Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.7% → 83.1%

Time: 37.5s

Alternatives: 30

Speedup: 0.5×

• 56.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 83.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := \left(t_1 + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\left(\left({\left(\sqrt[3]{c \cdot \left(t \cdot j\right)}\right)}^{3} + t_1\right) + i \cdot \left(a \cdot b - y \cdot j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{\left(x \cdot t - b \cdot i\right)}^{3}} \cdot \left(-a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ (+ t_1 (* b (- (* a i) (* z c)))) (* j (- (* t c) (* y i))))))
   (if (<= t_2 (- INFINITY))
     (-
      (+ (+ (pow (cbrt (* c (* t j))) 3.0) t_1) (* i (- (* a b) (* y j))))
      (* b (* z c)))
     (if (<= t_2 INFINITY)
       t_2
       (* (cbrt (pow (- (* x t) (* b i)) 3.0)) (- a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = (t_1 + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = ((pow(cbrt((c * (t * j))), 3.0) + t_1) + (i * ((a * b) - (y * j)))) - (b * (z * c));
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = cbrt(pow(((x * t) - (b * i)), 3.0)) * -a;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = (t_1 + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = ((Math.pow(Math.cbrt((c * (t * j))), 3.0) + t_1) + (i * ((a * b) - (y * j)))) - (b * (z * c));
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = Math.cbrt(Math.pow(((x * t) - (b * i)), 3.0)) * -a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(Float64((cbrt(Float64(c * Float64(t * j))) ^ 3.0) + t_1) + Float64(i * Float64(Float64(a * b) - Float64(y * j)))) - Float64(b * Float64(z * c)));
	elseif (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(cbrt((Float64(Float64(x * t) - Float64(b * i)) ^ 3.0)) * Float64(-a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(N[Power[N[Power[N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision] + t$95$1), $MachinePrecision] + N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$2, N[(N[Power[N[Power[N[(N[(x * t), $MachinePrecision] - N[(b * i), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision], 1/3], $MachinePrecision] * (-a)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 76.3%

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

   3. Taylor expanded in i around -inf 87.5%

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

      1. add-cube-cbrt 87.5%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right) + \left(\color{blue}{\left(\sqrt[3]{c \cdot \left(j \cdot t\right)} \cdot \sqrt[3]{c \cdot \left(j \cdot t\right)}\right) \cdot \sqrt[3]{c \cdot \left(j \cdot t\right)}} + x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) - b \cdot \left(c \cdot z\right) \]

      2. pow3 87.5%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right) + \left(\color{blue}{{\left(\sqrt[3]{c \cdot \left(j \cdot t\right)}\right)}^{3}} + x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) - b \cdot \left(c \cdot z\right) \]

   5. Applied egg-rr 87.5%

      \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right) + \left(\color{blue}{{\left(\sqrt[3]{c \cdot \left(j \cdot t\right)}\right)}^{3}} + x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) - b \cdot \left(c \cdot z\right) \]

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

   1. Initial program 90.9%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in a around inf 55.9%

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

      1. distribute-lft-out-- 55.9%

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

      2. *-commutative 55.9%

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

   5. Simplified 55.9%

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

      1. add-cbrt-cube 65.0%

         \[\leadsto a \cdot \left(-1 \cdot \color{blue}{\sqrt[3]{\left(\left(t \cdot x - i \cdot b\right) \cdot \left(t \cdot x - i \cdot b\right)\right) \cdot \left(t \cdot x - i \cdot b\right)}}\right) \]

      2. pow3 65.0%

         \[\leadsto a \cdot \left(-1 \cdot \sqrt[3]{\color{blue}{{\left(t \cdot x - i \cdot b\right)}^{3}}}\right) \]

   7. Applied egg-rr 65.0%

      \[\leadsto a \cdot \left(-1 \cdot \color{blue}{\sqrt[3]{{\left(t \cdot x - i \cdot b\right)}^{3}}}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \leq -\infty:\\ \;\;\;\;\left(\left({\left(\sqrt[3]{c \cdot \left(t \cdot j\right)}\right)}^{3} + x \cdot \left(y \cdot z - t \cdot a\right)\right) + i \cdot \left(a \cdot b - y \cdot j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{\left(x \cdot t - b \cdot i\right)}^{3}} \cdot \left(-a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 83.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := \left(t_1 + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\left(\left(c \cdot \left(t \cdot j\right) + t_1\right) + i \cdot \left(a \cdot b - y \cdot j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{\left(x \cdot t - b \cdot i\right)}^{3}} \cdot \left(-a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ (+ t_1 (* b (- (* a i) (* z c)))) (* j (- (* t c) (* y i))))))
   (if (<= t_2 (- INFINITY))
     (- (+ (+ (* c (* t j)) t_1) (* i (- (* a b) (* y j)))) (* b (* z c)))
     (if (<= t_2 INFINITY)
       t_2
       (* (cbrt (pow (- (* x t) (* b i)) 3.0)) (- a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = (t_1 + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (((c * (t * j)) + t_1) + (i * ((a * b) - (y * j)))) - (b * (z * c));
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = cbrt(pow(((x * t) - (b * i)), 3.0)) * -a;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = (t_1 + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (((c * (t * j)) + t_1) + (i * ((a * b) - (y * j)))) - (b * (z * c));
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = Math.cbrt(Math.pow(((x * t) - (b * i)), 3.0)) * -a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(c * Float64(t * j)) + t_1) + Float64(i * Float64(Float64(a * b) - Float64(y * j)))) - Float64(b * Float64(z * c)));
	elseif (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(cbrt((Float64(Float64(x * t) - Float64(b * i)) ^ 3.0)) * Float64(-a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$2, N[(N[Power[N[Power[N[(N[(x * t), $MachinePrecision] - N[(b * i), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision], 1/3], $MachinePrecision] * (-a)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 76.3%

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

   3. Taylor expanded in i around -inf 87.5%

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

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

   1. Initial program 90.9%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in a around inf 55.9%

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

      1. distribute-lft-out-- 55.9%

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

      2. *-commutative 55.9%

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

   5. Simplified 55.9%

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

      1. add-cbrt-cube 65.0%

         \[\leadsto a \cdot \left(-1 \cdot \color{blue}{\sqrt[3]{\left(\left(t \cdot x - i \cdot b\right) \cdot \left(t \cdot x - i \cdot b\right)\right) \cdot \left(t \cdot x - i \cdot b\right)}}\right) \]

      2. pow3 65.0%

         \[\leadsto a \cdot \left(-1 \cdot \sqrt[3]{\color{blue}{{\left(t \cdot x - i \cdot b\right)}^{3}}}\right) \]

   7. Applied egg-rr 65.0%

      \[\leadsto a \cdot \left(-1 \cdot \color{blue}{\sqrt[3]{{\left(t \cdot x - i \cdot b\right)}^{3}}}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \leq -\infty:\\ \;\;\;\;\left(\left(c \cdot \left(t \cdot j\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) + i \cdot \left(a \cdot b - y \cdot j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{\left(x \cdot t - b \cdot i\right)}^{3}} \cdot \left(-a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := \left(t_2 + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\left(\left(c \cdot \left(t \cdot j\right) + t_2\right) + t_1\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (+ (+ t_2 (* b (- (* a i) (* z c)))) (* j (- (* t c) (* y i))))))
   (if (<= t_3 (- INFINITY))
     (- (+ (+ (* c (* t j)) t_2) t_1) (* b (* z c)))
     (if (<= t_3 INFINITY) t_3 t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = (t_2 + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = (((c * (t * j)) + t_2) + t_1) - (b * (z * c));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	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 = i * ((a * b) - (y * j));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = (t_2 + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = (((c * (t * j)) + t_2) + t_1) - (b * (z * c));
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = x * ((y * z) - (t * a))
	t_3 = (t_2 + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)))
	tmp = 0
	if t_3 <= -math.inf:
		tmp = (((c * (t * j)) + t_2) + t_1) - (b * (z * c))
	elif t_3 <= math.inf:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(Float64(t_2 + Float64(b * Float64(Float64(a * i) - Float64(z * c)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(c * Float64(t * j)) + t_2) + t_1) - Float64(b * Float64(z * c)));
	elseif (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	t_2 = x * ((y * z) - (t * a));
	t_3 = (t_2 + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = (((c * (t * j)) + t_2) + t_1) - (b * (z * c));
	elseif (t_3 <= Inf)
		tmp = t_3;
	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[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$3, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 76.3%

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

   3. Taylor expanded in i around -inf 87.5%

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

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

   1. Initial program 90.9%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in i around inf 57.2%

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

      1. distribute-lft-out-- 57.2%

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

   5. Simplified 57.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.4%

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

Alternative 4: 82.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 86.9%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in i around inf 57.2%

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

      1. distribute-lft-out-- 57.2%

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

   5. Simplified 57.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.0%

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

Alternative 5: 51.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -660000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-295}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-202}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 50000 \lor \neg \left(y \leq 9 \cdot 10^{+93}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= y -660000.0)
     t_3
     (if (<= y -5.8e-295)
       t_2
       (if (<= y 6.5e-226)
         t_1
         (if (<= y 9.8e-202)
           (* z (* b (- c)))
           (if (<= y 3.7e-88)
             t_1
             (if (<= y 1.85e-44)
               t_2
               (if (<= y 6.6e-16)
                 t_1
                 (if (or (<= y 50000.0) (not (<= y 9e+93)))
                   t_3
                   (* c (- (* t 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 = t * ((c * j) - (x * a));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -660000.0) {
		tmp = t_3;
	} else if (y <= -5.8e-295) {
		tmp = t_2;
	} else if (y <= 6.5e-226) {
		tmp = t_1;
	} else if (y <= 9.8e-202) {
		tmp = z * (b * -c);
	} else if (y <= 3.7e-88) {
		tmp = t_1;
	} else if (y <= 1.85e-44) {
		tmp = t_2;
	} else if (y <= 6.6e-16) {
		tmp = t_1;
	} else if ((y <= 50000.0) || !(y <= 9e+93)) {
		tmp = t_3;
	} else {
		tmp = c * ((t * j) - (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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    t_2 = b * ((a * i) - (z * c))
    t_3 = y * ((x * z) - (i * j))
    if (y <= (-660000.0d0)) then
        tmp = t_3
    else if (y <= (-5.8d-295)) then
        tmp = t_2
    else if (y <= 6.5d-226) then
        tmp = t_1
    else if (y <= 9.8d-202) then
        tmp = z * (b * -c)
    else if (y <= 3.7d-88) then
        tmp = t_1
    else if (y <= 1.85d-44) then
        tmp = t_2
    else if (y <= 6.6d-16) then
        tmp = t_1
    else if ((y <= 50000.0d0) .or. (.not. (y <= 9d+93))) then
        tmp = t_3
    else
        tmp = c * ((t * j) - (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 t_1 = t * ((c * j) - (x * a));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -660000.0) {
		tmp = t_3;
	} else if (y <= -5.8e-295) {
		tmp = t_2;
	} else if (y <= 6.5e-226) {
		tmp = t_1;
	} else if (y <= 9.8e-202) {
		tmp = z * (b * -c);
	} else if (y <= 3.7e-88) {
		tmp = t_1;
	} else if (y <= 1.85e-44) {
		tmp = t_2;
	} else if (y <= 6.6e-16) {
		tmp = t_1;
	} else if ((y <= 50000.0) || !(y <= 9e+93)) {
		tmp = t_3;
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = b * ((a * i) - (z * c))
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -660000.0:
		tmp = t_3
	elif y <= -5.8e-295:
		tmp = t_2
	elif y <= 6.5e-226:
		tmp = t_1
	elif y <= 9.8e-202:
		tmp = z * (b * -c)
	elif y <= 3.7e-88:
		tmp = t_1
	elif y <= 1.85e-44:
		tmp = t_2
	elif y <= 6.6e-16:
		tmp = t_1
	elif (y <= 50000.0) or not (y <= 9e+93):
		tmp = t_3
	else:
		tmp = c * ((t * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -660000.0)
		tmp = t_3;
	elseif (y <= -5.8e-295)
		tmp = t_2;
	elseif (y <= 6.5e-226)
		tmp = t_1;
	elseif (y <= 9.8e-202)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (y <= 3.7e-88)
		tmp = t_1;
	elseif (y <= 1.85e-44)
		tmp = t_2;
	elseif (y <= 6.6e-16)
		tmp = t_1;
	elseif ((y <= 50000.0) || !(y <= 9e+93))
		tmp = t_3;
	else
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	t_2 = b * ((a * i) - (z * c));
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -660000.0)
		tmp = t_3;
	elseif (y <= -5.8e-295)
		tmp = t_2;
	elseif (y <= 6.5e-226)
		tmp = t_1;
	elseif (y <= 9.8e-202)
		tmp = z * (b * -c);
	elseif (y <= 3.7e-88)
		tmp = t_1;
	elseif (y <= 1.85e-44)
		tmp = t_2;
	elseif (y <= 6.6e-16)
		tmp = t_1;
	elseif ((y <= 50000.0) || ~((y <= 9e+93)))
		tmp = t_3;
	else
		tmp = c * ((t * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -660000.0], t$95$3, If[LessEqual[y, -5.8e-295], t$95$2, If[LessEqual[y, 6.5e-226], t$95$1, If[LessEqual[y, 9.8e-202], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e-88], t$95$1, If[LessEqual[y, 1.85e-44], t$95$2, If[LessEqual[y, 6.6e-16], t$95$1, If[Or[LessEqual[y, 50000.0], N[Not[LessEqual[y, 9e+93]], $MachinePrecision]], t$95$3, N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.6e5 or 6.59999999999999976e-16 < y < 5e4 or 8.99999999999999981e93 < y

   1. Initial program 57.9%

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

   3. Taylor expanded in y around inf 66.2%

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

      1. +-commutative 66.2%

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

      2. mul-1-neg 66.2%

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

      3. unsub-neg 66.2%

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

   5. Simplified 66.2%

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

   if -6.6e5 < y < -5.8000000000000003e-295 or 3.6999999999999997e-88 < y < 1.85e-44

   1. Initial program 76.4%

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

   3. Taylor expanded in b around inf 57.5%

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

      1. *-commutative 57.5%

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

   5. Simplified 57.5%

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

   if -5.8000000000000003e-295 < y < 6.50000000000000033e-226 or 9.8000000000000008e-202 < y < 3.6999999999999997e-88 or 1.85e-44 < y < 6.59999999999999976e-16

   1. Initial program 82.3%

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

   3. Taylor expanded in t around inf 69.7%

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

   4. Taylor expanded in a around 0 56.3%

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

      1. associate-*r* 62.9%

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

      2. +-commutative 62.9%

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

      3. mul-1-neg 62.9%

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

      4. *-commutative 62.9%

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

      5. associate-*l* 65.1%

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

      6. sub-neg 65.1%

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

      7. distribute-rgt-out-- 69.7%

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

   6. Simplified 69.7%

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

   if 6.50000000000000033e-226 < y < 9.8000000000000008e-202

   1. Initial program 60.7%

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

   3. Taylor expanded in z around inf 99.7%

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

      1. *-commutative 99.7%

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

      2. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around 0 99.7%

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

      1. neg-mul-1 99.7%

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

      2. distribute-lft-neg-in 99.7%

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

      3. *-commutative 99.7%

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

   8. Simplified 99.7%

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

   if 5e4 < y < 8.99999999999999981e93

   1. Initial program 82.9%

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

   3. Taylor expanded in c around inf 62.5%

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

      1. *-commutative 62.5%

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

   5. Simplified 62.5%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -660000:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-295}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-226}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-202}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-88}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 50000 \lor \neg \left(y \leq 9 \cdot 10^{+93}\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right) - b \cdot \left(z \cdot c\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -720000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.02 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 0.0016:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+94}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* x (* y z))))
        (t_2 (- (* a (- (* b i) (* x t))) (* b (* z c))))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= y -720000.0)
     t_3
     (if (<= y 1.7e-143)
       t_2
       (if (<= y 2.02e-88)
         t_1
         (if (<= y 1.1e-40)
           t_2
           (if (<= y 0.0016)
             t_1
             (if (<= y 2.9e+94)
               (+ (* t (* c j)) (* b (- (* a i) (* z c))))
               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 = (j * ((t * c) - (y * i))) + (x * (y * z));
	double t_2 = (a * ((b * i) - (x * t))) - (b * (z * c));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -720000.0) {
		tmp = t_3;
	} else if (y <= 1.7e-143) {
		tmp = t_2;
	} else if (y <= 2.02e-88) {
		tmp = t_1;
	} else if (y <= 1.1e-40) {
		tmp = t_2;
	} else if (y <= 0.0016) {
		tmp = t_1;
	} else if (y <= 2.9e+94) {
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	} 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 = (j * ((t * c) - (y * i))) + (x * (y * z))
    t_2 = (a * ((b * i) - (x * t))) - (b * (z * c))
    t_3 = y * ((x * z) - (i * j))
    if (y <= (-720000.0d0)) then
        tmp = t_3
    else if (y <= 1.7d-143) then
        tmp = t_2
    else if (y <= 2.02d-88) then
        tmp = t_1
    else if (y <= 1.1d-40) then
        tmp = t_2
    else if (y <= 0.0016d0) then
        tmp = t_1
    else if (y <= 2.9d+94) then
        tmp = (t * (c * j)) + (b * ((a * i) - (z * c)))
    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 = (j * ((t * c) - (y * i))) + (x * (y * z));
	double t_2 = (a * ((b * i) - (x * t))) - (b * (z * c));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -720000.0) {
		tmp = t_3;
	} else if (y <= 1.7e-143) {
		tmp = t_2;
	} else if (y <= 2.02e-88) {
		tmp = t_1;
	} else if (y <= 1.1e-40) {
		tmp = t_2;
	} else if (y <= 0.0016) {
		tmp = t_1;
	} else if (y <= 2.9e+94) {
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + (x * (y * z))
	t_2 = (a * ((b * i) - (x * t))) - (b * (z * c))
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -720000.0:
		tmp = t_3
	elif y <= 1.7e-143:
		tmp = t_2
	elif y <= 2.02e-88:
		tmp = t_1
	elif y <= 1.1e-40:
		tmp = t_2
	elif y <= 0.0016:
		tmp = t_1
	elif y <= 2.9e+94:
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(y * z)))
	t_2 = Float64(Float64(a * Float64(Float64(b * i) - Float64(x * t))) - Float64(b * Float64(z * c)))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -720000.0)
		tmp = t_3;
	elseif (y <= 1.7e-143)
		tmp = t_2;
	elseif (y <= 2.02e-88)
		tmp = t_1;
	elseif (y <= 1.1e-40)
		tmp = t_2;
	elseif (y <= 0.0016)
		tmp = t_1;
	elseif (y <= 2.9e+94)
		tmp = Float64(Float64(t * Float64(c * j)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((t * c) - (y * i))) + (x * (y * z));
	t_2 = (a * ((b * i) - (x * t))) - (b * (z * c));
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -720000.0)
		tmp = t_3;
	elseif (y <= 1.7e-143)
		tmp = t_2;
	elseif (y <= 2.02e-88)
		tmp = t_1;
	elseif (y <= 1.1e-40)
		tmp = t_2;
	elseif (y <= 0.0016)
		tmp = t_1;
	elseif (y <= 2.9e+94)
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	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[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -720000.0], t$95$3, If[LessEqual[y, 1.7e-143], t$95$2, If[LessEqual[y, 2.02e-88], t$95$1, If[LessEqual[y, 1.1e-40], t$95$2, If[LessEqual[y, 0.0016], t$95$1, If[LessEqual[y, 2.9e+94], N[(N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.2e5 or 2.8999999999999998e94 < y

   1. Initial program 57.1%

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

   3. Taylor expanded in y around inf 67.1%

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

      1. +-commutative 67.1%

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

      2. mul-1-neg 67.1%

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

      3. unsub-neg 67.1%

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

   5. Simplified 67.1%

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

   if -7.2e5 < y < 1.69999999999999992e-143 or 2.01999999999999994e-88 < y < 1.10000000000000004e-40

   1. Initial program 78.7%

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

   3. Taylor expanded in i around -inf 80.1%

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

   4. Taylor expanded in a around inf 71.0%

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

      1. +-commutative 71.0%

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

      2. mul-1-neg 71.0%

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

      3. unsub-neg 71.0%

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

      4. *-commutative 71.0%

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

   6. Simplified 71.0%

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

   if 1.69999999999999992e-143 < y < 2.01999999999999994e-88 or 1.10000000000000004e-40 < y < 0.00160000000000000008

   1. Initial program 70.3%

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

   3. Taylor expanded in b around 0 79.9%

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

   4. Taylor expanded in a around 0 80.0%

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

   if 0.00160000000000000008 < y < 2.8999999999999998e94

   1. Initial program 79.5%

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

   3. Taylor expanded in x around 0 76.3%

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

      1. *-commutative 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in c around inf 77.0%

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

      1. *-commutative 34.0%

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

      2. *-commutative 34.0%

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

      3. associate-*r* 33.6%

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

   8. Simplified 76.7%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -720000:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-143}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq 2.02 \cdot 10^{-88}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq 0.0016:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+94}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_4 := t_3 + t_1\\ t_5 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;i \leq -5.2 \cdot 10^{+149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1 \cdot 10^{+32}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -6.5 \cdot 10^{-20}:\\ \;\;\;\;t_5 + t_1\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{-199}:\\ \;\;\;\;t_5 + t_3\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{+43}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{+215}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (* i (- (* a b) (* y j))))
        (t_3 (* x (- (* y z) (* t a))))
        (t_4 (+ t_3 t_1))
        (t_5 (* j (- (* t c) (* y i)))))
   (if (<= i -5.2e+149)
     t_2
     (if (<= i -1e+32)
       t_4
       (if (<= i -6.5e-20)
         (+ t_5 t_1)
         (if (<= i 1.2e-199)
           (+ t_5 t_3)
           (if (<= i 2.7e+43)
             t_4
             (if (<= i 1.25e+215) (+ (* t (* c j)) 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 = b * ((a * i) - (z * c));
	double t_2 = i * ((a * b) - (y * j));
	double t_3 = x * ((y * z) - (t * a));
	double t_4 = t_3 + t_1;
	double t_5 = j * ((t * c) - (y * i));
	double tmp;
	if (i <= -5.2e+149) {
		tmp = t_2;
	} else if (i <= -1e+32) {
		tmp = t_4;
	} else if (i <= -6.5e-20) {
		tmp = t_5 + t_1;
	} else if (i <= 1.2e-199) {
		tmp = t_5 + t_3;
	} else if (i <= 2.7e+43) {
		tmp = t_4;
	} else if (i <= 1.25e+215) {
		tmp = (t * (c * j)) + 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) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = i * ((a * b) - (y * j))
    t_3 = x * ((y * z) - (t * a))
    t_4 = t_3 + t_1
    t_5 = j * ((t * c) - (y * i))
    if (i <= (-5.2d+149)) then
        tmp = t_2
    else if (i <= (-1d+32)) then
        tmp = t_4
    else if (i <= (-6.5d-20)) then
        tmp = t_5 + t_1
    else if (i <= 1.2d-199) then
        tmp = t_5 + t_3
    else if (i <= 2.7d+43) then
        tmp = t_4
    else if (i <= 1.25d+215) then
        tmp = (t * (c * j)) + 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 = b * ((a * i) - (z * c));
	double t_2 = i * ((a * b) - (y * j));
	double t_3 = x * ((y * z) - (t * a));
	double t_4 = t_3 + t_1;
	double t_5 = j * ((t * c) - (y * i));
	double tmp;
	if (i <= -5.2e+149) {
		tmp = t_2;
	} else if (i <= -1e+32) {
		tmp = t_4;
	} else if (i <= -6.5e-20) {
		tmp = t_5 + t_1;
	} else if (i <= 1.2e-199) {
		tmp = t_5 + t_3;
	} else if (i <= 2.7e+43) {
		tmp = t_4;
	} else if (i <= 1.25e+215) {
		tmp = (t * (c * j)) + t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = i * ((a * b) - (y * j))
	t_3 = x * ((y * z) - (t * a))
	t_4 = t_3 + t_1
	t_5 = j * ((t * c) - (y * i))
	tmp = 0
	if i <= -5.2e+149:
		tmp = t_2
	elif i <= -1e+32:
		tmp = t_4
	elif i <= -6.5e-20:
		tmp = t_5 + t_1
	elif i <= 1.2e-199:
		tmp = t_5 + t_3
	elif i <= 2.7e+43:
		tmp = t_4
	elif i <= 1.25e+215:
		tmp = (t * (c * j)) + t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_4 = Float64(t_3 + t_1)
	t_5 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (i <= -5.2e+149)
		tmp = t_2;
	elseif (i <= -1e+32)
		tmp = t_4;
	elseif (i <= -6.5e-20)
		tmp = Float64(t_5 + t_1);
	elseif (i <= 1.2e-199)
		tmp = Float64(t_5 + t_3);
	elseif (i <= 2.7e+43)
		tmp = t_4;
	elseif (i <= 1.25e+215)
		tmp = Float64(Float64(t * Float64(c * j)) + 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 = b * ((a * i) - (z * c));
	t_2 = i * ((a * b) - (y * j));
	t_3 = x * ((y * z) - (t * a));
	t_4 = t_3 + t_1;
	t_5 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (i <= -5.2e+149)
		tmp = t_2;
	elseif (i <= -1e+32)
		tmp = t_4;
	elseif (i <= -6.5e-20)
		tmp = t_5 + t_1;
	elseif (i <= 1.2e-199)
		tmp = t_5 + t_3;
	elseif (i <= 2.7e+43)
		tmp = t_4;
	elseif (i <= 1.25e+215)
		tmp = (t * (c * j)) + 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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -5.2e+149], t$95$2, If[LessEqual[i, -1e+32], t$95$4, If[LessEqual[i, -6.5e-20], N[(t$95$5 + t$95$1), $MachinePrecision], If[LessEqual[i, 1.2e-199], N[(t$95$5 + t$95$3), $MachinePrecision], If[LessEqual[i, 2.7e+43], t$95$4, If[LessEqual[i, 1.25e+215], N[(N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -5.19999999999999957e149 or 1.25e215 < i

   1. Initial program 57.3%

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

   3. Taylor expanded in i around inf 84.7%

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

      1. distribute-lft-out-- 84.7%

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

   5. Simplified 84.7%

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

   if -5.19999999999999957e149 < i < -1.00000000000000005e32 or 1.19999999999999998e-199 < i < 2.7000000000000002e43

   1. Initial program 71.4%

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

   3. Taylor expanded in j around 0 71.5%

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

      1. *-commutative 71.5%

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

      2. *-commutative 71.5%

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

   5. Simplified 71.5%

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

   if -1.00000000000000005e32 < i < -6.50000000000000032e-20

   1. Initial program 73.2%

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

   3. Taylor expanded in x around 0 80.4%

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

      1. *-commutative 80.4%

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

   5. Simplified 80.4%

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

   if -6.50000000000000032e-20 < i < 1.19999999999999998e-199

   1. Initial program 79.1%

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

   3. Taylor expanded in b around 0 79.3%

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

   if 2.7000000000000002e43 < i < 1.25e215

   1. Initial program 61.5%

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

   3. Taylor expanded in x around 0 61.5%

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

      1. *-commutative 61.5%

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

   5. Simplified 61.5%

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

   6. Taylor expanded in c around inf 70.3%

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

      1. *-commutative 28.0%

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

      2. *-commutative 28.0%

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

      3. associate-*r* 30.9%

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

   8. Simplified 70.3%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.2 \cdot 10^{+149}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq -6.5 \cdot 10^{-20}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{-199}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{+215}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 29.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -3.9 \cdot 10^{+46}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -3.6 \cdot 10^{+25}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;i \leq -100000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq 9 \cdot 10^{-293}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{-236}:\\ \;\;\;\;-t \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{-199}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 1.82 \cdot 10^{+106}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -3.9e+46)
   (* a (* b i))
   (if (<= i -3.6e+25)
     (* (* i j) (- y))
     (if (<= i -100000.0)
       (* b (* a i))
       (if (<= i 9e-293)
         (* t (* c j))
         (if (<= i 2.1e-236)
           (- (* t (* x a)))
           (if (<= i 2.1e-199)
             (* c (* t j))
             (if (<= i 1.82e+106) (* z (* x y)) (* (* y i) (- j))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -3.9e+46) {
		tmp = a * (b * i);
	} else if (i <= -3.6e+25) {
		tmp = (i * j) * -y;
	} else if (i <= -100000.0) {
		tmp = b * (a * i);
	} else if (i <= 9e-293) {
		tmp = t * (c * j);
	} else if (i <= 2.1e-236) {
		tmp = -(t * (x * a));
	} else if (i <= 2.1e-199) {
		tmp = c * (t * j);
	} else if (i <= 1.82e+106) {
		tmp = z * (x * y);
	} else {
		tmp = (y * i) * -j;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-3.9d+46)) then
        tmp = a * (b * i)
    else if (i <= (-3.6d+25)) then
        tmp = (i * j) * -y
    else if (i <= (-100000.0d0)) then
        tmp = b * (a * i)
    else if (i <= 9d-293) then
        tmp = t * (c * j)
    else if (i <= 2.1d-236) then
        tmp = -(t * (x * a))
    else if (i <= 2.1d-199) then
        tmp = c * (t * j)
    else if (i <= 1.82d+106) then
        tmp = z * (x * y)
    else
        tmp = (y * i) * -j
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -3.9e+46) {
		tmp = a * (b * i);
	} else if (i <= -3.6e+25) {
		tmp = (i * j) * -y;
	} else if (i <= -100000.0) {
		tmp = b * (a * i);
	} else if (i <= 9e-293) {
		tmp = t * (c * j);
	} else if (i <= 2.1e-236) {
		tmp = -(t * (x * a));
	} else if (i <= 2.1e-199) {
		tmp = c * (t * j);
	} else if (i <= 1.82e+106) {
		tmp = z * (x * y);
	} else {
		tmp = (y * i) * -j;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -3.9e+46:
		tmp = a * (b * i)
	elif i <= -3.6e+25:
		tmp = (i * j) * -y
	elif i <= -100000.0:
		tmp = b * (a * i)
	elif i <= 9e-293:
		tmp = t * (c * j)
	elif i <= 2.1e-236:
		tmp = -(t * (x * a))
	elif i <= 2.1e-199:
		tmp = c * (t * j)
	elif i <= 1.82e+106:
		tmp = z * (x * y)
	else:
		tmp = (y * i) * -j
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -3.9e+46)
		tmp = Float64(a * Float64(b * i));
	elseif (i <= -3.6e+25)
		tmp = Float64(Float64(i * j) * Float64(-y));
	elseif (i <= -100000.0)
		tmp = Float64(b * Float64(a * i));
	elseif (i <= 9e-293)
		tmp = Float64(t * Float64(c * j));
	elseif (i <= 2.1e-236)
		tmp = Float64(-Float64(t * Float64(x * a)));
	elseif (i <= 2.1e-199)
		tmp = Float64(c * Float64(t * j));
	elseif (i <= 1.82e+106)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(Float64(y * i) * Float64(-j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -3.9e+46)
		tmp = a * (b * i);
	elseif (i <= -3.6e+25)
		tmp = (i * j) * -y;
	elseif (i <= -100000.0)
		tmp = b * (a * i);
	elseif (i <= 9e-293)
		tmp = t * (c * j);
	elseif (i <= 2.1e-236)
		tmp = -(t * (x * a));
	elseif (i <= 2.1e-199)
		tmp = c * (t * j);
	elseif (i <= 1.82e+106)
		tmp = z * (x * y);
	else
		tmp = (y * i) * -j;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -3.9e+46], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.6e+25], N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[i, -100000.0], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 9e-293], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.1e-236], (-N[(t * N[(x * a), $MachinePrecision]), $MachinePrecision]), If[LessEqual[i, 2.1e-199], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.82e+106], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if i < -3.89999999999999995e46

   1. Initial program 58.0%

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

   3. Taylor expanded in x around 0 65.5%

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

      1. *-commutative 65.5%

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

   5. Simplified 65.5%

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

   6. Taylor expanded in a around inf 56.7%

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

   if -3.89999999999999995e46 < i < -3.60000000000000015e25

   1. Initial program 66.5%

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

   3. Taylor expanded in x around 0 68.2%

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

      1. *-commutative 68.2%

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

   5. Simplified 68.2%

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

   6. Taylor expanded in y around inf 55.2%

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

      1. mul-1-neg 55.2%

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

      2. associate-*r* 55.4%

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

   8. Simplified 55.4%

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

   if -3.60000000000000015e25 < i < -1e5

   1. Initial program 66.7%

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

   3. Taylor expanded in b around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in i around inf 100.0%

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

   if -1e5 < i < 9.0000000000000005e-293

   1. Initial program 75.6%

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

   3. Taylor expanded in j around inf 42.1%

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

   4. Taylor expanded in c around inf 37.9%

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

      1. *-commutative 37.9%

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

      2. *-commutative 37.9%

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

      3. associate-*r* 39.4%

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

   6. Simplified 39.4%

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

   if 9.0000000000000005e-293 < i < 2.09999999999999979e-236

   1. Initial program 88.7%

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

   3. Taylor expanded in t around inf 57.7%

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

   4. Taylor expanded in a around inf 57.0%

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

      1. mul-1-neg 57.0%

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

      2. *-commutative 57.0%

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

      3. distribute-rgt-neg-in 57.0%

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

   6. Simplified 57.0%

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

   if 2.09999999999999979e-236 < i < 2.10000000000000002e-199

   1. Initial program 90.0%

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

   3. Taylor expanded in j around inf 60.6%

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

   4. Taylor expanded in c around inf 50.8%

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

   if 2.10000000000000002e-199 < i < 1.8199999999999999e106

   1. Initial program 73.4%

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

   3. Taylor expanded in z around inf 53.5%

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

      1. *-commutative 53.5%

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

      2. *-commutative 53.5%

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

   5. Simplified 53.5%

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

   6. Taylor expanded in y around inf 32.0%

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

   if 1.8199999999999999e106 < i

   1. Initial program 62.7%

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

   3. Taylor expanded in j around inf 44.7%

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

   4. Taylor expanded in c around 0 38.2%

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

      1. neg-mul-1 38.2%

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

      2. distribute-lft-neg-in 38.2%

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

      3. *-commutative 38.2%

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

   6. Simplified 38.2%

      \[\leadsto j \cdot \color{blue}{\left(y \cdot \left(-i\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.9 \cdot 10^{+46}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -3.6 \cdot 10^{+25}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;i \leq -100000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq 9 \cdot 10^{-293}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{-236}:\\ \;\;\;\;-t \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{-199}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 1.82 \cdot 10^{+106}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 29.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{if}\;z \leq -20000000:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-78}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-256}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-117}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+161}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* x t) (- a))))
   (if (<= z -20000000.0)
     (* z (* b (- c)))
     (if (<= z -4.6e-78)
       (* a (* b i))
       (if (<= z -7.5e-256)
         (* t (* c j))
         (if (<= z 7e-277)
           t_1
           (if (<= z 7.8e-117)
             (* (* i j) (- y))
             (if (<= z 2.45e+30)
               t_1
               (if (<= z 7e+161) (* z (* x y)) (* b (* z (- c))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * t) * -a;
	double tmp;
	if (z <= -20000000.0) {
		tmp = z * (b * -c);
	} else if (z <= -4.6e-78) {
		tmp = a * (b * i);
	} else if (z <= -7.5e-256) {
		tmp = t * (c * j);
	} else if (z <= 7e-277) {
		tmp = t_1;
	} else if (z <= 7.8e-117) {
		tmp = (i * j) * -y;
	} else if (z <= 2.45e+30) {
		tmp = t_1;
	} else if (z <= 7e+161) {
		tmp = z * (x * y);
	} else {
		tmp = b * (z * -c);
	}
	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 = (x * t) * -a
    if (z <= (-20000000.0d0)) then
        tmp = z * (b * -c)
    else if (z <= (-4.6d-78)) then
        tmp = a * (b * i)
    else if (z <= (-7.5d-256)) then
        tmp = t * (c * j)
    else if (z <= 7d-277) then
        tmp = t_1
    else if (z <= 7.8d-117) then
        tmp = (i * j) * -y
    else if (z <= 2.45d+30) then
        tmp = t_1
    else if (z <= 7d+161) then
        tmp = z * (x * y)
    else
        tmp = b * (z * -c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * t) * -a;
	double tmp;
	if (z <= -20000000.0) {
		tmp = z * (b * -c);
	} else if (z <= -4.6e-78) {
		tmp = a * (b * i);
	} else if (z <= -7.5e-256) {
		tmp = t * (c * j);
	} else if (z <= 7e-277) {
		tmp = t_1;
	} else if (z <= 7.8e-117) {
		tmp = (i * j) * -y;
	} else if (z <= 2.45e+30) {
		tmp = t_1;
	} else if (z <= 7e+161) {
		tmp = z * (x * y);
	} else {
		tmp = b * (z * -c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * t) * -a
	tmp = 0
	if z <= -20000000.0:
		tmp = z * (b * -c)
	elif z <= -4.6e-78:
		tmp = a * (b * i)
	elif z <= -7.5e-256:
		tmp = t * (c * j)
	elif z <= 7e-277:
		tmp = t_1
	elif z <= 7.8e-117:
		tmp = (i * j) * -y
	elif z <= 2.45e+30:
		tmp = t_1
	elif z <= 7e+161:
		tmp = z * (x * y)
	else:
		tmp = b * (z * -c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * t) * Float64(-a))
	tmp = 0.0
	if (z <= -20000000.0)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (z <= -4.6e-78)
		tmp = Float64(a * Float64(b * i));
	elseif (z <= -7.5e-256)
		tmp = Float64(t * Float64(c * j));
	elseif (z <= 7e-277)
		tmp = t_1;
	elseif (z <= 7.8e-117)
		tmp = Float64(Float64(i * j) * Float64(-y));
	elseif (z <= 2.45e+30)
		tmp = t_1;
	elseif (z <= 7e+161)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(b * Float64(z * Float64(-c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * t) * -a;
	tmp = 0.0;
	if (z <= -20000000.0)
		tmp = z * (b * -c);
	elseif (z <= -4.6e-78)
		tmp = a * (b * i);
	elseif (z <= -7.5e-256)
		tmp = t * (c * j);
	elseif (z <= 7e-277)
		tmp = t_1;
	elseif (z <= 7.8e-117)
		tmp = (i * j) * -y;
	elseif (z <= 2.45e+30)
		tmp = t_1;
	elseif (z <= 7e+161)
		tmp = z * (x * y);
	else
		tmp = b * (z * -c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision]}, If[LessEqual[z, -20000000.0], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.6e-78], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.5e-256], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e-277], t$95$1, If[LessEqual[z, 7.8e-117], N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[z, 2.45e+30], t$95$1, If[LessEqual[z, 7e+161], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -2e7

   1. Initial program 52.8%

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

   3. Taylor expanded in z around inf 72.8%

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

      1. *-commutative 72.8%

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

      2. *-commutative 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in y around 0 45.0%

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

      1. neg-mul-1 45.0%

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

      2. distribute-lft-neg-in 45.0%

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

      3. *-commutative 45.0%

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

   8. Simplified 45.0%

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

   if -2e7 < z < -4.6000000000000004e-78

   1. Initial program 80.1%

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

   3. Taylor expanded in x around 0 60.0%

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

      1. *-commutative 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in a around inf 42.9%

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

   if -4.6000000000000004e-78 < z < -7.50000000000000005e-256

   1. Initial program 82.8%

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

   3. Taylor expanded in j around inf 51.6%

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

   4. Taylor expanded in c around inf 39.6%

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

      1. *-commutative 39.6%

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

      2. *-commutative 39.6%

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

      3. associate-*r* 42.3%

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

   6. Simplified 42.3%

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

   if -7.50000000000000005e-256 < z < 6.99999999999999966e-277 or 7.79999999999999984e-117 < z < 2.44999999999999992e30

   1. Initial program 67.4%

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

   3. Taylor expanded in a around inf 61.9%

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

      1. distribute-lft-out-- 61.9%

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

      2. *-commutative 61.9%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in t around inf 45.8%

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

      1. *-commutative 45.8%

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

   8. Simplified 45.8%

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

   if 6.99999999999999966e-277 < z < 7.79999999999999984e-117

   1. Initial program 81.4%

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

   3. Taylor expanded in x around 0 76.0%

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

      1. *-commutative 76.0%

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

   5. Simplified 76.0%

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

   6. Taylor expanded in y around inf 31.9%

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

      1. mul-1-neg 31.9%

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

      2. associate-*r* 34.6%

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

   8. Simplified 34.6%

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

   if 2.44999999999999992e30 < z < 6.99999999999999976e161

   1. Initial program 76.3%

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

   3. Taylor expanded in z around inf 71.5%

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

      1. *-commutative 71.5%

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

      2. *-commutative 71.5%

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

   5. Simplified 71.5%

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

   6. Taylor expanded in y around inf 59.5%

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

   if 6.99999999999999976e161 < z

   1. Initial program 66.6%

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

   3. Taylor expanded in b around inf 70.9%

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

      1. *-commutative 70.9%

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

   5. Simplified 70.9%

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

   6. Taylor expanded in i around 0 52.9%

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

      1. associate-*r* 52.9%

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

      2. neg-mul-1 52.9%

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

   8. Simplified 52.9%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(c \cdot z\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -20000000:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-78}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-256}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-277}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-117}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+30}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+161}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right) - b \cdot \left(z \cdot c\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -700000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-142}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* x (* y z))))
        (t_2 (- (* a (- (* b i) (* x t))) (* b (* z c))))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= y -700000.0)
     t_3
     (if (<= y 2.9e-142)
       t_2
       (if (<= y 1.7e-87)
         t_1
         (if (<= y 1.75e-41) t_2 (if (<= y 1.32e+135) 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 = (j * ((t * c) - (y * i))) + (x * (y * z));
	double t_2 = (a * ((b * i) - (x * t))) - (b * (z * c));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -700000.0) {
		tmp = t_3;
	} else if (y <= 2.9e-142) {
		tmp = t_2;
	} else if (y <= 1.7e-87) {
		tmp = t_1;
	} else if (y <= 1.75e-41) {
		tmp = t_2;
	} else if (y <= 1.32e+135) {
		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 = (j * ((t * c) - (y * i))) + (x * (y * z))
    t_2 = (a * ((b * i) - (x * t))) - (b * (z * c))
    t_3 = y * ((x * z) - (i * j))
    if (y <= (-700000.0d0)) then
        tmp = t_3
    else if (y <= 2.9d-142) then
        tmp = t_2
    else if (y <= 1.7d-87) then
        tmp = t_1
    else if (y <= 1.75d-41) then
        tmp = t_2
    else if (y <= 1.32d+135) 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 = (j * ((t * c) - (y * i))) + (x * (y * z));
	double t_2 = (a * ((b * i) - (x * t))) - (b * (z * c));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -700000.0) {
		tmp = t_3;
	} else if (y <= 2.9e-142) {
		tmp = t_2;
	} else if (y <= 1.7e-87) {
		tmp = t_1;
	} else if (y <= 1.75e-41) {
		tmp = t_2;
	} else if (y <= 1.32e+135) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + (x * (y * z))
	t_2 = (a * ((b * i) - (x * t))) - (b * (z * c))
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -700000.0:
		tmp = t_3
	elif y <= 2.9e-142:
		tmp = t_2
	elif y <= 1.7e-87:
		tmp = t_1
	elif y <= 1.75e-41:
		tmp = t_2
	elif y <= 1.32e+135:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(y * z)))
	t_2 = Float64(Float64(a * Float64(Float64(b * i) - Float64(x * t))) - Float64(b * Float64(z * c)))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -700000.0)
		tmp = t_3;
	elseif (y <= 2.9e-142)
		tmp = t_2;
	elseif (y <= 1.7e-87)
		tmp = t_1;
	elseif (y <= 1.75e-41)
		tmp = t_2;
	elseif (y <= 1.32e+135)
		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 = (j * ((t * c) - (y * i))) + (x * (y * z));
	t_2 = (a * ((b * i) - (x * t))) - (b * (z * c));
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -700000.0)
		tmp = t_3;
	elseif (y <= 2.9e-142)
		tmp = t_2;
	elseif (y <= 1.7e-87)
		tmp = t_1;
	elseif (y <= 1.75e-41)
		tmp = t_2;
	elseif (y <= 1.32e+135)
		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[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -700000.0], t$95$3, If[LessEqual[y, 2.9e-142], t$95$2, If[LessEqual[y, 1.7e-87], t$95$1, If[LessEqual[y, 1.75e-41], t$95$2, If[LessEqual[y, 1.32e+135], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7e5 or 1.32e135 < y

   1. Initial program 54.0%

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

   3. Taylor expanded in y around inf 67.1%

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

      1. +-commutative 67.1%

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

      2. mul-1-neg 67.1%

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

      3. unsub-neg 67.1%

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

   5. Simplified 67.1%

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

   if -7e5 < y < 2.8999999999999999e-142 or 1.6999999999999999e-87 < y < 1.75e-41

   1. Initial program 78.7%

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

   3. Taylor expanded in i around -inf 80.1%

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

   4. Taylor expanded in a around inf 71.0%

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

      1. +-commutative 71.0%

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

      2. mul-1-neg 71.0%

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

      3. unsub-neg 71.0%

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

      4. *-commutative 71.0%

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

   6. Simplified 71.0%

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

   if 2.8999999999999999e-142 < y < 1.6999999999999999e-87 or 1.75e-41 < y < 1.32e135

   1. Initial program 77.5%

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

   3. Taylor expanded in b around 0 67.6%

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

   4. Taylor expanded in a around 0 65.6%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -700000:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-142}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-87}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-41}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+135}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -112000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.45 \cdot 10^{-181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.08 \cdot 10^{-72}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.15 \cdot 10^{+214}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* x (- (* y z) (* t a)))))
        (t_2 (* i (- (* a b) (* y j)))))
   (if (<= i -112000.0)
     t_2
     (if (<= i 1.45e-181)
       t_1
       (if (<= i 1.08e-72)
         (* z (- (* x y) (* b c)))
         (if (<= i 1.3e+38)
           t_1
           (if (<= i 2.15e+214)
             (+ (* t (* c j)) (* b (- (* a i) (* z c))))
             t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -112000.0) {
		tmp = t_2;
	} else if (i <= 1.45e-181) {
		tmp = t_1;
	} else if (i <= 1.08e-72) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 1.3e+38) {
		tmp = t_1;
	} else if (i <= 2.15e+214) {
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	} 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 * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
    t_2 = i * ((a * b) - (y * j))
    if (i <= (-112000.0d0)) then
        tmp = t_2
    else if (i <= 1.45d-181) then
        tmp = t_1
    else if (i <= 1.08d-72) then
        tmp = z * ((x * y) - (b * c))
    else if (i <= 1.3d+38) then
        tmp = t_1
    else if (i <= 2.15d+214) then
        tmp = (t * (c * j)) + (b * ((a * i) - (z * c)))
    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 * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -112000.0) {
		tmp = t_2;
	} else if (i <= 1.45e-181) {
		tmp = t_1;
	} else if (i <= 1.08e-72) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 1.3e+38) {
		tmp = t_1;
	} else if (i <= 2.15e+214) {
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
	t_2 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -112000.0:
		tmp = t_2
	elif i <= 1.45e-181:
		tmp = t_1
	elif i <= 1.08e-72:
		tmp = z * ((x * y) - (b * c))
	elif i <= 1.3e+38:
		tmp = t_1
	elif i <= 2.15e+214:
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -112000.0)
		tmp = t_2;
	elseif (i <= 1.45e-181)
		tmp = t_1;
	elseif (i <= 1.08e-72)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (i <= 1.3e+38)
		tmp = t_1;
	elseif (i <= 2.15e+214)
		tmp = Float64(Float64(t * Float64(c * j)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	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 * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	t_2 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -112000.0)
		tmp = t_2;
	elseif (i <= 1.45e-181)
		tmp = t_1;
	elseif (i <= 1.08e-72)
		tmp = z * ((x * y) - (b * c));
	elseif (i <= 1.3e+38)
		tmp = t_1;
	elseif (i <= 2.15e+214)
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -112000.0], t$95$2, If[LessEqual[i, 1.45e-181], t$95$1, If[LessEqual[i, 1.08e-72], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.3e+38], t$95$1, If[LessEqual[i, 2.15e+214], N[(N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -112000 or 2.14999999999999991e214 < i

   1. Initial program 60.1%

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

   3. Taylor expanded in i around inf 76.4%

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

      1. distribute-lft-out-- 76.4%

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

   5. Simplified 76.4%

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

   if -112000 < i < 1.4499999999999999e-181 or 1.07999999999999998e-72 < i < 1.3e38

   1. Initial program 79.3%

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

   3. Taylor expanded in b around 0 74.8%

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

   if 1.4499999999999999e-181 < i < 1.07999999999999998e-72

   1. Initial program 74.6%

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

   3. Taylor expanded in z around inf 67.2%

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

      1. *-commutative 67.2%

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

      2. *-commutative 67.2%

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

   5. Simplified 67.2%

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

   if 1.3e38 < i < 2.14999999999999991e214

   1. Initial program 60.8%

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

   3. Taylor expanded in x around 0 58.4%

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

      1. *-commutative 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in c around inf 66.7%

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

      1. *-commutative 26.5%

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

      2. *-commutative 26.5%

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

      3. associate-*r* 29.2%

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

   8. Simplified 66.7%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -112000:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 1.45 \cdot 10^{-181}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 1.08 \cdot 10^{-72}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{+38}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 2.15 \cdot 10^{+214}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 44.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{if}\;b \leq -1.08 \cdot 10^{-36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-127}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-281}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 10^{-124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.54 \cdot 10^{-52}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y)))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* i (* j (- y)))))
   (if (<= b -1.08e-36)
     t_2
     (if (<= b -5e-127)
       (* t (* c j))
       (if (<= b 1.02e-281)
         t_3
         (if (<= b 1e-124)
           t_1
           (if (<= b 1.54e-52) t_3 (if (<= b 1.25e-9) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = i * (j * -y);
	double tmp;
	if (b <= -1.08e-36) {
		tmp = t_2;
	} else if (b <= -5e-127) {
		tmp = t * (c * j);
	} else if (b <= 1.02e-281) {
		tmp = t_3;
	} else if (b <= 1e-124) {
		tmp = t_1;
	} else if (b <= 1.54e-52) {
		tmp = t_3;
	} else if (b <= 1.25e-9) {
		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) :: t_3
    real(8) :: tmp
    t_1 = z * (x * y)
    t_2 = b * ((a * i) - (z * c))
    t_3 = i * (j * -y)
    if (b <= (-1.08d-36)) then
        tmp = t_2
    else if (b <= (-5d-127)) then
        tmp = t * (c * j)
    else if (b <= 1.02d-281) then
        tmp = t_3
    else if (b <= 1d-124) then
        tmp = t_1
    else if (b <= 1.54d-52) then
        tmp = t_3
    else if (b <= 1.25d-9) 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 = z * (x * y);
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = i * (j * -y);
	double tmp;
	if (b <= -1.08e-36) {
		tmp = t_2;
	} else if (b <= -5e-127) {
		tmp = t * (c * j);
	} else if (b <= 1.02e-281) {
		tmp = t_3;
	} else if (b <= 1e-124) {
		tmp = t_1;
	} else if (b <= 1.54e-52) {
		tmp = t_3;
	} else if (b <= 1.25e-9) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = b * ((a * i) - (z * c))
	t_3 = i * (j * -y)
	tmp = 0
	if b <= -1.08e-36:
		tmp = t_2
	elif b <= -5e-127:
		tmp = t * (c * j)
	elif b <= 1.02e-281:
		tmp = t_3
	elif b <= 1e-124:
		tmp = t_1
	elif b <= 1.54e-52:
		tmp = t_3
	elif b <= 1.25e-9:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(i * Float64(j * Float64(-y)))
	tmp = 0.0
	if (b <= -1.08e-36)
		tmp = t_2;
	elseif (b <= -5e-127)
		tmp = Float64(t * Float64(c * j));
	elseif (b <= 1.02e-281)
		tmp = t_3;
	elseif (b <= 1e-124)
		tmp = t_1;
	elseif (b <= 1.54e-52)
		tmp = t_3;
	elseif (b <= 1.25e-9)
		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 = z * (x * y);
	t_2 = b * ((a * i) - (z * c));
	t_3 = i * (j * -y);
	tmp = 0.0;
	if (b <= -1.08e-36)
		tmp = t_2;
	elseif (b <= -5e-127)
		tmp = t * (c * j);
	elseif (b <= 1.02e-281)
		tmp = t_3;
	elseif (b <= 1e-124)
		tmp = t_1;
	elseif (b <= 1.54e-52)
		tmp = t_3;
	elseif (b <= 1.25e-9)
		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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.08e-36], t$95$2, If[LessEqual[b, -5e-127], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.02e-281], t$95$3, If[LessEqual[b, 1e-124], t$95$1, If[LessEqual[b, 1.54e-52], t$95$3, If[LessEqual[b, 1.25e-9], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.08000000000000006e-36 or 1.25e-9 < b

   1. Initial program 72.1%

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

   3. Taylor expanded in b around inf 60.0%

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

      1. *-commutative 60.0%

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

   5. Simplified 60.0%

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

   if -1.08000000000000006e-36 < b < -4.9999999999999997e-127

   1. Initial program 64.1%

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

   3. Taylor expanded in j around inf 38.5%

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

   4. Taylor expanded in c around inf 38.8%

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

      1. *-commutative 38.8%

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

      2. *-commutative 38.8%

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

      3. associate-*r* 43.7%

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

   6. Simplified 43.7%

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

   if -4.9999999999999997e-127 < b < 1.01999999999999996e-281 or 9.99999999999999933e-125 < b < 1.53999999999999999e-52

   1. Initial program 57.7%

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

   3. Taylor expanded in i around inf 40.7%

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

      1. distribute-lft-out-- 40.7%

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

   5. Simplified 40.7%

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

   6. Taylor expanded in j around inf 39.3%

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

      1. associate-*r* 39.3%

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

      2. neg-mul-1 39.3%

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

   8. Simplified 39.3%

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

   if 1.01999999999999996e-281 < b < 9.99999999999999933e-125 or 1.53999999999999999e-52 < b < 1.25e-9

   1. Initial program 77.8%

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

   3. Taylor expanded in z around inf 51.5%

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

      1. *-commutative 51.5%

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

      2. *-commutative 51.5%

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

   5. Simplified 51.5%

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

   6. Taylor expanded in y around inf 47.4%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.08 \cdot 10^{-36}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-127}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-281}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;b \leq 10^{-124}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.54 \cdot 10^{-52}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-9}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 41.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;i \leq -3.3 \cdot 10^{+265}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;i \leq -5.9 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -6.2 \cdot 10^{+24}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;i \leq -58:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{-289}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 7 \cdot 10^{-161}:\\ \;\;\;\;-t \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= i -3.3e+265)
     (* (* y i) (- j))
     (if (<= i -5.9e+47)
       t_1
       (if (<= i -6.2e+24)
         (* (* i j) (- y))
         (if (<= i -58.0)
           t_1
           (if (<= i 1.25e-289)
             (* c (- (* t j) (* z b)))
             (if (<= i 7e-161) (- (* 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 = b * ((a * i) - (z * c));
	double tmp;
	if (i <= -3.3e+265) {
		tmp = (y * i) * -j;
	} else if (i <= -5.9e+47) {
		tmp = t_1;
	} else if (i <= -6.2e+24) {
		tmp = (i * j) * -y;
	} else if (i <= -58.0) {
		tmp = t_1;
	} else if (i <= 1.25e-289) {
		tmp = c * ((t * j) - (z * b));
	} else if (i <= 7e-161) {
		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 = b * ((a * i) - (z * c))
    if (i <= (-3.3d+265)) then
        tmp = (y * i) * -j
    else if (i <= (-5.9d+47)) then
        tmp = t_1
    else if (i <= (-6.2d+24)) then
        tmp = (i * j) * -y
    else if (i <= (-58.0d0)) then
        tmp = t_1
    else if (i <= 1.25d-289) then
        tmp = c * ((t * j) - (z * b))
    else if (i <= 7d-161) 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 = b * ((a * i) - (z * c));
	double tmp;
	if (i <= -3.3e+265) {
		tmp = (y * i) * -j;
	} else if (i <= -5.9e+47) {
		tmp = t_1;
	} else if (i <= -6.2e+24) {
		tmp = (i * j) * -y;
	} else if (i <= -58.0) {
		tmp = t_1;
	} else if (i <= 1.25e-289) {
		tmp = c * ((t * j) - (z * b));
	} else if (i <= 7e-161) {
		tmp = -(t * (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if i <= -3.3e+265:
		tmp = (y * i) * -j
	elif i <= -5.9e+47:
		tmp = t_1
	elif i <= -6.2e+24:
		tmp = (i * j) * -y
	elif i <= -58.0:
		tmp = t_1
	elif i <= 1.25e-289:
		tmp = c * ((t * j) - (z * b))
	elif i <= 7e-161:
		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(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (i <= -3.3e+265)
		tmp = Float64(Float64(y * i) * Float64(-j));
	elseif (i <= -5.9e+47)
		tmp = t_1;
	elseif (i <= -6.2e+24)
		tmp = Float64(Float64(i * j) * Float64(-y));
	elseif (i <= -58.0)
		tmp = t_1;
	elseif (i <= 1.25e-289)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (i <= 7e-161)
		tmp = Float64(-Float64(t * Float64(x * 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 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (i <= -3.3e+265)
		tmp = (y * i) * -j;
	elseif (i <= -5.9e+47)
		tmp = t_1;
	elseif (i <= -6.2e+24)
		tmp = (i * j) * -y;
	elseif (i <= -58.0)
		tmp = t_1;
	elseif (i <= 1.25e-289)
		tmp = c * ((t * j) - (z * b));
	elseif (i <= 7e-161)
		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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.3e+265], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[i, -5.9e+47], t$95$1, If[LessEqual[i, -6.2e+24], N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[i, -58.0], t$95$1, If[LessEqual[i, 1.25e-289], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7e-161], (-N[(t * N[(x * a), $MachinePrecision]), $MachinePrecision]), t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -3.2999999999999998e265

   1. Initial program 61.2%

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

   3. Taylor expanded in j around inf 80.1%

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

   4. Taylor expanded in c around 0 80.1%

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

      1. neg-mul-1 80.1%

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

      2. distribute-lft-neg-in 80.1%

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

      3. *-commutative 80.1%

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

   6. Simplified 80.1%

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

   if -3.2999999999999998e265 < i < -5.90000000000000034e47 or -6.20000000000000022e24 < i < -58 or 7.00000000000000039e-161 < i

   1. Initial program 64.9%

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

   3. Taylor expanded in b around inf 54.6%

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

      1. *-commutative 54.6%

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

   5. Simplified 54.6%

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

   if -5.90000000000000034e47 < i < -6.20000000000000022e24

   1. Initial program 66.5%

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

   3. Taylor expanded in x around 0 68.2%

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

      1. *-commutative 68.2%

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

   5. Simplified 68.2%

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

   6. Taylor expanded in y around inf 55.2%

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

      1. mul-1-neg 55.2%

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

      2. associate-*r* 55.4%

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

   8. Simplified 55.4%

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

   if -58 < i < 1.25000000000000007e-289

   1. Initial program 75.6%

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

   3. Taylor expanded in c around inf 53.0%

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

      1. *-commutative 53.0%

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

   5. Simplified 53.0%

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

   if 1.25000000000000007e-289 < i < 7.00000000000000039e-161

   1. Initial program 83.2%

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

   3. Taylor expanded in t around inf 59.8%

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

   4. Taylor expanded in a around inf 52.5%

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

      1. mul-1-neg 52.5%

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

      2. *-commutative 52.5%

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

      3. distribute-rgt-neg-in 52.5%

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

   6. Simplified 52.5%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.3 \cdot 10^{+265}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;i \leq -5.9 \cdot 10^{+47}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq -6.2 \cdot 10^{+24}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;i \leq -58:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{-289}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 7 \cdot 10^{-161}:\\ \;\;\;\;-t \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 57.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -112000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -3.6 \cdot 10^{-212}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 38000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;i \leq 2.45 \cdot 10^{+214}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))))
   (if (<= i -112000.0)
     t_1
     (if (<= i -3.6e-212)
       (+ (* j (- (* t c) (* y i))) (* x (* y z)))
       (if (<= i 38000.0)
         (- (* x (- (* y z) (* t a))) (* b (* z c)))
         (if (<= i 2.45e+214)
           (+ (* t (* c j)) (* b (- (* a i) (* z c))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -112000.0) {
		tmp = t_1;
	} else if (i <= -3.6e-212) {
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	} else if (i <= 38000.0) {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	} else if (i <= 2.45e+214) {
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    if (i <= (-112000.0d0)) then
        tmp = t_1
    else if (i <= (-3.6d-212)) then
        tmp = (j * ((t * c) - (y * i))) + (x * (y * z))
    else if (i <= 38000.0d0) then
        tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
    else if (i <= 2.45d+214) then
        tmp = (t * (c * j)) + (b * ((a * i) - (z * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -112000.0) {
		tmp = t_1;
	} else if (i <= -3.6e-212) {
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	} else if (i <= 38000.0) {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	} else if (i <= 2.45e+214) {
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -112000.0:
		tmp = t_1
	elif i <= -3.6e-212:
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z))
	elif i <= 38000.0:
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
	elif i <= 2.45e+214:
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -112000.0)
		tmp = t_1;
	elseif (i <= -3.6e-212)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(y * z)));
	elseif (i <= 38000.0)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(z * c)));
	elseif (i <= 2.45e+214)
		tmp = Float64(Float64(t * Float64(c * j)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -112000.0)
		tmp = t_1;
	elseif (i <= -3.6e-212)
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	elseif (i <= 38000.0)
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	elseif (i <= 2.45e+214)
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -112000.0], t$95$1, If[LessEqual[i, -3.6e-212], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 38000.0], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.45e+214], N[(N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -112000 or 2.45000000000000016e214 < i

   1. Initial program 60.1%

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

   3. Taylor expanded in i around inf 76.4%

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

      1. distribute-lft-out-- 76.4%

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

   5. Simplified 76.4%

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

   if -112000 < i < -3.6000000000000001e-212

   1. Initial program 76.3%

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

   3. Taylor expanded in b around 0 74.5%

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

   4. Taylor expanded in a around 0 61.9%

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

   if -3.6000000000000001e-212 < i < 38000

   1. Initial program 79.6%

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

   3. Taylor expanded in i around -inf 71.3%

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

   4. Taylor expanded in x around inf 64.1%

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

      1. *-commutative 64.1%

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

   6. Simplified 64.1%

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

   if 38000 < i < 2.45000000000000016e214

   1. Initial program 62.4%

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

   3. Taylor expanded in x around 0 60.1%

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

      1. *-commutative 60.1%

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

   5. Simplified 60.1%

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

   6. Taylor expanded in c around inf 65.1%

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

      1. *-commutative 26.4%

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

      2. *-commutative 26.4%

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

      3. associate-*r* 28.9%

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

   8. Simplified 65.1%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -112000:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -3.6 \cdot 10^{-212}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 38000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;i \leq 2.45 \cdot 10^{+214}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 44.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;i \leq -2.2 \cdot 10^{+265}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;i \leq -7 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1.5 \cdot 10^{+25}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq -1200 \lor \neg \left(i \leq 5.1 \cdot 10^{-155}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= i -2.2e+265)
     (* (* y i) (- j))
     (if (<= i -7e+44)
       t_1
       (if (<= i -1.5e+25)
         (* j (- (* t c) (* y i)))
         (if (or (<= i -1200.0) (not (<= i 5.1e-155)))
           t_1
           (* t (- (* c j) (* x a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (i <= -2.2e+265) {
		tmp = (y * i) * -j;
	} else if (i <= -7e+44) {
		tmp = t_1;
	} else if (i <= -1.5e+25) {
		tmp = j * ((t * c) - (y * i));
	} else if ((i <= -1200.0) || !(i <= 5.1e-155)) {
		tmp = t_1;
	} else {
		tmp = t * ((c * j) - (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) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (i <= (-2.2d+265)) then
        tmp = (y * i) * -j
    else if (i <= (-7d+44)) then
        tmp = t_1
    else if (i <= (-1.5d+25)) then
        tmp = j * ((t * c) - (y * i))
    else if ((i <= (-1200.0d0)) .or. (.not. (i <= 5.1d-155))) then
        tmp = t_1
    else
        tmp = t * ((c * j) - (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 t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (i <= -2.2e+265) {
		tmp = (y * i) * -j;
	} else if (i <= -7e+44) {
		tmp = t_1;
	} else if (i <= -1.5e+25) {
		tmp = j * ((t * c) - (y * i));
	} else if ((i <= -1200.0) || !(i <= 5.1e-155)) {
		tmp = t_1;
	} else {
		tmp = t * ((c * j) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if i <= -2.2e+265:
		tmp = (y * i) * -j
	elif i <= -7e+44:
		tmp = t_1
	elif i <= -1.5e+25:
		tmp = j * ((t * c) - (y * i))
	elif (i <= -1200.0) or not (i <= 5.1e-155):
		tmp = t_1
	else:
		tmp = t * ((c * j) - (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (i <= -2.2e+265)
		tmp = Float64(Float64(y * i) * Float64(-j));
	elseif (i <= -7e+44)
		tmp = t_1;
	elseif (i <= -1.5e+25)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif ((i <= -1200.0) || !(i <= 5.1e-155))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (i <= -2.2e+265)
		tmp = (y * i) * -j;
	elseif (i <= -7e+44)
		tmp = t_1;
	elseif (i <= -1.5e+25)
		tmp = j * ((t * c) - (y * i));
	elseif ((i <= -1200.0) || ~((i <= 5.1e-155)))
		tmp = t_1;
	else
		tmp = t * ((c * j) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.2e+265], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[i, -7e+44], t$95$1, If[LessEqual[i, -1.5e+25], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[i, -1200.0], N[Not[LessEqual[i, 5.1e-155]], $MachinePrecision]], t$95$1, N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -2.1999999999999999e265

   1. Initial program 61.2%

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

   3. Taylor expanded in j around inf 80.1%

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

   4. Taylor expanded in c around 0 80.1%

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

      1. neg-mul-1 80.1%

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

      2. distribute-lft-neg-in 80.1%

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

      3. *-commutative 80.1%

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

   6. Simplified 80.1%

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

   if -2.1999999999999999e265 < i < -6.9999999999999998e44 or -1.50000000000000003e25 < i < -1200 or 5.0999999999999996e-155 < i

   1. Initial program 64.4%

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

   3. Taylor expanded in b around inf 55.3%

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

      1. *-commutative 55.3%

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

   5. Simplified 55.3%

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

   if -6.9999999999999998e44 < i < -1.50000000000000003e25

   1. Initial program 66.5%

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

   3. Taylor expanded in j around inf 66.7%

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

   if -1200 < i < 5.0999999999999996e-155

   1. Initial program 78.4%

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

   3. Taylor expanded in t around inf 57.0%

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

   4. Taylor expanded in a around 0 48.7%

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

      1. associate-*r* 50.7%

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

      2. +-commutative 50.7%

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

      3. mul-1-neg 50.7%

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

      4. *-commutative 50.7%

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

      5. associate-*l* 56.0%

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

      6. sub-neg 56.0%

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

      7. distribute-rgt-out-- 57.0%

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

   6. Simplified 57.0%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.2 \cdot 10^{+265}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;i \leq -7 \cdot 10^{+44}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq -1.5 \cdot 10^{+25}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq -1200 \lor \neg \left(i \leq 5.1 \cdot 10^{-155}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{if}\;i \leq -1.9 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -2.3 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -105000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{-281}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 1.5 \cdot 10^{+106}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* i j) (- y))))
   (if (<= i -1.9e+49)
     (* a (* b i))
     (if (<= i -2.3e+24)
       t_1
       (if (<= i -105000.0)
         (* b (* a i))
         (if (<= i -5.2e-281)
           (* t (* c j))
           (if (<= i 1.5e+106) (* z (* x y)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * j) * -y;
	double tmp;
	if (i <= -1.9e+49) {
		tmp = a * (b * i);
	} else if (i <= -2.3e+24) {
		tmp = t_1;
	} else if (i <= -105000.0) {
		tmp = b * (a * i);
	} else if (i <= -5.2e-281) {
		tmp = t * (c * j);
	} else if (i <= 1.5e+106) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (i * j) * -y
    if (i <= (-1.9d+49)) then
        tmp = a * (b * i)
    else if (i <= (-2.3d+24)) then
        tmp = t_1
    else if (i <= (-105000.0d0)) then
        tmp = b * (a * i)
    else if (i <= (-5.2d-281)) then
        tmp = t * (c * j)
    else if (i <= 1.5d+106) then
        tmp = z * (x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * j) * -y;
	double tmp;
	if (i <= -1.9e+49) {
		tmp = a * (b * i);
	} else if (i <= -2.3e+24) {
		tmp = t_1;
	} else if (i <= -105000.0) {
		tmp = b * (a * i);
	} else if (i <= -5.2e-281) {
		tmp = t * (c * j);
	} else if (i <= 1.5e+106) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (i * j) * -y
	tmp = 0
	if i <= -1.9e+49:
		tmp = a * (b * i)
	elif i <= -2.3e+24:
		tmp = t_1
	elif i <= -105000.0:
		tmp = b * (a * i)
	elif i <= -5.2e-281:
		tmp = t * (c * j)
	elif i <= 1.5e+106:
		tmp = z * (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * j) * Float64(-y))
	tmp = 0.0
	if (i <= -1.9e+49)
		tmp = Float64(a * Float64(b * i));
	elseif (i <= -2.3e+24)
		tmp = t_1;
	elseif (i <= -105000.0)
		tmp = Float64(b * Float64(a * i));
	elseif (i <= -5.2e-281)
		tmp = Float64(t * Float64(c * j));
	elseif (i <= 1.5e+106)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (i * j) * -y;
	tmp = 0.0;
	if (i <= -1.9e+49)
		tmp = a * (b * i);
	elseif (i <= -2.3e+24)
		tmp = t_1;
	elseif (i <= -105000.0)
		tmp = b * (a * i);
	elseif (i <= -5.2e-281)
		tmp = t * (c * j);
	elseif (i <= 1.5e+106)
		tmp = z * (x * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision]}, If[LessEqual[i, -1.9e+49], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.3e+24], t$95$1, If[LessEqual[i, -105000.0], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -5.2e-281], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.5e+106], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -1.8999999999999999e49

   1. Initial program 58.0%

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

   3. Taylor expanded in x around 0 65.5%

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

      1. *-commutative 65.5%

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

   5. Simplified 65.5%

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

   6. Taylor expanded in a around inf 56.7%

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

   if -1.8999999999999999e49 < i < -2.2999999999999999e24 or 1.5e106 < i

   1. Initial program 63.3%

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

   3. Taylor expanded in x around 0 67.2%

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

      1. *-commutative 67.2%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in y around inf 40.8%

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

      1. mul-1-neg 40.8%

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

      2. associate-*r* 40.9%

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

   8. Simplified 40.9%

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

   if -2.2999999999999999e24 < i < -105000

   1. Initial program 66.7%

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

   3. Taylor expanded in b around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in i around inf 100.0%

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

   if -105000 < i < -5.2000000000000001e-281

   1. Initial program 76.5%

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

   3. Taylor expanded in j around inf 44.4%

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

   4. Taylor expanded in c around inf 39.7%

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

      1. *-commutative 39.7%

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

      2. *-commutative 39.7%

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

      3. associate-*r* 41.4%

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

   6. Simplified 41.4%

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

   if -5.2000000000000001e-281 < i < 1.5e106

   1. Initial program 76.5%

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

   3. Taylor expanded in z around inf 47.7%

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

      1. *-commutative 47.7%

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

      2. *-commutative 47.7%

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

   5. Simplified 47.7%

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

   6. Taylor expanded in y around inf 30.4%

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

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.9 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -2.3 \cdot 10^{+24}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;i \leq -105000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{-281}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 1.5 \cdot 10^{+106}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -9.5 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -2 \cdot 10^{+25}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;i \leq -115000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq -3.35 \cdot 10^{-286}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{+106}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -9.5e+45)
   (* a (* b i))
   (if (<= i -2e+25)
     (* (* i j) (- y))
     (if (<= i -115000.0)
       (* b (* a i))
       (if (<= i -3.35e-286)
         (* t (* c j))
         (if (<= i 1.7e+106) (* z (* x y)) (* (* y i) (- j))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -9.5e+45) {
		tmp = a * (b * i);
	} else if (i <= -2e+25) {
		tmp = (i * j) * -y;
	} else if (i <= -115000.0) {
		tmp = b * (a * i);
	} else if (i <= -3.35e-286) {
		tmp = t * (c * j);
	} else if (i <= 1.7e+106) {
		tmp = z * (x * y);
	} else {
		tmp = (y * i) * -j;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-9.5d+45)) then
        tmp = a * (b * i)
    else if (i <= (-2d+25)) then
        tmp = (i * j) * -y
    else if (i <= (-115000.0d0)) then
        tmp = b * (a * i)
    else if (i <= (-3.35d-286)) then
        tmp = t * (c * j)
    else if (i <= 1.7d+106) then
        tmp = z * (x * y)
    else
        tmp = (y * i) * -j
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -9.5e+45) {
		tmp = a * (b * i);
	} else if (i <= -2e+25) {
		tmp = (i * j) * -y;
	} else if (i <= -115000.0) {
		tmp = b * (a * i);
	} else if (i <= -3.35e-286) {
		tmp = t * (c * j);
	} else if (i <= 1.7e+106) {
		tmp = z * (x * y);
	} else {
		tmp = (y * i) * -j;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -9.5e+45:
		tmp = a * (b * i)
	elif i <= -2e+25:
		tmp = (i * j) * -y
	elif i <= -115000.0:
		tmp = b * (a * i)
	elif i <= -3.35e-286:
		tmp = t * (c * j)
	elif i <= 1.7e+106:
		tmp = z * (x * y)
	else:
		tmp = (y * i) * -j
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -9.5e+45)
		tmp = Float64(a * Float64(b * i));
	elseif (i <= -2e+25)
		tmp = Float64(Float64(i * j) * Float64(-y));
	elseif (i <= -115000.0)
		tmp = Float64(b * Float64(a * i));
	elseif (i <= -3.35e-286)
		tmp = Float64(t * Float64(c * j));
	elseif (i <= 1.7e+106)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(Float64(y * i) * Float64(-j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -9.5e+45)
		tmp = a * (b * i);
	elseif (i <= -2e+25)
		tmp = (i * j) * -y;
	elseif (i <= -115000.0)
		tmp = b * (a * i);
	elseif (i <= -3.35e-286)
		tmp = t * (c * j);
	elseif (i <= 1.7e+106)
		tmp = z * (x * y);
	else
		tmp = (y * i) * -j;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -9.5e+45], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2e+25], N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[i, -115000.0], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.35e-286], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.7e+106], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -9.4999999999999998e45

   1. Initial program 58.0%

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

   3. Taylor expanded in x around 0 65.5%

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

      1. *-commutative 65.5%

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

   5. Simplified 65.5%

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

   6. Taylor expanded in a around inf 56.7%

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

   if -9.4999999999999998e45 < i < -2.00000000000000018e25

   1. Initial program 66.5%

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

   3. Taylor expanded in x around 0 68.2%

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

      1. *-commutative 68.2%

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

   5. Simplified 68.2%

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

   6. Taylor expanded in y around inf 55.2%

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

      1. mul-1-neg 55.2%

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

      2. associate-*r* 55.4%

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

   8. Simplified 55.4%

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

   if -2.00000000000000018e25 < i < -115000

   1. Initial program 66.7%

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

   3. Taylor expanded in b around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in i around inf 100.0%

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

   if -115000 < i < -3.34999999999999998e-286

   1. Initial program 76.5%

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

   3. Taylor expanded in j around inf 44.4%

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

   4. Taylor expanded in c around inf 39.7%

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

      1. *-commutative 39.7%

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

      2. *-commutative 39.7%

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

      3. associate-*r* 41.4%

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

   6. Simplified 41.4%

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

   if -3.34999999999999998e-286 < i < 1.69999999999999997e106

   1. Initial program 76.5%

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

   3. Taylor expanded in z around inf 47.7%

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

      1. *-commutative 47.7%

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

      2. *-commutative 47.7%

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

   5. Simplified 47.7%

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

   6. Taylor expanded in y around inf 30.4%

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

   if 1.69999999999999997e106 < i

   1. Initial program 62.7%

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

   3. Taylor expanded in j around inf 44.7%

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

   4. Taylor expanded in c around 0 38.2%

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

      1. neg-mul-1 38.2%

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

      2. distribute-lft-neg-in 38.2%

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

      3. *-commutative 38.2%

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

   6. Simplified 38.2%

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

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9.5 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -2 \cdot 10^{+25}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;i \leq -115000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq -3.35 \cdot 10^{-286}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{+106}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 52.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-216}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* z (- (* x y) (* b c)))))
   (if (<= z -9.5e-9)
     t_2
     (if (<= z 3.15e-301)
       t_1
       (if (<= z 1.6e-216)
         (* j (- (* t c) (* y i)))
         (if (<= z 2.05e+24) 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 * ((c * j) - (x * a));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -9.5e-9) {
		tmp = t_2;
	} else if (z <= 3.15e-301) {
		tmp = t_1;
	} else if (z <= 1.6e-216) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= 2.05e+24) {
		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 * ((c * j) - (x * a))
    t_2 = z * ((x * y) - (b * c))
    if (z <= (-9.5d-9)) then
        tmp = t_2
    else if (z <= 3.15d-301) then
        tmp = t_1
    else if (z <= 1.6d-216) then
        tmp = j * ((t * c) - (y * i))
    else if (z <= 2.05d+24) 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 * ((c * j) - (x * a));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -9.5e-9) {
		tmp = t_2;
	} else if (z <= 3.15e-301) {
		tmp = t_1;
	} else if (z <= 1.6e-216) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= 2.05e+24) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -9.5e-9:
		tmp = t_2
	elif z <= 3.15e-301:
		tmp = t_1
	elif z <= 1.6e-216:
		tmp = j * ((t * c) - (y * i))
	elif z <= 2.05e+24:
		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(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -9.5e-9)
		tmp = t_2;
	elseif (z <= 3.15e-301)
		tmp = t_1;
	elseif (z <= 1.6e-216)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (z <= 2.05e+24)
		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 * ((c * j) - (x * a));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -9.5e-9)
		tmp = t_2;
	elseif (z <= 3.15e-301)
		tmp = t_1;
	elseif (z <= 1.6e-216)
		tmp = j * ((t * c) - (y * i));
	elseif (z <= 2.05e+24)
		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[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e-9], t$95$2, If[LessEqual[z, 3.15e-301], t$95$1, If[LessEqual[z, 1.6e-216], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+24], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5000000000000007e-9 or 2.05e24 < z

   1. Initial program 62.0%

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

   3. Taylor expanded in z around inf 69.1%

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

      1. *-commutative 69.1%

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

      2. *-commutative 69.1%

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

   5. Simplified 69.1%

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

   if -9.5000000000000007e-9 < z < 3.14999999999999981e-301 or 1.60000000000000013e-216 < z < 2.05e24

   1. Initial program 75.8%

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

   3. Taylor expanded in t around inf 55.7%

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

   4. Taylor expanded in a around 0 49.5%

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

      1. associate-*r* 50.3%

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

      2. +-commutative 50.3%

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

      3. mul-1-neg 50.3%

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

      4. *-commutative 50.3%

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

      5. associate-*l* 53.9%

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

      6. sub-neg 53.9%

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

      7. distribute-rgt-out-- 55.7%

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

   6. Simplified 55.7%

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

   if 3.14999999999999981e-301 < z < 1.60000000000000013e-216

   1. Initial program 85.1%

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

   3. Taylor expanded in j around inf 54.9%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-9}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{-301}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-216}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+24}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 52.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-300}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-215}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+21}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))))
   (if (<= z -2.4e-9)
     t_1
     (if (<= z 1.08e-300)
       (* t (- (* c j) (* x a)))
       (if (<= z 1.55e-215)
         (* j (- (* t c) (* y i)))
         (if (<= z 1.06e+21) (* a (- (* b i) (* x t))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -2.4e-9) {
		tmp = t_1;
	} else if (z <= 1.08e-300) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 1.55e-215) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= 1.06e+21) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    if (z <= (-2.4d-9)) then
        tmp = t_1
    else if (z <= 1.08d-300) then
        tmp = t * ((c * j) - (x * a))
    else if (z <= 1.55d-215) then
        tmp = j * ((t * c) - (y * i))
    else if (z <= 1.06d+21) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -2.4e-9) {
		tmp = t_1;
	} else if (z <= 1.08e-300) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 1.55e-215) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= 1.06e+21) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -2.4e-9:
		tmp = t_1
	elif z <= 1.08e-300:
		tmp = t * ((c * j) - (x * a))
	elif z <= 1.55e-215:
		tmp = j * ((t * c) - (y * i))
	elif z <= 1.06e+21:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -2.4e-9)
		tmp = t_1;
	elseif (z <= 1.08e-300)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (z <= 1.55e-215)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (z <= 1.06e+21)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -2.4e-9)
		tmp = t_1;
	elseif (z <= 1.08e-300)
		tmp = t * ((c * j) - (x * a));
	elseif (z <= 1.55e-215)
		tmp = j * ((t * c) - (y * i));
	elseif (z <= 1.06e+21)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e-9], t$95$1, If[LessEqual[z, 1.08e-300], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-215], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.06e+21], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.4e-9 or 1.06e21 < z

   1. Initial program 62.3%

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

   3. Taylor expanded in z around inf 68.6%

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

      1. *-commutative 68.6%

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

      2. *-commutative 68.6%

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

   5. Simplified 68.6%

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

   if -2.4e-9 < z < 1.08e-300

   1. Initial program 81.4%

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

   3. Taylor expanded in t around inf 56.8%

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

   4. Taylor expanded in a around 0 55.4%

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

      1. associate-*r* 56.8%

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

      2. +-commutative 56.8%

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

      3. mul-1-neg 56.8%

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

      4. *-commutative 56.8%

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

      5. associate-*l* 56.8%

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

      6. sub-neg 56.8%

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

      7. distribute-rgt-out-- 56.8%

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

   6. Simplified 56.8%

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

   if 1.08e-300 < z < 1.54999999999999997e-215

   1. Initial program 85.8%

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

   3. Taylor expanded in j around inf 57.1%

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

   if 1.54999999999999997e-215 < z < 1.06e21

   1. Initial program 66.7%

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

   3. Taylor expanded in a around inf 56.7%

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

      1. distribute-lft-out-- 56.7%

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

      2. *-commutative 56.7%

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

   5. Simplified 56.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x - i \cdot b\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-9}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-300}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-215}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+21}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 62.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;i \leq -110000:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{-158}:\\ \;\;\;\;t_1 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= i -110000.0)
     (* i (- (* a b) (* y j)))
     (if (<= i 7.2e-158)
       (+ t_1 (* x (- (* y z) (* t a))))
       (+ t_1 (* b (- (* a i) (* z c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (i <= -110000.0) {
		tmp = i * ((a * b) - (y * j));
	} else if (i <= 7.2e-158) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if (i <= (-110000.0d0)) then
        tmp = i * ((a * b) - (y * j))
    else if (i <= 7.2d-158) then
        tmp = t_1 + (x * ((y * z) - (t * a)))
    else
        tmp = t_1 + (b * ((a * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (i <= -110000.0) {
		tmp = i * ((a * b) - (y * j));
	} else if (i <= 7.2e-158) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if i <= -110000.0:
		tmp = i * ((a * b) - (y * j))
	elif i <= 7.2e-158:
		tmp = t_1 + (x * ((y * z) - (t * a)))
	else:
		tmp = t_1 + (b * ((a * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (i <= -110000.0)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (i <= 7.2e-158)
		tmp = Float64(t_1 + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (i <= -110000.0)
		tmp = i * ((a * b) - (y * j));
	elseif (i <= 7.2e-158)
		tmp = t_1 + (x * ((y * z) - (t * a)));
	else
		tmp = t_1 + (b * ((a * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -110000.0], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.2e-158], N[(t$95$1 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.1e5

   1. Initial program 59.6%

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

   3. Taylor expanded in i around inf 74.6%

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

      1. distribute-lft-out-- 74.6%

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

   5. Simplified 74.6%

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

   if -1.1e5 < i < 7.19999999999999982e-158

   1. Initial program 77.3%

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

   3. Taylor expanded in b around 0 74.6%

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

   if 7.19999999999999982e-158 < i

   1. Initial program 68.8%

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

   3. Taylor expanded in x around 0 62.0%

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

      1. *-commutative 62.0%

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

   5. Simplified 62.0%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -110000:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{-158}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5200000000000:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-237}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-162}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-18}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -5200000000000.0)
   (* i (* a b))
   (if (<= a -2.5e-237)
     (* z (* b (- c)))
     (if (<= a 5e-162)
       (* t (* c j))
       (if (<= a 1.15e-18) (* z (* x y)) (* b (* a i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -5200000000000.0) {
		tmp = i * (a * b);
	} else if (a <= -2.5e-237) {
		tmp = z * (b * -c);
	} else if (a <= 5e-162) {
		tmp = t * (c * j);
	} else if (a <= 1.15e-18) {
		tmp = z * (x * y);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-5200000000000.0d0)) then
        tmp = i * (a * b)
    else if (a <= (-2.5d-237)) then
        tmp = z * (b * -c)
    else if (a <= 5d-162) then
        tmp = t * (c * j)
    else if (a <= 1.15d-18) then
        tmp = z * (x * y)
    else
        tmp = b * (a * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -5200000000000.0) {
		tmp = i * (a * b);
	} else if (a <= -2.5e-237) {
		tmp = z * (b * -c);
	} else if (a <= 5e-162) {
		tmp = t * (c * j);
	} else if (a <= 1.15e-18) {
		tmp = z * (x * y);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -5200000000000.0:
		tmp = i * (a * b)
	elif a <= -2.5e-237:
		tmp = z * (b * -c)
	elif a <= 5e-162:
		tmp = t * (c * j)
	elif a <= 1.15e-18:
		tmp = z * (x * y)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -5200000000000.0)
		tmp = Float64(i * Float64(a * b));
	elseif (a <= -2.5e-237)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (a <= 5e-162)
		tmp = Float64(t * Float64(c * j));
	elseif (a <= 1.15e-18)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -5200000000000.0)
		tmp = i * (a * b);
	elseif (a <= -2.5e-237)
		tmp = z * (b * -c);
	elseif (a <= 5e-162)
		tmp = t * (c * j);
	elseif (a <= 1.15e-18)
		tmp = z * (x * y);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -5200000000000.0], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.5e-237], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e-162], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e-18], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -5.2e12

   1. Initial program 58.2%

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

   3. Taylor expanded in x around 0 48.6%

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

      1. *-commutative 48.6%

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

   5. Simplified 48.6%

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

   6. Taylor expanded in a around inf 44.1%

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

      1. associate-*r* 47.3%

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

   8. Simplified 47.3%

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

   if -5.2e12 < a < -2.5000000000000001e-237

   1. Initial program 76.7%

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

   3. Taylor expanded in z around inf 50.6%

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

      1. *-commutative 50.6%

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

      2. *-commutative 50.6%

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

   5. Simplified 50.6%

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

   6. Taylor expanded in y around 0 34.7%

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

      1. neg-mul-1 34.7%

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

      2. distribute-lft-neg-in 34.7%

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

      3. *-commutative 34.7%

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

   8. Simplified 34.7%

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

   if -2.5000000000000001e-237 < a < 5.00000000000000014e-162

   1. Initial program 83.5%

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

   3. Taylor expanded in j around inf 48.9%

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

   4. Taylor expanded in c around inf 36.4%

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

      1. *-commutative 36.4%

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

      2. *-commutative 36.4%

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

      3. associate-*r* 40.9%

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

   6. Simplified 40.9%

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

   if 5.00000000000000014e-162 < a < 1.15e-18

   1. Initial program 80.9%

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

   3. Taylor expanded in z around inf 46.4%

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

      1. *-commutative 46.4%

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

      2. *-commutative 46.4%

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

   5. Simplified 46.4%

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

   6. Taylor expanded in y around inf 33.8%

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

   if 1.15e-18 < a

   1. Initial program 56.7%

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

   3. Taylor expanded in b around inf 47.7%

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

      1. *-commutative 47.7%

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

   5. Simplified 47.7%

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

   6. Taylor expanded in i around inf 37.8%

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

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5200000000000:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-237}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-162}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-18}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 50.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -115000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{-198}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 2.15 \cdot 10^{+214}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))))
   (if (<= i -115000.0)
     t_1
     (if (<= i 1.02e-198)
       (+ (* j (- (* t c) (* y i))) (* x (* y z)))
       (if (<= i 2.15e+214) (* z (- (* x y) (* b c))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -115000.0) {
		tmp = t_1;
	} else if (i <= 1.02e-198) {
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	} else if (i <= 2.15e+214) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    if (i <= (-115000.0d0)) then
        tmp = t_1
    else if (i <= 1.02d-198) then
        tmp = (j * ((t * c) - (y * i))) + (x * (y * z))
    else if (i <= 2.15d+214) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -115000.0) {
		tmp = t_1;
	} else if (i <= 1.02e-198) {
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	} else if (i <= 2.15e+214) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -115000.0:
		tmp = t_1
	elif i <= 1.02e-198:
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z))
	elif i <= 2.15e+214:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -115000.0)
		tmp = t_1;
	elseif (i <= 1.02e-198)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(y * z)));
	elseif (i <= 2.15e+214)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -115000.0)
		tmp = t_1;
	elseif (i <= 1.02e-198)
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	elseif (i <= 2.15e+214)
		tmp = z * ((x * y) - (b * 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[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -115000.0], t$95$1, If[LessEqual[i, 1.02e-198], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.15e+214], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -115000 or 2.14999999999999991e214 < i

   1. Initial program 60.1%

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

   3. Taylor expanded in i around inf 76.4%

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

      1. distribute-lft-out-- 76.4%

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

   5. Simplified 76.4%

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

   if -115000 < i < 1.01999999999999997e-198

   1. Initial program 78.7%

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

   3. Taylor expanded in b around 0 76.6%

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

   4. Taylor expanded in a around 0 59.3%

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

   if 1.01999999999999997e-198 < i < 2.14999999999999991e214

   1. Initial program 70.6%

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

   3. Taylor expanded in z around inf 51.2%

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

      1. *-commutative 51.2%

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

      2. *-commutative 51.2%

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

   5. Simplified 51.2%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -115000:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{-198}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 2.15 \cdot 10^{+214}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 48.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.4 \cdot 10^{-128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -5.2 \cdot 10^{-223}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{+86}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= j -1.4e-128)
     t_1
     (if (<= j -5.2e-223)
       (* (* x t) (- a))
       (if (<= j 7.5e+86) (* b (- (* a i) (* z c))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.4e-128) {
		tmp = t_1;
	} else if (j <= -5.2e-223) {
		tmp = (x * t) * -a;
	} else if (j <= 7.5e+86) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if (j <= (-1.4d-128)) then
        tmp = t_1
    else if (j <= (-5.2d-223)) then
        tmp = (x * t) * -a
    else if (j <= 7.5d+86) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.4e-128) {
		tmp = t_1;
	} else if (j <= -5.2e-223) {
		tmp = (x * t) * -a;
	} else if (j <= 7.5e+86) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -1.4e-128:
		tmp = t_1
	elif j <= -5.2e-223:
		tmp = (x * t) * -a
	elif j <= 7.5e+86:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.4e-128)
		tmp = t_1;
	elseif (j <= -5.2e-223)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (j <= 7.5e+86)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.4e-128)
		tmp = t_1;
	elseif (j <= -5.2e-223)
		tmp = (x * t) * -a;
	elseif (j <= 7.5e+86)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.4e-128], t$95$1, If[LessEqual[j, -5.2e-223], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[j, 7.5e+86], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.3999999999999999e-128 or 7.4999999999999997e86 < j

   1. Initial program 70.4%

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

   3. Taylor expanded in j around inf 52.2%

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

   if -1.3999999999999999e-128 < j < -5.2e-223

   1. Initial program 63.6%

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

   3. Taylor expanded in a around inf 51.6%

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

      1. distribute-lft-out-- 51.6%

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

      2. *-commutative 51.6%

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

   5. Simplified 51.6%

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

   6. Taylor expanded in t around inf 39.2%

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

      1. *-commutative 39.2%

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

   8. Simplified 39.2%

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

   if -5.2e-223 < j < 7.4999999999999997e86

   1. Initial program 70.0%

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

   3. Taylor expanded in b around inf 56.9%

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

      1. *-commutative 56.9%

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

   5. Simplified 56.9%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.4 \cdot 10^{-128}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -5.2 \cdot 10^{-223}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{+86}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 48.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -220:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-170}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 2.15 \cdot 10^{+214}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))))
   (if (<= i -220.0)
     t_1
     (if (<= i 2.8e-170)
       (* t (- (* c j) (* x a)))
       (if (<= i 2.15e+214) (* z (- (* x y) (* b c))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -220.0) {
		tmp = t_1;
	} else if (i <= 2.8e-170) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 2.15e+214) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    if (i <= (-220.0d0)) then
        tmp = t_1
    else if (i <= 2.8d-170) then
        tmp = t * ((c * j) - (x * a))
    else if (i <= 2.15d+214) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -220.0) {
		tmp = t_1;
	} else if (i <= 2.8e-170) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 2.15e+214) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -220.0:
		tmp = t_1
	elif i <= 2.8e-170:
		tmp = t * ((c * j) - (x * a))
	elif i <= 2.15e+214:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -220.0)
		tmp = t_1;
	elseif (i <= 2.8e-170)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (i <= 2.15e+214)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -220.0)
		tmp = t_1;
	elseif (i <= 2.8e-170)
		tmp = t * ((c * j) - (x * a));
	elseif (i <= 2.15e+214)
		tmp = z * ((x * y) - (b * 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[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -220.0], t$95$1, If[LessEqual[i, 2.8e-170], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.15e+214], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -220 or 2.14999999999999991e214 < i

   1. Initial program 59.9%

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

   3. Taylor expanded in i around inf 74.8%

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

      1. distribute-lft-out-- 74.8%

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

   5. Simplified 74.8%

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

   if -220 < i < 2.79999999999999995e-170

   1. Initial program 77.8%

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

   3. Taylor expanded in t around inf 59.1%

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

   4. Taylor expanded in a around 0 51.2%

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

      1. associate-*r* 53.4%

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

      2. +-commutative 53.4%

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

      3. mul-1-neg 53.4%

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

      4. *-commutative 53.4%

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

      5. associate-*l* 57.9%

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

      6. sub-neg 57.9%

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

      7. distribute-rgt-out-- 59.1%

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

   6. Simplified 59.1%

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

   if 2.79999999999999995e-170 < i < 2.14999999999999991e214

   1. Initial program 71.6%

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

   3. Taylor expanded in z around inf 50.5%

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

      1. *-commutative 50.5%

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

      2. *-commutative 50.5%

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

   5. Simplified 50.5%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -220:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-170}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 2.15 \cdot 10^{+214}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 29.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -115000:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -6.3 \cdot 10^{-282}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{-83}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -115000.0)
   (* a (* b i))
   (if (<= i -6.3e-282)
     (* t (* c j))
     (if (<= i 1.6e-83) (* z (* x y)) (* b (* a i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -115000.0) {
		tmp = a * (b * i);
	} else if (i <= -6.3e-282) {
		tmp = t * (c * j);
	} else if (i <= 1.6e-83) {
		tmp = z * (x * y);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-115000.0d0)) then
        tmp = a * (b * i)
    else if (i <= (-6.3d-282)) then
        tmp = t * (c * j)
    else if (i <= 1.6d-83) then
        tmp = z * (x * y)
    else
        tmp = b * (a * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -115000.0) {
		tmp = a * (b * i);
	} else if (i <= -6.3e-282) {
		tmp = t * (c * j);
	} else if (i <= 1.6e-83) {
		tmp = z * (x * y);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -115000.0:
		tmp = a * (b * i)
	elif i <= -6.3e-282:
		tmp = t * (c * j)
	elif i <= 1.6e-83:
		tmp = z * (x * y)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -115000.0)
		tmp = Float64(a * Float64(b * i));
	elseif (i <= -6.3e-282)
		tmp = Float64(t * Float64(c * j));
	elseif (i <= 1.6e-83)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -115000.0)
		tmp = a * (b * i);
	elseif (i <= -6.3e-282)
		tmp = t * (c * j);
	elseif (i <= 1.6e-83)
		tmp = z * (x * y);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -115000.0], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -6.3e-282], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.6e-83], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if i < -115000

   1. Initial program 59.6%

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

   3. Taylor expanded in x around 0 65.9%

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

      1. *-commutative 65.9%

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

   5. Simplified 65.9%

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

   6. Taylor expanded in a around inf 51.2%

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

   if -115000 < i < -6.3e-282

   1. Initial program 76.5%

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

   3. Taylor expanded in j around inf 44.4%

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

   4. Taylor expanded in c around inf 39.7%

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

      1. *-commutative 39.7%

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

      2. *-commutative 39.7%

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

      3. associate-*r* 41.4%

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

   6. Simplified 41.4%

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

   if -6.3e-282 < i < 1.6000000000000001e-83

   1. Initial program 80.6%

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

   3. Taylor expanded in z around inf 50.4%

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

      1. *-commutative 50.4%

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

      2. *-commutative 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in y around inf 37.3%

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

   if 1.6000000000000001e-83 < i

   1. Initial program 65.8%

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

   3. Taylor expanded in b around inf 47.9%

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

      1. *-commutative 47.9%

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

   5. Simplified 47.9%

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

   6. Taylor expanded in i around inf 27.2%

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

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -115000:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -6.3 \cdot 10^{-282}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{-83}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 29.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -800 \lor \neg \left(t \leq 1.6 \cdot 10^{+191}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -800.0) (not (<= t 1.6e+191))) (* c (* t j)) (* a (* b i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -800.0) || !(t <= 1.6e+191)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-800.0d0)) .or. (.not. (t <= 1.6d+191))) then
        tmp = c * (t * j)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -800.0) || !(t <= 1.6e+191)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -800.0) or not (t <= 1.6e+191):
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -800.0) || !(t <= 1.6e+191))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -800.0) || ~((t <= 1.6e+191)))
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -800.0], N[Not[LessEqual[t, 1.6e+191]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -800 or 1.6000000000000001e191 < t

   1. Initial program 64.5%

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

   3. Taylor expanded in j around inf 46.1%

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

   4. Taylor expanded in c around inf 37.8%

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

   if -800 < t < 1.6000000000000001e191

   1. Initial program 72.4%

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

   3. Taylor expanded in x around 0 58.9%

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

      1. *-commutative 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in a around inf 30.6%

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

4. Final simplification 33.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -800 \lor \neg \left(t \leq 1.6 \cdot 10^{+191}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 29.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -950:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+193}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -950.0)
   (* j (* t c))
   (if (<= t 4e+193) (* a (* b i)) (* c (* t j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -950.0) {
		tmp = j * (t * c);
	} else if (t <= 4e+193) {
		tmp = a * (b * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-950.0d0)) then
        tmp = j * (t * c)
    else if (t <= 4d+193) then
        tmp = a * (b * i)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -950.0) {
		tmp = j * (t * c);
	} else if (t <= 4e+193) {
		tmp = a * (b * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -950.0:
		tmp = j * (t * c)
	elif t <= 4e+193:
		tmp = a * (b * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -950.0)
		tmp = Float64(j * Float64(t * c));
	elseif (t <= 4e+193)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -950.0)
		tmp = j * (t * c);
	elseif (t <= 4e+193)
		tmp = a * (b * i);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -950.0], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+193], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -950

   1. Initial program 65.0%

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

   3. Taylor expanded in j around inf 40.9%

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

   4. Taylor expanded in c around inf 32.4%

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

   if -950 < t < 4.00000000000000026e193

   1. Initial program 72.4%

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

   3. Taylor expanded in x around 0 58.9%

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

      1. *-commutative 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in a around inf 30.6%

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

   if 4.00000000000000026e193 < t

   1. Initial program 62.5%

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

   3. Taylor expanded in j around inf 63.4%

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

   4. Taylor expanded in c around inf 56.3%

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

4. Final simplification 33.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -950:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+193}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 27.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -98000:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 4.5 \cdot 10^{+190}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -98000.0)
   (* a (* b i))
   (if (<= i 4.5e+190) (* t (* c j)) (* b (* a i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -98000.0) {
		tmp = a * (b * i);
	} else if (i <= 4.5e+190) {
		tmp = t * (c * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-98000.0d0)) then
        tmp = a * (b * i)
    else if (i <= 4.5d+190) then
        tmp = t * (c * j)
    else
        tmp = b * (a * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -98000.0) {
		tmp = a * (b * i);
	} else if (i <= 4.5e+190) {
		tmp = t * (c * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -98000.0:
		tmp = a * (b * i)
	elif i <= 4.5e+190:
		tmp = t * (c * j)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -98000.0)
		tmp = Float64(a * Float64(b * i));
	elseif (i <= 4.5e+190)
		tmp = Float64(t * Float64(c * j));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -98000.0)
		tmp = a * (b * i);
	elseif (i <= 4.5e+190)
		tmp = t * (c * j);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -98000.0], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.5e+190], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -98000

   1. Initial program 59.6%

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

   3. Taylor expanded in x around 0 65.9%

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

      1. *-commutative 65.9%

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

   5. Simplified 65.9%

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

   6. Taylor expanded in a around inf 51.2%

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

   if -98000 < i < 4.4999999999999999e190

   1. Initial program 76.8%

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

   3. Taylor expanded in j around inf 33.8%

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

   4. Taylor expanded in c around inf 27.0%

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

      1. *-commutative 27.0%

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

      2. *-commutative 27.0%

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

      3. associate-*r* 28.2%

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

   6. Simplified 28.2%

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

   if 4.4999999999999999e190 < i

   1. Initial program 52.7%

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

   3. Taylor expanded in b around inf 49.2%

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

      1. *-commutative 49.2%

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

   5. Simplified 49.2%

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

   6. Taylor expanded in i around inf 36.1%

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

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -98000:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 4.5 \cdot 10^{+190}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 22.9% accurate, 5.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.6%

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

3. Taylor expanded in x around 0 57.9%

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

   1. *-commutative 57.9%

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

5. Simplified 57.9%

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

6. Taylor expanded in a around inf 24.1%

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

7. Final simplification 24.1%

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

Alternative 30: 22.7% accurate, 5.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.6%

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

3. Taylor expanded in b around inf 39.7%

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

   1. *-commutative 39.7%

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

5. Simplified 39.7%

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

6. Taylor expanded in i around inf 24.1%

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

7. Final simplification 24.1%

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

Developer target: 69.1% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024019 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

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

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