (x * t))) - (b * ((z * c) - (t * i)));
	} else if (y <= 3.9e+140) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -8.2e+149:
		tmp = t_1
	elif y <= 2.6e-46:
		tmp = ((c * (a * j)) - (a * (x * t))) - (b * ((z * c) - (t * i)))
	elif y <= 3.9e+140:
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
	else:
		tmp = t_1
	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)))
	tmp = 0.0
	if (y <= -8.2e+149)
		tmp = t_1;
	elseif (y <= 2.6e-46)
		tmp = Float64(Float64(Float64(c * Float64(a * j)) - Float64(a * Float64(x * t))) - Float64(b * Float64(Float64(z * c) - Float64(t * i))));
	elseif (y <= 3.9e+140)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	else
		tmp = t_1;
	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));
	tmp = 0.0;
	if (y <= -8.2e+149)
		tmp = t_1;
	elseif (y <= 2.6e-46)
		tmp = ((c * (a * j)) - (a * (x * t))) - (b * ((z * c) - (t * i)));
	elseif (y <= 3.9e+140)
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e+149], t$95$1, If[LessEqual[y, 2.6e-46], N[(N[(N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e+140], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.1999999999999992e149 or 3.89999999999999974e140 < y

   1. Initial program 53.0%

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

      1. cancel-sign-sub 53.0%

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

      2. cancel-sign-sub-inv 53.0%

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

      3. *-commutative 53.0%

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

      4. remove-double-neg 53.0%

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

      5. *-commutative 53.0%

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

   3. Simplified 53.0%

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

   4. Taylor expanded in y around -inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. distribute-rgt-neg-in 73.4%

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

      3. mul-1-neg 73.4%

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

      4. unsub-neg 73.4%

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

      5. *-commutative 73.4%

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

   6. Simplified 73.4%

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

   if -8.1999999999999992e149 < y < 2.6000000000000002e-46

   1. Initial program 81.2%

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

      1. cancel-sign-sub 81.2%

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

      2. cancel-sign-sub-inv 81.2%

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

      3. *-commutative 81.2%

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

      4. remove-double-neg 81.2%

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

      5. *-commutative 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in y around 0 75.1%

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

   if 2.6000000000000002e-46 < y < 3.89999999999999974e140

   1. Initial program 78.8%

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

      1. cancel-sign-sub 78.8%

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

      2. cancel-sign-sub-inv 78.8%

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

      3. *-commutative 78.8%

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

      4. remove-double-neg 78.8%

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

      5. *-commutative 78.8%

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

   3. Simplified 78.8%

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

   4. Taylor expanded in b around 0 81.3%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+149}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-46}:\\ \;\;\;\;\left(c \cdot \left(a \cdot j\right) - a \cdot \left(x \cdot t\right)\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+140}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 3: 51.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.55 \cdot 10^{+156}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-36}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-172}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-100}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 118:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* a (- (* c j) (* x t)))))
   (if (<= a -2.55e+156)
     t_3
     (if (<= a -4.4e-36)
       (* c (- (* a j) (* z b)))
       (if (<= a -7.5e-272)
         t_1
         (if (<= a 1.9e-172)
           t_2
           (if (<= a 2.9e-128)
             t_1
             (if (<= a 4.3e-100) t_2 (if (<= a 118.0) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.55e+156) {
		tmp = t_3;
	} else if (a <= -4.4e-36) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= -7.5e-272) {
		tmp = t_1;
	} else if (a <= 1.9e-172) {
		tmp = t_2;
	} else if (a <= 2.9e-128) {
		tmp = t_1;
	} else if (a <= 4.3e-100) {
		tmp = t_2;
	} else if (a <= 118.0) {
		tmp = t_1;
	} 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 * ((t * i) - (z * c))
    t_2 = y * ((x * z) - (i * j))
    t_3 = a * ((c * j) - (x * t))
    if (a <= (-2.55d+156)) then
        tmp = t_3
    else if (a <= (-4.4d-36)) then
        tmp = c * ((a * j) - (z * b))
    else if (a <= (-7.5d-272)) then
        tmp = t_1
    else if (a <= 1.9d-172) then
        tmp = t_2
    else if (a <= 2.9d-128) then
        tmp = t_1
    else if (a <= 4.3d-100) then
        tmp = t_2
    else if (a <= 118.0d0) then
        tmp = t_1
    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 * ((t * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.55e+156) {
		tmp = t_3;
	} else if (a <= -4.4e-36) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= -7.5e-272) {
		tmp = t_1;
	} else if (a <= 1.9e-172) {
		tmp = t_2;
	} else if (a <= 2.9e-128) {
		tmp = t_1;
	} else if (a <= 4.3e-100) {
		tmp = t_2;
	} else if (a <= 118.0) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = y * ((x * z) - (i * j))
	t_3 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -2.55e+156:
		tmp = t_3
	elif a <= -4.4e-36:
		tmp = c * ((a * j) - (z * b))
	elif a <= -7.5e-272:
		tmp = t_1
	elif a <= 1.9e-172:
		tmp = t_2
	elif a <= 2.9e-128:
		tmp = t_1
	elif a <= 4.3e-100:
		tmp = t_2
	elif a <= 118.0:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2.55e+156)
		tmp = t_3;
	elseif (a <= -4.4e-36)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (a <= -7.5e-272)
		tmp = t_1;
	elseif (a <= 1.9e-172)
		tmp = t_2;
	elseif (a <= 2.9e-128)
		tmp = t_1;
	elseif (a <= 4.3e-100)
		tmp = t_2;
	elseif (a <= 118.0)
		tmp = t_1;
	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 * ((t * i) - (z * c));
	t_2 = y * ((x * z) - (i * j));
	t_3 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -2.55e+156)
		tmp = t_3;
	elseif (a <= -4.4e-36)
		tmp = c * ((a * j) - (z * b));
	elseif (a <= -7.5e-272)
		tmp = t_1;
	elseif (a <= 1.9e-172)
		tmp = t_2;
	elseif (a <= 2.9e-128)
		tmp = t_1;
	elseif (a <= 4.3e-100)
		tmp = t_2;
	elseif (a <= 118.0)
		tmp = t_1;
	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[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.55e+156], t$95$3, If[LessEqual[a, -4.4e-36], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.5e-272], t$95$1, If[LessEqual[a, 1.9e-172], t$95$2, If[LessEqual[a, 2.9e-128], t$95$1, If[LessEqual[a, 4.3e-100], t$95$2, If[LessEqual[a, 118.0], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.55000000000000007e156 or 118 < a

   1. Initial program 64.7%

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

      1. cancel-sign-sub 64.7%

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

      2. cancel-sign-sub-inv 64.7%

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

      3. *-commutative 64.7%

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

      4. remove-double-neg 64.7%

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

      5. *-commutative 64.7%

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

   3. Simplified 64.7%

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

   4. Taylor expanded in a around inf 74.3%

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

      1. +-commutative 74.3%

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

      2. mul-1-neg 74.3%

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

      3. unsub-neg 74.3%

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

      4. *-commutative 74.3%

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

   6. Simplified 74.3%

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

   if -2.55000000000000007e156 < a < -4.3999999999999999e-36

   1. Initial program 83.6%

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

      1. cancel-sign-sub 83.6%

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

      2. cancel-sign-sub-inv 83.6%

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

      3. *-commutative 83.6%

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

      4. remove-double-neg 83.6%

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

      5. *-commutative 83.6%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in c around inf 53.2%

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

   if -4.3999999999999999e-36 < a < -7.50000000000000005e-272 or 1.89999999999999993e-172 < a < 2.9e-128 or 4.29999999999999998e-100 < a < 118

   1. Initial program 82.6%

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

      1. cancel-sign-sub 82.6%

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

      2. cancel-sign-sub-inv 82.6%

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

      3. *-commutative 82.6%

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

      4. remove-double-neg 82.6%

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

      5. *-commutative 82.6%

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

   3. Simplified 82.6%

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

   4. Taylor expanded in b around inf 72.8%

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

   if -7.50000000000000005e-272 < a < 1.89999999999999993e-172 or 2.9e-128 < a < 4.29999999999999998e-100

   1. Initial program 70.6%

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

      1. cancel-sign-sub 70.6%

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

      2. cancel-sign-sub-inv 70.6%

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

      3. *-commutative 70.6%

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

      4. remove-double-neg 70.6%

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

      5. *-commutative 70.6%

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

   3. Simplified 70.6%

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

   4. Taylor expanded in y around -inf 73.7%

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

      1. mul-1-neg 73.7%

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

      2. distribute-rgt-neg-in 73.7%

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

      3. mul-1-neg 73.7%

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

      4. unsub-neg 73.7%

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

      5. *-commutative 73.7%

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

   6. Simplified 73.7%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{+156}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-36}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-272}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-172}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-128}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-100}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 118:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 4: 60.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.95 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 9.2 \cdot 10^{+127}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - t \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -1.95e+43)
     t_1
     (if (<= j 9.2e+127)
       (- (* b (- (* t i) (* z c))) (* t (* x a)))
       (+ (* x (- (* y z) (* t a))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.95e+43) {
		tmp = t_1;
	} else if (j <= 9.2e+127) {
		tmp = (b * ((t * i) - (z * c))) - (t * (x * a));
	} else {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (j <= (-1.95d+43)) then
        tmp = t_1
    else if (j <= 9.2d+127) then
        tmp = (b * ((t * i) - (z * c))) - (t * (x * a))
    else
        tmp = (x * ((y * z) - (t * a))) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.95e+43) {
		tmp = t_1;
	} else if (j <= 9.2e+127) {
		tmp = (b * ((t * i) - (z * c))) - (t * (x * a));
	} else {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -1.95e+43:
		tmp = t_1
	elif j <= 9.2e+127:
		tmp = (b * ((t * i) - (z * c))) - (t * (x * a))
	else:
		tmp = (x * ((y * z) - (t * a))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.95e+43)
		tmp = t_1;
	elseif (j <= 9.2e+127)
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(t * Float64(x * a)));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.95e+43)
		tmp = t_1;
	elseif (j <= 9.2e+127)
		tmp = (b * ((t * i) - (z * c))) - (t * (x * a));
	else
		tmp = (x * ((y * z) - (t * a))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.95e+43], t$95$1, If[LessEqual[j, 9.2e+127], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.95e43

   1. Initial program 70.5%

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

      1. cancel-sign-sub 70.5%

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

      2. cancel-sign-sub-inv 70.5%

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

      3. *-commutative 70.5%

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

      4. remove-double-neg 70.5%

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

      5. *-commutative 70.5%

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

   3. Simplified 70.5%

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

   4. Taylor expanded in j around inf 66.6%

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

   if -1.95e43 < j < 9.2000000000000007e127

   1. Initial program 70.8%

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

      1. cancel-sign-sub 70.8%

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

      2. cancel-sign-sub-inv 70.8%

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

      3. *-commutative 70.8%

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

      4. remove-double-neg 70.8%

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

      5. *-commutative 70.8%

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

   3. Simplified 70.8%

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

   4. Taylor expanded in y around 0 69.9%

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

   5. Taylor expanded in j around 0 65.9%

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

      1. sub-neg 65.9%

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

      2. +-commutative 65.9%

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

      3. neg-mul-1 65.9%

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

      4. unsub-neg 65.9%

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

      5. *-commutative 65.9%

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

      6. *-commutative 65.9%

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

      7. distribute-rgt-neg-in 65.9%

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

      8. neg-sub0 65.9%

         \[\leadsto b \cdot \color{blue}{\left(0 - \left(c \cdot z - t \cdot i\right)\right)} - a \cdot \left(t \cdot x\right) \]

      9. associate-+l- 65.9%

         \[\leadsto b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + t \cdot i\right)} - a \cdot \left(t \cdot x\right) \]

      10. neg-sub0 65.9%

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

      11. +-commutative 65.9%

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

      12. *-commutative 65.9%

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

      13. sub-neg 65.9%

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

      14. *-commutative 65.9%

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

      15. associate-*l* 69.9%

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

      16. *-commutative 69.9%

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

   7. Simplified 69.9%

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

   if 9.2000000000000007e127 < j

   1. Initial program 85.3%

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

      1. cancel-sign-sub 85.3%

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

      2. cancel-sign-sub-inv 85.3%

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

      3. *-commutative 85.3%

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

      4. remove-double-neg 85.3%

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

      5. *-commutative 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in b around 0 83.3%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.95 \cdot 10^{+43}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 9.2 \cdot 10^{+127}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - t \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 5: 60.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -4.5 \cdot 10^{+43} \lor \neg \left(j \leq 2.5 \cdot 10^{+104}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - t \cdot \left(x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -4.5e+43) (not (<= j 2.5e+104)))
   (* j (- (* a c) (* y i)))
   (- (* b (- (* t i) (* z c))) (* t (* x a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -4.5e+43) || !(j <= 2.5e+104)) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = (b * ((t * i) - (z * c))) - (t * (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-4.5d+43)) .or. (.not. (j <= 2.5d+104))) then
        tmp = j * ((a * c) - (y * i))
    else
        tmp = (b * ((t * i) - (z * c))) - (t * (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -4.5e+43) || !(j <= 2.5e+104)) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = (b * ((t * i) - (z * c))) - (t * (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -4.5e+43) or not (j <= 2.5e+104):
		tmp = j * ((a * c) - (y * i))
	else:
		tmp = (b * ((t * i) - (z * c))) - (t * (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -4.5e+43) || !(j <= 2.5e+104))
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	else
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(t * Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -4.5e+43) || ~((j <= 2.5e+104)))
		tmp = j * ((a * c) - (y * i));
	else
		tmp = (b * ((t * i) - (z * c))) - (t * (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -4.5e+43], N[Not[LessEqual[j, 2.5e+104]], $MachinePrecision]], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -4.5e43 or 2.4999999999999998e104 < j

   1. Initial program 75.1%

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

      1. cancel-sign-sub 75.1%

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

      2. cancel-sign-sub-inv 75.1%

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

      3. *-commutative 75.1%

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

      4. remove-double-neg 75.1%

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

      5. *-commutative 75.1%

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

   3. Simplified 75.1%

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

   4. Taylor expanded in j around inf 69.7%

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

   if -4.5e43 < j < 2.4999999999999998e104

   1. Initial program 71.6%

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

      1. cancel-sign-sub 71.6%

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

      2. cancel-sign-sub-inv 71.6%

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

      3. *-commutative 71.6%

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

      4. remove-double-neg 71.6%

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

      5. *-commutative 71.6%

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

   3. Simplified 71.6%

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

   4. Taylor expanded in y around 0 70.6%

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

   5. Taylor expanded in j around 0 66.6%

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

      1. sub-neg 66.6%

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

      2. +-commutative 66.6%

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

      3. neg-mul-1 66.6%

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

      4. unsub-neg 66.6%

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

      5. *-commutative 66.6%

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

      6. *-commutative 66.6%

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

      7. distribute-rgt-neg-in 66.6%

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

      8. neg-sub0 66.6%

         \[\leadsto b \cdot \color{blue}{\left(0 - \left(c \cdot z - t \cdot i\right)\right)} - a \cdot \left(t \cdot x\right) \]

      9. associate-+l- 66.6%

         \[\leadsto b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + t \cdot i\right)} - a \cdot \left(t \cdot x\right) \]

      10. neg-sub0 66.6%

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

      11. +-commutative 66.6%

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

      12. *-commutative 66.6%

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

      13. sub-neg 66.6%

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

      14. *-commutative 66.6%

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

      15. associate-*l* 70.7%

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

      16. *-commutative 70.7%

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

   7. Simplified 70.7%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.5 \cdot 10^{+43} \lor \neg \left(j \leq 2.5 \cdot 10^{+104}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - t \cdot \left(x \cdot a\right)\\ \end{array} \]

Alternative 6: 51.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.7 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-35}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-199}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 1450:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -3.7e+156)
     t_1
     (if (<= a -2.4e-35)
       (* c (- (* a j) (* z b)))
       (if (<= a 1.02e-199)
         (* i (- (* t b) (* y j)))
         (if (<= a 1450.0) (* b (- (* t 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 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.7e+156) {
		tmp = t_1;
	} else if (a <= -2.4e-35) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= 1.02e-199) {
		tmp = i * ((t * b) - (y * j));
	} else if (a <= 1450.0) {
		tmp = b * ((t * 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 = a * ((c * j) - (x * t))
    if (a <= (-3.7d+156)) then
        tmp = t_1
    else if (a <= (-2.4d-35)) then
        tmp = c * ((a * j) - (z * b))
    else if (a <= 1.02d-199) then
        tmp = i * ((t * b) - (y * j))
    else if (a <= 1450.0d0) then
        tmp = b * ((t * 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 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.7e+156) {
		tmp = t_1;
	} else if (a <= -2.4e-35) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= 1.02e-199) {
		tmp = i * ((t * b) - (y * j));
	} else if (a <= 1450.0) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -3.7e+156:
		tmp = t_1
	elif a <= -2.4e-35:
		tmp = c * ((a * j) - (z * b))
	elif a <= 1.02e-199:
		tmp = i * ((t * b) - (y * j))
	elif a <= 1450.0:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -3.7e+156)
		tmp = t_1;
	elseif (a <= -2.4e-35)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (a <= 1.02e-199)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (a <= 1450.0)
		tmp = Float64(b * Float64(Float64(t * 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 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -3.7e+156)
		tmp = t_1;
	elseif (a <= -2.4e-35)
		tmp = c * ((a * j) - (z * b));
	elseif (a <= 1.02e-199)
		tmp = i * ((t * b) - (y * j));
	elseif (a <= 1450.0)
		tmp = b * ((t * 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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.7e+156], t$95$1, If[LessEqual[a, -2.4e-35], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.02e-199], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1450.0], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.70000000000000001e156 or 1450 < a

   1. Initial program 64.7%

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

      1. cancel-sign-sub 64.7%

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

      2. cancel-sign-sub-inv 64.7%

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

      3. *-commutative 64.7%

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

      4. remove-double-neg 64.7%

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

      5. *-commutative 64.7%

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

   3. Simplified 64.7%

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

   4. Taylor expanded in a around inf 74.3%

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

      1. +-commutative 74.3%

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

      2. mul-1-neg 74.3%

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

      3. unsub-neg 74.3%

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

      4. *-commutative 74.3%

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

   6. Simplified 74.3%

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

   if -3.70000000000000001e156 < a < -2.4000000000000001e-35

   1. Initial program 83.1%

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

      1. cancel-sign-sub 83.1%

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

      2. cancel-sign-sub-inv 83.1%

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

      3. *-commutative 83.1%

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

      4. remove-double-neg 83.1%

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

      5. *-commutative 83.1%

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

   3. Simplified 83.1%

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

   4. Taylor expanded in c around inf 54.5%

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

   if -2.4000000000000001e-35 < a < 1.02e-199

   1. Initial program 75.5%

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

      1. cancel-sign-sub 75.5%

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

      2. cancel-sign-sub-inv 75.5%

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

      3. *-commutative 75.5%

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

      4. remove-double-neg 75.5%

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

      5. *-commutative 75.5%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in i around inf 57.1%

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

      1. associate-*r* 57.1%

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

      2. neg-mul-1 57.1%

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

      3. cancel-sign-sub 57.1%

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

      4. +-commutative 57.1%

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

      5. mul-1-neg 57.1%

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

      6. unsub-neg 57.1%

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

   6. Simplified 57.1%

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

   if 1.02e-199 < a < 1450

   1. Initial program 83.1%

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

      1. cancel-sign-sub 83.1%

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

      2. cancel-sign-sub-inv 83.1%

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

      3. *-commutative 83.1%

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

      4. remove-double-neg 83.1%

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

      5. *-commutative 83.1%

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

   3. Simplified 83.1%

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

   4. Taylor expanded in b around inf 62.3%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+156}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-35}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-199}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 1450:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 7: 42.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.5 \cdot 10^{+177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-228}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-24}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -1.5e+177)
     t_1
     (if (<= a -6e-228)
       (* c (- (* a j) (* z b)))
       (if (<= a 5.3e-24) (* i (* t b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.5e+177) {
		tmp = t_1;
	} else if (a <= -6e-228) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= 5.3e-24) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-1.5d+177)) then
        tmp = t_1
    else if (a <= (-6d-228)) then
        tmp = c * ((a * j) - (z * b))
    else if (a <= 5.3d-24) then
        tmp = i * (t * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.5e+177) {
		tmp = t_1;
	} else if (a <= -6e-228) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= 5.3e-24) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.5e+177:
		tmp = t_1
	elif a <= -6e-228:
		tmp = c * ((a * j) - (z * b))
	elif a <= 5.3e-24:
		tmp = i * (t * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.5e+177)
		tmp = t_1;
	elseif (a <= -6e-228)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (a <= 5.3e-24)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.5e+177)
		tmp = t_1;
	elseif (a <= -6e-228)
		tmp = c * ((a * j) - (z * b));
	elseif (a <= 5.3e-24)
		tmp = i * (t * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.5e+177], t$95$1, If[LessEqual[a, -6e-228], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.3e-24], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.5e177 or 5.29999999999999969e-24 < a

   1. Initial program 64.8%

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

      1. cancel-sign-sub 64.8%

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

      2. cancel-sign-sub-inv 64.8%

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

      3. *-commutative 64.8%

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

      4. remove-double-neg 64.8%

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

      5. *-commutative 64.8%

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

   3. Simplified 64.8%

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

   4. Taylor expanded in a around inf 74.2%

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

      1. +-commutative 74.2%

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

      2. mul-1-neg 74.2%

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

      3. unsub-neg 74.2%

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

      4. *-commutative 74.2%

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

   6. Simplified 74.2%

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

   if -1.5e177 < a < -5.9999999999999999e-228

   1. Initial program 80.4%

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

      1. cancel-sign-sub 80.4%

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

      2. cancel-sign-sub-inv 80.4%

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

      3. *-commutative 80.4%

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

      4. remove-double-neg 80.4%

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

      5. *-commutative 80.4%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in c around inf 48.7%

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

   if -5.9999999999999999e-228 < a < 5.29999999999999969e-24

   1. Initial program 79.1%

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

      1. cancel-sign-sub 79.1%

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

      2. cancel-sign-sub-inv 79.1%

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

      3. *-commutative 79.1%

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

      4. remove-double-neg 79.1%

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

      5. *-commutative 79.1%

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

   3. Simplified 79.1%

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

   4. Taylor expanded in y around 0 48.9%

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

   5. Taylor expanded in i around inf 36.5%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+177}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-228}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-24}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 8: 51.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-32}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-23}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -1.55e+158)
     t_1
     (if (<= a -2.5e-32)
       (* c (- (* a j) (* z b)))
       (if (<= a 3.7e-23) (* i (- (* t b) (* y j))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.55e+158) {
		tmp = t_1;
	} else if (a <= -2.5e-32) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= 3.7e-23) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-1.55d+158)) then
        tmp = t_1
    else if (a <= (-2.5d-32)) then
        tmp = c * ((a * j) - (z * b))
    else if (a <= 3.7d-23) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.55e+158) {
		tmp = t_1;
	} else if (a <= -2.5e-32) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= 3.7e-23) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.55e+158:
		tmp = t_1
	elif a <= -2.5e-32:
		tmp = c * ((a * j) - (z * b))
	elif a <= 3.7e-23:
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.55e+158)
		tmp = t_1;
	elseif (a <= -2.5e-32)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (a <= 3.7e-23)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.55e+158)
		tmp = t_1;
	elseif (a <= -2.5e-32)
		tmp = c * ((a * j) - (z * b));
	elseif (a <= 3.7e-23)
		tmp = i * ((t * b) - (y * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.55e+158], t$95$1, If[LessEqual[a, -2.5e-32], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.7e-23], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.5500000000000001e158 or 3.7000000000000003e-23 < a

   1. Initial program 64.2%

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

      1. cancel-sign-sub 64.2%

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

      2. cancel-sign-sub-inv 64.2%

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

      3. *-commutative 64.2%

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

      4. remove-double-neg 64.2%

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

      5. *-commutative 64.2%

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

   3. Simplified 64.2%

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

   4. Taylor expanded in a around inf 73.5%

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

      1. +-commutative 73.5%

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

      2. mul-1-neg 73.5%

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

      3. unsub-neg 73.5%

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

      4. *-commutative 73.5%

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

   6. Simplified 73.5%

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

   if -1.5500000000000001e158 < a < -2.5e-32

   1. Initial program 83.1%

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

      1. cancel-sign-sub 83.1%

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

      2. cancel-sign-sub-inv 83.1%

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

      3. *-commutative 83.1%

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

      4. remove-double-neg 83.1%

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

      5. *-commutative 83.1%

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

   3. Simplified 83.1%

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

   4. Taylor expanded in c around inf 54.5%

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

   if -2.5e-32 < a < 3.7000000000000003e-23

   1. Initial program 79.4%

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

      1. cancel-sign-sub 79.4%

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

      2. cancel-sign-sub-inv 79.4%

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

      3. *-commutative 79.4%

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

      4. remove-double-neg 79.4%

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

      5. *-commutative 79.4%

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

   3. Simplified 79.4%

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

   4. Taylor expanded in i around inf 54.6%

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

      1. associate-*r* 54.6%

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

      2. neg-mul-1 54.6%

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

      3. cancel-sign-sub 54.6%

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

      4. +-commutative 54.6%

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

      5. mul-1-neg 54.6%

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

      6. unsub-neg 54.6%

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

   6. Simplified 54.6%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+158}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-32}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-23}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 9: 30.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(x \cdot \left(-a\right)\right)\\ t_2 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;j \leq -8.8 \cdot 10^{+33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -4.4 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 3 \cdot 10^{-128}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 0.032:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* x (- a)))) (t_2 (* a (* c j))))
   (if (<= j -8.8e+33)
     t_2
     (if (<= j -4.4e-146)
       t_1
       (if (<= j 3e-128) (* t (* b i)) (if (<= j 0.032) 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 = t * (x * -a);
	double t_2 = a * (c * j);
	double tmp;
	if (j <= -8.8e+33) {
		tmp = t_2;
	} else if (j <= -4.4e-146) {
		tmp = t_1;
	} else if (j <= 3e-128) {
		tmp = t * (b * i);
	} else if (j <= 0.032) {
		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 = t * (x * -a)
    t_2 = a * (c * j)
    if (j <= (-8.8d+33)) then
        tmp = t_2
    else if (j <= (-4.4d-146)) then
        tmp = t_1
    else if (j <= 3d-128) then
        tmp = t * (b * i)
    else if (j <= 0.032d0) 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 = t * (x * -a);
	double t_2 = a * (c * j);
	double tmp;
	if (j <= -8.8e+33) {
		tmp = t_2;
	} else if (j <= -4.4e-146) {
		tmp = t_1;
	} else if (j <= 3e-128) {
		tmp = t * (b * i);
	} else if (j <= 0.032) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (x * -a)
	t_2 = a * (c * j)
	tmp = 0
	if j <= -8.8e+33:
		tmp = t_2
	elif j <= -4.4e-146:
		tmp = t_1
	elif j <= 3e-128:
		tmp = t * (b * i)
	elif j <= 0.032:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(x * Float64(-a)))
	t_2 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (j <= -8.8e+33)
		tmp = t_2;
	elseif (j <= -4.4e-146)
		tmp = t_1;
	elseif (j <= 3e-128)
		tmp = Float64(t * Float64(b * i));
	elseif (j <= 0.032)
		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 = t * (x * -a);
	t_2 = a * (c * j);
	tmp = 0.0;
	if (j <= -8.8e+33)
		tmp = t_2;
	elseif (j <= -4.4e-146)
		tmp = t_1;
	elseif (j <= 3e-128)
		tmp = t * (b * i);
	elseif (j <= 0.032)
		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[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -8.8e+33], t$95$2, If[LessEqual[j, -4.4e-146], t$95$1, If[LessEqual[j, 3e-128], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 0.032], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -8.79999999999999975e33 or 0.032000000000000001 < j

   1. Initial program 74.5%

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

      1. cancel-sign-sub 74.5%

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

      2. cancel-sign-sub-inv 74.5%

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

      3. *-commutative 74.5%

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

      4. remove-double-neg 74.5%

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

      5. *-commutative 74.5%

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

   3. Simplified 74.5%

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

   4. Taylor expanded in a around inf 52.1%

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

      1. +-commutative 52.1%

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

      2. mul-1-neg 52.1%

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

      3. unsub-neg 52.1%

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

      4. *-commutative 52.1%

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

   6. Simplified 52.1%

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

   7. Taylor expanded in j around inf 47.4%

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

   if -8.79999999999999975e33 < j < -4.4e-146 or 2.99999999999999978e-128 < j < 0.032000000000000001

   1. Initial program 75.4%

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

      1. cancel-sign-sub 75.4%

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

      2. cancel-sign-sub-inv 75.4%

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

      3. *-commutative 75.4%

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

      4. remove-double-neg 75.4%

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

      5. *-commutative 75.4%

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

   3. Simplified 75.4%

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

   4. Taylor expanded in t around inf 56.4%

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

      1. distribute-lft-out-- 56.4%

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

      2. associate-*r* 56.4%

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

      3. mul-1-neg 56.4%

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

      4. *-commutative 56.4%

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

   6. Simplified 56.4%

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

   7. Taylor expanded in a around inf 37.0%

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

      1. *-commutative 37.0%

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

      2. associate-*l* 40.1%

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

      3. *-commutative 40.1%

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

   9. Simplified 40.1%

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

   if -4.4e-146 < j < 2.99999999999999978e-128

   1. Initial program 68.6%

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

      1. cancel-sign-sub 68.6%

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

      2. cancel-sign-sub-inv 68.6%

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

      3. *-commutative 68.6%

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

      4. remove-double-neg 68.6%

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

      5. *-commutative 68.6%

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

   3. Simplified 68.6%

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

      1. add-cbrt-cube 65.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{\sqrt[3]{\left(\left(j \cdot \left(a \cdot c - y \cdot i\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)}} \]

   5. Applied egg-rr 65.6%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{\sqrt[3]{\left(\left(j \cdot \left(a \cdot c - y \cdot i\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)}} \]

   6. Taylor expanded in y around inf 58.6%

      \[\leadsto \left(\color{blue}{y \cdot \left(z \cdot x\right)} - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \sqrt[3]{\left(\left(j \cdot \left(a \cdot c - y \cdot i\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 57.4%

         \[\leadsto \left(\color{blue}{\left(y \cdot z\right) \cdot x} - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \sqrt[3]{\left(\left(j \cdot \left(a \cdot c - y \cdot i\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

      2. *-commutative 57.4%

         \[\leadsto \left(\color{blue}{\left(z \cdot y\right)} \cdot x - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \sqrt[3]{\left(\left(j \cdot \left(a \cdot c - y \cdot i\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

      3. associate-*l* 60.2%

         \[\leadsto \left(\color{blue}{z \cdot \left(y \cdot x\right)} - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \sqrt[3]{\left(\left(j \cdot \left(a \cdot c - y \cdot i\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   8. Simplified 60.2%

      \[\leadsto \left(\color{blue}{z \cdot \left(y \cdot x\right)} - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \sqrt[3]{\left(\left(j \cdot \left(a \cdot c - y \cdot i\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   9. Taylor expanded in t around inf 40.6%

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

       1. *-commutative 40.6%

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

       2. associate-*l* 40.9%

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

       3. *-commutative 40.9%

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

   11. Simplified 40.9%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8.8 \cdot 10^{+33}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -4.4 \cdot 10^{-146}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{-128}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 0.032:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 10: 29.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{if}\;z \leq -4 \cdot 10^{+190}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3100000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-219}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* z (- b)))))
   (if (<= z -4e+190)
     (* x (* y z))
     (if (<= z -3100000.0)
       t_1
       (if (<= z -9.2e-219)
         (* a (* c j))
         (if (<= z 4.6e+87) (* t (* x (- a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (z * -b);
	double tmp;
	if (z <= -4e+190) {
		tmp = x * (y * z);
	} else if (z <= -3100000.0) {
		tmp = t_1;
	} else if (z <= -9.2e-219) {
		tmp = a * (c * j);
	} else if (z <= 4.6e+87) {
		tmp = t * (x * -a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (z * -b)
    if (z <= (-4d+190)) then
        tmp = x * (y * z)
    else if (z <= (-3100000.0d0)) then
        tmp = t_1
    else if (z <= (-9.2d-219)) then
        tmp = a * (c * j)
    else if (z <= 4.6d+87) then
        tmp = t * (x * -a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (z * -b);
	double tmp;
	if (z <= -4e+190) {
		tmp = x * (y * z);
	} else if (z <= -3100000.0) {
		tmp = t_1;
	} else if (z <= -9.2e-219) {
		tmp = a * (c * j);
	} else if (z <= 4.6e+87) {
		tmp = t * (x * -a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (z * -b)
	tmp = 0
	if z <= -4e+190:
		tmp = x * (y * z)
	elif z <= -3100000.0:
		tmp = t_1
	elif z <= -9.2e-219:
		tmp = a * (c * j)
	elif z <= 4.6e+87:
		tmp = t * (x * -a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(z * Float64(-b)))
	tmp = 0.0
	if (z <= -4e+190)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= -3100000.0)
		tmp = t_1;
	elseif (z <= -9.2e-219)
		tmp = Float64(a * Float64(c * j));
	elseif (z <= 4.6e+87)
		tmp = Float64(t * Float64(x * Float64(-a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (z * -b);
	tmp = 0.0;
	if (z <= -4e+190)
		tmp = x * (y * z);
	elseif (z <= -3100000.0)
		tmp = t_1;
	elseif (z <= -9.2e-219)
		tmp = a * (c * j);
	elseif (z <= 4.6e+87)
		tmp = t * (x * -a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e+190], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3100000.0], t$95$1, If[LessEqual[z, -9.2e-219], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+87], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.0000000000000003e190

   1. Initial program 79.0%

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

      1. cancel-sign-sub 79.0%

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

      2. cancel-sign-sub-inv 79.0%

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

      3. *-commutative 79.0%

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

      4. remove-double-neg 79.0%

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

      5. *-commutative 79.0%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in z around inf 79.3%

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

   5. Taylor expanded in y around inf 61.1%

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

      1. associate-*r* 66.2%

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

   7. Simplified 66.2%

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

   if -4.0000000000000003e190 < z < -3.1e6 or 4.6000000000000003e87 < z

   1. Initial program 61.5%

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

      1. cancel-sign-sub 61.5%

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

      2. cancel-sign-sub-inv 61.5%

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

      3. *-commutative 61.5%

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

      4. remove-double-neg 61.5%

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

      5. *-commutative 61.5%

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

   3. Simplified 61.5%

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

   4. Taylor expanded in y around 0 60.7%

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

   5. Taylor expanded in z around inf 43.8%

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

      1. associate-*r* 43.8%

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

      2. neg-mul-1 43.8%

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

   7. Simplified 43.8%

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

   if -3.1e6 < z < -9.19999999999999954e-219

   1. Initial program 79.6%

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

      1. cancel-sign-sub 79.6%

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

      2. cancel-sign-sub-inv 79.6%

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

      3. *-commutative 79.6%

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

      4. remove-double-neg 79.6%

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

      5. *-commutative 79.6%

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

   3. Simplified 79.6%

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

   4. Taylor expanded in a around inf 58.6%

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

      1. +-commutative 58.6%

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

      2. mul-1-neg 58.6%

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

      3. unsub-neg 58.6%

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

      4. *-commutative 58.6%

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

   6. Simplified 58.6%

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

   7. Taylor expanded in j around inf 45.3%

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

   if -9.19999999999999954e-219 < z < 4.6000000000000003e87

   1. Initial program 79.0%

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

      1. cancel-sign-sub 79.0%

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

      2. cancel-sign-sub-inv 79.0%

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

      3. *-commutative 79.0%

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

      4. remove-double-neg 79.0%

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

      5. *-commutative 79.0%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in t around inf 61.7%

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

      1. distribute-lft-out-- 61.7%

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

      2. associate-*r* 61.7%

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

      3. mul-1-neg 61.7%

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

      4. *-commutative 61.7%

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

   6. Simplified 61.7%

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

   7. Taylor expanded in a around inf 29.7%

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

      1. *-commutative 29.7%

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

      2. associate-*l* 36.7%

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

      3. *-commutative 36.7%

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

   9. Simplified 36.7%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+190}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3100000:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-219}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 11: 28.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+185}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -6800000:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-216}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+88}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -1.22e+185)
   (* x (* y z))
   (if (<= z -6800000.0)
     (* z (* b (- c)))
     (if (<= z -1e-216)
       (* a (* c j))
       (if (<= z 4.8e+88) (* t (* x (- a))) (* c (* z (- b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.22e+185) {
		tmp = x * (y * z);
	} else if (z <= -6800000.0) {
		tmp = z * (b * -c);
	} else if (z <= -1e-216) {
		tmp = a * (c * j);
	} else if (z <= 4.8e+88) {
		tmp = t * (x * -a);
	} else {
		tmp = c * (z * -b);
	}
	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 (z <= (-1.22d+185)) then
        tmp = x * (y * z)
    else if (z <= (-6800000.0d0)) then
        tmp = z * (b * -c)
    else if (z <= (-1d-216)) then
        tmp = a * (c * j)
    else if (z <= 4.8d+88) then
        tmp = t * (x * -a)
    else
        tmp = c * (z * -b)
    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 (z <= -1.22e+185) {
		tmp = x * (y * z);
	} else if (z <= -6800000.0) {
		tmp = z * (b * -c);
	} else if (z <= -1e-216) {
		tmp = a * (c * j);
	} else if (z <= 4.8e+88) {
		tmp = t * (x * -a);
	} else {
		tmp = c * (z * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -1.22e+185:
		tmp = x * (y * z)
	elif z <= -6800000.0:
		tmp = z * (b * -c)
	elif z <= -1e-216:
		tmp = a * (c * j)
	elif z <= 4.8e+88:
		tmp = t * (x * -a)
	else:
		tmp = c * (z * -b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -1.22e+185)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= -6800000.0)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (z <= -1e-216)
		tmp = Float64(a * Float64(c * j));
	elseif (z <= 4.8e+88)
		tmp = Float64(t * Float64(x * Float64(-a)));
	else
		tmp = Float64(c * Float64(z * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -1.22e+185)
		tmp = x * (y * z);
	elseif (z <= -6800000.0)
		tmp = z * (b * -c);
	elseif (z <= -1e-216)
		tmp = a * (c * j);
	elseif (z <= 4.8e+88)
		tmp = t * (x * -a);
	else
		tmp = c * (z * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -1.22e+185], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6800000.0], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1e-216], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e+88], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.22000000000000002e185

   1. Initial program 79.0%

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

      1. cancel-sign-sub 79.0%

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

      2. cancel-sign-sub-inv 79.0%

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

      3. *-commutative 79.0%

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

      4. remove-double-neg 79.0%

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

      5. *-commutative 79.0%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in z around inf 79.3%

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

   5. Taylor expanded in y around inf 61.1%

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

      1. associate-*r* 66.2%

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

   7. Simplified 66.2%

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

   if -1.22000000000000002e185 < z < -6.8e6

   1. Initial program 63.3%

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

      1. cancel-sign-sub 63.3%

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

      2. cancel-sign-sub-inv 63.3%

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

      3. *-commutative 63.3%

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

      4. remove-double-neg 63.3%

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

      5. *-commutative 63.3%

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

   3. Simplified 63.3%

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

   4. Taylor expanded in z around inf 51.2%

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

   5. Taylor expanded in y around 0 40.4%

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

      1. neg-mul-1 40.4%

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

      2. distribute-rgt-neg-in 40.4%

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

   7. Simplified 40.4%

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

   if -6.8e6 < z < -1e-216

   1. Initial program 79.6%

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

      1. cancel-sign-sub 79.6%

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

      2. cancel-sign-sub-inv 79.6%

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

      3. *-commutative 79.6%

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

      4. remove-double-neg 79.6%

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

      5. *-commutative 79.6%

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

   3. Simplified 79.6%

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

   4. Taylor expanded in a around inf 58.6%

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

      1. +-commutative 58.6%

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

      2. mul-1-neg 58.6%

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

      3. unsub-neg 58.6%

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

      4. *-commutative 58.6%

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

   6. Simplified 58.6%

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

   7. Taylor expanded in j around inf 45.3%

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

   if -1e-216 < z < 4.7999999999999998e88

   1. Initial program 79.0%

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

      1. cancel-sign-sub 79.0%

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

      2. cancel-sign-sub-inv 79.0%

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

      3. *-commutative 79.0%

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

      4. remove-double-neg 79.0%

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

      5. *-commutative 79.0%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in t around inf 61.7%

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

      1. distribute-lft-out-- 61.7%

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

      2. associate-*r* 61.7%

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

      3. mul-1-neg 61.7%

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

      4. *-commutative 61.7%

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

   6. Simplified 61.7%

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

   7. Taylor expanded in a around inf 29.7%

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

      1. *-commutative 29.7%

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

      2. associate-*l* 36.7%

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

      3. *-commutative 36.7%

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

   9. Simplified 36.7%

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

   if 4.7999999999999998e88 < z

   1. Initial program 59.4%

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

      1. cancel-sign-sub 59.4%

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

      2. cancel-sign-sub-inv 59.4%

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

      3. *-commutative 59.4%

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

      4. remove-double-neg 59.4%

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

      5. *-commutative 59.4%

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

   3. Simplified 59.4%

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

   4. Taylor expanded in y around 0 59.6%

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

   5. Taylor expanded in z around inf 47.7%

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

      1. associate-*r* 47.7%

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

      2. neg-mul-1 47.7%

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

   7. Simplified 47.7%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+185}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -6800000:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-216}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+88}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 12: 42.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -4.1 \cdot 10^{+139}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{+104}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -4.1e+139)
   (* t (* b i))
   (if (<= i 3.8e+104) (* a (- (* c j) (* x t))) (* b (* t i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -4.1e+139) {
		tmp = t * (b * i);
	} else if (i <= 3.8e+104) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-4.1d+139)) then
        tmp = t * (b * i)
    else if (i <= 3.8d+104) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -4.1e+139) {
		tmp = t * (b * i);
	} else if (i <= 3.8e+104) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -4.1e+139:
		tmp = t * (b * i)
	elif i <= 3.8e+104:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -4.1e+139)
		tmp = Float64(t * Float64(b * i));
	elseif (i <= 3.8e+104)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -4.1e+139)
		tmp = t * (b * i);
	elseif (i <= 3.8e+104)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -4.1e+139], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.8e+104], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -4.1000000000000002e139

   1. Initial program 57.7%

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

      1. cancel-sign-sub 57.7%

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

      2. cancel-sign-sub-inv 57.7%

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

      3. *-commutative 57.7%

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

      4. remove-double-neg 57.7%

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

      5. *-commutative 57.7%

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

   3. Simplified 57.7%

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

      1. add-cbrt-cube 49.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{\sqrt[3]{\left(\left(j \cdot \left(a \cdot c - y \cdot i\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)}} \]

   5. Applied egg-rr 49.1%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{\sqrt[3]{\left(\left(j \cdot \left(a \cdot c - y \cdot i\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)}} \]

   6. Taylor expanded in y around inf 52.0%

      \[\leadsto \left(\color{blue}{y \cdot \left(z \cdot x\right)} - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \sqrt[3]{\left(\left(j \cdot \left(a \cdot c - y \cdot i\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 49.1%

         \[\leadsto \left(\color{blue}{\left(y \cdot z\right) \cdot x} - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \sqrt[3]{\left(\left(j \cdot \left(a \cdot c - y \cdot i\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

      2. *-commutative 49.1%

         \[\leadsto \left(\color{blue}{\left(z \cdot y\right)} \cdot x - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \sqrt[3]{\left(\left(j \cdot \left(a \cdot c - y \cdot i\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

      3. associate-*l* 52.0%

         \[\leadsto \left(\color{blue}{z \cdot \left(y \cdot x\right)} - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \sqrt[3]{\left(\left(j \cdot \left(a \cdot c - y \cdot i\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   8. Simplified 52.0%

      \[\leadsto \left(\color{blue}{z \cdot \left(y \cdot x\right)} - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \sqrt[3]{\left(\left(j \cdot \left(a \cdot c - y \cdot i\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   9. Taylor expanded in t around inf 49.6%

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

       1. *-commutative 49.6%

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

       2. associate-*l* 55.0%

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

       3. *-commutative 55.0%

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

   11. Simplified 55.0%

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

   if -4.1000000000000002e139 < i < 3.79999999999999969e104

   1. Initial program 76.8%

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

      1. cancel-sign-sub 76.8%

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

      2. cancel-sign-sub-inv 76.8%

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

      3. *-commutative 76.8%

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

      4. remove-double-neg 76.8%

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

      5. *-commutative 76.8%

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

   3. Simplified 76.8%

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

   4. Taylor expanded in a around inf 51.7%

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

      1. +-commutative 51.7%

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

      2. mul-1-neg 51.7%

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

      3. unsub-neg 51.7%

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

      4. *-commutative 51.7%

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

   6. Simplified 51.7%

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

   if 3.79999999999999969e104 < i

   1. Initial program 70.0%

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

      1. cancel-sign-sub 70.0%

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

      2. cancel-sign-sub-inv 70.0%

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

      3. *-commutative 70.0%

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

      4. remove-double-neg 70.0%

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

      5. *-commutative 70.0%

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

   3. Simplified 70.0%

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

   4. Taylor expanded in b around inf 65.6%

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

   5. Taylor expanded in i around inf 53.7%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.1 \cdot 10^{+139}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{+104}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 13: 30.2% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.6 \cdot 10^{+26} \lor \neg \left(j \leq 4.8 \cdot 10^{-104}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1.6e+26) (not (<= j 4.8e-104))) (* a (* c j)) (* i (* t b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.6e+26) || !(j <= 4.8e-104)) {
		tmp = a * (c * j);
	} else {
		tmp = i * (t * b);
	}
	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 <= (-1.6d+26)) .or. (.not. (j <= 4.8d-104))) then
        tmp = a * (c * j)
    else
        tmp = i * (t * b)
    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 <= -1.6e+26) || !(j <= 4.8e-104)) {
		tmp = a * (c * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -1.6e+26) or not (j <= 4.8e-104):
		tmp = a * (c * j)
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -1.6e+26) || !(j <= 4.8e-104))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -1.6e+26) || ~((j <= 4.8e-104)))
		tmp = a * (c * j);
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -1.6e+26], N[Not[LessEqual[j, 4.8e-104]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.60000000000000014e26 or 4.8000000000000001e-104 < j

   1. Initial program 75.5%

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

      1. cancel-sign-sub 75.5%

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

      2. cancel-sign-sub-inv 75.5%

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

      3. *-commutative 75.5%

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

      4. remove-double-neg 75.5%

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

      5. *-commutative 75.5%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in a around inf 52.3%

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

      1. +-commutative 52.3%

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

      2. mul-1-neg 52.3%

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

      3. unsub-neg 52.3%

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

      4. *-commutative 52.3%

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

   6. Simplified 52.3%

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

   7. Taylor expanded in j around inf 44.4%

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

   if -1.60000000000000014e26 < j < 4.8000000000000001e-104

   1. Initial program 69.9%

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

      1. cancel-sign-sub 69.9%

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

      2. cancel-sign-sub-inv 69.9%

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

      3. *-commutative 69.9%

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

      4. remove-double-neg 69.9%

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

      5. *-commutative 69.9%

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

   3. Simplified 69.9%

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

   4. Taylor expanded in y around 0 69.4%

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

   5. Taylor expanded in i around inf 33.0%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.6 \cdot 10^{+26} \lor \neg \left(j \leq 4.8 \cdot 10^{-104}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]

Alternative 14: 30.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -4.2 \cdot 10^{+26} \lor \neg \left(j \leq 5.8 \cdot 10^{-94}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -4.2e+26) (not (<= j 5.8e-94))) (* a (* c j)) (* t (* 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 <= -4.2e+26) || !(j <= 5.8e-94)) {
		tmp = a * (c * j);
	} else {
		tmp = t * (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 <= (-4.2d+26)) .or. (.not. (j <= 5.8d-94))) then
        tmp = a * (c * j)
    else
        tmp = t * (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 <= -4.2e+26) || !(j <= 5.8e-94)) {
		tmp = a * (c * j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -4.2e+26) or not (j <= 5.8e-94):
		tmp = a * (c * j)
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -4.2e+26) || !(j <= 5.8e-94))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(t * 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 <= -4.2e+26) || ~((j <= 5.8e-94)))
		tmp = a * (c * j);
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -4.2e+26], N[Not[LessEqual[j, 5.8e-94]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -4.2000000000000002e26 or 5.79999999999999991e-94 < j

   1. Initial program 75.5%

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

      1. cancel-sign-sub 75.5%

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

      2. cancel-sign-sub-inv 75.5%

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

      3. *-commutative 75.5%

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

      4. remove-double-neg 75.5%

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

      5. *-commutative 75.5%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in a around inf 52.3%

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

      1. +-commutative 52.3%

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

      2. mul-1-neg 52.3%

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

      3. unsub-neg 52.3%

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

      4. *-commutative 52.3%

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

   6. Simplified 52.3%

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

   7. Taylor expanded in j around inf 44.4%

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

   if -4.2000000000000002e26 < j < 5.79999999999999991e-94

   1. Initial program 69.9%

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

      1. cancel-sign-sub 69.9%

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

      2. cancel-sign-sub-inv 69.9%

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

      3. *-commutative 69.9%

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

      4. remove-double-neg 69.9%

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

      5. *-commutative 69.9%

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

   3. Simplified 69.9%

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

      1. add-cbrt-cube 61.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{\sqrt[3]{\left(\left(j \cdot \left(a \cdot c - y \cdot i\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)}} \]

   5. Applied egg-rr 61.8%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{\sqrt[3]{\left(\left(j \cdot \left(a \cdot c - y \cdot i\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)}} \]

   6. Taylor expanded in y around inf 52.7%

      \[\leadsto \left(\color{blue}{y \cdot \left(z \cdot x\right)} - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \sqrt[3]{\left(\left(j \cdot \left(a \cdot c - y \cdot i\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 50.1%

         \[\leadsto \left(\color{blue}{\left(y \cdot z\right) \cdot x} - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \sqrt[3]{\left(\left(j \cdot \left(a \cdot c - y \cdot i\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

      2. *-commutative 50.1%

         \[\leadsto \left(\color{blue}{\left(z \cdot y\right)} \cdot x - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \sqrt[3]{\left(\left(j \cdot \left(a \cdot c - y \cdot i\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

      3. associate-*l* 53.7%

         \[\leadsto \left(\color{blue}{z \cdot \left(y \cdot x\right)} - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \sqrt[3]{\left(\left(j \cdot \left(a \cdot c - y \cdot i\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   8. Simplified 53.7%

      \[\leadsto \left(\color{blue}{z \cdot \left(y \cdot x\right)} - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \sqrt[3]{\left(\left(j \cdot \left(a \cdot c - y \cdot i\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)\right) \cdot \left(j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   9. Taylor expanded in t around inf 33.0%

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

       1. *-commutative 33.0%

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

       2. associate-*l* 34.1%

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

       3. *-commutative 34.1%

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

   11. Simplified 34.1%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.2 \cdot 10^{+26} \lor \neg \left(j \leq 5.8 \cdot 10^{-94}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 15: 22.7% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.1%

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

   1. cancel-sign-sub 73.1%

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

   2. cancel-sign-sub-inv 73.1%

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

   3. *-commutative 73.1%

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

   4. remove-double-neg 73.1%

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

   5. *-commutative 73.1%

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

3. Simplified 73.1%

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

4. Taylor expanded in a around inf 45.6%

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

   1. +-commutative 45.6%

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

   2. mul-1-neg 45.6%

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

   3. unsub-neg 45.6%

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

   4. *-commutative 45.6%

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

6. Simplified 45.6%

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

7. Taylor expanded in j around inf 29.3%

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

8. Final simplification 29.3%

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

Developer target: 59.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023229 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

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