Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.8% → 81.7%

Time: 30.0s

Alternatives: 21

Speedup: 0.5×

• 59.2% 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: 73.8% 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: 81.7% accurate, 0.2× speedup

Math

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

FPCore

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(j * t$95$2), $MachinePrecision] + t$95$1), $MachinePrecision], Infinity], N[(j * t$95$2 + t$95$1), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $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 91.1%

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

      1. +-commutative 91.1%

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

      2. fma-def 91.1%

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

      3. *-commutative 91.1%

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

      4. *-commutative 91.1%

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

      5. cancel-sign-sub-inv 91.1%

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

      6. cancel-sign-sub 91.1%

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

      7. remove-double-neg 91.1%

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

      8. *-commutative 91.1%

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

      9. *-commutative 91.1%

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

   3. Simplified 91.1%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in z around inf 63.0%

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

      1. *-commutative 63.0%

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

   4. Simplified 63.0%

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

4. Final simplification 85.5%

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

Alternative 2: 81.7% accurate, 0.5× speedup

Math

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

FPCore

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

Java

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

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + ((b * ((a * i) - (z * c))) - (x * ((t * a) - (y * z))))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = z * ((x * y) - (b * c))
	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(Float64(b * Float64(Float64(a * i) - Float64(z * c))) - Float64(x * Float64(Float64(t * a) - Float64(y * z)))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * 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))) + ((b * ((a * i) - (z * c))) - (x * ((t * a) - (y * z))));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = z * ((x * y) - (b * c));
	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[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $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 91.1%

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

   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. Taylor expanded in z around inf 63.0%

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

      1. *-commutative 63.0%

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

   4. Simplified 63.0%

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

4. Final simplification 85.5%

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

Alternative 3: 62.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t_1 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{if}\;b \leq -5.2 \cdot 10^{+147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.35 \cdot 10^{-20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-156}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+30}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(t \cdot j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (- t_1 (* x (- (* t a) (* y z))))))
   (if (<= b -5.2e+147)
     t_1
     (if (<= b -2.35e-20)
       t_2
       (if (<= b -6e-156)
         (* j (- (* t c) (* y i)))
         (if (<= b 4.6e+30)
           (- (+ (* x (- (* y z) (* t a))) (* c (* t j))) (* b (* 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 = b * ((a * i) - (z * c));
	double t_2 = t_1 - (x * ((t * a) - (y * z)));
	double tmp;
	if (b <= -5.2e+147) {
		tmp = t_1;
	} else if (b <= -2.35e-20) {
		tmp = t_2;
	} else if (b <= -6e-156) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 4.6e+30) {
		tmp = ((x * ((y * z) - (t * a))) + (c * (t * j))) - (b * (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 = b * ((a * i) - (z * c))
    t_2 = t_1 - (x * ((t * a) - (y * z)))
    if (b <= (-5.2d+147)) then
        tmp = t_1
    else if (b <= (-2.35d-20)) then
        tmp = t_2
    else if (b <= (-6d-156)) then
        tmp = j * ((t * c) - (y * i))
    else if (b <= 4.6d+30) then
        tmp = ((x * ((y * z) - (t * a))) + (c * (t * j))) - (b * (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 = b * ((a * i) - (z * c));
	double t_2 = t_1 - (x * ((t * a) - (y * z)));
	double tmp;
	if (b <= -5.2e+147) {
		tmp = t_1;
	} else if (b <= -2.35e-20) {
		tmp = t_2;
	} else if (b <= -6e-156) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 4.6e+30) {
		tmp = ((x * ((y * z) - (t * a))) + (c * (t * j))) - (b * (z * c));
	} 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 = t_1 - (x * ((t * a) - (y * z)))
	tmp = 0
	if b <= -5.2e+147:
		tmp = t_1
	elif b <= -2.35e-20:
		tmp = t_2
	elif b <= -6e-156:
		tmp = j * ((t * c) - (y * i))
	elif b <= 4.6e+30:
		tmp = ((x * ((y * z) - (t * a))) + (c * (t * j))) - (b * (z * c))
	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(t_1 - Float64(x * Float64(Float64(t * a) - Float64(y * z))))
	tmp = 0.0
	if (b <= -5.2e+147)
		tmp = t_1;
	elseif (b <= -2.35e-20)
		tmp = t_2;
	elseif (b <= -6e-156)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (b <= 4.6e+30)
		tmp = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(c * Float64(t * j))) - Float64(b * 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 = b * ((a * i) - (z * c));
	t_2 = t_1 - (x * ((t * a) - (y * z)));
	tmp = 0.0;
	if (b <= -5.2e+147)
		tmp = t_1;
	elseif (b <= -2.35e-20)
		tmp = t_2;
	elseif (b <= -6e-156)
		tmp = j * ((t * c) - (y * i));
	elseif (b <= 4.6e+30)
		tmp = ((x * ((y * z) - (t * a))) + (c * (t * j))) - (b * (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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.2e+147], t$95$1, If[LessEqual[b, -2.35e-20], t$95$2, If[LessEqual[b, -6e-156], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.6e+30], N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.1999999999999997e147

   1. Initial program 47.9%

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

   2. Taylor expanded in b around inf 77.5%

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

      1. *-commutative 77.5%

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

   4. Simplified 77.5%

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

   if -5.1999999999999997e147 < b < -2.35000000000000007e-20 or 4.6e30 < b

   1. Initial program 80.3%

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

   2. Taylor expanded in j around 0 73.9%

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

   if -2.35000000000000007e-20 < b < -6e-156

   1. Initial program 74.3%

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

   2. Taylor expanded in j around inf 63.1%

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

   if -6e-156 < b < 4.6e30

   1. Initial program 74.9%

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

   2. Taylor expanded in i around 0 64.9%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.35 \cdot 10^{-20}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-156}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+30}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(t \cdot j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \]

Alternative 4: 66.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.25 \cdot 10^{+73} \lor \neg \left(j \leq 1.05 \cdot 10^{+20}\right) \land \left(j \leq 3.1 \cdot 10^{+141} \lor \neg \left(j \leq 2.8 \cdot 10^{+166}\right)\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -2.25e+73)
         (and (not (<= j 1.05e+20))
              (or (<= j 3.1e+141) (not (<= j 2.8e+166)))))
   (* j (- (* t c) (* y i)))
   (- (* b (- (* a i) (* z c))) (* x (- (* t a) (* y z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -2.25e+73) || (!(j <= 1.05e+20) && ((j <= 3.1e+141) || !(j <= 2.8e+166)))) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = (b * ((a * i) - (z * c))) - (x * ((t * a) - (y * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-2.25d+73)) .or. (.not. (j <= 1.05d+20)) .and. (j <= 3.1d+141) .or. (.not. (j <= 2.8d+166))) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = (b * ((a * i) - (z * c))) - (x * ((t * a) - (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -2.25e+73) || (!(j <= 1.05e+20) && ((j <= 3.1e+141) || !(j <= 2.8e+166)))) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = (b * ((a * i) - (z * c))) - (x * ((t * a) - (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -2.25e+73) or (not (j <= 1.05e+20) and ((j <= 3.1e+141) or not (j <= 2.8e+166))):
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = (b * ((a * i) - (z * c))) - (x * ((t * a) - (y * z)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -2.25e+73) || (!(j <= 1.05e+20) && ((j <= 3.1e+141) || !(j <= 2.8e+166))))
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -2.25e+73) || (~((j <= 1.05e+20)) && ((j <= 3.1e+141) || ~((j <= 2.8e+166)))))
		tmp = j * ((t * c) - (y * i));
	else
		tmp = (b * ((a * i) - (z * c))) - (x * ((t * a) - (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -2.25e+73], And[N[Not[LessEqual[j, 1.05e+20]], $MachinePrecision], Or[LessEqual[j, 3.1e+141], N[Not[LessEqual[j, 2.8e+166]], $MachinePrecision]]]], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -2.24999999999999992e73 or 1.05e20 < j < 3.10000000000000004e141 or 2.79999999999999996e166 < j

   1. Initial program 73.9%

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

   2. Taylor expanded in j around inf 64.5%

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

   if -2.24999999999999992e73 < j < 1.05e20 or 3.10000000000000004e141 < j < 2.79999999999999996e166

   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. Taylor expanded in j around 0 73.1%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.25 \cdot 10^{+73} \lor \neg \left(j \leq 1.05 \cdot 10^{+20}\right) \land \left(j \leq 3.1 \cdot 10^{+141} \lor \neg \left(j \leq 2.8 \cdot 10^{+166}\right)\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \]

Alternative 5: 51.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{+78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -0.00042:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-269}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-176}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+141}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -7e+78)
     t_2
     (if (<= y -5.4e+32)
       t_1
       (if (<= y -0.00042)
         t_2
         (if (<= y 9e-269)
           (* c (- (* t j) (* z b)))
           (if (<= y 3.7e-176)
             (* t (- (* c j) (* x a)))
             (if (<= y 1.3e+141) 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 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -7e+78) {
		tmp = t_2;
	} else if (y <= -5.4e+32) {
		tmp = t_1;
	} else if (y <= -0.00042) {
		tmp = t_2;
	} else if (y <= 9e-269) {
		tmp = c * ((t * j) - (z * b));
	} else if (y <= 3.7e-176) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 1.3e+141) {
		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 = b * ((a * i) - (z * c))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-7d+78)) then
        tmp = t_2
    else if (y <= (-5.4d+32)) then
        tmp = t_1
    else if (y <= (-0.00042d0)) then
        tmp = t_2
    else if (y <= 9d-269) then
        tmp = c * ((t * j) - (z * b))
    else if (y <= 3.7d-176) then
        tmp = t * ((c * j) - (x * a))
    else if (y <= 1.3d+141) 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 = b * ((a * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -7e+78) {
		tmp = t_2;
	} else if (y <= -5.4e+32) {
		tmp = t_1;
	} else if (y <= -0.00042) {
		tmp = t_2;
	} else if (y <= 9e-269) {
		tmp = c * ((t * j) - (z * b));
	} else if (y <= 3.7e-176) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 1.3e+141) {
		tmp = 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 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -7e+78:
		tmp = t_2
	elif y <= -5.4e+32:
		tmp = t_1
	elif y <= -0.00042:
		tmp = t_2
	elif y <= 9e-269:
		tmp = c * ((t * j) - (z * b))
	elif y <= 3.7e-176:
		tmp = t * ((c * j) - (x * a))
	elif y <= 1.3e+141:
		tmp = 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(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -7e+78)
		tmp = t_2;
	elseif (y <= -5.4e+32)
		tmp = t_1;
	elseif (y <= -0.00042)
		tmp = t_2;
	elseif (y <= 9e-269)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (y <= 3.7e-176)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (y <= 1.3e+141)
		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 = b * ((a * i) - (z * c));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -7e+78)
		tmp = t_2;
	elseif (y <= -5.4e+32)
		tmp = t_1;
	elseif (y <= -0.00042)
		tmp = t_2;
	elseif (y <= 9e-269)
		tmp = c * ((t * j) - (z * b));
	elseif (y <= 3.7e-176)
		tmp = t * ((c * j) - (x * a));
	elseif (y <= 1.3e+141)
		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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e+78], t$95$2, If[LessEqual[y, -5.4e+32], t$95$1, If[LessEqual[y, -0.00042], t$95$2, If[LessEqual[y, 9e-269], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e-176], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+141], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.0000000000000003e78 or -5.40000000000000025e32 < y < -4.2000000000000002e-4 or 1.3e141 < y

   1. Initial program 64.2%

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

   2. Taylor expanded in y around inf 73.5%

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

      1. +-commutative 73.5%

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

      2. mul-1-neg 73.5%

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

      3. unsub-neg 73.5%

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

   4. Simplified 73.5%

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

   if -7.0000000000000003e78 < y < -5.40000000000000025e32 or 3.69999999999999984e-176 < y < 1.3e141

   1. Initial program 71.7%

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

   2. Taylor expanded in b around inf 57.7%

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

      1. *-commutative 57.7%

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

   4. Simplified 57.7%

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

   if -4.2000000000000002e-4 < y < 9.0000000000000003e-269

   1. Initial program 79.2%

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

   2. Taylor expanded in c around inf 60.2%

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

      1. *-commutative 60.2%

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

      2. *-commutative 60.2%

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

   4. Simplified 60.2%

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

   if 9.0000000000000003e-269 < y < 3.69999999999999984e-176

   1. Initial program 91.0%

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

   2. Taylor expanded in t around inf 70.4%

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

      1. +-commutative 70.4%

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

      2. mul-1-neg 70.4%

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

      3. unsub-neg 70.4%

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

      4. *-commutative 70.4%

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

      5. *-commutative 70.4%

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

   4. Simplified 70.4%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+78}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+32}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -0.00042:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-269}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-176}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+141}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 6: 50.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;y \leq -0.00035:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-270}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-176}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+139}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= y -2.8e+140)
     t_1
     (if (<= y -1.35e+32)
       (* z (- (* x y) (* b c)))
       (if (<= y -0.00035)
         t_1
         (if (<= y 7.5e-270)
           (* c (- (* t j) (* z b)))
           (if (<= y 4.2e-176)
             (* t (- (* c j) (* x a)))
             (if (<= y 1.7e+139) (* 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 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2.8e+140) {
		tmp = t_1;
	} else if (y <= -1.35e+32) {
		tmp = z * ((x * y) - (b * c));
	} else if (y <= -0.00035) {
		tmp = t_1;
	} else if (y <= 7.5e-270) {
		tmp = c * ((t * j) - (z * b));
	} else if (y <= 4.2e-176) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 1.7e+139) {
		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 = y * ((x * z) - (i * j))
    if (y <= (-2.8d+140)) then
        tmp = t_1
    else if (y <= (-1.35d+32)) then
        tmp = z * ((x * y) - (b * c))
    else if (y <= (-0.00035d0)) then
        tmp = t_1
    else if (y <= 7.5d-270) then
        tmp = c * ((t * j) - (z * b))
    else if (y <= 4.2d-176) then
        tmp = t * ((c * j) - (x * a))
    else if (y <= 1.7d+139) 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 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2.8e+140) {
		tmp = t_1;
	} else if (y <= -1.35e+32) {
		tmp = z * ((x * y) - (b * c));
	} else if (y <= -0.00035) {
		tmp = t_1;
	} else if (y <= 7.5e-270) {
		tmp = c * ((t * j) - (z * b));
	} else if (y <= 4.2e-176) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 1.7e+139) {
		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 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -2.8e+140:
		tmp = t_1
	elif y <= -1.35e+32:
		tmp = z * ((x * y) - (b * c))
	elif y <= -0.00035:
		tmp = t_1
	elif y <= 7.5e-270:
		tmp = c * ((t * j) - (z * b))
	elif y <= 4.2e-176:
		tmp = t * ((c * j) - (x * a))
	elif y <= 1.7e+139:
		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(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -2.8e+140)
		tmp = t_1;
	elseif (y <= -1.35e+32)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (y <= -0.00035)
		tmp = t_1;
	elseif (y <= 7.5e-270)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (y <= 4.2e-176)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (y <= 1.7e+139)
		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 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -2.8e+140)
		tmp = t_1;
	elseif (y <= -1.35e+32)
		tmp = z * ((x * y) - (b * c));
	elseif (y <= -0.00035)
		tmp = t_1;
	elseif (y <= 7.5e-270)
		tmp = c * ((t * j) - (z * b));
	elseif (y <= 4.2e-176)
		tmp = t * ((c * j) - (x * a));
	elseif (y <= 1.7e+139)
		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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.8e+140], t$95$1, If[LessEqual[y, -1.35e+32], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -0.00035], t$95$1, If[LessEqual[y, 7.5e-270], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e-176], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+139], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.79999999999999983e140 or -1.35000000000000006e32 < y < -3.49999999999999996e-4 or 1.7000000000000001e139 < y

   1. Initial program 65.2%

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

   2. Taylor expanded in y around inf 75.6%

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

      1. +-commutative 75.6%

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

      2. mul-1-neg 75.6%

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

      3. unsub-neg 75.6%

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

   4. Simplified 75.6%

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

   if -2.79999999999999983e140 < y < -1.35000000000000006e32

   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. Taylor expanded in z around inf 68.4%

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

      1. *-commutative 68.4%

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

   4. Simplified 68.4%

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

   if -3.49999999999999996e-4 < y < 7.4999999999999997e-270

   1. Initial program 79.2%

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

   2. Taylor expanded in c around inf 60.2%

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

      1. *-commutative 60.2%

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

      2. *-commutative 60.2%

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

   4. Simplified 60.2%

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

   if 7.4999999999999997e-270 < y < 4.19999999999999984e-176

   1. Initial program 91.0%

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

   2. Taylor expanded in t around inf 70.4%

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

      1. +-commutative 70.4%

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

      2. mul-1-neg 70.4%

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

      3. unsub-neg 70.4%

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

      4. *-commutative 70.4%

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

      5. *-commutative 70.4%

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

   4. Simplified 70.4%

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

   if 4.19999999999999984e-176 < y < 1.7000000000000001e139

   1. Initial program 73.6%

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

   2. Taylor expanded in b around inf 55.3%

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

      1. *-commutative 55.3%

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

   4. Simplified 55.3%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;y \leq -0.00035:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-270}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-176}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+139}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 7: 52.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -1.06 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-63}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{-158}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-171}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))) (t_2 (* z (- (* x y) (* b c)))))
   (if (<= z -1.06e+41)
     t_2
     (if (<= z -1.95e-63)
       (* a (- (* b i) (* x t)))
       (if (<= z -1.62e-158)
         (* j (- (* t c) (* y i)))
         (if (<= z -1.8e-199)
           t_1
           (if (<= z 1.25e-171)
             (* t (- (* c j) (* x a)))
             (if (<= z 6.6e-53) 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 = i * ((a * b) - (y * j));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.06e+41) {
		tmp = t_2;
	} else if (z <= -1.95e-63) {
		tmp = a * ((b * i) - (x * t));
	} else if (z <= -1.62e-158) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= -1.8e-199) {
		tmp = t_1;
	} else if (z <= 1.25e-171) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 6.6e-53) {
		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 = i * ((a * b) - (y * j))
    t_2 = z * ((x * y) - (b * c))
    if (z <= (-1.06d+41)) then
        tmp = t_2
    else if (z <= (-1.95d-63)) then
        tmp = a * ((b * i) - (x * t))
    else if (z <= (-1.62d-158)) then
        tmp = j * ((t * c) - (y * i))
    else if (z <= (-1.8d-199)) then
        tmp = t_1
    else if (z <= 1.25d-171) then
        tmp = t * ((c * j) - (x * a))
    else if (z <= 6.6d-53) 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 = i * ((a * b) - (y * j));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.06e+41) {
		tmp = t_2;
	} else if (z <= -1.95e-63) {
		tmp = a * ((b * i) - (x * t));
	} else if (z <= -1.62e-158) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= -1.8e-199) {
		tmp = t_1;
	} else if (z <= 1.25e-171) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 6.6e-53) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -1.06e+41:
		tmp = t_2
	elif z <= -1.95e-63:
		tmp = a * ((b * i) - (x * t))
	elif z <= -1.62e-158:
		tmp = j * ((t * c) - (y * i))
	elif z <= -1.8e-199:
		tmp = t_1
	elif z <= 1.25e-171:
		tmp = t * ((c * j) - (x * a))
	elif z <= 6.6e-53:
		tmp = t_1
	else:
		tmp = t_2
	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(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -1.06e+41)
		tmp = t_2;
	elseif (z <= -1.95e-63)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (z <= -1.62e-158)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (z <= -1.8e-199)
		tmp = t_1;
	elseif (z <= 1.25e-171)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (z <= 6.6e-53)
		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 = i * ((a * b) - (y * j));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -1.06e+41)
		tmp = t_2;
	elseif (z <= -1.95e-63)
		tmp = a * ((b * i) - (x * t));
	elseif (z <= -1.62e-158)
		tmp = j * ((t * c) - (y * i));
	elseif (z <= -1.8e-199)
		tmp = t_1;
	elseif (z <= 1.25e-171)
		tmp = t * ((c * j) - (x * a));
	elseif (z <= 6.6e-53)
		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[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.06e+41], t$95$2, If[LessEqual[z, -1.95e-63], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.62e-158], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.8e-199], t$95$1, If[LessEqual[z, 1.25e-171], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e-53], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.06e41 or 6.60000000000000009e-53 < z

   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. Taylor expanded in z around inf 72.8%

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

      1. *-commutative 72.8%

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

   4. Simplified 72.8%

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

   if -1.06e41 < z < -1.95000000000000011e-63

   1. Initial program 91.4%

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

   2. Taylor expanded in a around -inf 59.1%

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

   if -1.95000000000000011e-63 < z < -1.62000000000000002e-158

   1. Initial program 91.8%

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

   2. Taylor expanded in j around inf 70.2%

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

   if -1.62000000000000002e-158 < z < -1.8000000000000001e-199 or 1.24999999999999998e-171 < z < 6.60000000000000009e-53

   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. Taylor expanded in i around inf 69.8%

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

      1. distribute-lft-out-- 69.8%

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

      2. *-commutative 69.8%

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

   4. Simplified 69.8%

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

   if -1.8000000000000001e-199 < z < 1.24999999999999998e-171

   1. Initial program 75.1%

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

   2. Taylor expanded in t around inf 60.0%

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

      1. +-commutative 60.0%

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

      2. mul-1-neg 60.0%

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

      3. unsub-neg 60.0%

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

      4. *-commutative 60.0%

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

      5. *-commutative 60.0%

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

   4. Simplified 60.0%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+41}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-63}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{-158}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-199}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-171}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-53}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 8: 52.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -7.8 \cdot 10^{+73}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-234}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* b (- (* a i) (* z c)))))
   (if (<= b -7.8e+73)
     t_3
     (if (<= b -2.8e-17)
       t_2
       (if (<= b -8e-177)
         t_1
         (if (<= b -2.4e-234) t_2 (if (<= b 8.5e+21) 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));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -7.8e+73) {
		tmp = t_3;
	} else if (b <= -2.8e-17) {
		tmp = t_2;
	} else if (b <= -8e-177) {
		tmp = t_1;
	} else if (b <= -2.4e-234) {
		tmp = t_2;
	} else if (b <= 8.5e+21) {
		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))
    t_2 = x * ((y * z) - (t * a))
    t_3 = b * ((a * i) - (z * c))
    if (b <= (-7.8d+73)) then
        tmp = t_3
    else if (b <= (-2.8d-17)) then
        tmp = t_2
    else if (b <= (-8d-177)) then
        tmp = t_1
    else if (b <= (-2.4d-234)) then
        tmp = t_2
    else if (b <= 8.5d+21) 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));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -7.8e+73) {
		tmp = t_3;
	} else if (b <= -2.8e-17) {
		tmp = t_2;
	} else if (b <= -8e-177) {
		tmp = t_1;
	} else if (b <= -2.4e-234) {
		tmp = t_2;
	} else if (b <= 8.5e+21) {
		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))
	t_2 = x * ((y * z) - (t * a))
	t_3 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -7.8e+73:
		tmp = t_3
	elif b <= -2.8e-17:
		tmp = t_2
	elif b <= -8e-177:
		tmp = t_1
	elif b <= -2.4e-234:
		tmp = t_2
	elif b <= 8.5e+21:
		tmp = t_1
	else:
		tmp = t_3
	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)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -7.8e+73)
		tmp = t_3;
	elseif (b <= -2.8e-17)
		tmp = t_2;
	elseif (b <= -8e-177)
		tmp = t_1;
	elseif (b <= -2.4e-234)
		tmp = t_2;
	elseif (b <= 8.5e+21)
		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));
	t_2 = x * ((y * z) - (t * a));
	t_3 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -7.8e+73)
		tmp = t_3;
	elseif (b <= -2.8e-17)
		tmp = t_2;
	elseif (b <= -8e-177)
		tmp = t_1;
	elseif (b <= -2.4e-234)
		tmp = t_2;
	elseif (b <= 8.5e+21)
		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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.8e+73], t$95$3, If[LessEqual[b, -2.8e-17], t$95$2, If[LessEqual[b, -8e-177], t$95$1, If[LessEqual[b, -2.4e-234], t$95$2, If[LessEqual[b, 8.5e+21], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.8000000000000002e73 or 8.5e21 < b

   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. Taylor expanded in b around inf 69.5%

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

      1. *-commutative 69.5%

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

   4. Simplified 69.5%

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

   if -7.8000000000000002e73 < b < -2.7999999999999999e-17 or -7.99999999999999962e-177 < b < -2.3999999999999999e-234

   1. Initial program 81.5%

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

   2. Taylor expanded in j around 0 85.1%

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

   3. Taylor expanded in x around inf 69.6%

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

   if -2.7999999999999999e-17 < b < -7.99999999999999962e-177 or -2.3999999999999999e-234 < b < 8.5e21

   1. Initial program 74.1%

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

   2. Taylor expanded in j around inf 55.8%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{+73}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-177}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-234}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+21}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 9: 29.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot b\right) \cdot \left(-c\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-124}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-70}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 28500:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z b) (- c))) (t_2 (* z (* x y))))
   (if (<= x -9.5e+38)
     t_2
     (if (<= x -1.65e-77)
       t_1
       (if (<= x -3.4e-124)
         (* b (* a i))
         (if (<= x -1.2e-300)
           t_1
           (if (<= x 1.8e-70) (* c (* t j)) (if (<= x 28500.0) 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 * b) * -c;
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -9.5e+38) {
		tmp = t_2;
	} else if (x <= -1.65e-77) {
		tmp = t_1;
	} else if (x <= -3.4e-124) {
		tmp = b * (a * i);
	} else if (x <= -1.2e-300) {
		tmp = t_1;
	} else if (x <= 1.8e-70) {
		tmp = c * (t * j);
	} else if (x <= 28500.0) {
		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 = (z * b) * -c
    t_2 = z * (x * y)
    if (x <= (-9.5d+38)) then
        tmp = t_2
    else if (x <= (-1.65d-77)) then
        tmp = t_1
    else if (x <= (-3.4d-124)) then
        tmp = b * (a * i)
    else if (x <= (-1.2d-300)) then
        tmp = t_1
    else if (x <= 1.8d-70) then
        tmp = c * (t * j)
    else if (x <= 28500.0d0) 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 * b) * -c;
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -9.5e+38) {
		tmp = t_2;
	} else if (x <= -1.65e-77) {
		tmp = t_1;
	} else if (x <= -3.4e-124) {
		tmp = b * (a * i);
	} else if (x <= -1.2e-300) {
		tmp = t_1;
	} else if (x <= 1.8e-70) {
		tmp = c * (t * j);
	} else if (x <= 28500.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * b) * -c
	t_2 = z * (x * y)
	tmp = 0
	if x <= -9.5e+38:
		tmp = t_2
	elif x <= -1.65e-77:
		tmp = t_1
	elif x <= -3.4e-124:
		tmp = b * (a * i)
	elif x <= -1.2e-300:
		tmp = t_1
	elif x <= 1.8e-70:
		tmp = c * (t * j)
	elif x <= 28500.0:
		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(z * b) * Float64(-c))
	t_2 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -9.5e+38)
		tmp = t_2;
	elseif (x <= -1.65e-77)
		tmp = t_1;
	elseif (x <= -3.4e-124)
		tmp = Float64(b * Float64(a * i));
	elseif (x <= -1.2e-300)
		tmp = t_1;
	elseif (x <= 1.8e-70)
		tmp = Float64(c * Float64(t * j));
	elseif (x <= 28500.0)
		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 * b) * -c;
	t_2 = z * (x * y);
	tmp = 0.0;
	if (x <= -9.5e+38)
		tmp = t_2;
	elseif (x <= -1.65e-77)
		tmp = t_1;
	elseif (x <= -3.4e-124)
		tmp = b * (a * i);
	elseif (x <= -1.2e-300)
		tmp = t_1;
	elseif (x <= 1.8e-70)
		tmp = c * (t * j);
	elseif (x <= 28500.0)
		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[(z * b), $MachinePrecision] * (-c)), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.5e+38], t$95$2, If[LessEqual[x, -1.65e-77], t$95$1, If[LessEqual[x, -3.4e-124], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.2e-300], t$95$1, If[LessEqual[x, 1.8e-70], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 28500.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.4999999999999995e38 or 28500 < x

   1. Initial program 78.2%

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

   2. Taylor expanded in a around 0 60.9%

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

      1. associate--l+ 60.9%

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

      2. associate-*r* 60.8%

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

      3. associate-*r* 59.8%

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

      4. distribute-rgt-out-- 62.6%

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

      5. fma-def 65.5%

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

      6. *-commutative 65.5%

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

      7. *-commutative 65.5%

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

      8. fma-def 62.6%

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

      9. +-commutative 62.6%

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

      10. fma-def 62.6%

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

      11. fma-neg 62.6%

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

      12. *-commutative 62.6%

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

      13. distribute-rgt-neg-in 62.6%

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

   4. Simplified 62.6%

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

   5. Taylor expanded in x around inf 42.3%

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

      1. *-commutative 42.3%

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

      2. associate-*r* 40.3%

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

   7. Simplified 40.3%

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

   8. Taylor expanded in y around 0 42.3%

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

   10. Simplified 45.7%

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

   if -9.4999999999999995e38 < x < -1.64999999999999996e-77 or -3.4000000000000001e-124 < x < -1.2e-300 or 1.8000000000000001e-70 < x < 28500

   1. Initial program 68.4%

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

   2. Taylor expanded in a around 0 57.4%

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

      1. associate--l+ 57.4%

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

      2. associate-*r* 59.4%

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

      3. associate-*r* 62.1%

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

      4. distribute-rgt-out-- 64.2%

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

      5. fma-def 66.3%

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

      6. *-commutative 66.3%

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

      7. *-commutative 66.3%

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

      8. fma-def 64.2%

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

      9. +-commutative 64.2%

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

      10. fma-def 66.3%

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

      11. fma-neg 66.3%

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

      12. *-commutative 66.3%

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

      13. distribute-rgt-neg-in 66.3%

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

   4. Simplified 66.3%

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

   5. Taylor expanded in b around inf 43.2%

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

      1. *-commutative 43.2%

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

      2. associate-*r* 46.1%

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

      3. associate-*l* 46.1%

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

      4. *-commutative 46.1%

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

      5. mul-1-neg 46.1%

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

      6. *-commutative 46.1%

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

      7. distribute-rgt-neg-in 46.1%

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

   7. Simplified 46.1%

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

   if -1.64999999999999996e-77 < x < -3.4000000000000001e-124

   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. Taylor expanded in b around inf 78.3%

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

      1. *-commutative 78.3%

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

   4. Simplified 78.3%

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

   5. Taylor expanded in a around inf 67.1%

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

      1. *-commutative 67.1%

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

   7. Simplified 67.1%

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

   if -1.2e-300 < x < 1.8000000000000001e-70

   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. Taylor expanded in a around 0 63.1%

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

      1. associate--l+ 63.1%

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

      2. associate-*r* 73.9%

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

      3. associate-*r* 76.1%

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

      4. distribute-rgt-out-- 76.1%

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

      5. fma-def 78.3%

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

      6. *-commutative 78.3%

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

      7. *-commutative 78.3%

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

      8. fma-def 76.1%

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

      9. +-commutative 76.1%

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

      10. fma-def 76.1%

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

      11. fma-neg 76.1%

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

      12. *-commutative 76.1%

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

      13. distribute-rgt-neg-in 76.1%

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

   4. Simplified 76.1%

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

   5. Taylor expanded in t around inf 35.0%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-77}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-124}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-300}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-70}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 28500:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 10: 29.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot b\right) \cdot \left(-c\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.52 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-119}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{-70}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;x \leq 60000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z b) (- c))) (t_2 (* z (* x y))))
   (if (<= x -1e+39)
     t_2
     (if (<= x -1.52e-77)
       t_1
       (if (<= x -2.2e-119)
         (* b (* a i))
         (if (<= x 1e-149)
           t_1
           (if (<= x 1.42e-70)
             (* (* y i) (- j))
             (if (<= x 60000.0) 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 * b) * -c;
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -1e+39) {
		tmp = t_2;
	} else if (x <= -1.52e-77) {
		tmp = t_1;
	} else if (x <= -2.2e-119) {
		tmp = b * (a * i);
	} else if (x <= 1e-149) {
		tmp = t_1;
	} else if (x <= 1.42e-70) {
		tmp = (y * i) * -j;
	} else if (x <= 60000.0) {
		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 = (z * b) * -c
    t_2 = z * (x * y)
    if (x <= (-1d+39)) then
        tmp = t_2
    else if (x <= (-1.52d-77)) then
        tmp = t_1
    else if (x <= (-2.2d-119)) then
        tmp = b * (a * i)
    else if (x <= 1d-149) then
        tmp = t_1
    else if (x <= 1.42d-70) then
        tmp = (y * i) * -j
    else if (x <= 60000.0d0) 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 * b) * -c;
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -1e+39) {
		tmp = t_2;
	} else if (x <= -1.52e-77) {
		tmp = t_1;
	} else if (x <= -2.2e-119) {
		tmp = b * (a * i);
	} else if (x <= 1e-149) {
		tmp = t_1;
	} else if (x <= 1.42e-70) {
		tmp = (y * i) * -j;
	} else if (x <= 60000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * b) * -c
	t_2 = z * (x * y)
	tmp = 0
	if x <= -1e+39:
		tmp = t_2
	elif x <= -1.52e-77:
		tmp = t_1
	elif x <= -2.2e-119:
		tmp = b * (a * i)
	elif x <= 1e-149:
		tmp = t_1
	elif x <= 1.42e-70:
		tmp = (y * i) * -j
	elif x <= 60000.0:
		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(z * b) * Float64(-c))
	t_2 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -1e+39)
		tmp = t_2;
	elseif (x <= -1.52e-77)
		tmp = t_1;
	elseif (x <= -2.2e-119)
		tmp = Float64(b * Float64(a * i));
	elseif (x <= 1e-149)
		tmp = t_1;
	elseif (x <= 1.42e-70)
		tmp = Float64(Float64(y * i) * Float64(-j));
	elseif (x <= 60000.0)
		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 * b) * -c;
	t_2 = z * (x * y);
	tmp = 0.0;
	if (x <= -1e+39)
		tmp = t_2;
	elseif (x <= -1.52e-77)
		tmp = t_1;
	elseif (x <= -2.2e-119)
		tmp = b * (a * i);
	elseif (x <= 1e-149)
		tmp = t_1;
	elseif (x <= 1.42e-70)
		tmp = (y * i) * -j;
	elseif (x <= 60000.0)
		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[(z * b), $MachinePrecision] * (-c)), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e+39], t$95$2, If[LessEqual[x, -1.52e-77], t$95$1, If[LessEqual[x, -2.2e-119], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1e-149], t$95$1, If[LessEqual[x, 1.42e-70], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[x, 60000.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.9999999999999994e38 or 6e4 < x

   1. Initial program 78.2%

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

   2. Taylor expanded in a around 0 60.9%

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

      1. associate--l+ 60.9%

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

      2. associate-*r* 60.8%

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

      3. associate-*r* 59.8%

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

      4. distribute-rgt-out-- 62.6%

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

      5. fma-def 65.5%

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

      6. *-commutative 65.5%

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

      7. *-commutative 65.5%

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

      8. fma-def 62.6%

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

      9. +-commutative 62.6%

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

      10. fma-def 62.6%

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

      11. fma-neg 62.6%

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

      12. *-commutative 62.6%

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

      13. distribute-rgt-neg-in 62.6%

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

   4. Simplified 62.6%

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

   5. Taylor expanded in x around inf 42.3%

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

      1. *-commutative 42.3%

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

      2. associate-*r* 40.3%

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

   7. Simplified 40.3%

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

   8. Taylor expanded in y around 0 42.3%

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

   10. Simplified 45.7%

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

   if -9.9999999999999994e38 < x < -1.52e-77 or -2.2000000000000001e-119 < x < 9.99999999999999979e-150 or 1.42000000000000002e-70 < x < 6e4

   1. Initial program 68.1%

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

   2. Taylor expanded in a around 0 57.6%

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

      1. associate--l+ 57.6%

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

      2. associate-*r* 62.9%

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

      3. associate-*r* 65.7%

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

      4. distribute-rgt-out-- 67.3%

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

      5. fma-def 69.6%

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

      6. *-commutative 69.6%

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

      7. *-commutative 69.6%

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

      8. fma-def 67.3%

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

      9. +-commutative 67.3%

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

      10. fma-def 68.8%

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

      11. fma-neg 68.8%

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

      12. *-commutative 68.8%

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

      13. distribute-rgt-neg-in 68.8%

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

   4. Simplified 68.8%

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

   5. Taylor expanded in b around inf 42.4%

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

      1. *-commutative 42.4%

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

      2. associate-*r* 43.2%

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

      3. associate-*l* 43.2%

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

      4. *-commutative 43.2%

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

      5. mul-1-neg 43.2%

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

      6. *-commutative 43.2%

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

      7. distribute-rgt-neg-in 43.2%

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

   7. Simplified 43.2%

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

   if -1.52e-77 < x < -2.2000000000000001e-119

   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. Taylor expanded in b around inf 78.3%

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

      1. *-commutative 78.3%

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

   4. Simplified 78.3%

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

   5. Taylor expanded in a around inf 67.1%

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

      1. *-commutative 67.1%

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

   7. Simplified 67.1%

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

   if 9.99999999999999979e-150 < x < 1.42000000000000002e-70

   1. Initial program 83.9%

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

   2. Taylor expanded in j around inf 75.9%

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

   3. Taylor expanded in c around 0 51.6%

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

      1. associate-*r* 51.6%

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

      2. neg-mul-1 51.6%

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

      3. *-commutative 51.6%

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

   5. Simplified 51.6%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+39}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -1.52 \cdot 10^{-77}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-119}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 10^{-149}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{-70}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;x \leq 60000:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 11: 29.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot b\right) \cdot \left(-c\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{+39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-115}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{elif}\;x \leq 60000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z b) (- c))) (t_2 (* z (* x y))))
   (if (<= x -7.8e+39)
     t_2
     (if (<= x -5e-78)
       t_1
       (if (<= x -1.4e-115)
         (* b (* a i))
         (if (<= x 2.5e-150)
           t_1
           (if (<= x 1.1e-70)
             (* y (- (* i j)))
             (if (<= x 60000.0) 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 * b) * -c;
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -7.8e+39) {
		tmp = t_2;
	} else if (x <= -5e-78) {
		tmp = t_1;
	} else if (x <= -1.4e-115) {
		tmp = b * (a * i);
	} else if (x <= 2.5e-150) {
		tmp = t_1;
	} else if (x <= 1.1e-70) {
		tmp = y * -(i * j);
	} else if (x <= 60000.0) {
		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 = (z * b) * -c
    t_2 = z * (x * y)
    if (x <= (-7.8d+39)) then
        tmp = t_2
    else if (x <= (-5d-78)) then
        tmp = t_1
    else if (x <= (-1.4d-115)) then
        tmp = b * (a * i)
    else if (x <= 2.5d-150) then
        tmp = t_1
    else if (x <= 1.1d-70) then
        tmp = y * -(i * j)
    else if (x <= 60000.0d0) 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 * b) * -c;
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -7.8e+39) {
		tmp = t_2;
	} else if (x <= -5e-78) {
		tmp = t_1;
	} else if (x <= -1.4e-115) {
		tmp = b * (a * i);
	} else if (x <= 2.5e-150) {
		tmp = t_1;
	} else if (x <= 1.1e-70) {
		tmp = y * -(i * j);
	} else if (x <= 60000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * b) * -c
	t_2 = z * (x * y)
	tmp = 0
	if x <= -7.8e+39:
		tmp = t_2
	elif x <= -5e-78:
		tmp = t_1
	elif x <= -1.4e-115:
		tmp = b * (a * i)
	elif x <= 2.5e-150:
		tmp = t_1
	elif x <= 1.1e-70:
		tmp = y * -(i * j)
	elif x <= 60000.0:
		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(z * b) * Float64(-c))
	t_2 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -7.8e+39)
		tmp = t_2;
	elseif (x <= -5e-78)
		tmp = t_1;
	elseif (x <= -1.4e-115)
		tmp = Float64(b * Float64(a * i));
	elseif (x <= 2.5e-150)
		tmp = t_1;
	elseif (x <= 1.1e-70)
		tmp = Float64(y * Float64(-Float64(i * j)));
	elseif (x <= 60000.0)
		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 * b) * -c;
	t_2 = z * (x * y);
	tmp = 0.0;
	if (x <= -7.8e+39)
		tmp = t_2;
	elseif (x <= -5e-78)
		tmp = t_1;
	elseif (x <= -1.4e-115)
		tmp = b * (a * i);
	elseif (x <= 2.5e-150)
		tmp = t_1;
	elseif (x <= 1.1e-70)
		tmp = y * -(i * j);
	elseif (x <= 60000.0)
		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[(z * b), $MachinePrecision] * (-c)), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.8e+39], t$95$2, If[LessEqual[x, -5e-78], t$95$1, If[LessEqual[x, -1.4e-115], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e-150], t$95$1, If[LessEqual[x, 1.1e-70], N[(y * (-N[(i * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[x, 60000.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.8000000000000002e39 or 6e4 < x

   1. Initial program 78.2%

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

   2. Taylor expanded in a around 0 60.9%

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

      1. associate--l+ 60.9%

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

      2. associate-*r* 60.8%

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

      3. associate-*r* 59.8%

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

      4. distribute-rgt-out-- 62.6%

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

      5. fma-def 65.5%

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

      6. *-commutative 65.5%

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

      7. *-commutative 65.5%

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

      8. fma-def 62.6%

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

      9. +-commutative 62.6%

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

      10. fma-def 62.6%

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

      11. fma-neg 62.6%

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

      12. *-commutative 62.6%

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

      13. distribute-rgt-neg-in 62.6%

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

   4. Simplified 62.6%

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

   5. Taylor expanded in x around inf 42.3%

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

      1. *-commutative 42.3%

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

      2. associate-*r* 40.3%

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

   7. Simplified 40.3%

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

   8. Taylor expanded in y around 0 42.3%

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

   10. Simplified 45.7%

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

   if -7.8000000000000002e39 < x < -4.9999999999999996e-78 or -1.39999999999999994e-115 < x < 2.49999999999999995e-150 or 1.0999999999999999e-70 < x < 6e4

   1. Initial program 68.1%

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

   2. Taylor expanded in a around 0 57.6%

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

      1. associate--l+ 57.6%

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

      2. associate-*r* 62.9%

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

      3. associate-*r* 65.7%

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

      4. distribute-rgt-out-- 67.3%

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

      5. fma-def 69.6%

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

      6. *-commutative 69.6%

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

      7. *-commutative 69.6%

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

      8. fma-def 67.3%

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

      9. +-commutative 67.3%

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

      10. fma-def 68.8%

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

      11. fma-neg 68.8%

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

      12. *-commutative 68.8%

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

      13. distribute-rgt-neg-in 68.8%

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

   4. Simplified 68.8%

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

   5. Taylor expanded in b around inf 42.4%

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

      1. *-commutative 42.4%

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

      2. associate-*r* 43.2%

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

      3. associate-*l* 43.2%

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

      4. *-commutative 43.2%

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

      5. mul-1-neg 43.2%

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

      6. *-commutative 43.2%

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

      7. distribute-rgt-neg-in 43.2%

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

   7. Simplified 43.2%

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

   if -4.9999999999999996e-78 < x < -1.39999999999999994e-115

   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. Taylor expanded in b around inf 78.3%

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

      1. *-commutative 78.3%

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

   4. Simplified 78.3%

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

   5. Taylor expanded in a around inf 67.1%

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

      1. *-commutative 67.1%

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

   7. Simplified 67.1%

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

   if 2.49999999999999995e-150 < x < 1.0999999999999999e-70

   1. Initial program 83.9%

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

   2. Taylor expanded in j around inf 75.9%

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

   3. Taylor expanded in c around 0 43.9%

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

      1. associate-*r* 51.6%

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

      2. associate-*r* 51.6%

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

      3. *-commutative 51.6%

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

      4. mul-1-neg 51.6%

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

      5. distribute-rgt-neg-in 51.6%

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

   5. Simplified 51.6%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+39}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-78}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-115}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-150}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{elif}\;x \leq 60000:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 12: 29.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot b\right) \cdot \left(-c\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{-122}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-150}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{elif}\;x \leq 33000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z b) (- c))) (t_2 (* z (* x y))))
   (if (<= x -2.2e+37)
     t_2
     (if (<= x -8.2e-78)
       t_1
       (if (<= x -6.4e-122)
         (* b (* a i))
         (if (<= x 9.5e-150)
           (* (* z c) (- b))
           (if (<= x 1.15e-70)
             (* y (- (* i j)))
             (if (<= x 33000.0) 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 * b) * -c;
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -2.2e+37) {
		tmp = t_2;
	} else if (x <= -8.2e-78) {
		tmp = t_1;
	} else if (x <= -6.4e-122) {
		tmp = b * (a * i);
	} else if (x <= 9.5e-150) {
		tmp = (z * c) * -b;
	} else if (x <= 1.15e-70) {
		tmp = y * -(i * j);
	} else if (x <= 33000.0) {
		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 = (z * b) * -c
    t_2 = z * (x * y)
    if (x <= (-2.2d+37)) then
        tmp = t_2
    else if (x <= (-8.2d-78)) then
        tmp = t_1
    else if (x <= (-6.4d-122)) then
        tmp = b * (a * i)
    else if (x <= 9.5d-150) then
        tmp = (z * c) * -b
    else if (x <= 1.15d-70) then
        tmp = y * -(i * j)
    else if (x <= 33000.0d0) 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 * b) * -c;
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -2.2e+37) {
		tmp = t_2;
	} else if (x <= -8.2e-78) {
		tmp = t_1;
	} else if (x <= -6.4e-122) {
		tmp = b * (a * i);
	} else if (x <= 9.5e-150) {
		tmp = (z * c) * -b;
	} else if (x <= 1.15e-70) {
		tmp = y * -(i * j);
	} else if (x <= 33000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * b) * -c
	t_2 = z * (x * y)
	tmp = 0
	if x <= -2.2e+37:
		tmp = t_2
	elif x <= -8.2e-78:
		tmp = t_1
	elif x <= -6.4e-122:
		tmp = b * (a * i)
	elif x <= 9.5e-150:
		tmp = (z * c) * -b
	elif x <= 1.15e-70:
		tmp = y * -(i * j)
	elif x <= 33000.0:
		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(z * b) * Float64(-c))
	t_2 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -2.2e+37)
		tmp = t_2;
	elseif (x <= -8.2e-78)
		tmp = t_1;
	elseif (x <= -6.4e-122)
		tmp = Float64(b * Float64(a * i));
	elseif (x <= 9.5e-150)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (x <= 1.15e-70)
		tmp = Float64(y * Float64(-Float64(i * j)));
	elseif (x <= 33000.0)
		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 * b) * -c;
	t_2 = z * (x * y);
	tmp = 0.0;
	if (x <= -2.2e+37)
		tmp = t_2;
	elseif (x <= -8.2e-78)
		tmp = t_1;
	elseif (x <= -6.4e-122)
		tmp = b * (a * i);
	elseif (x <= 9.5e-150)
		tmp = (z * c) * -b;
	elseif (x <= 1.15e-70)
		tmp = y * -(i * j);
	elseif (x <= 33000.0)
		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[(z * b), $MachinePrecision] * (-c)), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.2e+37], t$95$2, If[LessEqual[x, -8.2e-78], t$95$1, If[LessEqual[x, -6.4e-122], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.5e-150], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[x, 1.15e-70], N[(y * (-N[(i * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[x, 33000.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.2000000000000001e37 or 33000 < x

   1. Initial program 78.2%

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

   2. Taylor expanded in a around 0 60.9%

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

      1. associate--l+ 60.9%

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

      2. associate-*r* 60.8%

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

      3. associate-*r* 59.8%

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

      4. distribute-rgt-out-- 62.6%

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

      5. fma-def 65.5%

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

      6. *-commutative 65.5%

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

      7. *-commutative 65.5%

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

      8. fma-def 62.6%

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

      9. +-commutative 62.6%

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

      10. fma-def 62.6%

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

      11. fma-neg 62.6%

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

      12. *-commutative 62.6%

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

      13. distribute-rgt-neg-in 62.6%

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

   4. Simplified 62.6%

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

   5. Taylor expanded in x around inf 42.3%

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

      1. *-commutative 42.3%

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

      2. associate-*r* 40.3%

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

   7. Simplified 40.3%

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

   8. Taylor expanded in y around 0 42.3%

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

   10. Simplified 45.7%

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

   if -2.2000000000000001e37 < x < -8.1999999999999996e-78 or 1.15e-70 < x < 33000

   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. Taylor expanded in a around 0 54.9%

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

      1. associate--l+ 54.9%

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

      2. associate-*r* 54.9%

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

      3. associate-*r* 60.3%

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

      4. distribute-rgt-out-- 60.3%

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

      5. fma-def 64.3%

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

      6. *-commutative 64.3%

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

      7. *-commutative 64.3%

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

      8. fma-def 60.3%

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

      9. +-commutative 60.3%

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

      10. fma-def 64.4%

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

      11. fma-neg 64.4%

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

      12. *-commutative 64.4%

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

      13. distribute-rgt-neg-in 64.4%

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

   4. Simplified 64.4%

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

   5. Taylor expanded in b around inf 41.8%

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

      1. *-commutative 41.8%

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

      2. associate-*r* 47.4%

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

      3. associate-*l* 47.4%

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

      4. *-commutative 47.4%

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

      5. mul-1-neg 47.4%

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

      6. *-commutative 47.4%

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

      7. distribute-rgt-neg-in 47.4%

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

   7. Simplified 47.4%

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

   if -8.1999999999999996e-78 < x < -6.4000000000000004e-122

   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. Taylor expanded in b around inf 78.3%

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

      1. *-commutative 78.3%

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

   4. Simplified 78.3%

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

   5. Taylor expanded in a around inf 67.1%

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

      1. *-commutative 67.1%

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

   7. Simplified 67.1%

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

   if -6.4000000000000004e-122 < x < 9.50000000000000013e-150

   1. Initial program 70.1%

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

   2. Taylor expanded in a around 0 59.3%

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

      1. associate--l+ 59.3%

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

      2. associate-*r* 67.9%

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

      3. associate-*r* 69.1%

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

      4. distribute-rgt-out-- 71.7%

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

      5. fma-def 72.9%

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

      6. *-commutative 72.9%

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

      7. *-commutative 72.9%

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

      8. fma-def 71.7%

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

      9. +-commutative 71.7%

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

      10. fma-def 71.7%

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

      11. fma-neg 71.7%

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

      12. *-commutative 71.7%

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

      13. distribute-rgt-neg-in 71.7%

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

   4. Simplified 71.7%

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

   5. Taylor expanded in b around inf 42.8%

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

      1. associate-*r* 42.8%

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

      2. neg-mul-1 42.8%

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

   7. Simplified 42.8%

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

   if 9.50000000000000013e-150 < x < 1.15e-70

   1. Initial program 83.9%

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

   2. Taylor expanded in j around inf 75.9%

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

   3. Taylor expanded in c around 0 43.9%

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

      1. associate-*r* 51.6%

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

      2. associate-*r* 51.6%

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

      3. *-commutative 51.6%

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

      4. mul-1-neg 51.6%

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

      5. distribute-rgt-neg-in 51.6%

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

   5. Simplified 51.6%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+37}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-78}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{-122}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-150}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{elif}\;x \leq 33000:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 13: 42.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -8.8 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-153}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{-248}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-175}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -8.8e-83)
     t_1
     (if (<= b -1.9e-153)
       (* (* y i) (- j))
       (if (<= b 6.4e-248)
         (* z (* x y))
         (if (<= b 1.25e-175) (* c (* t j)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -8.8e-83) {
		tmp = t_1;
	} else if (b <= -1.9e-153) {
		tmp = (y * i) * -j;
	} else if (b <= 6.4e-248) {
		tmp = z * (x * y);
	} else if (b <= 1.25e-175) {
		tmp = c * (t * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-8.8d-83)) then
        tmp = t_1
    else if (b <= (-1.9d-153)) then
        tmp = (y * i) * -j
    else if (b <= 6.4d-248) then
        tmp = z * (x * y)
    else if (b <= 1.25d-175) then
        tmp = c * (t * j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -8.8e-83) {
		tmp = t_1;
	} else if (b <= -1.9e-153) {
		tmp = (y * i) * -j;
	} else if (b <= 6.4e-248) {
		tmp = z * (x * y);
	} else if (b <= 1.25e-175) {
		tmp = c * (t * j);
	} 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 b <= -8.8e-83:
		tmp = t_1
	elif b <= -1.9e-153:
		tmp = (y * i) * -j
	elif b <= 6.4e-248:
		tmp = z * (x * y)
	elif b <= 1.25e-175:
		tmp = c * (t * j)
	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 (b <= -8.8e-83)
		tmp = t_1;
	elseif (b <= -1.9e-153)
		tmp = Float64(Float64(y * i) * Float64(-j));
	elseif (b <= 6.4e-248)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 1.25e-175)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -8.8e-83)
		tmp = t_1;
	elseif (b <= -1.9e-153)
		tmp = (y * i) * -j;
	elseif (b <= 6.4e-248)
		tmp = z * (x * y);
	elseif (b <= 1.25e-175)
		tmp = c * (t * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.8e-83], t$95$1, If[LessEqual[b, -1.9e-153], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[b, 6.4e-248], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.25e-175], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8.8000000000000003e-83 or 1.25e-175 < b

   1. Initial program 72.9%

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

   2. Taylor expanded in b around inf 54.5%

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

      1. *-commutative 54.5%

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

   4. Simplified 54.5%

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

   if -8.8000000000000003e-83 < b < -1.90000000000000011e-153

   1. Initial program 76.1%

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

   2. Taylor expanded in j around inf 76.2%

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

   3. Taylor expanded in c around 0 59.4%

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

      1. associate-*r* 59.4%

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

      2. neg-mul-1 59.4%

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

      3. *-commutative 59.4%

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

   5. Simplified 59.4%

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

   if -1.90000000000000011e-153 < b < 6.40000000000000035e-248

   1. Initial program 74.2%

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

   2. Taylor expanded in a around 0 65.7%

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

      1. associate--l+ 65.7%

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

      2. associate-*r* 68.6%

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

      3. associate-*r* 74.0%

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

      4. distribute-rgt-out-- 74.0%

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

      5. fma-def 76.9%

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

      6. *-commutative 76.9%

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

      7. *-commutative 76.9%

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

      8. fma-def 74.0%

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

      9. +-commutative 74.0%

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

      10. fma-def 74.0%

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

      11. fma-neg 74.0%

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

      12. *-commutative 74.0%

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

      13. distribute-rgt-neg-in 74.0%

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

   4. Simplified 74.0%

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

   5. Taylor expanded in x around inf 38.6%

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

      1. *-commutative 38.6%

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

      2. associate-*r* 35.9%

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

   7. Simplified 35.9%

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

   8. Taylor expanded in y around 0 38.6%

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

   10. Simplified 44.1%

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

   if 6.40000000000000035e-248 < b < 1.25e-175

   1. Initial program 67.7%

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

   2. Taylor expanded in a around 0 67.7%

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

      1. associate--l+ 67.7%

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

      2. associate-*r* 67.7%

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

      3. associate-*r* 76.1%

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

      4. distribute-rgt-out-- 76.1%

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

      5. fma-def 76.1%

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

      6. *-commutative 76.1%

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

      7. *-commutative 76.1%

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

      8. fma-def 76.1%

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

      9. +-commutative 76.1%

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

      10. fma-def 76.1%

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

      11. fma-neg 76.1%

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

      12. *-commutative 76.1%

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

      13. distribute-rgt-neg-in 76.1%

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

   4. Simplified 76.1%

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

   5. Taylor expanded in t around inf 67.1%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.8 \cdot 10^{-83}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-153}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{-248}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-175}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 14: 44.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -9.8 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{-152}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-250}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+43}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -9.8e-80)
     t_1
     (if (<= b -5.6e-152)
       (* (* y i) (- j))
       (if (<= b 4.5e-250)
         (* z (* x y))
         (if (<= b 5.6e+43) (* c (- (* t j) (* z b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -9.8e-80) {
		tmp = t_1;
	} else if (b <= -5.6e-152) {
		tmp = (y * i) * -j;
	} else if (b <= 4.5e-250) {
		tmp = z * (x * y);
	} else if (b <= 5.6e+43) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-9.8d-80)) then
        tmp = t_1
    else if (b <= (-5.6d-152)) then
        tmp = (y * i) * -j
    else if (b <= 4.5d-250) then
        tmp = z * (x * y)
    else if (b <= 5.6d+43) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -9.8e-80) {
		tmp = t_1;
	} else if (b <= -5.6e-152) {
		tmp = (y * i) * -j;
	} else if (b <= 4.5e-250) {
		tmp = z * (x * y);
	} else if (b <= 5.6e+43) {
		tmp = c * ((t * j) - (z * b));
	} 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 b <= -9.8e-80:
		tmp = t_1
	elif b <= -5.6e-152:
		tmp = (y * i) * -j
	elif b <= 4.5e-250:
		tmp = z * (x * y)
	elif b <= 5.6e+43:
		tmp = c * ((t * j) - (z * b))
	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 (b <= -9.8e-80)
		tmp = t_1;
	elseif (b <= -5.6e-152)
		tmp = Float64(Float64(y * i) * Float64(-j));
	elseif (b <= 4.5e-250)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 5.6e+43)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -9.8e-80)
		tmp = t_1;
	elseif (b <= -5.6e-152)
		tmp = (y * i) * -j;
	elseif (b <= 4.5e-250)
		tmp = z * (x * y);
	elseif (b <= 5.6e+43)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.8e-80], t$95$1, If[LessEqual[b, -5.6e-152], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[b, 4.5e-250], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.6e+43], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.79999999999999981e-80 or 5.60000000000000038e43 < b

   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. Taylor expanded in b around inf 63.0%

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

      1. *-commutative 63.0%

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

   4. Simplified 63.0%

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

   if -9.79999999999999981e-80 < b < -5.59999999999999969e-152

   1. Initial program 76.1%

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

   2. Taylor expanded in j around inf 76.2%

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

   3. Taylor expanded in c around 0 59.4%

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

      1. associate-*r* 59.4%

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

      2. neg-mul-1 59.4%

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

      3. *-commutative 59.4%

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

   5. Simplified 59.4%

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

   if -5.59999999999999969e-152 < b < 4.49999999999999993e-250

   1. Initial program 74.2%

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

   2. Taylor expanded in a around 0 65.7%

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

      1. associate--l+ 65.7%

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

      2. associate-*r* 68.6%

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

      3. associate-*r* 74.0%

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

      4. distribute-rgt-out-- 74.0%

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

      5. fma-def 76.9%

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

      6. *-commutative 76.9%

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

      7. *-commutative 76.9%

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

      8. fma-def 74.0%

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

      9. +-commutative 74.0%

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

      10. fma-def 74.0%

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

      11. fma-neg 74.0%

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

      12. *-commutative 74.0%

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

      13. distribute-rgt-neg-in 74.0%

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

   4. Simplified 74.0%

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

   5. Taylor expanded in x around inf 38.6%

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

      1. *-commutative 38.6%

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

      2. associate-*r* 35.9%

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

   7. Simplified 35.9%

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

   8. Taylor expanded in y around 0 38.6%

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

   10. Simplified 44.1%

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

   if 4.49999999999999993e-250 < b < 5.60000000000000038e43

   1. Initial program 74.9%

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

   2. Taylor expanded in c around inf 48.0%

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

      1. *-commutative 48.0%

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

      2. *-commutative 48.0%

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

   4. Simplified 48.0%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.8 \cdot 10^{-80}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{-152}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-250}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+43}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 15: 51.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -5 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-158}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))) (t_2 (* z (- (* x y) (* b c)))))
   (if (<= z -5e+44)
     t_2
     (if (<= z -5.5e-63)
       t_1
       (if (<= z -2.65e-158)
         (* j (- (* t c) (* y i)))
         (if (<= z 1.2e-72) 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 = a * ((b * i) - (x * t));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -5e+44) {
		tmp = t_2;
	} else if (z <= -5.5e-63) {
		tmp = t_1;
	} else if (z <= -2.65e-158) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= 1.2e-72) {
		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 = a * ((b * i) - (x * t))
    t_2 = z * ((x * y) - (b * c))
    if (z <= (-5d+44)) then
        tmp = t_2
    else if (z <= (-5.5d-63)) then
        tmp = t_1
    else if (z <= (-2.65d-158)) then
        tmp = j * ((t * c) - (y * i))
    else if (z <= 1.2d-72) 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 = a * ((b * i) - (x * t));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -5e+44) {
		tmp = t_2;
	} else if (z <= -5.5e-63) {
		tmp = t_1;
	} else if (z <= -2.65e-158) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= 1.2e-72) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -5e+44:
		tmp = t_2
	elif z <= -5.5e-63:
		tmp = t_1
	elif z <= -2.65e-158:
		tmp = j * ((t * c) - (y * i))
	elif z <= 1.2e-72:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -5e+44)
		tmp = t_2;
	elseif (z <= -5.5e-63)
		tmp = t_1;
	elseif (z <= -2.65e-158)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (z <= 1.2e-72)
		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 = a * ((b * i) - (x * t));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -5e+44)
		tmp = t_2;
	elseif (z <= -5.5e-63)
		tmp = t_1;
	elseif (z <= -2.65e-158)
		tmp = j * ((t * c) - (y * i));
	elseif (z <= 1.2e-72)
		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[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+44], t$95$2, If[LessEqual[z, -5.5e-63], t$95$1, If[LessEqual[z, -2.65e-158], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e-72], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.9999999999999996e44 or 1.2e-72 < z

   1. Initial program 65.3%

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

   2. Taylor expanded in z around inf 71.3%

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

      1. *-commutative 71.3%

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

   4. Simplified 71.3%

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

   if -4.9999999999999996e44 < z < -5.50000000000000043e-63 or -2.6499999999999999e-158 < z < 1.2e-72

   1. Initial program 78.9%

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

   2. Taylor expanded in a around -inf 54.5%

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

   if -5.50000000000000043e-63 < z < -2.6499999999999999e-158

   1. Initial program 91.8%

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

   2. Taylor expanded in j around inf 70.2%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+44}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-63}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-158}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-72}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 16: 52.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{-22} \lor \neg \left(b \leq 6 \cdot 10^{+21}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.1e-22) (not (<= b 6e+21)))
   (* b (- (* a i) (* z c)))
   (* j (- (* t c) (* y 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 ((b <= -1.1e-22) || !(b <= 6e+21)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = j * ((t * c) - (y * 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 ((b <= (-1.1d-22)) .or. (.not. (b <= 6d+21))) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = j * ((t * c) - (y * 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 ((b <= -1.1e-22) || !(b <= 6e+21)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = j * ((t * c) - (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.1e-22) or not (b <= 6e+21):
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = j * ((t * c) - (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.1e-22) || !(b <= 6e+21))
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -1.1e-22) || ~((b <= 6e+21)))
		tmp = b * ((a * i) - (z * c));
	else
		tmp = j * ((t * c) - (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.1e-22], N[Not[LessEqual[b, 6e+21]], $MachinePrecision]], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.1e-22 or 6e21 < b

   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. Taylor expanded in b around inf 63.7%

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

      1. *-commutative 63.7%

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

   4. Simplified 63.7%

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

   if -1.1e-22 < b < 6e21

   1. Initial program 75.9%

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

   2. Taylor expanded in j around inf 53.8%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{-22} \lor \neg \left(b \leq 6 \cdot 10^{+21}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 17: 30.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-226}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* b i))))
   (if (<= a -1.9e-24)
     t_1
     (if (<= a 3e-226) (* t (* c j)) (if (<= a 3.8e+63) (* x (* y z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double tmp;
	if (a <= -1.9e-24) {
		tmp = t_1;
	} else if (a <= 3e-226) {
		tmp = t * (c * j);
	} else if (a <= 3.8e+63) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * i)
    if (a <= (-1.9d-24)) then
        tmp = t_1
    else if (a <= 3d-226) then
        tmp = t * (c * j)
    else if (a <= 3.8d+63) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double tmp;
	if (a <= -1.9e-24) {
		tmp = t_1;
	} else if (a <= 3e-226) {
		tmp = t * (c * j);
	} else if (a <= 3.8e+63) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (b * i)
	tmp = 0
	if a <= -1.9e-24:
		tmp = t_1
	elif a <= 3e-226:
		tmp = t * (c * j)
	elif a <= 3.8e+63:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (a <= -1.9e-24)
		tmp = t_1;
	elseif (a <= 3e-226)
		tmp = Float64(t * Float64(c * j));
	elseif (a <= 3.8e+63)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (b * i);
	tmp = 0.0;
	if (a <= -1.9e-24)
		tmp = t_1;
	elseif (a <= 3e-226)
		tmp = t * (c * j);
	elseif (a <= 3.8e+63)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.9e-24], t$95$1, If[LessEqual[a, 3e-226], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e+63], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.90000000000000013e-24 or 3.8000000000000001e63 < a

   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. Taylor expanded in b around inf 57.1%

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

      1. *-commutative 57.1%

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

   4. Simplified 57.1%

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

   5. Taylor expanded in a around inf 40.2%

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

   if -1.90000000000000013e-24 < a < 2.99999999999999995e-226

   1. Initial program 80.7%

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

   2. Taylor expanded in j around inf 48.7%

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

   3. Taylor expanded in c around inf 25.7%

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

      1. *-commutative 25.7%

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

      2. *-commutative 25.7%

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

      3. associate-*r* 26.9%

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

   5. Simplified 26.9%

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

   if 2.99999999999999995e-226 < a < 3.8000000000000001e63

   1. Initial program 75.9%

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

   2. Taylor expanded in a around 0 68.2%

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

      1. associate--l+ 68.2%

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

      2. associate-*r* 68.2%

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

      3. associate-*r* 74.5%

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

      4. distribute-rgt-out-- 79.3%

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

      5. fma-def 82.5%

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

      6. *-commutative 82.5%

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

      7. *-commutative 82.5%

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

      8. fma-def 79.3%

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

      9. +-commutative 79.3%

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

      10. fma-def 79.3%

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

      11. fma-neg 79.3%

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

      12. *-commutative 79.3%

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

      13. distribute-rgt-neg-in 79.3%

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

   4. Simplified 79.3%

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

   5. Taylor expanded in x around inf 40.5%

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

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-24}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-226}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 18: 30.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b\right)\\ \mathbf{if}\;a \leq -3 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-226}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* a b))))
   (if (<= a -3e-25)
     t_1
     (if (<= a 3.2e-226)
       (* t (* c j))
       (if (<= a 8.8e+63) (* x (* y z)) 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);
	double tmp;
	if (a <= -3e-25) {
		tmp = t_1;
	} else if (a <= 3.2e-226) {
		tmp = t * (c * j);
	} else if (a <= 8.8e+63) {
		tmp = x * (y * z);
	} 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)
    if (a <= (-3d-25)) then
        tmp = t_1
    else if (a <= 3.2d-226) then
        tmp = t * (c * j)
    else if (a <= 8.8d+63) then
        tmp = x * (y * z)
    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);
	double tmp;
	if (a <= -3e-25) {
		tmp = t_1;
	} else if (a <= 3.2e-226) {
		tmp = t * (c * j);
	} else if (a <= 8.8e+63) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (a * b)
	tmp = 0
	if a <= -3e-25:
		tmp = t_1
	elif a <= 3.2e-226:
		tmp = t * (c * j)
	elif a <= 8.8e+63:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(a * b))
	tmp = 0.0
	if (a <= -3e-25)
		tmp = t_1;
	elseif (a <= 3.2e-226)
		tmp = Float64(t * Float64(c * j));
	elseif (a <= 8.8e+63)
		tmp = Float64(x * Float64(y * z));
	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);
	tmp = 0.0;
	if (a <= -3e-25)
		tmp = t_1;
	elseif (a <= 3.2e-226)
		tmp = t * (c * j);
	elseif (a <= 8.8e+63)
		tmp = x * (y * z);
	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[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3e-25], t$95$1, If[LessEqual[a, 3.2e-226], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.8e+63], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.9999999999999998e-25 or 8.7999999999999995e63 < a

   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. Taylor expanded in b around inf 57.1%

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

      1. *-commutative 57.1%

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

   4. Simplified 57.1%

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

   5. Taylor expanded in a around inf 40.2%

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

      1. associate-*r* 41.8%

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

   7. Simplified 41.8%

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

   if -2.9999999999999998e-25 < a < 3.19999999999999982e-226

   1. Initial program 80.7%

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

   2. Taylor expanded in j around inf 48.7%

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

   3. Taylor expanded in c around inf 25.7%

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

      1. *-commutative 25.7%

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

      2. *-commutative 25.7%

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

      3. associate-*r* 26.9%

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

   5. Simplified 26.9%

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

   if 3.19999999999999982e-226 < a < 8.7999999999999995e63

   1. Initial program 75.9%

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

   2. Taylor expanded in a around 0 68.2%

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

      1. associate--l+ 68.2%

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

      2. associate-*r* 68.2%

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

      3. associate-*r* 74.5%

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

      4. distribute-rgt-out-- 79.3%

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

      5. fma-def 82.5%

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

      6. *-commutative 82.5%

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

      7. *-commutative 82.5%

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

      8. fma-def 79.3%

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

      9. +-commutative 79.3%

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

      10. fma-def 79.3%

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

      11. fma-neg 79.3%

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

      12. *-commutative 79.3%

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

      13. distribute-rgt-neg-in 79.3%

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

   4. Simplified 79.3%

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

   5. Taylor expanded in x around inf 40.5%

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

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-25}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-226}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 19: 30.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b\right)\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.15 \cdot 10^{-226}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* a b))))
   (if (<= a -1.9e-25)
     t_1
     (if (<= a 3.15e-226)
       (* t (* c j))
       (if (<= a 2.9e+63) (* 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 * (a * b);
	double tmp;
	if (a <= -1.9e-25) {
		tmp = t_1;
	} else if (a <= 3.15e-226) {
		tmp = t * (c * j);
	} else if (a <= 2.9e+63) {
		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 * (a * b)
    if (a <= (-1.9d-25)) then
        tmp = t_1
    else if (a <= 3.15d-226) then
        tmp = t * (c * j)
    else if (a <= 2.9d+63) 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 * (a * b);
	double tmp;
	if (a <= -1.9e-25) {
		tmp = t_1;
	} else if (a <= 3.15e-226) {
		tmp = t * (c * j);
	} else if (a <= 2.9e+63) {
		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 * (a * b)
	tmp = 0
	if a <= -1.9e-25:
		tmp = t_1
	elif a <= 3.15e-226:
		tmp = t * (c * j)
	elif a <= 2.9e+63:
		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(i * Float64(a * b))
	tmp = 0.0
	if (a <= -1.9e-25)
		tmp = t_1;
	elseif (a <= 3.15e-226)
		tmp = Float64(t * Float64(c * j));
	elseif (a <= 2.9e+63)
		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 * (a * b);
	tmp = 0.0;
	if (a <= -1.9e-25)
		tmp = t_1;
	elseif (a <= 3.15e-226)
		tmp = t * (c * j);
	elseif (a <= 2.9e+63)
		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[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.9e-25], t$95$1, If[LessEqual[a, 3.15e-226], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e+63], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.8999999999999999e-25 or 2.8999999999999999e63 < a

   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. Taylor expanded in b around inf 57.1%

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

      1. *-commutative 57.1%

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

   4. Simplified 57.1%

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

   5. Taylor expanded in a around inf 40.2%

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

      1. associate-*r* 41.8%

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

   7. Simplified 41.8%

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

   if -1.8999999999999999e-25 < a < 3.1499999999999999e-226

   1. Initial program 80.7%

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

   2. Taylor expanded in j around inf 48.7%

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

   3. Taylor expanded in c around inf 25.7%

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

      1. *-commutative 25.7%

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

      2. *-commutative 25.7%

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

      3. associate-*r* 26.9%

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

   5. Simplified 26.9%

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

   if 3.1499999999999999e-226 < a < 2.8999999999999999e63

   1. Initial program 75.9%

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

   2. Taylor expanded in a around 0 68.2%

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

      1. associate--l+ 68.2%

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

      2. associate-*r* 68.2%

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

      3. associate-*r* 74.5%

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

      4. distribute-rgt-out-- 79.3%

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

      5. fma-def 82.5%

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

      6. *-commutative 82.5%

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

      7. *-commutative 82.5%

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

      8. fma-def 79.3%

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

      9. +-commutative 79.3%

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

      10. fma-def 79.3%

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

      11. fma-neg 79.3%

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

      12. *-commutative 79.3%

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

      13. distribute-rgt-neg-in 79.3%

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

   4. Simplified 79.3%

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

   5. Taylor expanded in x around inf 40.5%

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

      1. *-commutative 40.5%

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

      2. associate-*r* 35.7%

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

   7. Simplified 35.7%

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

   8. Taylor expanded in y around 0 40.5%

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

   10. Simplified 42.0%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-25}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 3.15 \cdot 10^{-226}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 20: 31.6% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -5.6 \cdot 10^{+34} \lor \neg \left(i \leq 0.0062\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -5.6e+34) (not (<= i 0.0062))) (* 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 ((i <= -5.6e+34) || !(i <= 0.0062)) {
		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 ((i <= (-5.6d+34)) .or. (.not. (i <= 0.0062d0))) 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 ((i <= -5.6e+34) || !(i <= 0.0062)) {
		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 (i <= -5.6e+34) or not (i <= 0.0062):
		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 ((i <= -5.6e+34) || !(i <= 0.0062))
		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 ((i <= -5.6e+34) || ~((i <= 0.0062)))
		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[Or[LessEqual[i, -5.6e+34], N[Not[LessEqual[i, 0.0062]], $MachinePrecision]], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -5.60000000000000016e34 or 0.00619999999999999978 < i

   1. Initial program 68.4%

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

   2. Taylor expanded in b around inf 51.9%

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

      1. *-commutative 51.9%

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

   4. Simplified 51.9%

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

   5. Taylor expanded in a around inf 39.2%

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

   if -5.60000000000000016e34 < i < 0.00619999999999999978

   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. Taylor expanded in a around 0 65.4%

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

      1. associate--l+ 65.4%

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

      2. associate-*r* 68.0%

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

      3. associate-*r* 70.5%

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

      4. distribute-rgt-out-- 73.2%

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

      5. fma-def 74.6%

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

      6. *-commutative 74.6%

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

      7. *-commutative 74.6%

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

      8. fma-def 73.2%

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

      9. +-commutative 73.2%

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

      10. fma-def 73.9%

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

      11. fma-neg 73.9%

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

      12. *-commutative 73.9%

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

      13. distribute-rgt-neg-in 73.9%

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

   4. Simplified 73.9%

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

   5. Taylor expanded in t around inf 26.5%

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

4. Final simplification 32.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.6 \cdot 10^{+34} \lor \neg \left(i \leq 0.0062\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]

Alternative 21: 22.8% 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 73.0%

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

2. Taylor expanded in b around inf 43.5%

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

   1. *-commutative 43.5%

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

4. Simplified 43.5%

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

5. Taylor expanded in a around inf 22.4%

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

6. Final simplification 22.4%

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

Developer target: 69.0% 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 2023310 
(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)))))