Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.5% → 81.9%

Time: 19.0s

Alternatives: 25

Speedup: 0.5×

• 58.8% 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: 73.5% 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: 81.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(i * N[(j * N[(N[(N[(t * c), $MachinePrecision] / i), $MachinePrecision] - y), $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 92.2%

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

   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. Step-by-step derivation

      1. +-commutative 0.0%

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

      2. fma-define 6.4%

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

      3. *-commutative 6.4%

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

      4. *-commutative 6.4%

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

      5. cancel-sign-sub-inv 6.4%

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

      6. cancel-sign-sub 6.4%

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

      7. sub-neg 6.4%

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

      8. sub-neg 6.4%

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

      9. *-commutative 6.4%

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

      10. fmm-def 6.4%

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

      11. *-commutative 6.4%

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

      12. distribute-rgt-neg-out 6.4%

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

      13. remove-double-neg 6.4%

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

      14. *-commutative 6.4%

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

      15. *-commutative 6.4%

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

   3. Simplified 6.4%

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

   5. Taylor expanded in i around inf 6.4%

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

      1. *-commutative 6.4%

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

   7. Simplified 6.4%

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

   8. Taylor expanded in j around inf 50.5%

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

4. Final simplification 84.5%

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

Alternative 2: 68.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right) + t\_1\\ t_3 := y \cdot \left(\left(\left(x \cdot z - \frac{x \cdot \left(t \cdot a\right)}{y}\right) - i \cdot j\right) + a \cdot \frac{b \cdot i}{y}\right)\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+25}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-210}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-143}:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + t\_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-44}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (+ (* j (- (* t c) (* y i))) t_1))
        (t_3
         (*
          y
          (+
           (- (- (* x z) (/ (* x (* t a)) y)) (* i j))
           (* a (/ (* b i) y))))))
   (if (<= y -1.5e+25)
     t_3
     (if (<= y -3.5e-210)
       t_2
       (if (<= y 4.6e-143)
         (+ (- (* c (* t j)) (* a (* x t))) t_1)
         (if (<= y 2.5e-44) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = (j * ((t * c) - (y * i))) + t_1;
	double t_3 = y * ((((x * z) - ((x * (t * a)) / y)) - (i * j)) + (a * ((b * i) / y)));
	double tmp;
	if (y <= -1.5e+25) {
		tmp = t_3;
	} else if (y <= -3.5e-210) {
		tmp = t_2;
	} else if (y <= 4.6e-143) {
		tmp = ((c * (t * j)) - (a * (x * t))) + t_1;
	} else if (y <= 2.5e-44) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = (j * ((t * c) - (y * i))) + t_1
    t_3 = y * ((((x * z) - ((x * (t * a)) / y)) - (i * j)) + (a * ((b * i) / y)))
    if (y <= (-1.5d+25)) then
        tmp = t_3
    else if (y <= (-3.5d-210)) then
        tmp = t_2
    else if (y <= 4.6d-143) then
        tmp = ((c * (t * j)) - (a * (x * t))) + t_1
    else if (y <= 2.5d-44) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = (j * ((t * c) - (y * i))) + t_1;
	double t_3 = y * ((((x * z) - ((x * (t * a)) / y)) - (i * j)) + (a * ((b * i) / y)));
	double tmp;
	if (y <= -1.5e+25) {
		tmp = t_3;
	} else if (y <= -3.5e-210) {
		tmp = t_2;
	} else if (y <= 4.6e-143) {
		tmp = ((c * (t * j)) - (a * (x * t))) + t_1;
	} else if (y <= 2.5e-44) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = (j * ((t * c) - (y * i))) + t_1
	t_3 = y * ((((x * z) - ((x * (t * a)) / y)) - (i * j)) + (a * ((b * i) / y)))
	tmp = 0
	if y <= -1.5e+25:
		tmp = t_3
	elif y <= -3.5e-210:
		tmp = t_2
	elif y <= 4.6e-143:
		tmp = ((c * (t * j)) - (a * (x * t))) + t_1
	elif y <= 2.5e-44:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + t_1)
	t_3 = Float64(y * Float64(Float64(Float64(Float64(x * z) - Float64(Float64(x * Float64(t * a)) / y)) - Float64(i * j)) + Float64(a * Float64(Float64(b * i) / y))))
	tmp = 0.0
	if (y <= -1.5e+25)
		tmp = t_3;
	elseif (y <= -3.5e-210)
		tmp = t_2;
	elseif (y <= 4.6e-143)
		tmp = Float64(Float64(Float64(c * Float64(t * j)) - Float64(a * Float64(x * t))) + t_1);
	elseif (y <= 2.5e-44)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = (j * ((t * c) - (y * i))) + t_1;
	t_3 = y * ((((x * z) - ((x * (t * a)) / y)) - (i * j)) + (a * ((b * i) / y)));
	tmp = 0.0;
	if (y <= -1.5e+25)
		tmp = t_3;
	elseif (y <= -3.5e-210)
		tmp = t_2;
	elseif (y <= 4.6e-143)
		tmp = ((c * (t * j)) - (a * (x * t))) + t_1;
	elseif (y <= 2.5e-44)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(N[(N[(x * z), $MachinePrecision] - N[(N[(x * N[(t * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(b * i), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e+25], t$95$3, If[LessEqual[y, -3.5e-210], t$95$2, If[LessEqual[y, 4.6e-143], N[(N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[y, 2.5e-44], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.50000000000000003e25 or 2.50000000000000019e-44 < y

   1. Initial program 69.5%

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

   3. Taylor expanded in c around 0 67.8%

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

   4. Taylor expanded in y around inf 76.0%

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

      1. sub-neg 76.0%

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

      2. neg-mul-1 76.0%

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

      3. +-commutative 76.0%

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

      4. unsub-neg 76.0%

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

      5. +-commutative 76.0%

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

      6. mul-1-neg 76.0%

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

      7. unsub-neg 76.0%

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

      8. *-commutative 76.0%

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

      9. associate-*r* 78.9%

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

      10. *-commutative 78.9%

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

      11. mul-1-neg 78.9%

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

      12. remove-double-neg 78.9%

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

      13. associate-/l* 80.4%

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

   6. Simplified 80.4%

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

   if -1.50000000000000003e25 < y < -3.50000000000000015e-210 or 4.60000000000000023e-143 < y < 2.50000000000000019e-44

   1. Initial program 81.3%

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

   3. Taylor expanded in x around 0 73.9%

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

   if -3.50000000000000015e-210 < y < 4.60000000000000023e-143

   1. Initial program 81.8%

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

   3. Taylor expanded in y around 0 79.7%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+25}:\\ \;\;\;\;y \cdot \left(\left(\left(x \cdot z - \frac{x \cdot \left(t \cdot a\right)}{y}\right) - i \cdot j\right) + a \cdot \frac{b \cdot i}{y}\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-210}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-143}:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-44}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(\left(x \cdot z - \frac{x \cdot \left(t \cdot a\right)}{y}\right) - i \cdot j\right) + a \cdot \frac{b \cdot i}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 55.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{-230}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-156}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+186}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))))
   (if (<= z -4.2e+128)
     t_1
     (if (<= z 1e-230)
       (+ (* x (- (* y z) (* t a))) (* a (* b i)))
       (if (<= z 3.4e-156)
         (* t (- (* c j) (* x a)))
         (if (<= z 1.95e+186)
           (+ (* x (* y z)) (* 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 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -4.2e+128) {
		tmp = t_1;
	} else if (z <= 1e-230) {
		tmp = (x * ((y * z) - (t * a))) + (a * (b * i));
	} else if (z <= 3.4e-156) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 1.95e+186) {
		tmp = (x * (y * z)) + (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 = z * ((x * y) - (b * c))
    if (z <= (-4.2d+128)) then
        tmp = t_1
    else if (z <= 1d-230) then
        tmp = (x * ((y * z) - (t * a))) + (a * (b * i))
    else if (z <= 3.4d-156) then
        tmp = t * ((c * j) - (x * a))
    else if (z <= 1.95d+186) then
        tmp = (x * (y * z)) + (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 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -4.2e+128) {
		tmp = t_1;
	} else if (z <= 1e-230) {
		tmp = (x * ((y * z) - (t * a))) + (a * (b * i));
	} else if (z <= 3.4e-156) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 1.95e+186) {
		tmp = (x * (y * z)) + (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 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -4.2e+128:
		tmp = t_1
	elif z <= 1e-230:
		tmp = (x * ((y * z) - (t * a))) + (a * (b * i))
	elif z <= 3.4e-156:
		tmp = t * ((c * j) - (x * a))
	elif z <= 1.95e+186:
		tmp = (x * (y * z)) + (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(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -4.2e+128)
		tmp = t_1;
	elseif (z <= 1e-230)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(a * Float64(b * i)));
	elseif (z <= 3.4e-156)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (z <= 1.95e+186)
		tmp = Float64(Float64(x * Float64(y * z)) + 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 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -4.2e+128)
		tmp = t_1;
	elseif (z <= 1e-230)
		tmp = (x * ((y * z) - (t * a))) + (a * (b * i));
	elseif (z <= 3.4e-156)
		tmp = t * ((c * j) - (x * a));
	elseif (z <= 1.95e+186)
		tmp = (x * (y * z)) + (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[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+128], t$95$1, If[LessEqual[z, 1e-230], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e-156], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e+186], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.1999999999999999e128 or 1.95000000000000005e186 < z

   1. Initial program 61.3%

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

   3. Taylor expanded in z around inf 70.0%

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

      1. *-commutative 70.0%

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

   5. Simplified 70.0%

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

   if -4.1999999999999999e128 < z < 1.00000000000000005e-230

   1. Initial program 80.6%

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

   3. Taylor expanded in j around 0 66.9%

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

   4. Taylor expanded in c around 0 66.1%

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

      1. cancel-sign-sub-inv 66.1%

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

      2. cancel-sign-sub-inv 66.1%

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

      3. *-commutative 66.1%

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

      4. associate-*r* 66.1%

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

      5. neg-mul-1 66.1%

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

      6. *-commutative 66.1%

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

   6. Simplified 66.1%

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

   if 1.00000000000000005e-230 < z < 3.3999999999999999e-156

   1. Initial program 74.6%

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

   3. Taylor expanded in t around inf 69.9%

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

      1. +-commutative 69.9%

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

      2. mul-1-neg 69.9%

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

      3. unsub-neg 69.9%

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

      4. *-commutative 69.9%

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

   5. Simplified 69.9%

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

   if 3.3999999999999999e-156 < z < 1.95000000000000005e186

   1. Initial program 79.9%

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

   3. Taylor expanded in j around 0 69.7%

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

   4. Taylor expanded in y around inf 69.1%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+128}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 10^{-230}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-156}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+186}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 29.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{if}\;i \leq -1.18 \cdot 10^{+155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -2.85 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq -8.2 \cdot 10^{-273}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{-171}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{-78}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* i (- j)))))
   (if (<= i -1.18e+155)
     t_1
     (if (<= i -2.85e-109)
       (* x (* t (- a)))
       (if (<= i -8.2e-273)
         (* z (* x y))
         (if (<= i 2.3e-171)
           (* (* z b) (- c))
           (if (<= i 1.8e-78) (* a (* t (- x))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (i * -j);
	double tmp;
	if (i <= -1.18e+155) {
		tmp = t_1;
	} else if (i <= -2.85e-109) {
		tmp = x * (t * -a);
	} else if (i <= -8.2e-273) {
		tmp = z * (x * y);
	} else if (i <= 2.3e-171) {
		tmp = (z * b) * -c;
	} else if (i <= 1.8e-78) {
		tmp = a * (t * -x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (i * -j)
    if (i <= (-1.18d+155)) then
        tmp = t_1
    else if (i <= (-2.85d-109)) then
        tmp = x * (t * -a)
    else if (i <= (-8.2d-273)) then
        tmp = z * (x * y)
    else if (i <= 2.3d-171) then
        tmp = (z * b) * -c
    else if (i <= 1.8d-78) then
        tmp = a * (t * -x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (i * -j);
	double tmp;
	if (i <= -1.18e+155) {
		tmp = t_1;
	} else if (i <= -2.85e-109) {
		tmp = x * (t * -a);
	} else if (i <= -8.2e-273) {
		tmp = z * (x * y);
	} else if (i <= 2.3e-171) {
		tmp = (z * b) * -c;
	} else if (i <= 1.8e-78) {
		tmp = a * (t * -x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (i * -j)
	tmp = 0
	if i <= -1.18e+155:
		tmp = t_1
	elif i <= -2.85e-109:
		tmp = x * (t * -a)
	elif i <= -8.2e-273:
		tmp = z * (x * y)
	elif i <= 2.3e-171:
		tmp = (z * b) * -c
	elif i <= 1.8e-78:
		tmp = a * (t * -x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(i * Float64(-j)))
	tmp = 0.0
	if (i <= -1.18e+155)
		tmp = t_1;
	elseif (i <= -2.85e-109)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (i <= -8.2e-273)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 2.3e-171)
		tmp = Float64(Float64(z * b) * Float64(-c));
	elseif (i <= 1.8e-78)
		tmp = Float64(a * Float64(t * Float64(-x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (i * -j);
	tmp = 0.0;
	if (i <= -1.18e+155)
		tmp = t_1;
	elseif (i <= -2.85e-109)
		tmp = x * (t * -a);
	elseif (i <= -8.2e-273)
		tmp = z * (x * y);
	elseif (i <= 2.3e-171)
		tmp = (z * b) * -c;
	elseif (i <= 1.8e-78)
		tmp = a * (t * -x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.18e+155], t$95$1, If[LessEqual[i, -2.85e-109], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -8.2e-273], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.3e-171], N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision], If[LessEqual[i, 1.8e-78], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -1.18e155 or 1.8000000000000001e-78 < i

   1. Initial program 69.0%

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

   3. Taylor expanded in c around 0 62.1%

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

   4. Taylor expanded in a around 0 47.6%

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

      1. +-commutative 47.6%

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

      2. mul-1-neg 47.6%

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

      3. unsub-neg 47.6%

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

      4. associate-*r* 48.2%

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

   6. Simplified 48.2%

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

   7. Taylor expanded in x around 0 40.5%

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

      1. neg-mul-1 40.5%

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

      2. associate-*r* 41.1%

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

      3. *-commutative 41.1%

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

      4. distribute-lft-neg-out 41.1%

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

      5. *-commutative 41.1%

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

      6. distribute-rgt-neg-in 41.1%

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

   9. Simplified 41.1%

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

   if -1.18e155 < i < -2.84999999999999989e-109

   1. Initial program 82.7%

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

   3. Taylor expanded in c around 0 69.0%

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

   4. Taylor expanded in i around 0 61.6%

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

   5. Taylor expanded in y around 0 45.7%

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

      1. mul-1-neg 45.7%

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

      2. distribute-lft-neg-out 45.7%

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

      3. *-commutative 45.7%

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

   7. Simplified 45.7%

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

   if -2.84999999999999989e-109 < i < -8.2000000000000008e-273

   1. Initial program 81.9%

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

   3. Taylor expanded in b around inf 72.1%

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

   4. Taylor expanded in y around inf 31.4%

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

      1. associate-*r* 34.1%

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

      2. *-commutative 34.1%

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

      3. +-commutative 34.1%

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

      4. mul-1-neg 34.1%

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

      5. unsub-neg 34.1%

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

      6. associate-/l* 31.0%

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

      7. associate-/l* 31.0%

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

   6. Simplified 31.0%

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

   7. Taylor expanded in x around inf 34.8%

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

      1. *-commutative 34.8%

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

      2. *-commutative 34.8%

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

      3. associate-*r* 45.0%

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

   9. Simplified 45.0%

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

   if -8.2000000000000008e-273 < i < 2.29999999999999978e-171

   1. Initial program 75.0%

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

   3. Taylor expanded in c around inf 58.9%

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

      1. *-commutative 58.9%

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

      2. *-commutative 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in t around 0 49.2%

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

      1. mul-1-neg 49.2%

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

      2. *-commutative 49.2%

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

      3. distribute-rgt-neg-in 49.2%

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

   8. Simplified 49.2%

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

   if 2.29999999999999978e-171 < i < 1.8000000000000001e-78

   1. Initial program 77.8%

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

   3. Taylor expanded in a around inf 56.5%

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

      1. distribute-lft-out-- 56.5%

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

      2. *-commutative 56.5%

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

      3. *-commutative 56.5%

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

   5. Simplified 56.5%

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

   6. Taylor expanded in x around inf 51.9%

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

      1. associate-*r* 51.9%

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

      2. neg-mul-1 51.9%

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

   8. Simplified 51.9%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.18 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -2.85 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq -8.2 \cdot 10^{-273}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{-171}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{-78}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 28.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot \left(-a\right)\right)\\ t_2 := y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{if}\;i \leq -2 \cdot 10^{+155}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -4.5 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -1.8 \cdot 10^{-276}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-171}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* t (- a)))) (t_2 (* y (* i (- j)))))
   (if (<= i -2e+155)
     t_2
     (if (<= i -4.5e-106)
       t_1
       (if (<= i -1.8e-276)
         (* z (* x y))
         (if (<= i 2e-171) (* (* z b) (- c)) (if (<= i 3.7e-82) 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 * (t * -a);
	double t_2 = y * (i * -j);
	double tmp;
	if (i <= -2e+155) {
		tmp = t_2;
	} else if (i <= -4.5e-106) {
		tmp = t_1;
	} else if (i <= -1.8e-276) {
		tmp = z * (x * y);
	} else if (i <= 2e-171) {
		tmp = (z * b) * -c;
	} else if (i <= 3.7e-82) {
		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 * (t * -a)
    t_2 = y * (i * -j)
    if (i <= (-2d+155)) then
        tmp = t_2
    else if (i <= (-4.5d-106)) then
        tmp = t_1
    else if (i <= (-1.8d-276)) then
        tmp = z * (x * y)
    else if (i <= 2d-171) then
        tmp = (z * b) * -c
    else if (i <= 3.7d-82) 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 * (t * -a);
	double t_2 = y * (i * -j);
	double tmp;
	if (i <= -2e+155) {
		tmp = t_2;
	} else if (i <= -4.5e-106) {
		tmp = t_1;
	} else if (i <= -1.8e-276) {
		tmp = z * (x * y);
	} else if (i <= 2e-171) {
		tmp = (z * b) * -c;
	} else if (i <= 3.7e-82) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (t * -a)
	t_2 = y * (i * -j)
	tmp = 0
	if i <= -2e+155:
		tmp = t_2
	elif i <= -4.5e-106:
		tmp = t_1
	elif i <= -1.8e-276:
		tmp = z * (x * y)
	elif i <= 2e-171:
		tmp = (z * b) * -c
	elif i <= 3.7e-82:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(t * Float64(-a)))
	t_2 = Float64(y * Float64(i * Float64(-j)))
	tmp = 0.0
	if (i <= -2e+155)
		tmp = t_2;
	elseif (i <= -4.5e-106)
		tmp = t_1;
	elseif (i <= -1.8e-276)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 2e-171)
		tmp = Float64(Float64(z * b) * Float64(-c));
	elseif (i <= 3.7e-82)
		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 * (t * -a);
	t_2 = y * (i * -j);
	tmp = 0.0;
	if (i <= -2e+155)
		tmp = t_2;
	elseif (i <= -4.5e-106)
		tmp = t_1;
	elseif (i <= -1.8e-276)
		tmp = z * (x * y);
	elseif (i <= 2e-171)
		tmp = (z * b) * -c;
	elseif (i <= 3.7e-82)
		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[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2e+155], t$95$2, If[LessEqual[i, -4.5e-106], t$95$1, If[LessEqual[i, -1.8e-276], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2e-171], N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision], If[LessEqual[i, 3.7e-82], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -2.00000000000000001e155 or 3.7000000000000001e-82 < i

   1. Initial program 69.0%

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

   3. Taylor expanded in c around 0 62.1%

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

   4. Taylor expanded in a around 0 47.6%

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

      1. +-commutative 47.6%

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

      2. mul-1-neg 47.6%

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

      3. unsub-neg 47.6%

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

      4. associate-*r* 48.2%

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

   6. Simplified 48.2%

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

   7. Taylor expanded in x around 0 40.5%

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

      1. neg-mul-1 40.5%

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

      2. associate-*r* 41.1%

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

      3. *-commutative 41.1%

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

      4. distribute-lft-neg-out 41.1%

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

      5. *-commutative 41.1%

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

      6. distribute-rgt-neg-in 41.1%

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

   9. Simplified 41.1%

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

   if -2.00000000000000001e155 < i < -4.49999999999999955e-106 or 2e-171 < i < 3.7000000000000001e-82

   1. Initial program 81.3%

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

   3. Taylor expanded in c around 0 67.7%

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

   4. Taylor expanded in i around 0 62.5%

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

   5. Taylor expanded in y around 0 46.3%

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

      1. mul-1-neg 46.3%

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

      2. distribute-lft-neg-out 46.3%

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

      3. *-commutative 46.3%

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

   7. Simplified 46.3%

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

   if -4.49999999999999955e-106 < i < -1.79999999999999997e-276

   1. Initial program 81.9%

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

   3. Taylor expanded in b around inf 72.1%

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

   4. Taylor expanded in y around inf 31.4%

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

      1. associate-*r* 34.1%

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

      2. *-commutative 34.1%

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

      3. +-commutative 34.1%

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

      4. mul-1-neg 34.1%

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

      5. unsub-neg 34.1%

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

      6. associate-/l* 31.0%

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

      7. associate-/l* 31.0%

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

   6. Simplified 31.0%

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

   7. Taylor expanded in x around inf 34.8%

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

      1. *-commutative 34.8%

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

      2. *-commutative 34.8%

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

      3. associate-*r* 45.0%

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

   9. Simplified 45.0%

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

   if -1.79999999999999997e-276 < i < 2e-171

   1. Initial program 75.0%

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

   3. Taylor expanded in c around inf 58.9%

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

      1. *-commutative 58.9%

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

      2. *-commutative 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in t around 0 49.2%

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

      1. mul-1-neg 49.2%

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

      2. *-commutative 49.2%

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

      3. distribute-rgt-neg-in 49.2%

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

   8. Simplified 49.2%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -4.5 \cdot 10^{-106}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq -1.8 \cdot 10^{-276}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-171}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 28.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot \left(-a\right)\right)\\ t_2 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;i \leq -1.5 \cdot 10^{+155}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -6.2 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -3 \cdot 10^{-263}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 3.35 \cdot 10^{-171}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;i \leq 2.15 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* t (- a)))) (t_2 (* i (* y (- j)))))
   (if (<= i -1.5e+155)
     t_2
     (if (<= i -6.2e-106)
       t_1
       (if (<= i -3e-263)
         (* z (* x y))
         (if (<= i 3.35e-171)
           (* (* z b) (- c))
           (if (<= i 2.15e-79) 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 * (t * -a);
	double t_2 = i * (y * -j);
	double tmp;
	if (i <= -1.5e+155) {
		tmp = t_2;
	} else if (i <= -6.2e-106) {
		tmp = t_1;
	} else if (i <= -3e-263) {
		tmp = z * (x * y);
	} else if (i <= 3.35e-171) {
		tmp = (z * b) * -c;
	} else if (i <= 2.15e-79) {
		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 * (t * -a)
    t_2 = i * (y * -j)
    if (i <= (-1.5d+155)) then
        tmp = t_2
    else if (i <= (-6.2d-106)) then
        tmp = t_1
    else if (i <= (-3d-263)) then
        tmp = z * (x * y)
    else if (i <= 3.35d-171) then
        tmp = (z * b) * -c
    else if (i <= 2.15d-79) 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 * (t * -a);
	double t_2 = i * (y * -j);
	double tmp;
	if (i <= -1.5e+155) {
		tmp = t_2;
	} else if (i <= -6.2e-106) {
		tmp = t_1;
	} else if (i <= -3e-263) {
		tmp = z * (x * y);
	} else if (i <= 3.35e-171) {
		tmp = (z * b) * -c;
	} else if (i <= 2.15e-79) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (t * -a)
	t_2 = i * (y * -j)
	tmp = 0
	if i <= -1.5e+155:
		tmp = t_2
	elif i <= -6.2e-106:
		tmp = t_1
	elif i <= -3e-263:
		tmp = z * (x * y)
	elif i <= 3.35e-171:
		tmp = (z * b) * -c
	elif i <= 2.15e-79:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(t * Float64(-a)))
	t_2 = Float64(i * Float64(y * Float64(-j)))
	tmp = 0.0
	if (i <= -1.5e+155)
		tmp = t_2;
	elseif (i <= -6.2e-106)
		tmp = t_1;
	elseif (i <= -3e-263)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 3.35e-171)
		tmp = Float64(Float64(z * b) * Float64(-c));
	elseif (i <= 2.15e-79)
		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 * (t * -a);
	t_2 = i * (y * -j);
	tmp = 0.0;
	if (i <= -1.5e+155)
		tmp = t_2;
	elseif (i <= -6.2e-106)
		tmp = t_1;
	elseif (i <= -3e-263)
		tmp = z * (x * y);
	elseif (i <= 3.35e-171)
		tmp = (z * b) * -c;
	elseif (i <= 2.15e-79)
		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[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.5e+155], t$95$2, If[LessEqual[i, -6.2e-106], t$95$1, If[LessEqual[i, -3e-263], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.35e-171], N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision], If[LessEqual[i, 2.15e-79], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.5000000000000001e155 or 2.14999999999999991e-79 < i

   1. Initial program 69.0%

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

   3. Taylor expanded in c around 0 62.1%

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

   4. Taylor expanded in a around 0 47.6%

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

      1. +-commutative 47.6%

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

      2. mul-1-neg 47.6%

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

      3. unsub-neg 47.6%

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

      4. associate-*r* 48.2%

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

   6. Simplified 48.2%

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

   7. Taylor expanded in x around 0 40.5%

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

      1. neg-mul-1 40.5%

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

      2. distribute-rgt-neg-in 40.5%

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

      3. distribute-lft-neg-in 40.5%

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

   9. Simplified 40.5%

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

   if -1.5000000000000001e155 < i < -6.19999999999999971e-106 or 3.34999999999999981e-171 < i < 2.14999999999999991e-79

   1. Initial program 81.3%

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

   3. Taylor expanded in c around 0 67.7%

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

   4. Taylor expanded in i around 0 62.5%

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

   5. Taylor expanded in y around 0 46.3%

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

      1. mul-1-neg 46.3%

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

      2. distribute-lft-neg-out 46.3%

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

      3. *-commutative 46.3%

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

   7. Simplified 46.3%

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

   if -6.19999999999999971e-106 < i < -3e-263

   1. Initial program 81.9%

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

   3. Taylor expanded in b around inf 72.1%

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

   4. Taylor expanded in y around inf 31.4%

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

      1. associate-*r* 34.1%

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

      2. *-commutative 34.1%

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

      3. +-commutative 34.1%

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

      4. mul-1-neg 34.1%

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

      5. unsub-neg 34.1%

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

      6. associate-/l* 31.0%

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

      7. associate-/l* 31.0%

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

   6. Simplified 31.0%

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

   7. Taylor expanded in x around inf 34.8%

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

      1. *-commutative 34.8%

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

      2. *-commutative 34.8%

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

      3. associate-*r* 45.0%

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

   9. Simplified 45.0%

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

   if -3e-263 < i < 3.34999999999999981e-171

   1. Initial program 75.0%

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

   3. Taylor expanded in c around inf 58.9%

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

      1. *-commutative 58.9%

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

      2. *-commutative 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in t around 0 49.2%

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

      1. mul-1-neg 49.2%

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

      2. *-commutative 49.2%

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

      3. distribute-rgt-neg-in 49.2%

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

   8. Simplified 49.2%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.5 \cdot 10^{+155}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -6.2 \cdot 10^{-106}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq -3 \cdot 10^{-263}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 3.35 \cdot 10^{-171}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;i \leq 2.15 \cdot 10^{-79}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 28.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;i \leq -4 \cdot 10^{+164}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -2.65 \cdot 10^{-80}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq -4.5 \cdot 10^{-273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{-165}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))) (t_2 (* i (* y (- j)))))
   (if (<= i -4e+164)
     t_2
     (if (<= i -2.65e-80)
       (* b (* a i))
       (if (<= i -4.5e-273)
         t_1
         (if (<= i 1.7e-165)
           (* (* z b) (- c))
           (if (<= i 2.3e-27) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double t_2 = i * (y * -j);
	double tmp;
	if (i <= -4e+164) {
		tmp = t_2;
	} else if (i <= -2.65e-80) {
		tmp = b * (a * i);
	} else if (i <= -4.5e-273) {
		tmp = t_1;
	} else if (i <= 1.7e-165) {
		tmp = (z * b) * -c;
	} else if (i <= 2.3e-27) {
		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 * (x * y)
    t_2 = i * (y * -j)
    if (i <= (-4d+164)) then
        tmp = t_2
    else if (i <= (-2.65d-80)) then
        tmp = b * (a * i)
    else if (i <= (-4.5d-273)) then
        tmp = t_1
    else if (i <= 1.7d-165) then
        tmp = (z * b) * -c
    else if (i <= 2.3d-27) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double t_2 = i * (y * -j);
	double tmp;
	if (i <= -4e+164) {
		tmp = t_2;
	} else if (i <= -2.65e-80) {
		tmp = b * (a * i);
	} else if (i <= -4.5e-273) {
		tmp = t_1;
	} else if (i <= 1.7e-165) {
		tmp = (z * b) * -c;
	} else if (i <= 2.3e-27) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = i * (y * -j)
	tmp = 0
	if i <= -4e+164:
		tmp = t_2
	elif i <= -2.65e-80:
		tmp = b * (a * i)
	elif i <= -4.5e-273:
		tmp = t_1
	elif i <= 1.7e-165:
		tmp = (z * b) * -c
	elif i <= 2.3e-27:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(i * Float64(y * Float64(-j)))
	tmp = 0.0
	if (i <= -4e+164)
		tmp = t_2;
	elseif (i <= -2.65e-80)
		tmp = Float64(b * Float64(a * i));
	elseif (i <= -4.5e-273)
		tmp = t_1;
	elseif (i <= 1.7e-165)
		tmp = Float64(Float64(z * b) * Float64(-c));
	elseif (i <= 2.3e-27)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	t_2 = i * (y * -j);
	tmp = 0.0;
	if (i <= -4e+164)
		tmp = t_2;
	elseif (i <= -2.65e-80)
		tmp = b * (a * i);
	elseif (i <= -4.5e-273)
		tmp = t_1;
	elseif (i <= 1.7e-165)
		tmp = (z * b) * -c;
	elseif (i <= 2.3e-27)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4e+164], t$95$2, If[LessEqual[i, -2.65e-80], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -4.5e-273], t$95$1, If[LessEqual[i, 1.7e-165], N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision], If[LessEqual[i, 2.3e-27], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -4e164 or 2.2999999999999999e-27 < i

   1. Initial program 68.2%

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

   3. Taylor expanded in c around 0 64.2%

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

   4. Taylor expanded in a around 0 50.2%

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

      1. +-commutative 50.2%

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

      2. mul-1-neg 50.2%

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

      3. unsub-neg 50.2%

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

      4. associate-*r* 50.8%

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

   6. Simplified 50.8%

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

   7. Taylor expanded in x around 0 43.3%

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

      1. neg-mul-1 43.3%

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

      2. distribute-rgt-neg-in 43.3%

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

      3. distribute-lft-neg-in 43.3%

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

   9. Simplified 43.3%

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

   if -4e164 < i < -2.65000000000000013e-80

   1. Initial program 84.3%

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

   3. Taylor expanded in b around inf 46.8%

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

      1. *-commutative 46.8%

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

   5. Simplified 46.8%

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

   6. Taylor expanded in a around inf 28.2%

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

      1. *-commutative 28.2%

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

   8. Simplified 28.2%

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

   if -2.65000000000000013e-80 < i < -4.4999999999999996e-273 or 1.7e-165 < i < 2.2999999999999999e-27

   1. Initial program 79.7%

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

   3. Taylor expanded in b around inf 71.1%

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

   4. Taylor expanded in y around inf 32.1%

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

      1. associate-*r* 33.2%

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

      2. *-commutative 33.2%

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

      3. +-commutative 33.2%

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

      4. mul-1-neg 33.2%

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

      5. unsub-neg 33.2%

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

      6. associate-/l* 31.7%

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

      7. associate-/l* 31.7%

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

   6. Simplified 31.7%

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

   7. Taylor expanded in x around inf 32.2%

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

      1. *-commutative 32.2%

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

      2. *-commutative 32.2%

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

      3. associate-*r* 38.5%

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

   9. Simplified 38.5%

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

   if -4.4999999999999996e-273 < i < 1.7e-165

   1. Initial program 73.7%

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

   3. Taylor expanded in c around inf 55.8%

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

      1. *-commutative 55.8%

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

      2. *-commutative 55.8%

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

   5. Simplified 55.8%

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

   6. Taylor expanded in t around 0 46.6%

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

      1. mul-1-neg 46.6%

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

      2. *-commutative 46.6%

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

      3. distribute-rgt-neg-in 46.6%

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

   8. Simplified 46.6%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4 \cdot 10^{+164}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -2.65 \cdot 10^{-80}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq -4.5 \cdot 10^{-273}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{-165}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{-27}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -6 \cdot 10^{+155}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -3.1 \cdot 10^{+69}:\\ \;\;\;\;b \cdot \left(a \cdot \left(i - \frac{z \cdot c}{a}\right)\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-23}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(a - j \cdot \frac{y}{b}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -6e+155)
   (* i (- (* a b) (* y j)))
   (if (<= i -3.1e+69)
     (* b (* a (- i (/ (* z c) a))))
     (if (<= i 3.2e-82)
       (* x (- (* y z) (* t a)))
       (if (<= i 2e-23)
         (* z (- (* x y) (* b c)))
         (* (* b i) (- a (* j (/ y b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -6e+155) {
		tmp = i * ((a * b) - (y * j));
	} else if (i <= -3.1e+69) {
		tmp = b * (a * (i - ((z * c) / a)));
	} else if (i <= 3.2e-82) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 2e-23) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = (b * i) * (a - (j * (y / b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-6d+155)) then
        tmp = i * ((a * b) - (y * j))
    else if (i <= (-3.1d+69)) then
        tmp = b * (a * (i - ((z * c) / a)))
    else if (i <= 3.2d-82) then
        tmp = x * ((y * z) - (t * a))
    else if (i <= 2d-23) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = (b * i) * (a - (j * (y / b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -6e+155) {
		tmp = i * ((a * b) - (y * j));
	} else if (i <= -3.1e+69) {
		tmp = b * (a * (i - ((z * c) / a)));
	} else if (i <= 3.2e-82) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 2e-23) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = (b * i) * (a - (j * (y / b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -6e+155:
		tmp = i * ((a * b) - (y * j))
	elif i <= -3.1e+69:
		tmp = b * (a * (i - ((z * c) / a)))
	elif i <= 3.2e-82:
		tmp = x * ((y * z) - (t * a))
	elif i <= 2e-23:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = (b * i) * (a - (j * (y / b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -6e+155)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (i <= -3.1e+69)
		tmp = Float64(b * Float64(a * Float64(i - Float64(Float64(z * c) / a))));
	elseif (i <= 3.2e-82)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (i <= 2e-23)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = Float64(Float64(b * i) * Float64(a - Float64(j * Float64(y / b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -6e+155)
		tmp = i * ((a * b) - (y * j));
	elseif (i <= -3.1e+69)
		tmp = b * (a * (i - ((z * c) / a)));
	elseif (i <= 3.2e-82)
		tmp = x * ((y * z) - (t * a));
	elseif (i <= 2e-23)
		tmp = z * ((x * y) - (b * c));
	else
		tmp = (b * i) * (a - (j * (y / b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -6e+155], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.1e+69], N[(b * N[(a * N[(i - N[(N[(z * c), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.2e-82], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2e-23], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * i), $MachinePrecision] * N[(a - N[(j * N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -6.0000000000000003e155

   1. Initial program 63.3%

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

   3. Taylor expanded in i around inf 63.4%

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

      1. distribute-lft-out-- 63.4%

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

      2. *-commutative 63.4%

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

   5. Simplified 63.4%

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

   if -6.0000000000000003e155 < i < -3.0999999999999998e69

   1. Initial program 83.1%

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

   3. Taylor expanded in b around inf 58.8%

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

      1. *-commutative 58.8%

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

   5. Simplified 58.8%

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

   6. Taylor expanded in a around inf 74.6%

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

      1. associate-*r/ 74.6%

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

      2. neg-mul-1 74.6%

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

      3. distribute-rgt-neg-in 74.6%

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

   8. Simplified 74.6%

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

   if -3.0999999999999998e69 < i < 3.2000000000000001e-82

   1. Initial program 79.6%

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

   3. Taylor expanded in c around 0 59.9%

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

   4. Taylor expanded in i around 0 60.0%

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

   if 3.2000000000000001e-82 < i < 1.99999999999999992e-23

   1. Initial program 75.4%

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

   3. Taylor expanded in z around inf 66.9%

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

      1. *-commutative 66.9%

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

   5. Simplified 66.9%

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

   if 1.99999999999999992e-23 < i

   1. Initial program 70.5%

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

   3. Taylor expanded in b around inf 64.6%

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

   4. Taylor expanded in i around inf 59.7%

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

      1. associate-*r* 62.5%

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

      2. *-commutative 62.5%

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

      3. mul-1-neg 62.5%

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

      4. unsub-neg 62.5%

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

      5. associate-/l* 67.1%

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

   6. Simplified 67.1%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6 \cdot 10^{+155}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -3.1 \cdot 10^{+69}:\\ \;\;\;\;b \cdot \left(a \cdot \left(i - \frac{z \cdot c}{a}\right)\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-23}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(a - j \cdot \frac{y}{b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;b \leq -9.4 \cdot 10^{+52}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* j (- (* t c) (* y i)))))
   (if (<= b -9.4e+52)
     (+ t_2 t_1)
     (if (<= b 1.8e-22)
       (+ (* x (- (* y z) (* t a))) t_2)
       (+ (- (* c (* t j)) (* a (* x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (b <= -9.4e+52) {
		tmp = t_2 + t_1;
	} else if (b <= 1.8e-22) {
		tmp = (x * ((y * z) - (t * a))) + t_2;
	} else {
		tmp = ((c * (t * j)) - (a * (x * t))) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = j * ((t * c) - (y * i))
    if (b <= (-9.4d+52)) then
        tmp = t_2 + t_1
    else if (b <= 1.8d-22) then
        tmp = (x * ((y * z) - (t * a))) + t_2
    else
        tmp = ((c * (t * j)) - (a * (x * t))) + 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 t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (b <= -9.4e+52) {
		tmp = t_2 + t_1;
	} else if (b <= 1.8e-22) {
		tmp = (x * ((y * z) - (t * a))) + t_2;
	} else {
		tmp = ((c * (t * j)) - (a * (x * t))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if b <= -9.4e+52:
		tmp = t_2 + t_1
	elif b <= 1.8e-22:
		tmp = (x * ((y * z) - (t * a))) + t_2
	else:
		tmp = ((c * (t * j)) - (a * (x * t))) + 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)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (b <= -9.4e+52)
		tmp = Float64(t_2 + t_1);
	elseif (b <= 1.8e-22)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_2);
	else
		tmp = Float64(Float64(Float64(c * Float64(t * j)) - Float64(a * Float64(x * t))) + 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));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (b <= -9.4e+52)
		tmp = t_2 + t_1;
	elseif (b <= 1.8e-22)
		tmp = (x * ((y * z) - (t * a))) + t_2;
	else
		tmp = ((c * (t * j)) - (a * (x * t))) + 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]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.4e+52], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[b, 1.8e-22], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], N[(N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.3999999999999999e52

   1. Initial program 76.4%

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

   3. Taylor expanded in x around 0 80.9%

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

   if -9.3999999999999999e52 < b < 1.7999999999999999e-22

   1. Initial program 75.7%

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

   3. Taylor expanded in b around 0 75.5%

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

   if 1.7999999999999999e-22 < b

   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. Add Preprocessing

   3. Taylor expanded in y around 0 68.7%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.4 \cdot 10^{+52}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -9.5 \cdot 10^{-38}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(c \cdot \frac{t}{i} - y\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{-164}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.9 \cdot 10^{+174}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(\frac{t \cdot c}{i} - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -9.5e-38)
   (* (* i j) (- (* c (/ t i)) y))
   (if (<= j 5e-164)
     (- (* x (- (* y z) (* t a))) (* b (* z c)))
     (if (<= j 2.9e+174)
       (+ (* x (* y z)) (* b (- (* a i) (* z c))))
       (* i (* j (- (/ (* t c) i) y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -9.5e-38) {
		tmp = (i * j) * ((c * (t / i)) - y);
	} else if (j <= 5e-164) {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	} else if (j <= 2.9e+174) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else {
		tmp = i * (j * (((t * c) / i) - y));
	}
	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 <= (-9.5d-38)) then
        tmp = (i * j) * ((c * (t / i)) - y)
    else if (j <= 5d-164) then
        tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
    else if (j <= 2.9d+174) then
        tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
    else
        tmp = i * (j * (((t * c) / i) - y))
    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 <= -9.5e-38) {
		tmp = (i * j) * ((c * (t / i)) - y);
	} else if (j <= 5e-164) {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	} else if (j <= 2.9e+174) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else {
		tmp = i * (j * (((t * c) / i) - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -9.5e-38:
		tmp = (i * j) * ((c * (t / i)) - y)
	elif j <= 5e-164:
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
	elif j <= 2.9e+174:
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
	else:
		tmp = i * (j * (((t * c) / i) - y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -9.5e-38)
		tmp = Float64(Float64(i * j) * Float64(Float64(c * Float64(t / i)) - y));
	elseif (j <= 5e-164)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(z * c)));
	elseif (j <= 2.9e+174)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(i * Float64(j * Float64(Float64(Float64(t * c) / i) - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -9.5e-38)
		tmp = (i * j) * ((c * (t / i)) - y);
	elseif (j <= 5e-164)
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	elseif (j <= 2.9e+174)
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	else
		tmp = i * (j * (((t * c) / i) - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -9.5e-38], N[(N[(i * j), $MachinePrecision] * N[(N[(c * N[(t / i), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5e-164], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.9e+174], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(j * N[(N[(N[(t * c), $MachinePrecision] / i), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -9.5000000000000009e-38

   1. Initial program 70.2%

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

      1. +-commutative 70.2%

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

      2. fma-define 70.2%

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

      3. *-commutative 70.2%

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

      4. *-commutative 70.2%

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

      5. cancel-sign-sub-inv 70.2%

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

      6. cancel-sign-sub 70.2%

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

      7. sub-neg 70.2%

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

      8. sub-neg 70.2%

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

      9. *-commutative 70.2%

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

      10. fmm-def 70.2%

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

      11. *-commutative 70.2%

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

      12. distribute-rgt-neg-out 70.2%

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

      13. remove-double-neg 70.2%

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

      14. *-commutative 70.2%

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

      15. *-commutative 70.2%

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

   3. Simplified 70.2%

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

   5. Taylor expanded in i around inf 69.0%

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

      1. *-commutative 69.0%

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

   7. Simplified 69.0%

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

   8. Taylor expanded in j around inf 61.8%

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

      1. associate-*r* 59.3%

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

      2. associate-/l* 61.9%

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

   10. Simplified 61.9%

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

   if -9.5000000000000009e-38 < j < 4.99999999999999962e-164

   1. Initial program 77.3%

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

   3. Taylor expanded in j around 0 74.5%

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

   4. Taylor expanded in i around 0 69.4%

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

      1. cancel-sign-sub-inv 69.4%

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

      2. cancel-sign-sub-inv 69.4%

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

      3. *-commutative 69.4%

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

   6. Simplified 69.4%

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

   if 4.99999999999999962e-164 < j < 2.9e174

   1. Initial program 75.6%

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

   3. Taylor expanded in j around 0 67.7%

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

   4. Taylor expanded in y around inf 62.2%

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

   if 2.9e174 < j

   1. Initial program 84.8%

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

      1. +-commutative 84.8%

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

      2. fma-define 89.8%

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

      3. *-commutative 89.8%

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

      4. *-commutative 89.8%

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

      5. cancel-sign-sub-inv 89.8%

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

      6. cancel-sign-sub 89.8%

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

      7. sub-neg 89.8%

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

      8. sub-neg 89.8%

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

      9. *-commutative 89.8%

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

      10. fmm-def 89.8%

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

      11. *-commutative 89.8%

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

      12. distribute-rgt-neg-out 89.8%

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

      13. remove-double-neg 89.8%

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

      14. *-commutative 89.8%

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

      15. *-commutative 89.8%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in i around inf 89.8%

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

      1. *-commutative 89.8%

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

   7. Simplified 89.8%

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

   8. Taylor expanded in j around inf 85.6%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.5 \cdot 10^{-38}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(c \cdot \frac{t}{i} - y\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{-164}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.9 \cdot 10^{+174}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(\frac{t \cdot c}{i} - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.4 \cdot 10^{-37}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(c \cdot \frac{t}{i} - y\right)\\ \mathbf{elif}\;j \leq -3.05 \cdot 10^{-266}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{+186}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(\frac{t \cdot c}{i} - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.4e-37)
   (* (* i j) (- (* c (/ t i)) y))
   (if (<= j -3.05e-266)
     (* x (- (* y z) (* t a)))
     (if (<= j 7.5e+186)
       (+ (* x (* y z)) (* b (- (* a i) (* z c))))
       (* i (* j (- (/ (* t c) i) y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.4e-37) {
		tmp = (i * j) * ((c * (t / i)) - y);
	} else if (j <= -3.05e-266) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 7.5e+186) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else {
		tmp = i * (j * (((t * c) / i) - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-1.4d-37)) then
        tmp = (i * j) * ((c * (t / i)) - y)
    else if (j <= (-3.05d-266)) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= 7.5d+186) then
        tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
    else
        tmp = i * (j * (((t * c) / i) - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.4e-37) {
		tmp = (i * j) * ((c * (t / i)) - y);
	} else if (j <= -3.05e-266) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 7.5e+186) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else {
		tmp = i * (j * (((t * c) / i) - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -1.4e-37:
		tmp = (i * j) * ((c * (t / i)) - y)
	elif j <= -3.05e-266:
		tmp = x * ((y * z) - (t * a))
	elif j <= 7.5e+186:
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
	else:
		tmp = i * (j * (((t * c) / i) - y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.4e-37)
		tmp = Float64(Float64(i * j) * Float64(Float64(c * Float64(t / i)) - y));
	elseif (j <= -3.05e-266)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= 7.5e+186)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(i * Float64(j * Float64(Float64(Float64(t * c) / i) - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -1.4e-37)
		tmp = (i * j) * ((c * (t / i)) - y);
	elseif (j <= -3.05e-266)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= 7.5e+186)
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	else
		tmp = i * (j * (((t * c) / i) - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1.4e-37], N[(N[(i * j), $MachinePrecision] * N[(N[(c * N[(t / i), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.05e-266], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.5e+186], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(j * N[(N[(N[(t * c), $MachinePrecision] / i), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.4000000000000001e-37

   1. Initial program 70.2%

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

      1. +-commutative 70.2%

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

      2. fma-define 70.2%

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

      3. *-commutative 70.2%

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

      4. *-commutative 70.2%

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

      5. cancel-sign-sub-inv 70.2%

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

      6. cancel-sign-sub 70.2%

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

      7. sub-neg 70.2%

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

      8. sub-neg 70.2%

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

      9. *-commutative 70.2%

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

      10. fmm-def 70.2%

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

      11. *-commutative 70.2%

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

      12. distribute-rgt-neg-out 70.2%

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

      13. remove-double-neg 70.2%

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

      14. *-commutative 70.2%

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

      15. *-commutative 70.2%

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

   3. Simplified 70.2%

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

   5. Taylor expanded in i around inf 69.0%

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

      1. *-commutative 69.0%

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

   7. Simplified 69.0%

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

   8. Taylor expanded in j around inf 61.8%

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

      1. associate-*r* 59.3%

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

      2. associate-/l* 61.9%

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

   10. Simplified 61.9%

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

   if -1.4000000000000001e-37 < j < -3.05e-266

   1. Initial program 82.5%

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

   3. Taylor expanded in c around 0 74.8%

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

   4. Taylor expanded in i around 0 65.0%

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

   if -3.05e-266 < j < 7.4999999999999998e186

   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. Add Preprocessing

   3. Taylor expanded in j around 0 68.6%

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

   4. Taylor expanded in y around inf 61.0%

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

   if 7.4999999999999998e186 < j

   1. Initial program 84.8%

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

      1. +-commutative 84.8%

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

      2. fma-define 89.8%

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

      3. *-commutative 89.8%

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

      4. *-commutative 89.8%

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

      5. cancel-sign-sub-inv 89.8%

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

      6. cancel-sign-sub 89.8%

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

      7. sub-neg 89.8%

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

      8. sub-neg 89.8%

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

      9. *-commutative 89.8%

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

      10. fmm-def 89.8%

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

      11. *-commutative 89.8%

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

      12. distribute-rgt-neg-out 89.8%

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

      13. remove-double-neg 89.8%

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

      14. *-commutative 89.8%

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

      15. *-commutative 89.8%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in i around inf 89.8%

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

      1. *-commutative 89.8%

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

   7. Simplified 89.8%

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

   8. Taylor expanded in j around inf 85.6%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.4 \cdot 10^{-37}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(c \cdot \frac{t}{i} - y\right)\\ \mathbf{elif}\;j \leq -3.05 \cdot 10^{-266}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{+186}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(\frac{t \cdot c}{i} - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4.3 \cdot 10^{+117}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-302}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-122}:\\ \;\;\;\;i \cdot \left(j \cdot \left(\frac{t \cdot c}{i} - y\right)\right)\\ \mathbf{elif}\;b \leq 2.85 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -4.3e+117)
     t_2
     (if (<= b -3.2e-302)
       t_1
       (if (<= b 4.8e-122)
         (* i (* j (- (/ (* t c) i) y)))
         (if (<= b 2.85e+60) 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));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -4.3e+117) {
		tmp = t_2;
	} else if (b <= -3.2e-302) {
		tmp = t_1;
	} else if (b <= 4.8e-122) {
		tmp = i * (j * (((t * c) / i) - y));
	} else if (b <= 2.85e+60) {
		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))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-4.3d+117)) then
        tmp = t_2
    else if (b <= (-3.2d-302)) then
        tmp = t_1
    else if (b <= 4.8d-122) then
        tmp = i * (j * (((t * c) / i) - y))
    else if (b <= 2.85d+60) 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));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -4.3e+117) {
		tmp = t_2;
	} else if (b <= -3.2e-302) {
		tmp = t_1;
	} else if (b <= 4.8e-122) {
		tmp = i * (j * (((t * c) / i) - y));
	} else if (b <= 2.85e+60) {
		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))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -4.3e+117:
		tmp = t_2
	elif b <= -3.2e-302:
		tmp = t_1
	elif b <= 4.8e-122:
		tmp = i * (j * (((t * c) / i) - y))
	elif b <= 2.85e+60:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -4.3e+117)
		tmp = t_2;
	elseif (b <= -3.2e-302)
		tmp = t_1;
	elseif (b <= 4.8e-122)
		tmp = Float64(i * Float64(j * Float64(Float64(Float64(t * c) / i) - y)));
	elseif (b <= 2.85e+60)
		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));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -4.3e+117)
		tmp = t_2;
	elseif (b <= -3.2e-302)
		tmp = t_1;
	elseif (b <= 4.8e-122)
		tmp = i * (j * (((t * c) / i) - y));
	elseif (b <= 2.85e+60)
		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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.3e+117], t$95$2, If[LessEqual[b, -3.2e-302], t$95$1, If[LessEqual[b, 4.8e-122], N[(i * N[(j * N[(N[(N[(t * c), $MachinePrecision] / i), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.85e+60], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.29999999999999998e117 or 2.84999999999999989e60 < b

   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. Add Preprocessing

   3. Taylor expanded in b around inf 69.9%

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

      1. *-commutative 69.9%

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

   5. Simplified 69.9%

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

   if -4.29999999999999998e117 < b < -3.19999999999999978e-302 or 4.79999999999999975e-122 < b < 2.84999999999999989e60

   1. Initial program 77.1%

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

   3. Taylor expanded in c around 0 66.2%

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

   4. Taylor expanded in i around 0 60.0%

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

   if -3.19999999999999978e-302 < b < 4.79999999999999975e-122

   1. Initial program 72.6%

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

      1. +-commutative 72.6%

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

      2. fma-define 74.9%

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

      3. *-commutative 74.9%

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

      4. *-commutative 74.9%

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

      5. cancel-sign-sub-inv 74.9%

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

      6. cancel-sign-sub 74.9%

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

      7. sub-neg 74.9%

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

      8. sub-neg 74.9%

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

      9. *-commutative 74.9%

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

      10. fmm-def 74.9%

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

      11. *-commutative 74.9%

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

      12. distribute-rgt-neg-out 74.9%

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

      13. remove-double-neg 74.9%

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

      14. *-commutative 74.9%

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

      15. *-commutative 74.9%

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

   3. Simplified 74.9%

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

   5. Taylor expanded in i around inf 70.3%

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

      1. *-commutative 70.3%

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

   7. Simplified 70.3%

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

   8. Taylor expanded in j around inf 60.5%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.3 \cdot 10^{+117}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-302}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-122}:\\ \;\;\;\;i \cdot \left(j \cdot \left(\frac{t \cdot c}{i} - y\right)\right)\\ \mathbf{elif}\;b \leq 2.85 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 68.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;b \leq -4.5 \cdot 10^{+52}:\\ \;\;\;\;t\_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(a \cdot i - \frac{a \cdot \left(x \cdot t\right)}{b}\right) - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= b -4.5e+52)
     (+ t_1 (* b (- (* a i) (* z c))))
     (if (<= b 1.8e-21)
       (+ (* x (- (* y z) (* t a))) t_1)
       (* b (- (- (* a i) (/ (* a (* x t)) b)) (* z c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (b <= -4.5e+52) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else if (b <= 1.8e-21) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else {
		tmp = b * (((a * i) - ((a * (x * t)) / b)) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if (b <= (-4.5d+52)) then
        tmp = t_1 + (b * ((a * i) - (z * c)))
    else if (b <= 1.8d-21) then
        tmp = (x * ((y * z) - (t * a))) + t_1
    else
        tmp = b * (((a * i) - ((a * (x * t)) / b)) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (b <= -4.5e+52) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else if (b <= 1.8e-21) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else {
		tmp = b * (((a * i) - ((a * (x * t)) / b)) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if b <= -4.5e+52:
		tmp = t_1 + (b * ((a * i) - (z * c)))
	elif b <= 1.8e-21:
		tmp = (x * ((y * z) - (t * a))) + t_1
	else:
		tmp = b * (((a * i) - ((a * (x * t)) / b)) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (b <= -4.5e+52)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (b <= 1.8e-21)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	else
		tmp = Float64(b * Float64(Float64(Float64(a * i) - Float64(Float64(a * Float64(x * t)) / b)) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (b <= -4.5e+52)
		tmp = t_1 + (b * ((a * i) - (z * c)));
	elseif (b <= 1.8e-21)
		tmp = (x * ((y * z) - (t * a))) + t_1;
	else
		tmp = b * (((a * i) - ((a * (x * t)) / b)) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.5e+52], N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.8e-21], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(b * N[(N[(N[(a * i), $MachinePrecision] - N[(N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.5e52

   1. Initial program 76.4%

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

   3. Taylor expanded in x around 0 80.9%

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

   if -4.5e52 < b < 1.79999999999999995e-21

   1. Initial program 75.7%

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

   3. Taylor expanded in b around 0 75.5%

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

   if 1.79999999999999995e-21 < b

   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. Add Preprocessing

   3. Taylor expanded in b around inf 76.7%

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

   4. Taylor expanded in a around inf 67.2%

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

      1. associate-*r/ 67.2%

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

      2. associate-*r* 67.2%

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

      3. neg-mul-1 67.2%

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

   6. Simplified 67.2%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+52}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(a \cdot i - \frac{a \cdot \left(x \cdot t\right)}{b}\right) - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 67.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 10^{-21}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(a \cdot i - \frac{a \cdot \left(x \cdot t\right)}{b}\right) - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -1.1e+36)
   (+ (* x (* y z)) (* b (- (* a i) (* z c))))
   (if (<= b 1e-21)
     (+ (* x (- (* y z) (* t a))) (* j (- (* t c) (* y i))))
     (* b (- (- (* a i) (/ (* a (* x t)) b)) (* z c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -1.1e+36) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else if (b <= 1e-21) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	} else {
		tmp = b * (((a * i) - ((a * (x * t)) / b)) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-1.1d+36)) then
        tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
    else if (b <= 1d-21) then
        tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
    else
        tmp = b * (((a * i) - ((a * (x * t)) / b)) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -1.1e+36) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else if (b <= 1e-21) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	} else {
		tmp = b * (((a * i) - ((a * (x * t)) / b)) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -1.1e+36:
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
	elif b <= 1e-21:
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
	else:
		tmp = b * (((a * i) - ((a * (x * t)) / b)) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -1.1e+36)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (b <= 1e-21)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))));
	else
		tmp = Float64(b * Float64(Float64(Float64(a * i) - Float64(Float64(a * Float64(x * t)) / b)) - Float64(z * c)));
	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+36)
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	elseif (b <= 1e-21)
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	else
		tmp = b * (((a * i) - ((a * (x * t)) / b)) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -1.1e+36], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e-21], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(N[(a * i), $MachinePrecision] - N[(N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.1e36

   1. Initial program 76.3%

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

   3. Taylor expanded in j around 0 70.4%

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

   4. Taylor expanded in y around inf 78.5%

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

   if -1.1e36 < b < 9.99999999999999908e-22

   1. Initial program 75.7%

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

   3. Taylor expanded in b around 0 75.5%

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

   if 9.99999999999999908e-22 < b

   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. Add Preprocessing

   3. Taylor expanded in b around inf 76.7%

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

   4. Taylor expanded in a around inf 67.2%

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

      1. associate-*r/ 67.2%

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

      2. associate-*r* 67.2%

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

      3. neg-mul-1 67.2%

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

   6. Simplified 67.2%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 10^{-21}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(a \cdot i - \frac{a \cdot \left(x \cdot t\right)}{b}\right) - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 57.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.8 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(a \cdot i - \frac{a \cdot \left(x \cdot t\right)}{b}\right) - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -8.8e+39)
   (+ (* x (* y z)) (* b (- (* a i) (* z c))))
   (if (<= b 3.7e-22)
     (+ (* x (- (* y z) (* t a))) (* a (* b i)))
     (* b (- (- (* a i) (/ (* a (* x t)) b)) (* z c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -8.8e+39) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else if (b <= 3.7e-22) {
		tmp = (x * ((y * z) - (t * a))) + (a * (b * i));
	} else {
		tmp = b * (((a * i) - ((a * (x * t)) / b)) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-8.8d+39)) then
        tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
    else if (b <= 3.7d-22) then
        tmp = (x * ((y * z) - (t * a))) + (a * (b * i))
    else
        tmp = b * (((a * i) - ((a * (x * t)) / b)) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -8.8e+39) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else if (b <= 3.7e-22) {
		tmp = (x * ((y * z) - (t * a))) + (a * (b * i));
	} else {
		tmp = b * (((a * i) - ((a * (x * t)) / b)) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -8.8e+39:
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
	elif b <= 3.7e-22:
		tmp = (x * ((y * z) - (t * a))) + (a * (b * i))
	else:
		tmp = b * (((a * i) - ((a * (x * t)) / b)) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -8.8e+39)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (b <= 3.7e-22)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(a * Float64(b * i)));
	else
		tmp = Float64(b * Float64(Float64(Float64(a * i) - Float64(Float64(a * Float64(x * t)) / b)) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -8.8e+39)
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	elseif (b <= 3.7e-22)
		tmp = (x * ((y * z) - (t * a))) + (a * (b * i));
	else
		tmp = b * (((a * i) - ((a * (x * t)) / b)) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -8.8e+39], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.7e-22], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(N[(a * i), $MachinePrecision] - N[(N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.8000000000000006e39

   1. Initial program 76.3%

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

   3. Taylor expanded in j around 0 70.4%

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

   4. Taylor expanded in y around inf 78.5%

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

   if -8.8000000000000006e39 < b < 3.7e-22

   1. Initial program 75.7%

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

   3. Taylor expanded in j around 0 57.3%

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

   4. Taylor expanded in c around 0 59.9%

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

      1. cancel-sign-sub-inv 59.9%

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

      2. cancel-sign-sub-inv 59.9%

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

      3. *-commutative 59.9%

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

      4. associate-*r* 59.9%

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

      5. neg-mul-1 59.9%

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

      6. *-commutative 59.9%

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

   6. Simplified 59.9%

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

   if 3.7e-22 < b

   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. Add Preprocessing

   3. Taylor expanded in b around inf 76.7%

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

   4. Taylor expanded in a around inf 67.2%

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

      1. associate-*r/ 67.2%

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

      2. associate-*r* 67.2%

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

      3. neg-mul-1 67.2%

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

   6. Simplified 67.2%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.8 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(a \cdot i - \frac{a \cdot \left(x \cdot t\right)}{b}\right) - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -15.2:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{-301}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+95}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -15.2)
     t_1
     (if (<= b -5.6e-301)
       (* t (- (* c j) (* x a)))
       (if (<= b 9.2e+95) (* j (- (* t c) (* y i))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -15.2) {
		tmp = t_1;
	} else if (b <= -5.6e-301) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 9.2e+95) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-15.2d0)) then
        tmp = t_1
    else if (b <= (-5.6d-301)) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= 9.2d+95) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -15.2) {
		tmp = t_1;
	} else if (b <= -5.6e-301) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 9.2e+95) {
		tmp = j * ((t * c) - (y * i));
	} 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 <= -15.2:
		tmp = t_1
	elif b <= -5.6e-301:
		tmp = t * ((c * j) - (x * a))
	elif b <= 9.2e+95:
		tmp = j * ((t * c) - (y * i))
	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 <= -15.2)
		tmp = t_1;
	elseif (b <= -5.6e-301)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= 9.2e+95)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -15.2)
		tmp = t_1;
	elseif (b <= -5.6e-301)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= 9.2e+95)
		tmp = j * ((t * c) - (y * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -15.2], t$95$1, If[LessEqual[b, -5.6e-301], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.2e+95], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -15.199999999999999 or 9.19999999999999989e95 < b

   1. Initial program 75.5%

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

   3. Taylor expanded in b around inf 65.2%

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

      1. *-commutative 65.2%

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

   5. Simplified 65.2%

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

   if -15.199999999999999 < b < -5.6000000000000002e-301

   1. Initial program 80.6%

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

   3. Taylor expanded in t around inf 47.8%

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

      1. +-commutative 47.8%

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

      2. mul-1-neg 47.8%

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

      3. unsub-neg 47.8%

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

      4. *-commutative 47.8%

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

   5. Simplified 47.8%

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

   if -5.6000000000000002e-301 < b < 9.19999999999999989e95

   1. Initial program 70.4%

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

   3. Taylor expanded in j around inf 51.9%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -15.2:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{-301}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+95}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 49.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -20:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-102}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+96}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -20.0)
     t_1
     (if (<= b -2.7e-102)
       (* a (* t (- x)))
       (if (<= b 1.75e+96) (* j (- (* t c) (* y i))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -20.0) {
		tmp = t_1;
	} else if (b <= -2.7e-102) {
		tmp = a * (t * -x);
	} else if (b <= 1.75e+96) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-20.0d0)) then
        tmp = t_1
    else if (b <= (-2.7d-102)) then
        tmp = a * (t * -x)
    else if (b <= 1.75d+96) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -20.0) {
		tmp = t_1;
	} else if (b <= -2.7e-102) {
		tmp = a * (t * -x);
	} else if (b <= 1.75e+96) {
		tmp = j * ((t * c) - (y * i));
	} 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 <= -20.0:
		tmp = t_1
	elif b <= -2.7e-102:
		tmp = a * (t * -x)
	elif b <= 1.75e+96:
		tmp = j * ((t * c) - (y * i))
	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 <= -20.0)
		tmp = t_1;
	elseif (b <= -2.7e-102)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (b <= 1.75e+96)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -20.0)
		tmp = t_1;
	elseif (b <= -2.7e-102)
		tmp = a * (t * -x);
	elseif (b <= 1.75e+96)
		tmp = j * ((t * c) - (y * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -20.0], t$95$1, If[LessEqual[b, -2.7e-102], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.75e+96], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -20 or 1.7499999999999999e96 < b

   1. Initial program 75.2%

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

   3. Taylor expanded in b around inf 65.8%

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

      1. *-commutative 65.8%

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

   5. Simplified 65.8%

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

   if -20 < b < -2.7e-102

   1. Initial program 89.2%

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

   3. Taylor expanded in a around inf 57.3%

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

      1. distribute-lft-out-- 57.3%

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

      2. *-commutative 57.3%

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

      3. *-commutative 57.3%

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

   5. Simplified 57.3%

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

   6. Taylor expanded in x around inf 46.1%

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

      1. associate-*r* 46.1%

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

      2. neg-mul-1 46.1%

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

   8. Simplified 46.1%

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

   if -2.7e-102 < b < 1.7499999999999999e96

   1. Initial program 72.4%

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

   3. Taylor expanded in j around inf 46.0%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -20:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-102}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+96}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 41.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq 2.16 \cdot 10^{-184}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 6.1 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -4.4e+85)
   (* x (* t (- a)))
   (if (<= a 2.16e-184)
     (* c (- (* t j) (* z b)))
     (if (<= a 6.1e-109) (* x (* y z)) (* b (- (* a i) (* z c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -4.4e+85) {
		tmp = x * (t * -a);
	} else if (a <= 2.16e-184) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 6.1e-109) {
		tmp = x * (y * z);
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-4.4d+85)) then
        tmp = x * (t * -a)
    else if (a <= 2.16d-184) then
        tmp = c * ((t * j) - (z * b))
    else if (a <= 6.1d-109) then
        tmp = x * (y * z)
    else
        tmp = b * ((a * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -4.4e+85) {
		tmp = x * (t * -a);
	} else if (a <= 2.16e-184) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 6.1e-109) {
		tmp = x * (y * z);
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -4.4e+85:
		tmp = x * (t * -a)
	elif a <= 2.16e-184:
		tmp = c * ((t * j) - (z * b))
	elif a <= 6.1e-109:
		tmp = x * (y * z)
	else:
		tmp = b * ((a * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -4.4e+85)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (a <= 2.16e-184)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (a <= 6.1e-109)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -4.4e+85)
		tmp = x * (t * -a);
	elseif (a <= 2.16e-184)
		tmp = c * ((t * j) - (z * b));
	elseif (a <= 6.1e-109)
		tmp = x * (y * z);
	else
		tmp = b * ((a * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -4.4e+85], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.16e-184], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.1e-109], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.4000000000000003e85

   1. Initial program 67.1%

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

   3. Taylor expanded in c around 0 69.0%

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

   4. Taylor expanded in i around 0 54.8%

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

   5. Taylor expanded in y around 0 47.7%

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

      1. mul-1-neg 47.7%

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

      2. distribute-lft-neg-out 47.7%

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

      3. *-commutative 47.7%

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

   7. Simplified 47.7%

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

   if -4.4000000000000003e85 < a < 2.15999999999999991e-184

   1. Initial program 83.8%

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

   3. Taylor expanded in c around inf 47.4%

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

      1. *-commutative 47.4%

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

      2. *-commutative 47.4%

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

   5. Simplified 47.4%

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

   if 2.15999999999999991e-184 < a < 6.0999999999999997e-109

   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. Add Preprocessing

   3. Taylor expanded in c around 0 75.6%

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

   4. Taylor expanded in i around 0 61.3%

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

   5. Taylor expanded in y around inf 55.9%

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

   if 6.0999999999999997e-109 < a

   1. Initial program 70.9%

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

   3. Taylor expanded in b around inf 53.5%

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

      1. *-commutative 53.5%

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

   5. Simplified 53.5%

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

Alternative 19: 41.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.15 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-168}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -1.15e+17)
     t_1
     (if (<= b -3e-168)
       (* a (* t (- x)))
       (if (<= b 2.2e-11) (* y (* x 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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.15e+17) {
		tmp = t_1;
	} else if (b <= -3e-168) {
		tmp = a * (t * -x);
	} else if (b <= 2.2e-11) {
		tmp = y * (x * 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 = b * ((a * i) - (z * c))
    if (b <= (-1.15d+17)) then
        tmp = t_1
    else if (b <= (-3d-168)) then
        tmp = a * (t * -x)
    else if (b <= 2.2d-11) then
        tmp = y * (x * 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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.15e+17) {
		tmp = t_1;
	} else if (b <= -3e-168) {
		tmp = a * (t * -x);
	} else if (b <= 2.2e-11) {
		tmp = y * (x * z);
	} 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 <= -1.15e+17:
		tmp = t_1
	elif b <= -3e-168:
		tmp = a * (t * -x)
	elif b <= 2.2e-11:
		tmp = y * (x * z)
	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 <= -1.15e+17)
		tmp = t_1;
	elseif (b <= -3e-168)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (b <= 2.2e-11)
		tmp = Float64(y * Float64(x * 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 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.15e+17)
		tmp = t_1;
	elseif (b <= -3e-168)
		tmp = a * (t * -x);
	elseif (b <= 2.2e-11)
		tmp = y * (x * 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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.15e+17], t$95$1, If[LessEqual[b, -3e-168], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.2e-11], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.15e17 or 2.2000000000000002e-11 < b

   1. Initial program 75.0%

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

   3. Taylor expanded in b around inf 60.9%

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

      1. *-commutative 60.9%

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

   5. Simplified 60.9%

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

   if -1.15e17 < b < -2.99999999999999991e-168

   1. Initial program 83.6%

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

   3. Taylor expanded in a around inf 47.4%

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

      1. distribute-lft-out-- 47.4%

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

      2. *-commutative 47.4%

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

      3. *-commutative 47.4%

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

   5. Simplified 47.4%

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

   6. Taylor expanded in x around inf 40.1%

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

      1. associate-*r* 40.1%

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

      2. neg-mul-1 40.1%

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

   8. Simplified 40.1%

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

   if -2.99999999999999991e-168 < b < 2.2000000000000002e-11

   1. Initial program 71.9%

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

   3. Taylor expanded in c around 0 66.0%

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

   4. Taylor expanded in a around 0 44.1%

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

      1. +-commutative 44.1%

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

      2. mul-1-neg 44.1%

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

      3. unsub-neg 44.1%

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

      4. associate-*r* 45.6%

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

   6. Simplified 45.6%

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

   7. Taylor expanded in x around inf 33.0%

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

      1. *-commutative 33.0%

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

      2. associate-*l* 34.1%

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

   9. Simplified 34.1%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+17}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-168}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 50.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.96 \cdot 10^{+118} \lor \neg \left(b \leq 1.75 \cdot 10^{+65}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.96e+118) (not (<= b 1.75e+65)))
   (* b (- (* a i) (* z c)))
   (* x (- (* y z) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.96e+118) || !(b <= 1.75e+65)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-1.96d+118)) .or. (.not. (b <= 1.75d+65))) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = x * ((y * z) - (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.96e+118) || !(b <= 1.75e+65)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.96e+118) or not (b <= 1.75e+65):
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = x * ((y * z) - (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.96e+118) || !(b <= 1.75e+65))
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -1.96e+118) || ~((b <= 1.75e+65)))
		tmp = b * ((a * i) - (z * c));
	else
		tmp = x * ((y * z) - (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.96e+118], N[Not[LessEqual[b, 1.75e+65]], $MachinePrecision]], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.96e118 or 1.75e65 < b

   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. Add Preprocessing

   3. Taylor expanded in b around inf 69.9%

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

      1. *-commutative 69.9%

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

   5. Simplified 69.9%

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

   if -1.96e118 < b < 1.75e65

   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. Add Preprocessing

   3. Taylor expanded in c around 0 65.5%

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

   4. Taylor expanded in i around 0 55.2%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.96 \cdot 10^{+118} \lor \neg \left(b \leq 1.75 \cdot 10^{+65}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 28.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-106} \lor \neg \left(z \leq 1.85 \cdot 10^{+93}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -4.5e-106) (not (<= z 1.85e+93))) (* y (* x z)) (* a (* b i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -4.5e-106) || !(z <= 1.85e+93)) {
		tmp = y * (x * z);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((z <= (-4.5d-106)) .or. (.not. (z <= 1.85d+93))) then
        tmp = y * (x * z)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -4.5e-106) || !(z <= 1.85e+93)) {
		tmp = y * (x * z);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -4.5e-106) or not (z <= 1.85e+93):
		tmp = y * (x * z)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -4.5e-106) || !(z <= 1.85e+93))
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -4.5e-106) || ~((z <= 1.85e+93)))
		tmp = y * (x * z);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -4.5e-106], N[Not[LessEqual[z, 1.85e+93]], $MachinePrecision]], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.49999999999999955e-106 or 1.84999999999999994e93 < z

   1. Initial program 70.6%

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

   3. Taylor expanded in c around 0 53.5%

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

   4. Taylor expanded in a around 0 39.5%

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

      1. +-commutative 39.5%

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

      2. mul-1-neg 39.5%

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

      3. unsub-neg 39.5%

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

      4. associate-*r* 41.9%

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

   6. Simplified 41.9%

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

   7. Taylor expanded in x around inf 36.1%

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

      1. *-commutative 36.1%

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

      2. associate-*l* 39.0%

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

   9. Simplified 39.0%

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

   if -4.49999999999999955e-106 < z < 1.84999999999999994e93

   1. Initial program 80.1%

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

   3. Taylor expanded in b around inf 36.7%

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

      1. *-commutative 36.7%

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

   5. Simplified 36.7%

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

   6. Taylor expanded in a around inf 30.7%

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

      1. *-commutative 30.7%

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

   8. Simplified 30.7%

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

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-106} \lor \neg \left(z \leq 1.85 \cdot 10^{+93}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 28.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-106}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+92}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -2.9e-106)
   (* z (* x y))
   (if (<= z 2.4e+92) (* a (* b i)) (* y (* x 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 (z <= -2.9e-106) {
		tmp = z * (x * y);
	} else if (z <= 2.4e+92) {
		tmp = a * (b * i);
	} else {
		tmp = y * (x * 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 (z <= (-2.9d-106)) then
        tmp = z * (x * y)
    else if (z <= 2.4d+92) then
        tmp = a * (b * i)
    else
        tmp = y * (x * 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 (z <= -2.9e-106) {
		tmp = z * (x * y);
	} else if (z <= 2.4e+92) {
		tmp = a * (b * i);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -2.9e-106:
		tmp = z * (x * y)
	elif z <= 2.4e+92:
		tmp = a * (b * i)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -2.9e-106)
		tmp = Float64(z * Float64(x * y));
	elseif (z <= 2.4e+92)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -2.9e-106)
		tmp = z * (x * y);
	elseif (z <= 2.4e+92)
		tmp = a * (b * i);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -2.9e-106], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+92], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9e-106

   1. Initial program 66.7%

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

   3. Taylor expanded in b around inf 58.3%

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

   4. Taylor expanded in y around inf 41.1%

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

      1. associate-*r* 41.8%

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

      2. *-commutative 41.8%

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

      3. +-commutative 41.8%

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

      4. mul-1-neg 41.8%

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

      5. unsub-neg 41.8%

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

      6. associate-/l* 39.2%

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

      7. associate-/l* 38.0%

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

   6. Simplified 38.0%

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

   7. Taylor expanded in x around inf 31.8%

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

      1. *-commutative 31.8%

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

      2. *-commutative 31.8%

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

      3. associate-*r* 34.2%

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

   9. Simplified 34.2%

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

   if -2.9e-106 < z < 2.40000000000000005e92

   1. Initial program 80.1%

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

   3. Taylor expanded in b around inf 36.7%

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

      1. *-commutative 36.7%

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

   5. Simplified 36.7%

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

   6. Taylor expanded in a around inf 30.7%

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

      1. *-commutative 30.7%

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

   8. Simplified 30.7%

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

   if 2.40000000000000005e92 < z

   1. Initial program 76.2%

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

   3. Taylor expanded in c around 0 43.0%

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

   4. Taylor expanded in a around 0 36.8%

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

      1. +-commutative 36.8%

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

      2. mul-1-neg 36.8%

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

      3. unsub-neg 36.8%

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

      4. associate-*r* 40.5%

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

   6. Simplified 40.5%

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

   7. Taylor expanded in x around inf 42.2%

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

      1. *-commutative 42.2%

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

      2. associate-*l* 46.0%

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

   9. Simplified 46.0%

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

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-106}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+92}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 28.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-28}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -2.2e-28)
   (* a (* b i))
   (if (<= a 2.95e-104) (* x (* y z)) (* b (* a i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -2.2e-28) {
		tmp = a * (b * i);
	} else if (a <= 2.95e-104) {
		tmp = x * (y * z);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-2.2d-28)) then
        tmp = a * (b * i)
    else if (a <= 2.95d-104) then
        tmp = x * (y * z)
    else
        tmp = b * (a * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -2.2e-28) {
		tmp = a * (b * i);
	} else if (a <= 2.95e-104) {
		tmp = x * (y * z);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -2.2e-28:
		tmp = a * (b * i)
	elif a <= 2.95e-104:
		tmp = x * (y * z)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -2.2e-28)
		tmp = Float64(a * Float64(b * i));
	elseif (a <= 2.95e-104)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -2.2e-28)
		tmp = a * (b * i);
	elseif (a <= 2.95e-104)
		tmp = x * (y * z);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -2.2e-28], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.95e-104], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.19999999999999996e-28

   1. Initial program 74.7%

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

   3. Taylor expanded in b around inf 39.0%

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

      1. *-commutative 39.0%

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

   5. Simplified 39.0%

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

   6. Taylor expanded in a around inf 31.5%

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

      1. *-commutative 31.5%

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

   8. Simplified 31.5%

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

   if -2.19999999999999996e-28 < a < 2.9500000000000002e-104

   1. Initial program 80.1%

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

   3. Taylor expanded in c around 0 51.6%

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

   4. Taylor expanded in i around 0 43.9%

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

   5. Taylor expanded in y around inf 37.1%

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

   if 2.9500000000000002e-104 < a

   1. Initial program 70.9%

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

   3. Taylor expanded in b around inf 53.5%

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

      1. *-commutative 53.5%

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

   5. Simplified 53.5%

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

   6. Taylor expanded in a around inf 33.2%

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

      1. *-commutative 33.2%

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

   8. Simplified 33.2%

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

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-28}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 22.0% accurate, 5.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 75.3%

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

3. Taylor expanded in b around inf 37.5%

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

   1. *-commutative 37.5%

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

5. Simplified 37.5%

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

6. Taylor expanded in a around inf 21.5%

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

   1. *-commutative 21.5%

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

8. Simplified 21.5%

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

9. Final simplification 21.5%

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

Alternative 25: 22.2% accurate, 5.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 75.3%

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

3. Taylor expanded in b around inf 37.5%

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

   1. *-commutative 37.5%

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

5. Simplified 37.5%

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

6. Taylor expanded in a around inf 20.5%

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

   1. *-commutative 20.5%

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

8. Simplified 20.5%

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

9. Final simplification 20.5%

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

Developer Target 1: 68.7% 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 2024170 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -1015122364899489/125000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -942510763643697/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (if (< t -238547917063487/3125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 10535888557455487/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* 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)))))