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

Percentage Accurate: 73.1% → 80.7%

Time: 20.4s

Alternatives: 27

Speedup: 0.7×

• 57.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 80.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\\ t_3 := a \cdot c - y \cdot i\\ t_4 := t\_2 + j \cdot t\_3\\ \mathbf{if}\;t\_4 \leq 5 \cdot 10^{+285}:\\ \;\;\;\;\mathsf{fma}\left(j, t\_3, t\_2\right)\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;\left(a \cdot \left(c \cdot j - x \cdot t\right) + y \cdot \left(x \cdot z - i \cdot j\right)\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (+ (* x (- (* y z) (* t a))) t_1))
        (t_3 (- (* a c) (* y i)))
        (t_4 (+ t_2 (* j t_3))))
   (if (<= t_4 5e+285)
     (fma j t_3 t_2)
     (if (<= t_4 INFINITY)
       (+ (+ (* a (- (* c j) (* x t))) (* y (- (* x z) (* i j)))) t_1)
       (* i (- (* t b) (* y j)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = (x * ((y * z) - (t * a))) + t_1;
	double t_3 = (a * c) - (y * i);
	double t_4 = t_2 + (j * t_3);
	double tmp;
	if (t_4 <= 5e+285) {
		tmp = fma(j, t_3, t_2);
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = ((a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))) + t_1;
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1)
	t_3 = Float64(Float64(a * c) - Float64(y * i))
	t_4 = Float64(t_2 + Float64(j * t_3))
	tmp = 0.0
	if (t_4 <= 5e+285)
		tmp = fma(j, t_3, t_2);
	elseif (t_4 <= Inf)
		tmp = Float64(Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(y * Float64(Float64(x * z) - Float64(i * j)))) + t_1);
	else
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 + N[(j * t$95$3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, 5e+285], N[(j * t$95$3 + t$95$2), $MachinePrecision], If[LessEqual[t$95$4, Infinity], N[(N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < 5.00000000000000016e285

   1. Initial program 97.7%

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

      1. +-commutative 97.7%

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

      2. fma-define 97.7%

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

      3. *-commutative 97.7%

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

      4. *-commutative 97.7%

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

   3. Simplified 97.7%

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

   if 5.00000000000000016e285 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 83.4%

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

      1. +-commutative 83.4%

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

      2. fma-define 83.4%

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

      3. *-commutative 83.4%

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

      4. *-commutative 83.4%

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

   3. Simplified 83.4%

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

   5. Taylor expanded in y around 0 90.4%

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

   7. Simplified 90.4%

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

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

   1. Initial program 0.0%

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

      1. +-commutative 0.0%

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

      2. fma-define 7.7%

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

      3. *-commutative 7.7%

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

      4. *-commutative 7.7%

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

   3. Simplified 7.7%

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

   5. Taylor expanded in y around 0 23.2%

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

   7. Simplified 29.0%

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

   8. Taylor expanded in i around inf 52.9%

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

      1. +-commutative 52.9%

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

      2. mul-1-neg 52.9%

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

      3. unsub-neg 52.9%

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

      4. *-commutative 52.9%

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

      5. *-commutative 52.9%

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

   10. Simplified 52.9%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq 5 \cdot 10^{+285}:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{elif}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\left(a \cdot \left(c \cdot j - x \cdot t\right) + y \cdot \left(x \cdot z - i \cdot j\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 80.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;t\_2 \leq 5 \cdot 10^{+285}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\left(a \cdot \left(c \cdot j - x \cdot t\right) + y \cdot \left(x \cdot z - i \cdot j\right)\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (+ (+ (* x (- (* y z) (* t a))) t_1) (* j (- (* a c) (* y i))))))
   (if (<= t_2 5e+285)
     t_2
     (if (<= t_2 INFINITY)
       (+ (+ (* a (- (* c j) (* x t))) (* y (- (* x z) (* i j)))) t_1)
       (* i (- (* t b) (* y j)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = ((x * ((y * z) - (t * a))) + t_1) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_2 <= 5e+285) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = ((a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))) + t_1;
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = ((x * ((y * z) - (t * a))) + t_1) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_2 <= 5e+285) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = ((a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))) + t_1;
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = ((x * ((y * z) - (t * a))) + t_1) + (j * ((a * c) - (y * i)))
	tmp = 0
	if t_2 <= 5e+285:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = ((a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))) + t_1
	else:
		tmp = i * ((t * b) - (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_2 <= 5e+285)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(y * Float64(Float64(x * z) - Float64(i * j)))) + t_1);
	else
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = ((x * ((y * z) - (t * a))) + t_1) + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (t_2 <= 5e+285)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = ((a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))) + t_1;
	else
		tmp = i * ((t * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 5e+285], t$95$2, If[LessEqual[t$95$2, Infinity], N[(N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < 5.00000000000000016e285

   1. Initial program 97.7%

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

   if 5.00000000000000016e285 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 83.4%

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

      1. +-commutative 83.4%

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

      2. fma-define 83.4%

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

      3. *-commutative 83.4%

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

      4. *-commutative 83.4%

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

   3. Simplified 83.4%

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

   5. Taylor expanded in y around 0 90.4%

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

   7. Simplified 90.4%

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

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

   1. Initial program 0.0%

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

      1. +-commutative 0.0%

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

      2. fma-define 7.7%

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

      3. *-commutative 7.7%

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

      4. *-commutative 7.7%

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

   3. Simplified 7.7%

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

   5. Taylor expanded in y around 0 23.2%

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

   7. Simplified 29.0%

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

   8. Taylor expanded in i around inf 52.9%

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

      1. +-commutative 52.9%

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

      2. mul-1-neg 52.9%

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

      3. unsub-neg 52.9%

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

      4. *-commutative 52.9%

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

      5. *-commutative 52.9%

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

   10. Simplified 52.9%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq 5 \cdot 10^{+285}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\left(a \cdot \left(c \cdot j - x \cdot t\right) + y \cdot \left(x \cdot z - i \cdot j\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -4.4 \cdot 10^{+23}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t\_1\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{+116}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j - x \cdot t\right) + y \cdot \left(x \cdot z - i \cdot j\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -4.4e+23)
     (+ (* j (- (* a c) (* y i))) t_1)
     (if (<= x 1.18e+116)
       (+
        (+ (* a (- (* c j) (* x t))) (* y (- (* x z) (* i j))))
        (* b (- (* t i) (* z c))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -4.4e+23) {
		tmp = (j * ((a * c) - (y * i))) + t_1;
	} else if (x <= 1.18e+116) {
		tmp = ((a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-4.4d+23)) then
        tmp = (j * ((a * c) - (y * i))) + t_1
    else if (x <= 1.18d+116) then
        tmp = ((a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))) + (b * ((t * i) - (z * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -4.4e+23) {
		tmp = (j * ((a * c) - (y * i))) + t_1;
	} else if (x <= 1.18e+116) {
		tmp = ((a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -4.4e+23:
		tmp = (j * ((a * c) - (y * i))) + t_1
	elif x <= 1.18e+116:
		tmp = ((a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))) + (b * ((t * i) - (z * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -4.4e+23)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + t_1);
	elseif (x <= 1.18e+116)
		tmp = Float64(Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(y * Float64(Float64(x * z) - Float64(i * j)))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -4.4e+23)
		tmp = (j * ((a * c) - (y * i))) + t_1;
	elseif (x <= 1.18e+116)
		tmp = ((a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))) + (b * ((t * i) - (z * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.4e+23], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 1.18e+116], N[(N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.40000000000000017e23

   1. Initial program 80.7%

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

      1. +-commutative 80.7%

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

      2. fma-define 84.2%

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

      3. *-commutative 84.2%

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

      4. *-commutative 84.2%

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

   3. Simplified 84.2%

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

   5. Taylor expanded in b around 0 81.0%

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

   if -4.40000000000000017e23 < x < 1.1799999999999999e116

   1. Initial program 76.1%

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

      1. +-commutative 76.1%

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

      2. fma-define 76.2%

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

      3. *-commutative 76.2%

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

      4. *-commutative 76.2%

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

   3. Simplified 76.2%

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

   5. Taylor expanded in y around 0 85.2%

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

   7. Simplified 85.8%

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

   if 1.1799999999999999e116 < x

   1. Initial program 60.8%

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

      1. +-commutative 60.8%

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

      2. fma-define 65.1%

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

      3. *-commutative 65.1%

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

      4. *-commutative 65.1%

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

   3. Simplified 65.1%

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

   5. Taylor expanded in y around 0 43.9%

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

   7. Simplified 46.0%

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

   8. Taylor expanded in j around inf 46.0%

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

      1. associate-/l* 46.0%

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

   10. Simplified 46.0%

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

   11. Taylor expanded in x around inf 71.9%

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

       1. +-commutative 71.9%

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

       2. mul-1-neg 71.9%

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

       3. unsub-neg 71.9%

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

   13. Simplified 71.9%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+23}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{+116}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j - x \cdot t\right) + y \cdot \left(x \cdot z - i \cdot j\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.1 \cdot 10^{-57} \lor \neg \left(b \leq 1.1 \cdot 10^{+49}\right):\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) - y \cdot \left(i \cdot \left(j - x \cdot \frac{z}{i}\right)\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -4.1e-57) (not (<= b 1.1e+49)))
   (+
    (- (* a (* c j)) (* y (* i (- j (* x (/ z i))))))
    (* b (- (* t i) (* z c))))
   (+ (* j (- (* a c) (* y i))) (* 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 <= -4.1e-57) || !(b <= 1.1e+49)) {
		tmp = ((a * (c * j)) - (y * (i * (j - (x * (z / i)))))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (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 <= (-4.1d-57)) .or. (.not. (b <= 1.1d+49))) then
        tmp = ((a * (c * j)) - (y * (i * (j - (x * (z / i)))))) + (b * ((t * i) - (z * c)))
    else
        tmp = (j * ((a * c) - (y * i))) + (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 <= -4.1e-57) || !(b <= 1.1e+49)) {
		tmp = ((a * (c * j)) - (y * (i * (j - (x * (z / i)))))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -4.1e-57) or not (b <= 1.1e+49):
		tmp = ((a * (c * j)) - (y * (i * (j - (x * (z / i)))))) + (b * ((t * i) - (z * c)))
	else:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -4.1e-57) || !(b <= 1.1e+49))
		tmp = Float64(Float64(Float64(a * Float64(c * j)) - Float64(y * Float64(i * Float64(j - Float64(x * Float64(z / i)))))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + 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 <= -4.1e-57) || ~((b <= 1.1e+49)))
		tmp = ((a * (c * j)) - (y * (i * (j - (x * (z / i)))))) + (b * ((t * i) - (z * c)));
	else
		tmp = (j * ((a * c) - (y * i))) + (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, -4.1e-57], N[Not[LessEqual[b, 1.1e+49]], $MachinePrecision]], N[(N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] - N[(y * N[(i * N[(j - N[(x * N[(z / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.1000000000000001e-57 or 1.1e49 < b

   1. Initial program 68.7%

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

      1. +-commutative 68.7%

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

      2. fma-define 71.1%

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

      3. *-commutative 71.1%

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

      4. *-commutative 71.1%

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

   3. Simplified 71.1%

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

   5. Taylor expanded in y around 0 74.1%

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

   7. Simplified 75.6%

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

   8. Taylor expanded in j around inf 74.9%

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

      1. associate-/l* 73.4%

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

   10. Simplified 73.4%

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

   11. Taylor expanded in c around inf 74.3%

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

       1. *-commutative 74.3%

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

   13. Simplified 74.3%

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

   14. Taylor expanded in i around inf 74.4%

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

       1. neg-mul-1 74.4%

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

       2. +-commutative 74.4%

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

       3. unsub-neg 74.4%

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

       4. associate-/l* 72.9%

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

   16. Simplified 72.9%

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

   if -4.1000000000000001e-57 < b < 1.1e49

   1. Initial program 80.0%

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

      1. +-commutative 80.0%

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

      2. fma-define 80.8%

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

      3. *-commutative 80.8%

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

      4. *-commutative 80.8%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in b around 0 81.9%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.1 \cdot 10^{-57} \lor \neg \left(b \leq 1.1 \cdot 10^{+49}\right):\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) - y \cdot \left(i \cdot \left(j - x \cdot \frac{z}{i}\right)\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;b \leq -1.85 \cdot 10^{-56}:\\ \;\;\;\;\left(t\_2 - y \cdot \left(j \cdot \left(i - x \cdot \frac{z}{j}\right)\right)\right) + t\_1\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+47}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t\_2 - y \cdot \left(i \cdot \left(j - x \cdot \frac{z}{i}\right)\right)\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* a (* c j))))
   (if (<= b -1.85e-56)
     (+ (- t_2 (* y (* j (- i (* x (/ z j)))))) t_1)
     (if (<= b 6e+47)
       (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))
       (+ (- t_2 (* y (* i (- j (* x (/ z 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 * ((t * i) - (z * c));
	double t_2 = a * (c * j);
	double tmp;
	if (b <= -1.85e-56) {
		tmp = (t_2 - (y * (j * (i - (x * (z / j)))))) + t_1;
	} else if (b <= 6e+47) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (t_2 - (y * (i * (j - (x * (z / i)))))) + 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 * ((t * i) - (z * c))
    t_2 = a * (c * j)
    if (b <= (-1.85d-56)) then
        tmp = (t_2 - (y * (j * (i - (x * (z / j)))))) + t_1
    else if (b <= 6d+47) then
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else
        tmp = (t_2 - (y * (i * (j - (x * (z / i)))))) + 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 * ((t * i) - (z * c));
	double t_2 = a * (c * j);
	double tmp;
	if (b <= -1.85e-56) {
		tmp = (t_2 - (y * (j * (i - (x * (z / j)))))) + t_1;
	} else if (b <= 6e+47) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (t_2 - (y * (i * (j - (x * (z / i)))))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * (c * j)
	tmp = 0
	if b <= -1.85e-56:
		tmp = (t_2 - (y * (j * (i - (x * (z / j)))))) + t_1
	elif b <= 6e+47:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	else:
		tmp = (t_2 - (y * (i * (j - (x * (z / i)))))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (b <= -1.85e-56)
		tmp = Float64(Float64(t_2 - Float64(y * Float64(j * Float64(i - Float64(x * Float64(z / j)))))) + t_1);
	elseif (b <= 6e+47)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = Float64(Float64(t_2 - Float64(y * Float64(i * Float64(j - Float64(x * Float64(z / i)))))) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = a * (c * j);
	tmp = 0.0;
	if (b <= -1.85e-56)
		tmp = (t_2 - (y * (j * (i - (x * (z / j)))))) + t_1;
	elseif (b <= 6e+47)
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	else
		tmp = (t_2 - (y * (i * (j - (x * (z / i)))))) + 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[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.85e-56], N[(N[(t$95$2 - N[(y * N[(j * N[(i - N[(x * N[(z / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, 6e+47], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$2 - N[(y * N[(i * N[(j - N[(x * N[(z / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.8500000000000001e-56

   1. Initial program 71.6%

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

      1. +-commutative 71.6%

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

      2. fma-define 75.9%

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

      3. *-commutative 75.9%

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

      4. *-commutative 75.9%

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

   3. Simplified 75.9%

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

   5. Taylor expanded in y around 0 71.5%

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

   7. Simplified 74.3%

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

   8. Taylor expanded in j around inf 73.0%

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

      1. associate-/l* 73.0%

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

   10. Simplified 73.0%

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

   11. Taylor expanded in c around inf 73.3%

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

       1. *-commutative 73.3%

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

   13. Simplified 73.3%

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

   if -1.8500000000000001e-56 < b < 6.0000000000000003e47

   1. Initial program 80.0%

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

      1. +-commutative 80.0%

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

      2. fma-define 80.8%

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

      3. *-commutative 80.8%

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

      4. *-commutative 80.8%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in b around 0 81.9%

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

   if 6.0000000000000003e47 < b

   1. Initial program 65.1%

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

      1. +-commutative 65.1%

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

      2. fma-define 65.1%

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

      3. *-commutative 65.1%

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

      4. *-commutative 65.1%

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

   3. Simplified 65.1%

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

   5. Taylor expanded in y around 0 77.2%

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

   7. Simplified 77.2%

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

   8. Taylor expanded in j around inf 77.2%

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

      1. associate-/l* 73.8%

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

   10. Simplified 73.8%

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

   11. Taylor expanded in c around inf 75.6%

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

       1. *-commutative 75.6%

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

   13. Simplified 75.6%

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

   14. Taylor expanded in i around inf 79.0%

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

       1. neg-mul-1 79.0%

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

       2. +-commutative 79.0%

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

       3. unsub-neg 79.0%

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

       4. associate-/l* 79.0%

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

   16. Simplified 79.0%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.85 \cdot 10^{-56}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) - y \cdot \left(j \cdot \left(i - x \cdot \frac{z}{j}\right)\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+47}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) - y \cdot \left(i \cdot \left(j - x \cdot \frac{z}{i}\right)\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5.8 \cdot 10^{+146}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-110}:\\ \;\;\;\;t\_1 + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+148}:\\ \;\;\;\;t\_1 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -5.8e+146)
     t_2
     (if (<= b -1.35e-110)
       (+ t_1 (* z (- (* x y) (* b c))))
       (if (<= b 7.8e+148) (+ t_1 (* x (- (* y z) (* t a)))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.8e+146) {
		tmp = t_2;
	} else if (b <= -1.35e-110) {
		tmp = t_1 + (z * ((x * y) - (b * c)));
	} else if (b <= 7.8e+148) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-5.8d+146)) then
        tmp = t_2
    else if (b <= (-1.35d-110)) then
        tmp = t_1 + (z * ((x * y) - (b * c)))
    else if (b <= 7.8d+148) then
        tmp = t_1 + (x * ((y * z) - (t * a)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.8e+146) {
		tmp = t_2;
	} else if (b <= -1.35e-110) {
		tmp = t_1 + (z * ((x * y) - (b * c)));
	} else if (b <= 7.8e+148) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -5.8e+146:
		tmp = t_2
	elif b <= -1.35e-110:
		tmp = t_1 + (z * ((x * y) - (b * c)))
	elif b <= 7.8e+148:
		tmp = t_1 + (x * ((y * z) - (t * a)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -5.8e+146)
		tmp = t_2;
	elseif (b <= -1.35e-110)
		tmp = Float64(t_1 + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	elseif (b <= 7.8e+148)
		tmp = Float64(t_1 + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -5.8e+146)
		tmp = t_2;
	elseif (b <= -1.35e-110)
		tmp = t_1 + (z * ((x * y) - (b * c)));
	elseif (b <= 7.8e+148)
		tmp = t_1 + (x * ((y * z) - (t * a)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.8e+146], t$95$2, If[LessEqual[b, -1.35e-110], N[(t$95$1 + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.8e+148], N[(t$95$1 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.7999999999999997e146 or 7.80000000000000004e148 < b

   1. Initial program 64.3%

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

      1. +-commutative 64.3%

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

      2. fma-define 67.3%

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

      3. *-commutative 67.3%

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

      4. *-commutative 67.3%

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

   3. Simplified 67.3%

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

   5. Taylor expanded in y around 0 71.6%

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

   7. Simplified 71.6%

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

   8. Taylor expanded in b around inf 67.9%

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

      1. *-commutative 67.9%

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

   10. Simplified 67.9%

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

   if -5.7999999999999997e146 < b < -1.3499999999999999e-110

   1. Initial program 77.6%

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

   3. Taylor expanded in z around inf 66.0%

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

      1. *-commutative 66.0%

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

   5. Simplified 66.0%

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

   if -1.3499999999999999e-110 < b < 7.80000000000000004e148

   1. Initial program 78.0%

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

      1. +-commutative 78.0%

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

      2. fma-define 78.7%

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

      3. *-commutative 78.7%

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

      4. *-commutative 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in b around 0 79.1%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+146}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-110}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+148}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-280}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-71}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+156}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))))
   (if (<= t -4.6e+88)
     t_1
     (if (<= t -2.2e-280)
       (- (* j (- (* a c) (* y i))) (* b (* z c)))
       (if (<= t 5.1e-71)
         (- (* c (- (* a j) (* z b))) (* i (* y j)))
         (if (<= t 3.4e+156) (* x (- (* y z) (* t a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -4.6e+88) {
		tmp = t_1;
	} else if (t <= -2.2e-280) {
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	} else if (t <= 5.1e-71) {
		tmp = (c * ((a * j) - (z * b))) - (i * (y * j));
	} else if (t <= 3.4e+156) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    if (t <= (-4.6d+88)) then
        tmp = t_1
    else if (t <= (-2.2d-280)) then
        tmp = (j * ((a * c) - (y * i))) - (b * (z * c))
    else if (t <= 5.1d-71) then
        tmp = (c * ((a * j) - (z * b))) - (i * (y * j))
    else if (t <= 3.4d+156) then
        tmp = x * ((y * z) - (t * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -4.6e+88) {
		tmp = t_1;
	} else if (t <= -2.2e-280) {
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	} else if (t <= 5.1e-71) {
		tmp = (c * ((a * j) - (z * b))) - (i * (y * j));
	} else if (t <= 3.4e+156) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -4.6e+88:
		tmp = t_1
	elif t <= -2.2e-280:
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c))
	elif t <= 5.1e-71:
		tmp = (c * ((a * j) - (z * b))) - (i * (y * j))
	elif t <= 3.4e+156:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -4.6e+88)
		tmp = t_1;
	elseif (t <= -2.2e-280)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(b * Float64(z * c)));
	elseif (t <= 5.1e-71)
		tmp = Float64(Float64(c * Float64(Float64(a * j) - Float64(z * b))) - Float64(i * Float64(y * j)));
	elseif (t <= 3.4e+156)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -4.6e+88)
		tmp = t_1;
	elseif (t <= -2.2e-280)
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	elseif (t <= 5.1e-71)
		tmp = (c * ((a * j) - (z * b))) - (i * (y * j));
	elseif (t <= 3.4e+156)
		tmp = x * ((y * z) - (t * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.6e+88], t$95$1, If[LessEqual[t, -2.2e-280], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.1e-71], N[(N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e+156], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.6000000000000003e88 or 3.4000000000000001e156 < t

   1. Initial program 62.7%

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

      1. +-commutative 62.7%

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

      2. fma-define 65.1%

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

      3. *-commutative 65.1%

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

      4. *-commutative 65.1%

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

   3. Simplified 65.1%

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

   5. Taylor expanded in y around 0 66.6%

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

   7. Simplified 67.8%

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

   8. Taylor expanded in t around inf 71.2%

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

      1. +-commutative 71.2%

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

      2. mul-1-neg 71.2%

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

      3. unsub-neg 71.2%

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

      4. *-commutative 71.2%

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

      5. *-commutative 71.2%

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

   10. Simplified 71.2%

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

   if -4.6000000000000003e88 < t < -2.2000000000000001e-280

   1. Initial program 81.5%

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

      1. +-commutative 81.5%

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

      2. fma-define 81.5%

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

      3. *-commutative 81.5%

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

      4. *-commutative 81.5%

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

   3. Simplified 81.5%

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

   5. Taylor expanded in x around 0 62.8%

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

   6. Taylor expanded in c around inf 58.0%

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

      1. *-commutative 58.0%

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

   8. Simplified 58.0%

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

   if -2.2000000000000001e-280 < t < 5.1000000000000003e-71

   1. Initial program 83.2%

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

      1. +-commutative 83.2%

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

      2. fma-define 85.1%

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

      3. *-commutative 85.1%

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

      4. *-commutative 85.1%

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

   3. Simplified 85.1%

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

   5. Taylor expanded in x around 0 74.1%

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

   6. Taylor expanded in c around inf 70.5%

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

      1. *-commutative 70.5%

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

   8. Simplified 70.5%

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

   9. Taylor expanded in a around 0 66.8%

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

       1. associate--l+ 66.8%

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

       2. *-commutative 66.8%

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

       3. associate-*r* 72.1%

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

       4. cancel-sign-sub-inv 72.1%

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

       5. *-commutative 72.1%

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

       6. associate-*r* 81.4%

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

       7. mul-1-neg 81.4%

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

       8. distribute-rgt-in 83.2%

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

       9. mul-1-neg 83.2%

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

       10. sub-neg 83.2%

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

       11. +-commutative 83.2%

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

       12. sub-neg 83.2%

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

       13. mul-1-neg 83.2%

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

       14. +-commutative 83.2%

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

       15. mul-1-neg 83.2%

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

   11. Simplified 83.2%

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

   if 5.1000000000000003e-71 < t < 3.4000000000000001e156

   1. Initial program 72.9%

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

      1. +-commutative 72.9%

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

      2. fma-define 75.4%

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

      3. *-commutative 75.4%

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

      4. *-commutative 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in y around 0 60.3%

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

   7. Simplified 62.8%

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

   8. Taylor expanded in j around inf 62.8%

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

      1. associate-/l* 62.8%

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

   10. Simplified 62.8%

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

   11. Taylor expanded in x around inf 66.0%

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

       1. +-commutative 66.0%

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

       2. mul-1-neg 66.0%

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

       3. unsub-neg 66.0%

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

   13. Simplified 66.0%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+88}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-280}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-71}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+156}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -2 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.65 \cdot 10^{-278}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-71}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+155}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))))
   (if (<= t -2e+86)
     t_1
     (if (<= t -2.65e-278)
       (* y (- (* x z) (* i j)))
       (if (<= t 1.08e-71)
         (* c (- (* a j) (* z b)))
         (if (<= t 3.5e+155) (* x (- (* y z) (* t a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -2e+86) {
		tmp = t_1;
	} else if (t <= -2.65e-278) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 1.08e-71) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= 3.5e+155) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    if (t <= (-2d+86)) then
        tmp = t_1
    else if (t <= (-2.65d-278)) then
        tmp = y * ((x * z) - (i * j))
    else if (t <= 1.08d-71) then
        tmp = c * ((a * j) - (z * b))
    else if (t <= 3.5d+155) then
        tmp = x * ((y * z) - (t * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -2e+86) {
		tmp = t_1;
	} else if (t <= -2.65e-278) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 1.08e-71) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= 3.5e+155) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -2e+86:
		tmp = t_1
	elif t <= -2.65e-278:
		tmp = y * ((x * z) - (i * j))
	elif t <= 1.08e-71:
		tmp = c * ((a * j) - (z * b))
	elif t <= 3.5e+155:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -2e+86)
		tmp = t_1;
	elseif (t <= -2.65e-278)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (t <= 1.08e-71)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (t <= 3.5e+155)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -2e+86)
		tmp = t_1;
	elseif (t <= -2.65e-278)
		tmp = y * ((x * z) - (i * j));
	elseif (t <= 1.08e-71)
		tmp = c * ((a * j) - (z * b));
	elseif (t <= 3.5e+155)
		tmp = x * ((y * z) - (t * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e+86], t$95$1, If[LessEqual[t, -2.65e-278], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.08e-71], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+155], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2e86 or 3.49999999999999985e155 < t

   1. Initial program 63.6%

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

      1. +-commutative 63.6%

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

      2. fma-define 65.9%

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

      3. *-commutative 65.9%

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

      4. *-commutative 65.9%

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

   3. Simplified 65.9%

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

   5. Taylor expanded in y around 0 67.3%

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

   7. Simplified 68.5%

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

   8. Taylor expanded in t around inf 70.7%

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

      1. +-commutative 70.7%

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

      2. mul-1-neg 70.7%

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

      3. unsub-neg 70.7%

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

      4. *-commutative 70.7%

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

      5. *-commutative 70.7%

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

   10. Simplified 70.7%

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

   if -2e86 < t < -2.65e-278

   1. Initial program 80.8%

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

      1. +-commutative 80.8%

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

      2. fma-define 80.8%

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

      3. *-commutative 80.8%

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

      4. *-commutative 80.8%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in y around inf 52.2%

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

      1. +-commutative 52.2%

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

      2. mul-1-neg 52.2%

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

      3. unsub-neg 52.2%

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

      4. *-commutative 52.2%

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

   7. Simplified 52.2%

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

   if -2.65e-278 < t < 1.08e-71

   1. Initial program 83.5%

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

      1. +-commutative 83.5%

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

      2. fma-define 85.4%

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

      3. *-commutative 85.4%

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

      4. *-commutative 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in c around inf 69.7%

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

   if 1.08e-71 < t < 3.49999999999999985e155

   1. Initial program 72.9%

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

      1. +-commutative 72.9%

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

      2. fma-define 75.4%

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

      3. *-commutative 75.4%

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

      4. *-commutative 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in y around 0 60.3%

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

   7. Simplified 62.8%

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

   8. Taylor expanded in j around inf 62.8%

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

      1. associate-/l* 62.8%

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

   10. Simplified 62.8%

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

   11. Taylor expanded in x around inf 66.0%

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

       1. +-commutative 66.0%

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

       2. mul-1-neg 66.0%

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

       3. unsub-neg 66.0%

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

   13. Simplified 66.0%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2.65 \cdot 10^{-278}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-71}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+155}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.2 \cdot 10^{+200}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-24}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{-288}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 100000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))))
   (if (<= c -1.2e+200)
     t_1
     (if (<= c -5.5e-24)
       (* a (- (* c j) (* x t)))
       (if (<= c 1.6e-288)
         (* i (- (* t b) (* y j)))
         (if (<= c 100000.0) (* x (- (* y z) (* t a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.2e+200) {
		tmp = t_1;
	} else if (c <= -5.5e-24) {
		tmp = a * ((c * j) - (x * t));
	} else if (c <= 1.6e-288) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= 100000.0) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a * j) - (z * b))
    if (c <= (-1.2d+200)) then
        tmp = t_1
    else if (c <= (-5.5d-24)) then
        tmp = a * ((c * j) - (x * t))
    else if (c <= 1.6d-288) then
        tmp = i * ((t * b) - (y * j))
    else if (c <= 100000.0d0) then
        tmp = x * ((y * z) - (t * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.2e+200) {
		tmp = t_1;
	} else if (c <= -5.5e-24) {
		tmp = a * ((c * j) - (x * t));
	} else if (c <= 1.6e-288) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= 100000.0) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -1.2e+200:
		tmp = t_1
	elif c <= -5.5e-24:
		tmp = a * ((c * j) - (x * t))
	elif c <= 1.6e-288:
		tmp = i * ((t * b) - (y * j))
	elif c <= 100000.0:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.2e+200)
		tmp = t_1;
	elseif (c <= -5.5e-24)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (c <= 1.6e-288)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (c <= 100000.0)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.2e+200)
		tmp = t_1;
	elseif (c <= -5.5e-24)
		tmp = a * ((c * j) - (x * t));
	elseif (c <= 1.6e-288)
		tmp = i * ((t * b) - (y * j));
	elseif (c <= 100000.0)
		tmp = x * ((y * z) - (t * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.2e+200], t$95$1, If[LessEqual[c, -5.5e-24], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.6e-288], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 100000.0], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.2e200 or 1e5 < c

   1. Initial program 70.1%

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

      1. +-commutative 70.1%

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

      2. fma-define 71.2%

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

      3. *-commutative 71.2%

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

      4. *-commutative 71.2%

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

   3. Simplified 71.2%

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

   5. Taylor expanded in c around inf 70.6%

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

   if -1.2e200 < c < -5.4999999999999999e-24

   1. Initial program 71.0%

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

      1. +-commutative 71.0%

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

      2. fma-define 71.0%

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

      3. *-commutative 71.0%

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

      4. *-commutative 71.0%

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

   3. Simplified 71.0%

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

   5. Taylor expanded in a around inf 56.3%

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

      1. +-commutative 56.3%

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

      2. mul-1-neg 56.3%

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

      3. unsub-neg 56.3%

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

   7. Simplified 56.3%

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

   if -5.4999999999999999e-24 < c < 1.6e-288

   1. Initial program 73.8%

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

      1. +-commutative 73.8%

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

      2. fma-define 75.3%

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

      3. *-commutative 75.3%

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

      4. *-commutative 75.3%

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

   3. Simplified 75.3%

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

   5. Taylor expanded in y around 0 74.0%

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

   7. Simplified 74.0%

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

   8. Taylor expanded in i around inf 53.0%

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

      1. +-commutative 53.0%

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

      2. mul-1-neg 53.0%

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

      3. unsub-neg 53.0%

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

      4. *-commutative 53.0%

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

      5. *-commutative 53.0%

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

   10. Simplified 53.0%

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

   if 1.6e-288 < c < 1e5

   1. Initial program 82.1%

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

      1. +-commutative 82.1%

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

      2. fma-define 85.1%

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

      3. *-commutative 85.1%

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

      4. *-commutative 85.1%

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

   3. Simplified 85.1%

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

   5. Taylor expanded in y around 0 83.8%

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

   7. Simplified 85.3%

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

   8. Taylor expanded in j around inf 82.4%

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

      1. associate-/l* 79.4%

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

   10. Simplified 79.4%

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

   11. Taylor expanded in x around inf 62.4%

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

       1. +-commutative 62.4%

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

       2. mul-1-neg 62.4%

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

       3. unsub-neg 62.4%

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

   13. Simplified 62.4%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.2 \cdot 10^{+200}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-24}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{-288}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 100000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -2.8 \cdot 10^{-103}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 2.85 \cdot 10^{-294}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 8.6 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -2.8e-103)
     t_2
     (if (<= i 2.85e-294)
       t_1
       (if (<= i 2.6e-179)
         (* c (- (* a j) (* z b)))
         (if (<= i 8.6e-26) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -2.8e-103) {
		tmp = t_2;
	} else if (i <= 2.85e-294) {
		tmp = t_1;
	} else if (i <= 2.6e-179) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 8.6e-26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = i * ((t * b) - (y * j))
    if (i <= (-2.8d-103)) then
        tmp = t_2
    else if (i <= 2.85d-294) then
        tmp = t_1
    else if (i <= 2.6d-179) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 8.6d-26) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -2.8e-103) {
		tmp = t_2;
	} else if (i <= 2.85e-294) {
		tmp = t_1;
	} else if (i <= 2.6e-179) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 8.6e-26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -2.8e-103:
		tmp = t_2
	elif i <= 2.85e-294:
		tmp = t_1
	elif i <= 2.6e-179:
		tmp = c * ((a * j) - (z * b))
	elif i <= 8.6e-26:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -2.8e-103)
		tmp = t_2;
	elseif (i <= 2.85e-294)
		tmp = t_1;
	elseif (i <= 2.6e-179)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 8.6e-26)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -2.8e-103)
		tmp = t_2;
	elseif (i <= 2.85e-294)
		tmp = t_1;
	elseif (i <= 2.6e-179)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 8.6e-26)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.8e-103], t$95$2, If[LessEqual[i, 2.85e-294], t$95$1, If[LessEqual[i, 2.6e-179], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8.6e-26], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -2.80000000000000023e-103 or 8.59999999999999976e-26 < i

   1. Initial program 67.9%

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

      1. +-commutative 67.9%

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

      2. fma-define 69.3%

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

      3. *-commutative 69.3%

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

      4. *-commutative 69.3%

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

   3. Simplified 69.3%

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

   5. Taylor expanded in y around 0 69.9%

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

   7. Simplified 70.6%

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

   8. Taylor expanded in i around inf 55.8%

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

      1. +-commutative 55.8%

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

      2. mul-1-neg 55.8%

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

      3. unsub-neg 55.8%

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

      4. *-commutative 55.8%

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

      5. *-commutative 55.8%

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

   10. Simplified 55.8%

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

   if -2.80000000000000023e-103 < i < 2.85000000000000016e-294 or 2.60000000000000005e-179 < i < 8.59999999999999976e-26

   1. Initial program 81.1%

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

      1. +-commutative 81.1%

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

      2. fma-define 83.5%

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

      3. *-commutative 83.5%

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

      4. *-commutative 83.5%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in a around inf 62.1%

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

      1. +-commutative 62.1%

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

      2. mul-1-neg 62.1%

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

      3. unsub-neg 62.1%

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

   7. Simplified 62.1%

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

   if 2.85000000000000016e-294 < i < 2.60000000000000005e-179

   1. Initial program 88.5%

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

      1. +-commutative 88.5%

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

      2. fma-define 88.6%

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

      3. *-commutative 88.6%

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

      4. *-commutative 88.6%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in c around inf 59.8%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.8 \cdot 10^{-103}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 2.85 \cdot 10^{-294}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 8.6 \cdot 10^{-26}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 68.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{-78} \lor \neg \left(x \leq 4.5 \cdot 10^{-94}\right):\\ \;\;\;\;t\_1 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (or (<= x -2.7e-78) (not (<= x 4.5e-94)))
     (+ t_1 (* x (- (* y z) (* t a))))
     (+ t_1 (* b (- (* t i) (* z c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if ((x <= -2.7e-78) || !(x <= 4.5e-94)) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if ((x <= (-2.7d-78)) .or. (.not. (x <= 4.5d-94))) then
        tmp = t_1 + (x * ((y * z) - (t * a)))
    else
        tmp = t_1 + (b * ((t * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if ((x <= -2.7e-78) || !(x <= 4.5e-94)) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if (x <= -2.7e-78) or not (x <= 4.5e-94):
		tmp = t_1 + (x * ((y * z) - (t * a)))
	else:
		tmp = t_1 + (b * ((t * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if ((x <= -2.7e-78) || !(x <= 4.5e-94))
		tmp = Float64(t_1 + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if ((x <= -2.7e-78) || ~((x <= 4.5e-94)))
		tmp = t_1 + (x * ((y * z) - (t * a)));
	else
		tmp = t_1 + (b * ((t * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -2.7e-78], N[Not[LessEqual[x, 4.5e-94]], $MachinePrecision]], N[(t$95$1 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.69999999999999994e-78 or 4.5000000000000002e-94 < x

   1. Initial program 76.9%

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

      1. +-commutative 76.9%

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

      2. fma-define 79.4%

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

      3. *-commutative 79.4%

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

      4. *-commutative 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in b around 0 74.9%

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

   if -2.69999999999999994e-78 < x < 4.5000000000000002e-94

   1. Initial program 70.1%

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

      1. +-commutative 70.1%

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

      2. fma-define 70.2%

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

      3. *-commutative 70.2%

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

      4. *-commutative 70.2%

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

   3. Simplified 70.2%

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

   5. Taylor expanded in x around 0 73.6%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-78} \lor \neg \left(x \leq 4.5 \cdot 10^{-94}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+120} \lor \neg \left(b \leq 8.2 \cdot 10^{+148}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -4.8e+120) (not (<= b 8.2e+148)))
   (* b (- (* t i) (* z c)))
   (+ (* j (- (* a c) (* y i))) (* 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 <= -4.8e+120) || !(b <= 8.2e+148)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (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 <= (-4.8d+120)) .or. (.not. (b <= 8.2d+148))) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = (j * ((a * c) - (y * i))) + (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 <= -4.8e+120) || !(b <= 8.2e+148)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -4.8e+120) or not (b <= 8.2e+148):
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -4.8e+120) || !(b <= 8.2e+148))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + 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 <= -4.8e+120) || ~((b <= 8.2e+148)))
		tmp = b * ((t * i) - (z * c));
	else
		tmp = (j * ((a * c) - (y * i))) + (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, -4.8e+120], N[Not[LessEqual[b, 8.2e+148]], $MachinePrecision]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.80000000000000002e120 or 8.1999999999999996e148 < b

   1. Initial program 65.0%

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

      1. +-commutative 65.0%

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

      2. fma-define 69.1%

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

      3. *-commutative 69.1%

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

      4. *-commutative 69.1%

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

   3. Simplified 69.1%

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

   5. Taylor expanded in y around 0 71.7%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in b around inf 67.0%

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

      1. *-commutative 67.0%

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

   10. Simplified 67.0%

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

   if -4.80000000000000002e120 < b < 8.1999999999999996e148

   1. Initial program 78.2%

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

      1. +-commutative 78.2%

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

      2. fma-define 78.8%

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

      3. *-commutative 78.8%

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

      4. *-commutative 78.8%

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

   3. Simplified 78.8%

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

   5. Taylor expanded in b around 0 74.4%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+120} \lor \neg \left(b \leq 8.2 \cdot 10^{+148}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 28.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{if}\;c \leq -3.1 \cdot 10^{+200}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;c \leq -1.15 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{-284}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* t (- x)))))
   (if (<= c -3.1e+200)
     (* c (* z (- b)))
     (if (<= c -1.15e-32)
       t_1
       (if (<= c 2.15e-284)
         (* i (* t b))
         (if (<= c 4.7e-11) t_1 (* c (* a j))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (t * -x);
	double tmp;
	if (c <= -3.1e+200) {
		tmp = c * (z * -b);
	} else if (c <= -1.15e-32) {
		tmp = t_1;
	} else if (c <= 2.15e-284) {
		tmp = i * (t * b);
	} else if (c <= 4.7e-11) {
		tmp = t_1;
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t * -x)
    if (c <= (-3.1d+200)) then
        tmp = c * (z * -b)
    else if (c <= (-1.15d-32)) then
        tmp = t_1
    else if (c <= 2.15d-284) then
        tmp = i * (t * b)
    else if (c <= 4.7d-11) then
        tmp = t_1
    else
        tmp = c * (a * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (t * -x);
	double tmp;
	if (c <= -3.1e+200) {
		tmp = c * (z * -b);
	} else if (c <= -1.15e-32) {
		tmp = t_1;
	} else if (c <= 2.15e-284) {
		tmp = i * (t * b);
	} else if (c <= 4.7e-11) {
		tmp = t_1;
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (t * -x)
	tmp = 0
	if c <= -3.1e+200:
		tmp = c * (z * -b)
	elif c <= -1.15e-32:
		tmp = t_1
	elif c <= 2.15e-284:
		tmp = i * (t * b)
	elif c <= 4.7e-11:
		tmp = t_1
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(t * Float64(-x)))
	tmp = 0.0
	if (c <= -3.1e+200)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (c <= -1.15e-32)
		tmp = t_1;
	elseif (c <= 2.15e-284)
		tmp = Float64(i * Float64(t * b));
	elseif (c <= 4.7e-11)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (t * -x);
	tmp = 0.0;
	if (c <= -3.1e+200)
		tmp = c * (z * -b);
	elseif (c <= -1.15e-32)
		tmp = t_1;
	elseif (c <= 2.15e-284)
		tmp = i * (t * b);
	elseif (c <= 4.7e-11)
		tmp = t_1;
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.1e+200], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.15e-32], t$95$1, If[LessEqual[c, 2.15e-284], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.7e-11], t$95$1, N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -3.09999999999999994e200

   1. Initial program 72.8%

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

      1. +-commutative 72.8%

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

      2. fma-define 72.8%

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

      3. *-commutative 72.8%

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

      4. *-commutative 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in y around 0 61.1%

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

   7. Simplified 65.1%

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

   8. Taylor expanded in z around inf 58.3%

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

      1. +-commutative 58.3%

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

      2. mul-1-neg 58.3%

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

      3. unsub-neg 58.3%

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

      4. *-commutative 58.3%

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

      5. *-commutative 58.3%

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

   10. Simplified 58.3%

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

   11. Taylor expanded in y around 0 51.0%

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

       1. mul-1-neg 51.0%

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

       2. *-commutative 51.0%

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

       3. associate-*r* 54.5%

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

       4. *-commutative 54.5%

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

       5. distribute-lft-neg-in 54.5%

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

       6. *-commutative 54.5%

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

   13. Simplified 54.5%

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

   if -3.09999999999999994e200 < c < -1.15e-32 or 2.1500000000000001e-284 < c < 4.69999999999999993e-11

   1. Initial program 80.3%

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

      1. +-commutative 80.3%

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

      2. fma-define 81.3%

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

      3. *-commutative 81.3%

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

      4. *-commutative 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in a around inf 47.9%

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

      1. +-commutative 47.9%

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

      2. mul-1-neg 47.9%

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

      3. unsub-neg 47.9%

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

   7. Simplified 47.9%

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

   8. Taylor expanded in c around 0 40.7%

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

      1. associate-*r* 40.7%

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

      2. mul-1-neg 40.7%

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

      3. *-commutative 40.7%

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

   10. Simplified 40.7%

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

   if -1.15e-32 < c < 2.1500000000000001e-284

   1. Initial program 73.0%

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

      1. +-commutative 73.0%

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

      2. fma-define 74.5%

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

      3. *-commutative 74.5%

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

      4. *-commutative 74.5%

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

   3. Simplified 74.5%

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

   5. Taylor expanded in y around 0 71.7%

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

   7. Simplified 71.7%

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

   8. Taylor expanded in t around inf 44.0%

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

      1. +-commutative 44.0%

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

      2. mul-1-neg 44.0%

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

      3. unsub-neg 44.0%

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

      4. *-commutative 44.0%

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

      5. *-commutative 44.0%

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

   10. Simplified 44.0%

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

   11. Taylor expanded in i around inf 33.4%

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

       1. associate-*r* 31.2%

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

       2. *-commutative 31.2%

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

       3. associate-*r* 34.8%

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

   13. Simplified 34.8%

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

   if 4.69999999999999993e-11 < c

   1. Initial program 67.9%

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

      1. +-commutative 67.9%

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

      2. fma-define 70.9%

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

      3. *-commutative 70.9%

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

      4. *-commutative 70.9%

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

   3. Simplified 70.9%

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

   5. Taylor expanded in a around inf 46.0%

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

      1. +-commutative 46.0%

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

      2. mul-1-neg 46.0%

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

      3. unsub-neg 46.0%

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

   7. Simplified 46.0%

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

   8. Taylor expanded in c around inf 44.6%

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

      1. +-commutative 44.6%

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

      2. mul-1-neg 44.6%

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

      3. unsub-neg 44.6%

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

      4. *-commutative 44.6%

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

      5. associate-/l* 44.6%

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

      6. associate-/l* 43.2%

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

   10. Simplified 43.2%

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

   11. Taylor expanded in c around inf 39.1%

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

       1. *-commutative 39.1%

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

       2. associate-*l* 39.1%

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

       3. *-commutative 39.1%

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

   13. Simplified 39.1%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.1 \cdot 10^{+200}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;c \leq -1.15 \cdot 10^{-32}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{-284}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{-11}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 30.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;y \leq -68000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-287}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-249}:\\ \;\;\;\;-z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;y \leq 8000000000:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* y (- j)))))
   (if (<= y -68000000000000.0)
     t_1
     (if (<= y 4.4e-287)
       (* c (* a j))
       (if (<= y 2.3e-249)
         (- (* z (* b c)))
         (if (<= y 8000000000.0) (* 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 = i * (y * -j);
	double tmp;
	if (y <= -68000000000000.0) {
		tmp = t_1;
	} else if (y <= 4.4e-287) {
		tmp = c * (a * j);
	} else if (y <= 2.3e-249) {
		tmp = -(z * (b * c));
	} else if (y <= 8000000000.0) {
		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 = i * (y * -j)
    if (y <= (-68000000000000.0d0)) then
        tmp = t_1
    else if (y <= 4.4d-287) then
        tmp = c * (a * j)
    else if (y <= 2.3d-249) then
        tmp = -(z * (b * c))
    else if (y <= 8000000000.0d0) 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 = i * (y * -j);
	double tmp;
	if (y <= -68000000000000.0) {
		tmp = t_1;
	} else if (y <= 4.4e-287) {
		tmp = c * (a * j);
	} else if (y <= 2.3e-249) {
		tmp = -(z * (b * c));
	} else if (y <= 8000000000.0) {
		tmp = a * (t * -x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (y * -j)
	tmp = 0
	if y <= -68000000000000.0:
		tmp = t_1
	elif y <= 4.4e-287:
		tmp = c * (a * j)
	elif y <= 2.3e-249:
		tmp = -(z * (b * c))
	elif y <= 8000000000.0:
		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(i * Float64(y * Float64(-j)))
	tmp = 0.0
	if (y <= -68000000000000.0)
		tmp = t_1;
	elseif (y <= 4.4e-287)
		tmp = Float64(c * Float64(a * j));
	elseif (y <= 2.3e-249)
		tmp = Float64(-Float64(z * Float64(b * c)));
	elseif (y <= 8000000000.0)
		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 = i * (y * -j);
	tmp = 0.0;
	if (y <= -68000000000000.0)
		tmp = t_1;
	elseif (y <= 4.4e-287)
		tmp = c * (a * j);
	elseif (y <= 2.3e-249)
		tmp = -(z * (b * c));
	elseif (y <= 8000000000.0)
		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[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -68000000000000.0], t$95$1, If[LessEqual[y, 4.4e-287], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e-249], (-N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), If[LessEqual[y, 8000000000.0], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.8e13 or 8e9 < y

   1. Initial program 66.9%

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

      1. +-commutative 66.9%

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

      2. fma-define 69.1%

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

      3. *-commutative 69.1%

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

      4. *-commutative 69.1%

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

   3. Simplified 69.1%

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

   5. Taylor expanded in y around 0 73.5%

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

   7. Simplified 75.0%

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

   8. Taylor expanded in i around inf 47.5%

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

      1. +-commutative 47.5%

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

      2. mul-1-neg 47.5%

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

      3. unsub-neg 47.5%

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

      4. *-commutative 47.5%

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

      5. *-commutative 47.5%

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

   10. Simplified 47.5%

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

   11. Taylor expanded in t around 0 37.1%

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

       1. mul-1-neg 37.1%

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

       2. distribute-rgt-neg-in 37.1%

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

   13. Simplified 37.1%

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

   if -6.8e13 < y < 4.4e-287

   1. Initial program 83.6%

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

      1. +-commutative 83.6%

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

      2. fma-define 83.6%

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

      3. *-commutative 83.6%

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

      4. *-commutative 83.6%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in a around inf 49.6%

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

      1. +-commutative 49.6%

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

      2. mul-1-neg 49.6%

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

      3. unsub-neg 49.6%

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

   7. Simplified 49.6%

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

   8. Taylor expanded in c around inf 48.0%

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

      1. +-commutative 48.0%

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

      2. mul-1-neg 48.0%

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

      3. unsub-neg 48.0%

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

      4. *-commutative 48.0%

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

      5. associate-/l* 49.5%

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

      6. associate-/l* 49.5%

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

   10. Simplified 49.5%

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

   11. Taylor expanded in c around inf 33.9%

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

       1. *-commutative 33.9%

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

       2. associate-*l* 38.2%

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

       3. *-commutative 38.2%

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

   13. Simplified 38.2%

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

   if 4.4e-287 < y < 2.2999999999999998e-249

   1. Initial program 89.2%

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

      1. +-commutative 89.2%

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

      2. fma-define 89.2%

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

      3. *-commutative 89.2%

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

      4. *-commutative 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in y around 0 89.4%

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

   7. Simplified 89.4%

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

   8. Taylor expanded in z around inf 70.8%

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

      1. +-commutative 70.8%

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

      2. mul-1-neg 70.8%

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

      3. unsub-neg 70.8%

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

      4. *-commutative 70.8%

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

      5. *-commutative 70.8%

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

   10. Simplified 70.8%

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

   11. Taylor expanded in y around 0 70.8%

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

       1. mul-1-neg 70.8%

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

       2. *-commutative 70.8%

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

       3. distribute-rgt-neg-in 70.8%

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

   13. Simplified 70.8%

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

   if 2.2999999999999998e-249 < y < 8e9

   1. Initial program 79.4%

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

      1. +-commutative 79.4%

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

      2. fma-define 81.5%

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

      3. *-commutative 81.5%

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

      4. *-commutative 81.5%

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

   3. Simplified 81.5%

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

   5. Taylor expanded in a around inf 53.2%

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

      1. +-commutative 53.2%

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

      2. mul-1-neg 53.2%

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

      3. unsub-neg 53.2%

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

   7. Simplified 53.2%

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

   8. Taylor expanded in c around 0 45.0%

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

      1. associate-*r* 45.0%

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

      2. mul-1-neg 45.0%

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

      3. *-commutative 45.0%

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

   10. Simplified 45.0%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -68000000000000:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-287}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-249}:\\ \;\;\;\;-z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;y \leq 8000000000:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-288}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-255}:\\ \;\;\;\;-z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;y \leq 13000000:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* y (- j)))))
   (if (<= y -1.1e+18)
     t_1
     (if (<= y 2.1e-288)
       (* c (* a j))
       (if (<= y 1.1e-255)
         (- (* z (* b c)))
         (if (<= y 13000000.0) (* t (* a (- 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 = i * (y * -j);
	double tmp;
	if (y <= -1.1e+18) {
		tmp = t_1;
	} else if (y <= 2.1e-288) {
		tmp = c * (a * j);
	} else if (y <= 1.1e-255) {
		tmp = -(z * (b * c));
	} else if (y <= 13000000.0) {
		tmp = t * (a * -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 = i * (y * -j)
    if (y <= (-1.1d+18)) then
        tmp = t_1
    else if (y <= 2.1d-288) then
        tmp = c * (a * j)
    else if (y <= 1.1d-255) then
        tmp = -(z * (b * c))
    else if (y <= 13000000.0d0) then
        tmp = t * (a * -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 = i * (y * -j);
	double tmp;
	if (y <= -1.1e+18) {
		tmp = t_1;
	} else if (y <= 2.1e-288) {
		tmp = c * (a * j);
	} else if (y <= 1.1e-255) {
		tmp = -(z * (b * c));
	} else if (y <= 13000000.0) {
		tmp = t * (a * -x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (y * -j)
	tmp = 0
	if y <= -1.1e+18:
		tmp = t_1
	elif y <= 2.1e-288:
		tmp = c * (a * j)
	elif y <= 1.1e-255:
		tmp = -(z * (b * c))
	elif y <= 13000000.0:
		tmp = t * (a * -x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(y * Float64(-j)))
	tmp = 0.0
	if (y <= -1.1e+18)
		tmp = t_1;
	elseif (y <= 2.1e-288)
		tmp = Float64(c * Float64(a * j));
	elseif (y <= 1.1e-255)
		tmp = Float64(-Float64(z * Float64(b * c)));
	elseif (y <= 13000000.0)
		tmp = Float64(t * Float64(a * 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 = i * (y * -j);
	tmp = 0.0;
	if (y <= -1.1e+18)
		tmp = t_1;
	elseif (y <= 2.1e-288)
		tmp = c * (a * j);
	elseif (y <= 1.1e-255)
		tmp = -(z * (b * c));
	elseif (y <= 13000000.0)
		tmp = t * (a * -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[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.1e+18], t$95$1, If[LessEqual[y, 2.1e-288], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e-255], (-N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), If[LessEqual[y, 13000000.0], N[(t * N[(a * (-x)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.1e18 or 1.3e7 < y

   1. Initial program 66.9%

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

      1. +-commutative 66.9%

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

      2. fma-define 69.1%

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

      3. *-commutative 69.1%

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

      4. *-commutative 69.1%

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

   3. Simplified 69.1%

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

   5. Taylor expanded in y around 0 73.5%

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

   7. Simplified 75.0%

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

   8. Taylor expanded in i around inf 47.5%

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

      1. +-commutative 47.5%

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

      2. mul-1-neg 47.5%

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

      3. unsub-neg 47.5%

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

      4. *-commutative 47.5%

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

      5. *-commutative 47.5%

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

   10. Simplified 47.5%

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

   11. Taylor expanded in t around 0 37.1%

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

       1. mul-1-neg 37.1%

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

       2. distribute-rgt-neg-in 37.1%

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

   13. Simplified 37.1%

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

   if -1.1e18 < y < 2.09999999999999996e-288

   1. Initial program 83.6%

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

      1. +-commutative 83.6%

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

      2. fma-define 83.6%

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

      3. *-commutative 83.6%

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

      4. *-commutative 83.6%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in a around inf 49.6%

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

      1. +-commutative 49.6%

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

      2. mul-1-neg 49.6%

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

      3. unsub-neg 49.6%

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

   7. Simplified 49.6%

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

   8. Taylor expanded in c around inf 48.0%

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

      1. +-commutative 48.0%

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

      2. mul-1-neg 48.0%

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

      3. unsub-neg 48.0%

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

      4. *-commutative 48.0%

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

      5. associate-/l* 49.5%

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

      6. associate-/l* 49.5%

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

   10. Simplified 49.5%

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

   11. Taylor expanded in c around inf 33.9%

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

       1. *-commutative 33.9%

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

       2. associate-*l* 38.2%

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

       3. *-commutative 38.2%

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

   13. Simplified 38.2%

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

   if 2.09999999999999996e-288 < y < 1.1e-255

   1. Initial program 89.2%

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

      1. +-commutative 89.2%

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

      2. fma-define 89.2%

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

      3. *-commutative 89.2%

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

      4. *-commutative 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in y around 0 89.4%

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

   7. Simplified 89.4%

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

   8. Taylor expanded in z around inf 70.8%

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

      1. +-commutative 70.8%

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

      2. mul-1-neg 70.8%

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

      3. unsub-neg 70.8%

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

      4. *-commutative 70.8%

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

      5. *-commutative 70.8%

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

   10. Simplified 70.8%

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

   11. Taylor expanded in y around 0 70.8%

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

       1. mul-1-neg 70.8%

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

       2. *-commutative 70.8%

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

       3. distribute-rgt-neg-in 70.8%

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

   13. Simplified 70.8%

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

   if 1.1e-255 < y < 1.3e7

   1. Initial program 79.4%

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

      1. +-commutative 79.4%

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

      2. fma-define 81.5%

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

      3. *-commutative 81.5%

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

      4. *-commutative 81.5%

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

   3. Simplified 81.5%

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

   5. Taylor expanded in y around 0 69.4%

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

   7. Simplified 69.4%

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

   8. Taylor expanded in t around inf 57.2%

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

      1. +-commutative 57.2%

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

      2. mul-1-neg 57.2%

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

      3. unsub-neg 57.2%

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

      4. *-commutative 57.2%

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

      5. *-commutative 57.2%

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

   10. Simplified 57.2%

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

   11. Taylor expanded in i around 0 45.0%

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

       1. mul-1-neg 45.0%

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

       2. distribute-lft-neg-out 45.0%

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

       3. *-commutative 45.0%

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

       4. associate-*r* 44.9%

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

   13. Simplified 44.9%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+18}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-288}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-255}:\\ \;\;\;\;-z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;y \leq 13000000:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 58.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-69}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+155}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))))
   (if (<= t -7.2e+86)
     t_1
     (if (<= t 2.2e-69)
       (- (* c (- (* a j) (* z b))) (* i (* y j)))
       (if (<= t 3.6e+155) (* x (- (* y z) (* t a))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -7.2e+86) {
		tmp = t_1;
	} else if (t <= 2.2e-69) {
		tmp = (c * ((a * j) - (z * b))) - (i * (y * j));
	} else if (t <= 3.6e+155) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    if (t <= (-7.2d+86)) then
        tmp = t_1
    else if (t <= 2.2d-69) then
        tmp = (c * ((a * j) - (z * b))) - (i * (y * j))
    else if (t <= 3.6d+155) then
        tmp = x * ((y * z) - (t * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -7.2e+86) {
		tmp = t_1;
	} else if (t <= 2.2e-69) {
		tmp = (c * ((a * j) - (z * b))) - (i * (y * j));
	} else if (t <= 3.6e+155) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -7.2e+86:
		tmp = t_1
	elif t <= 2.2e-69:
		tmp = (c * ((a * j) - (z * b))) - (i * (y * j))
	elif t <= 3.6e+155:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -7.2e+86)
		tmp = t_1;
	elseif (t <= 2.2e-69)
		tmp = Float64(Float64(c * Float64(Float64(a * j) - Float64(z * b))) - Float64(i * Float64(y * j)));
	elseif (t <= 3.6e+155)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -7.2e+86)
		tmp = t_1;
	elseif (t <= 2.2e-69)
		tmp = (c * ((a * j) - (z * b))) - (i * (y * j));
	elseif (t <= 3.6e+155)
		tmp = x * ((y * z) - (t * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.2e+86], t$95$1, If[LessEqual[t, 2.2e-69], N[(N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e+155], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.20000000000000011e86 or 3.60000000000000007e155 < t

   1. Initial program 63.2%

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

      1. +-commutative 63.2%

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

      2. fma-define 65.6%

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

      3. *-commutative 65.6%

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

      4. *-commutative 65.6%

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

   3. Simplified 65.6%

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

   5. Taylor expanded in y around 0 66.9%

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

   7. Simplified 68.1%

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

   8. Taylor expanded in t around inf 71.5%

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

      1. +-commutative 71.5%

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

      2. mul-1-neg 71.5%

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

      3. unsub-neg 71.5%

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

      4. *-commutative 71.5%

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

      5. *-commutative 71.5%

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

   10. Simplified 71.5%

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

   if -7.20000000000000011e86 < t < 2.2e-69

   1. Initial program 82.0%

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

      1. +-commutative 82.0%

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

      2. fma-define 82.8%

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

      3. *-commutative 82.8%

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

      4. *-commutative 82.8%

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

   3. Simplified 82.8%

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

   5. Taylor expanded in x around 0 67.0%

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

   6. Taylor expanded in c around inf 62.6%

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

      1. *-commutative 62.6%

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

   8. Simplified 62.6%

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

   9. Taylor expanded in a around 0 57.5%

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

       1. associate--l+ 57.5%

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

       2. *-commutative 57.5%

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

       3. associate-*r* 57.4%

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

       4. cancel-sign-sub-inv 57.4%

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

       5. *-commutative 57.4%

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

       6. associate-*r* 61.1%

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

       7. mul-1-neg 61.1%

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

       8. distribute-rgt-in 62.6%

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

       9. mul-1-neg 62.6%

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

       10. sub-neg 62.6%

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

       11. +-commutative 62.6%

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

       12. sub-neg 62.6%

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

       13. mul-1-neg 62.6%

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

       14. +-commutative 62.6%

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

       15. mul-1-neg 62.6%

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

   11. Simplified 62.6%

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

   if 2.2e-69 < t < 3.60000000000000007e155

   1. Initial program 72.9%

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

      1. +-commutative 72.9%

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

      2. fma-define 75.4%

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

      3. *-commutative 75.4%

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

      4. *-commutative 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in y around 0 60.3%

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

   7. Simplified 62.8%

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

   8. Taylor expanded in j around inf 62.8%

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

      1. associate-/l* 62.8%

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

   10. Simplified 62.8%

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

   11. Taylor expanded in x around inf 66.0%

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

       1. +-commutative 66.0%

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

       2. mul-1-neg 66.0%

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

       3. unsub-neg 66.0%

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

   13. Simplified 66.0%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-69}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+155}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 55.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+26}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+114}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -1e+26)
   (* z (- (* x y) (* b c)))
   (if (<= z 3.2e+114)
     (+ (* j (- (* a c) (* y i))) (* b (* t i)))
     (* 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 (z <= -1e+26) {
		tmp = z * ((x * y) - (b * c));
	} else if (z <= 3.2e+114) {
		tmp = (j * ((a * c) - (y * i))) + (b * (t * i));
	} 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 (z <= (-1d+26)) then
        tmp = z * ((x * y) - (b * c))
    else if (z <= 3.2d+114) then
        tmp = (j * ((a * c) - (y * i))) + (b * (t * i))
    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 (z <= -1e+26) {
		tmp = z * ((x * y) - (b * c));
	} else if (z <= 3.2e+114) {
		tmp = (j * ((a * c) - (y * i))) + (b * (t * i));
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -1e+26:
		tmp = z * ((x * y) - (b * c))
	elif z <= 3.2e+114:
		tmp = (j * ((a * c) - (y * i))) + (b * (t * i))
	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 (z <= -1e+26)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (z <= 3.2e+114)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(b * Float64(t * i)));
	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 (z <= -1e+26)
		tmp = z * ((x * y) - (b * c));
	elseif (z <= 3.2e+114)
		tmp = (j * ((a * c) - (y * i))) + (b * (t * i));
	else
		tmp = x * ((y * z) - (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -1e+26], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+114], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.00000000000000005e26

   1. Initial program 67.1%

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

      1. +-commutative 67.1%

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

      2. fma-define 68.9%

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

      3. *-commutative 68.9%

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

      4. *-commutative 68.9%

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

   3. Simplified 68.9%

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

   5. Taylor expanded in y around 0 70.9%

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

   7. Simplified 70.9%

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

   8. Taylor expanded in z around inf 69.4%

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

      1. +-commutative 69.4%

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

      2. mul-1-neg 69.4%

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

      3. unsub-neg 69.4%

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

      4. *-commutative 69.4%

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

      5. *-commutative 69.4%

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

   10. Simplified 69.4%

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

   if -1.00000000000000005e26 < z < 3.2e114

   1. Initial program 82.5%

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

   3. Taylor expanded in i around inf 61.6%

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

      1. *-commutative 61.6%

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

   5. Simplified 61.6%

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

   if 3.2e114 < z

   1. Initial program 53.5%

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

      1. +-commutative 53.5%

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

      2. fma-define 55.8%

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

      3. *-commutative 55.8%

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

      4. *-commutative 55.8%

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

   3. Simplified 55.8%

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

   5. Taylor expanded in y around 0 58.4%

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

   7. Simplified 58.4%

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

   8. Taylor expanded in j around inf 51.7%

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

      1. associate-/l* 49.5%

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

   10. Simplified 49.5%

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

   11. Taylor expanded in x around inf 60.8%

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

       1. +-commutative 60.8%

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

       2. mul-1-neg 60.8%

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

       3. unsub-neg 60.8%

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

   13. Simplified 60.8%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+26}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+114}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 52.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -46:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-203}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 960:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))))
   (if (<= t -46.0)
     t_1
     (if (<= t -2.45e-203)
       (* j (- (* a c) (* y i)))
       (if (<= t 960.0) (* c (- (* a j) (* z b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -46.0) {
		tmp = t_1;
	} else if (t <= -2.45e-203) {
		tmp = j * ((a * c) - (y * i));
	} else if (t <= 960.0) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    if (t <= (-46.0d0)) then
        tmp = t_1
    else if (t <= (-2.45d-203)) then
        tmp = j * ((a * c) - (y * i))
    else if (t <= 960.0d0) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -46.0) {
		tmp = t_1;
	} else if (t <= -2.45e-203) {
		tmp = j * ((a * c) - (y * i));
	} else if (t <= 960.0) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -46.0:
		tmp = t_1
	elif t <= -2.45e-203:
		tmp = j * ((a * c) - (y * i))
	elif t <= 960.0:
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -46.0)
		tmp = t_1;
	elseif (t <= -2.45e-203)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (t <= 960.0)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -46.0)
		tmp = t_1;
	elseif (t <= -2.45e-203)
		tmp = j * ((a * c) - (y * i));
	elseif (t <= 960.0)
		tmp = c * ((a * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -46.0], t$95$1, If[LessEqual[t, -2.45e-203], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 960.0], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -46 or 960 < t

   1. Initial program 70.4%

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

      1. +-commutative 70.4%

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

      2. fma-define 72.7%

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

      3. *-commutative 72.7%

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

      4. *-commutative 72.7%

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

   3. Simplified 72.7%

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

   5. Taylor expanded in y around 0 66.6%

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

   7. Simplified 68.2%

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

   8. Taylor expanded in t around inf 61.2%

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

      1. +-commutative 61.2%

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

      2. mul-1-neg 61.2%

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

      3. unsub-neg 61.2%

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

      4. *-commutative 61.2%

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

      5. *-commutative 61.2%

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

   10. Simplified 61.2%

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

   if -46 < t < -2.45e-203

   1. Initial program 73.3%

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

      1. +-commutative 73.3%

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

      2. fma-define 73.3%

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

      3. *-commutative 73.3%

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

      4. *-commutative 73.3%

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

   3. Simplified 73.3%

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

   5. Taylor expanded in y around 0 75.8%

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

   7. Simplified 78.0%

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

   8. Taylor expanded in j around inf 48.9%

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

      1. mul-1-neg 48.9%

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

      2. distribute-lft-neg-out 48.9%

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

      3. +-commutative 48.9%

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

      4. cancel-sign-sub-inv 48.9%

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

      5. *-commutative 48.9%

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

   10. Simplified 48.9%

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

   if -2.45e-203 < t < 960

   1. Initial program 81.6%

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

      1. +-commutative 81.6%

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

      2. fma-define 82.9%

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

      3. *-commutative 82.9%

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

      4. *-commutative 82.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 82.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 58.6%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -46:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-203}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 960:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;y \leq -62000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-282}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;y \leq 3900:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* y (- j)))))
   (if (<= y -62000000000000.0)
     t_1
     (if (<= y 1.8e-282)
       (* c (* a j))
       (if (<= y 3900.0) (* t (* a (- 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 = i * (y * -j);
	double tmp;
	if (y <= -62000000000000.0) {
		tmp = t_1;
	} else if (y <= 1.8e-282) {
		tmp = c * (a * j);
	} else if (y <= 3900.0) {
		tmp = t * (a * -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 = i * (y * -j)
    if (y <= (-62000000000000.0d0)) then
        tmp = t_1
    else if (y <= 1.8d-282) then
        tmp = c * (a * j)
    else if (y <= 3900.0d0) then
        tmp = t * (a * -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 = i * (y * -j);
	double tmp;
	if (y <= -62000000000000.0) {
		tmp = t_1;
	} else if (y <= 1.8e-282) {
		tmp = c * (a * j);
	} else if (y <= 3900.0) {
		tmp = t * (a * -x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (y * -j)
	tmp = 0
	if y <= -62000000000000.0:
		tmp = t_1
	elif y <= 1.8e-282:
		tmp = c * (a * j)
	elif y <= 3900.0:
		tmp = t * (a * -x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(y * Float64(-j)))
	tmp = 0.0
	if (y <= -62000000000000.0)
		tmp = t_1;
	elseif (y <= 1.8e-282)
		tmp = Float64(c * Float64(a * j));
	elseif (y <= 3900.0)
		tmp = Float64(t * Float64(a * 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 = i * (y * -j);
	tmp = 0.0;
	if (y <= -62000000000000.0)
		tmp = t_1;
	elseif (y <= 1.8e-282)
		tmp = c * (a * j);
	elseif (y <= 3900.0)
		tmp = t * (a * -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[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -62000000000000.0], t$95$1, If[LessEqual[y, 1.8e-282], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3900.0], N[(t * N[(a * (-x)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.2e13 or 3900 < y

   1. Initial program 66.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 66.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 69.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 69.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 69.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 69.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 73.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(a \cdot \left(c \cdot j\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   7. Simplified 75.0%

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j - t \cdot x\right) + y \cdot \left(z \cdot x - i \cdot j\right)\right) + b \cdot \left(t \cdot i - c \cdot z\right)} \]

   8. Taylor expanded in i around inf 47.5%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   9. Step-by-step derivation

      1. +-commutative 47.5%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 47.5%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 47.5%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      4. *-commutative 47.5%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} - j \cdot y\right) \]

      5. *-commutative 47.5%

         \[\leadsto i \cdot \left(t \cdot b - \color{blue}{y \cdot j}\right) \]

   10. Simplified 47.5%

       \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   11. Taylor expanded in t around 0 37.1%

       \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg 37.1%

          \[\leadsto i \cdot \color{blue}{\left(-j \cdot y\right)} \]

       2. distribute-rgt-neg-in 37.1%

          \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(-y\right)\right)} \]

   13. Simplified 37.1%

       \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(-y\right)\right)} \]

   if -6.2e13 < y < 1.7999999999999999e-282

   1. Initial program 84.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 84.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 84.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 84.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 48.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 48.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 48.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 48.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   7. Simplified 48.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   8. Taylor expanded in c around inf 46.7%

      \[\leadsto \color{blue}{c \cdot \left(-1 \cdot \frac{a \cdot \left(t \cdot x\right)}{c} + a \cdot j\right)} \]
   9. Step-by-step derivation

      1. +-commutative 46.7%

         \[\leadsto c \cdot \color{blue}{\left(a \cdot j + -1 \cdot \frac{a \cdot \left(t \cdot x\right)}{c}\right)} \]

      2. mul-1-neg 46.7%

         \[\leadsto c \cdot \left(a \cdot j + \color{blue}{\left(-\frac{a \cdot \left(t \cdot x\right)}{c}\right)}\right) \]

      3. unsub-neg 46.7%

         \[\leadsto c \cdot \color{blue}{\left(a \cdot j - \frac{a \cdot \left(t \cdot x\right)}{c}\right)} \]

      4. *-commutative 46.7%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - \frac{a \cdot \left(t \cdot x\right)}{c}\right) \]

      5. associate-/l* 48.2%

         \[\leadsto c \cdot \left(j \cdot a - \color{blue}{a \cdot \frac{t \cdot x}{c}}\right) \]

      6. associate-/l* 48.2%

         \[\leadsto c \cdot \left(j \cdot a - a \cdot \color{blue}{\left(t \cdot \frac{x}{c}\right)}\right) \]

   10. Simplified 48.2%

       \[\leadsto \color{blue}{c \cdot \left(j \cdot a - a \cdot \left(t \cdot \frac{x}{c}\right)\right)} \]

   11. Taylor expanded in c around inf 33.0%

       \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   12. Step-by-step derivation

       1. *-commutative 33.0%

          \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

       2. associate-*l* 37.1%

          \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c} \]

       3. *-commutative 37.1%

          \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   13. Simplified 37.1%

       \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   if 1.7999999999999999e-282 < y < 3900

   1. Initial program 80.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 80.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 82.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 82.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 82.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 82.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(a \cdot \left(c \cdot j\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   7. Simplified 71.5%

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j - t \cdot x\right) + y \cdot \left(z \cdot x - i \cdot j\right)\right) + b \cdot \left(t \cdot i - c \cdot z\right)} \]

   8. Taylor expanded in t around inf 55.6%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)} \]
   9. Step-by-step derivation

      1. +-commutative 55.6%

         \[\leadsto t \cdot \color{blue}{\left(b \cdot i + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 55.6%

         \[\leadsto t \cdot \left(b \cdot i + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 55.6%

         \[\leadsto t \cdot \color{blue}{\left(b \cdot i - a \cdot x\right)} \]

      4. *-commutative 55.6%

         \[\leadsto t \cdot \left(\color{blue}{i \cdot b} - a \cdot x\right) \]

      5. *-commutative 55.6%

         \[\leadsto t \cdot \left(i \cdot b - \color{blue}{x \cdot a}\right) \]

   10. Simplified 55.6%

       \[\leadsto \color{blue}{t \cdot \left(i \cdot b - x \cdot a\right)} \]

   11. Taylor expanded in i around 0 43.1%

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg 43.1%

          \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

       2. distribute-lft-neg-out 43.1%

          \[\leadsto \color{blue}{\left(-a\right) \cdot \left(t \cdot x\right)} \]

       3. *-commutative 43.1%

          \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} \]

       4. associate-*r* 43.1%

          \[\leadsto \color{blue}{t \cdot \left(x \cdot \left(-a\right)\right)} \]

   13. Simplified 43.1%

       \[\leadsto \color{blue}{t \cdot \left(x \cdot \left(-a\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -62000000000000:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-282}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;y \leq 3900:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 51.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+122} \lor \neg \left(b \leq 5.3 \cdot 10^{+59}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.15e+122) (not (<= b 5.3e+59)))
   (* b (- (* t i) (* z c)))
   (* a (- (* c j) (* x t)))))

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 <= -1.15e+122) || !(b <= 5.3e+59)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	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 <= (-1.15d+122)) .or. (.not. (b <= 5.3d+59))) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = a * ((c * j) - (x * t))
    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 <= -1.15e+122) || !(b <= 5.3e+59)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.15e+122) or not (b <= 5.3e+59):
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.15e+122) || !(b <= 5.3e+59))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -1.15e+122) || ~((b <= 5.3e+59)))
		tmp = b * ((t * i) - (z * c));
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.15e+122], N[Not[LessEqual[b, 5.3e+59]], $MachinePrecision]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.15e122 or 5.2999999999999997e59 < b

   1. Initial program 66.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 66.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 68.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 68.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 68.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 68.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 74.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(a \cdot \left(c \cdot j\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   7. Simplified 74.6%

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j - t \cdot x\right) + y \cdot \left(z \cdot x - i \cdot j\right)\right) + b \cdot \left(t \cdot i - c \cdot z\right)} \]

   8. Taylor expanded in b around inf 60.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 60.6%

         \[\leadsto b \cdot \left(i \cdot t - \color{blue}{z \cdot c}\right) \]

   10. Simplified 60.6%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot t - z \cdot c\right)} \]

   if -1.15e122 < b < 5.2999999999999997e59

   1. Initial program 79.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 79.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 80.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 80.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 80.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 80.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 47.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 47.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 47.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 47.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   7. Simplified 47.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+122} \lor \neg \left(b \leq 5.3 \cdot 10^{+59}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 40.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+247} \lor \neg \left(y \leq 2.3 \cdot 10^{+15}\right):\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -8e+247) (not (<= y 2.3e+15)))
   (* i (* y (- j)))
   (* a (- (* c j) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -8e+247) || !(y <= 2.3e+15)) {
		tmp = i * (y * -j);
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	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 ((y <= (-8d+247)) .or. (.not. (y <= 2.3d+15))) then
        tmp = i * (y * -j)
    else
        tmp = a * ((c * j) - (x * t))
    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 ((y <= -8e+247) || !(y <= 2.3e+15)) {
		tmp = i * (y * -j);
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (y <= -8e+247) or not (y <= 2.3e+15):
		tmp = i * (y * -j)
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -8e+247) || !(y <= 2.3e+15))
		tmp = Float64(i * Float64(y * Float64(-j)));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((y <= -8e+247) || ~((y <= 2.3e+15)))
		tmp = i * (y * -j);
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[y, -8e+247], N[Not[LessEqual[y, 2.3e+15]], $MachinePrecision]], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.99999999999999962e247 or 2.3e15 < y

   1. Initial program 68.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 68.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 70.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 70.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 70.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 70.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 77.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(a \cdot \left(c \cdot j\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   7. Simplified 78.2%

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j - t \cdot x\right) + y \cdot \left(z \cdot x - i \cdot j\right)\right) + b \cdot \left(t \cdot i - c \cdot z\right)} \]

   8. Taylor expanded in i around inf 53.9%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   9. Step-by-step derivation

      1. +-commutative 53.9%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 53.9%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 53.9%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      4. *-commutative 53.9%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} - j \cdot y\right) \]

      5. *-commutative 53.9%

         \[\leadsto i \cdot \left(t \cdot b - \color{blue}{y \cdot j}\right) \]

   10. Simplified 53.9%

       \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   11. Taylor expanded in t around 0 44.7%

       \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg 44.7%

          \[\leadsto i \cdot \color{blue}{\left(-j \cdot y\right)} \]

       2. distribute-rgt-neg-in 44.7%

          \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(-y\right)\right)} \]

   13. Simplified 44.7%

       \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(-y\right)\right)} \]

   if -7.99999999999999962e247 < y < 2.3e15

   1. Initial program 77.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 77.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 78.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 78.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 78.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 78.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 47.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 47.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 47.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 47.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   7. Simplified 47.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+247} \lor \neg \left(y \leq 2.3 \cdot 10^{+15}\right):\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 31.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+18} \lor \neg \left(y \leq 1900\right):\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -9.5e+18) (not (<= y 1900.0))) (* i (* y (- j))) (* c (* a j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -9.5e+18) || !(y <= 1900.0)) {
		tmp = i * (y * -j);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((y <= (-9.5d+18)) .or. (.not. (y <= 1900.0d0))) then
        tmp = i * (y * -j)
    else
        tmp = c * (a * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -9.5e+18) || !(y <= 1900.0)) {
		tmp = i * (y * -j);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (y <= -9.5e+18) or not (y <= 1900.0):
		tmp = i * (y * -j)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -9.5e+18) || !(y <= 1900.0))
		tmp = Float64(i * Float64(y * Float64(-j)));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((y <= -9.5e+18) || ~((y <= 1900.0)))
		tmp = i * (y * -j);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[y, -9.5e+18], N[Not[LessEqual[y, 1900.0]], $MachinePrecision]], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.5e18 or 1900 < y

   1. Initial program 66.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 66.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 69.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 69.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 69.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 69.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 73.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(a \cdot \left(c \cdot j\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   7. Simplified 75.0%

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j - t \cdot x\right) + y \cdot \left(z \cdot x - i \cdot j\right)\right) + b \cdot \left(t \cdot i - c \cdot z\right)} \]

   8. Taylor expanded in i around inf 47.5%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   9. Step-by-step derivation

      1. +-commutative 47.5%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 47.5%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 47.5%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      4. *-commutative 47.5%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} - j \cdot y\right) \]

      5. *-commutative 47.5%

         \[\leadsto i \cdot \left(t \cdot b - \color{blue}{y \cdot j}\right) \]

   10. Simplified 47.5%

       \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   11. Taylor expanded in t around 0 37.1%

       \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg 37.1%

          \[\leadsto i \cdot \color{blue}{\left(-j \cdot y\right)} \]

       2. distribute-rgt-neg-in 37.1%

          \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(-y\right)\right)} \]

   13. Simplified 37.1%

       \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(-y\right)\right)} \]

   if -9.5e18 < y < 1900

   1. Initial program 82.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 82.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 83.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 83.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 83.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 83.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 50.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 50.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.7%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   7. Simplified 50.7%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   8. Taylor expanded in c around inf 48.4%

      \[\leadsto \color{blue}{c \cdot \left(-1 \cdot \frac{a \cdot \left(t \cdot x\right)}{c} + a \cdot j\right)} \]
   9. Step-by-step derivation

      1. +-commutative 48.4%

         \[\leadsto c \cdot \color{blue}{\left(a \cdot j + -1 \cdot \frac{a \cdot \left(t \cdot x\right)}{c}\right)} \]

      2. mul-1-neg 48.4%

         \[\leadsto c \cdot \left(a \cdot j + \color{blue}{\left(-\frac{a \cdot \left(t \cdot x\right)}{c}\right)}\right) \]

      3. unsub-neg 48.4%

         \[\leadsto c \cdot \color{blue}{\left(a \cdot j - \frac{a \cdot \left(t \cdot x\right)}{c}\right)} \]

      4. *-commutative 48.4%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - \frac{a \cdot \left(t \cdot x\right)}{c}\right) \]

      5. associate-/l* 49.2%

         \[\leadsto c \cdot \left(j \cdot a - \color{blue}{a \cdot \frac{t \cdot x}{c}}\right) \]

      6. associate-/l* 48.4%

         \[\leadsto c \cdot \left(j \cdot a - a \cdot \color{blue}{\left(t \cdot \frac{x}{c}\right)}\right) \]

   10. Simplified 48.4%

       \[\leadsto \color{blue}{c \cdot \left(j \cdot a - a \cdot \left(t \cdot \frac{x}{c}\right)\right)} \]

   11. Taylor expanded in c around inf 26.5%

       \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   12. Step-by-step derivation

       1. *-commutative 26.5%

          \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

       2. associate-*l* 29.6%

          \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c} \]

       3. *-commutative 29.6%

          \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   13. Simplified 29.6%

       \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+18} \lor \neg \left(y \leq 1900\right):\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 30.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+88} \lor \neg \left(b \leq 9.2 \cdot 10^{+148}\right):\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -4.4e+88) (not (<= b 9.2e+148))) (* t (* b i)) (* c (* a j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -4.4e+88) || !(b <= 9.2e+148)) {
		tmp = t * (b * i);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-4.4d+88)) .or. (.not. (b <= 9.2d+148))) then
        tmp = t * (b * i)
    else
        tmp = c * (a * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -4.4e+88) || !(b <= 9.2e+148)) {
		tmp = t * (b * i);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -4.4e+88) or not (b <= 9.2e+148):
		tmp = t * (b * i)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -4.4e+88) || !(b <= 9.2e+148))
		tmp = Float64(t * Float64(b * i));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -4.4e+88) || ~((b <= 9.2e+148)))
		tmp = t * (b * i);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -4.4e+88], N[Not[LessEqual[b, 9.2e+148]], $MachinePrecision]], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.40000000000000017e88 or 9.2000000000000002e148 < b

   1. Initial program 66.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 66.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 69.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 69.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 69.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 69.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 70.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(a \cdot \left(c \cdot j\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   7. Simplified 72.0%

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j - t \cdot x\right) + y \cdot \left(z \cdot x - i \cdot j\right)\right) + b \cdot \left(t \cdot i - c \cdot z\right)} \]

   8. Taylor expanded in i around inf 46.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   9. Step-by-step derivation

      1. +-commutative 46.2%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 46.2%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 46.2%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      4. *-commutative 46.2%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} - j \cdot y\right) \]

      5. *-commutative 46.2%

         \[\leadsto i \cdot \left(t \cdot b - \color{blue}{y \cdot j}\right) \]

   10. Simplified 46.2%

       \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   11. Taylor expanded in t around inf 37.6%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 40.4%

          \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

       2. *-commutative 40.4%

          \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot t \]

   13. Simplified 40.4%

       \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot t} \]

   if -4.40000000000000017e88 < b < 9.2000000000000002e148

   1. Initial program 78.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 78.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 78.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 78.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 78.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 78.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 45.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 45.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 45.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 45.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   7. Simplified 45.3%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   8. Taylor expanded in c around inf 41.1%

      \[\leadsto \color{blue}{c \cdot \left(-1 \cdot \frac{a \cdot \left(t \cdot x\right)}{c} + a \cdot j\right)} \]
   9. Step-by-step derivation

      1. +-commutative 41.1%

         \[\leadsto c \cdot \color{blue}{\left(a \cdot j + -1 \cdot \frac{a \cdot \left(t \cdot x\right)}{c}\right)} \]

      2. mul-1-neg 41.1%

         \[\leadsto c \cdot \left(a \cdot j + \color{blue}{\left(-\frac{a \cdot \left(t \cdot x\right)}{c}\right)}\right) \]

      3. unsub-neg 41.1%

         \[\leadsto c \cdot \color{blue}{\left(a \cdot j - \frac{a \cdot \left(t \cdot x\right)}{c}\right)} \]

      4. *-commutative 41.1%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - \frac{a \cdot \left(t \cdot x\right)}{c}\right) \]

      5. associate-/l* 41.6%

         \[\leadsto c \cdot \left(j \cdot a - \color{blue}{a \cdot \frac{t \cdot x}{c}}\right) \]

      6. associate-/l* 40.5%

         \[\leadsto c \cdot \left(j \cdot a - a \cdot \color{blue}{\left(t \cdot \frac{x}{c}\right)}\right) \]

   10. Simplified 40.5%

       \[\leadsto \color{blue}{c \cdot \left(j \cdot a - a \cdot \left(t \cdot \frac{x}{c}\right)\right)} \]

   11. Taylor expanded in c around inf 24.1%

       \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   12. Step-by-step derivation

       1. *-commutative 24.1%

          \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

       2. associate-*l* 26.9%

          \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c} \]

       3. *-commutative 26.9%

          \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   13. Simplified 26.9%

       \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+88} \lor \neg \left(b \leq 9.2 \cdot 10^{+148}\right):\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -7 \cdot 10^{+23} \lor \neg \left(c \leq 2.5 \cdot 10^{-111}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -7e+23) (not (<= c 2.5e-111))) (* c (* a j)) (* i (* t b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -7e+23) || !(c <= 2.5e-111)) {
		tmp = c * (a * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-7d+23)) .or. (.not. (c <= 2.5d-111))) then
        tmp = c * (a * j)
    else
        tmp = i * (t * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -7e+23) || !(c <= 2.5e-111)) {
		tmp = c * (a * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -7e+23) or not (c <= 2.5e-111):
		tmp = c * (a * j)
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -7e+23) || !(c <= 2.5e-111))
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -7e+23) || ~((c <= 2.5e-111)))
		tmp = c * (a * j);
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -7e+23], N[Not[LessEqual[c, 2.5e-111]], $MachinePrecision]], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -7.0000000000000004e23 or 2.5000000000000001e-111 < c

   1. Initial program 72.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 72.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 74.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 74.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 74.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 74.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 47.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 47.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 47.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 47.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   7. Simplified 47.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   8. Taylor expanded in c around inf 45.3%

      \[\leadsto \color{blue}{c \cdot \left(-1 \cdot \frac{a \cdot \left(t \cdot x\right)}{c} + a \cdot j\right)} \]
   9. Step-by-step derivation

      1. +-commutative 45.3%

         \[\leadsto c \cdot \color{blue}{\left(a \cdot j + -1 \cdot \frac{a \cdot \left(t \cdot x\right)}{c}\right)} \]

      2. mul-1-neg 45.3%

         \[\leadsto c \cdot \left(a \cdot j + \color{blue}{\left(-\frac{a \cdot \left(t \cdot x\right)}{c}\right)}\right) \]

      3. unsub-neg 45.3%

         \[\leadsto c \cdot \color{blue}{\left(a \cdot j - \frac{a \cdot \left(t \cdot x\right)}{c}\right)} \]

      4. *-commutative 45.3%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - \frac{a \cdot \left(t \cdot x\right)}{c}\right) \]

      5. associate-/l* 46.0%

         \[\leadsto c \cdot \left(j \cdot a - \color{blue}{a \cdot \frac{t \cdot x}{c}}\right) \]

      6. associate-/l* 44.0%

         \[\leadsto c \cdot \left(j \cdot a - a \cdot \color{blue}{\left(t \cdot \frac{x}{c}\right)}\right) \]

   10. Simplified 44.0%

       \[\leadsto \color{blue}{c \cdot \left(j \cdot a - a \cdot \left(t \cdot \frac{x}{c}\right)\right)} \]

   11. Taylor expanded in c around inf 31.9%

       \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   12. Step-by-step derivation

       1. *-commutative 31.9%

          \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

       2. associate-*l* 33.4%

          \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c} \]

       3. *-commutative 33.4%

          \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   13. Simplified 33.4%

       \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   if -7.0000000000000004e23 < c < 2.5000000000000001e-111

   1. Initial program 77.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 77.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 78.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 78.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 78.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 78.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 77.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(a \cdot \left(c \cdot j\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   7. Simplified 77.8%

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j - t \cdot x\right) + y \cdot \left(z \cdot x - i \cdot j\right)\right) + b \cdot \left(t \cdot i - c \cdot z\right)} \]

   8. Taylor expanded in t around inf 45.0%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)} \]
   9. Step-by-step derivation

      1. +-commutative 45.0%

         \[\leadsto t \cdot \color{blue}{\left(b \cdot i + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 45.0%

         \[\leadsto t \cdot \left(b \cdot i + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 45.0%

         \[\leadsto t \cdot \color{blue}{\left(b \cdot i - a \cdot x\right)} \]

      4. *-commutative 45.0%

         \[\leadsto t \cdot \left(\color{blue}{i \cdot b} - a \cdot x\right) \]

      5. *-commutative 45.0%

         \[\leadsto t \cdot \left(i \cdot b - \color{blue}{x \cdot a}\right) \]

   10. Simplified 45.0%

       \[\leadsto \color{blue}{t \cdot \left(i \cdot b - x \cdot a\right)} \]

   11. Taylor expanded in i around inf 27.0%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 24.8%

          \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

       2. *-commutative 24.8%

          \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot t \]

       3. associate-*r* 27.8%

          \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]

   13. Simplified 27.8%

       \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7 \cdot 10^{+23} \lor \neg \left(c \leq 2.5 \cdot 10^{-111}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 30.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -7.1 \cdot 10^{+19} \lor \neg \left(c \leq 8.8 \cdot 10^{-16}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -7.1e+19) (not (<= c 8.8e-16))) (* c (* a j)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -7.1e+19) || !(c <= 8.8e-16)) {
		tmp = c * (a * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-7.1d+19)) .or. (.not. (c <= 8.8d-16))) then
        tmp = c * (a * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -7.1e+19) || !(c <= 8.8e-16)) {
		tmp = c * (a * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -7.1e+19) or not (c <= 8.8e-16):
		tmp = c * (a * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -7.1e+19) || !(c <= 8.8e-16))
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -7.1e+19) || ~((c <= 8.8e-16)))
		tmp = c * (a * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -7.1e+19], N[Not[LessEqual[c, 8.8e-16]], $MachinePrecision]], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -7.1e19 or 8.80000000000000001e-16 < c

   1. Initial program 69.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 69.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 70.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 70.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 70.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 70.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 47.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 47.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 47.6%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 47.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   7. Simplified 47.6%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   8. Taylor expanded in c around inf 47.7%

      \[\leadsto \color{blue}{c \cdot \left(-1 \cdot \frac{a \cdot \left(t \cdot x\right)}{c} + a \cdot j\right)} \]
   9. Step-by-step derivation

      1. +-commutative 47.7%

         \[\leadsto c \cdot \color{blue}{\left(a \cdot j + -1 \cdot \frac{a \cdot \left(t \cdot x\right)}{c}\right)} \]

      2. mul-1-neg 47.7%

         \[\leadsto c \cdot \left(a \cdot j + \color{blue}{\left(-\frac{a \cdot \left(t \cdot x\right)}{c}\right)}\right) \]

      3. unsub-neg 47.7%

         \[\leadsto c \cdot \color{blue}{\left(a \cdot j - \frac{a \cdot \left(t \cdot x\right)}{c}\right)} \]

      4. *-commutative 47.7%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - \frac{a \cdot \left(t \cdot x\right)}{c}\right) \]

      5. associate-/l* 48.5%

         \[\leadsto c \cdot \left(j \cdot a - \color{blue}{a \cdot \frac{t \cdot x}{c}}\right) \]

      6. associate-/l* 46.2%

         \[\leadsto c \cdot \left(j \cdot a - a \cdot \color{blue}{\left(t \cdot \frac{x}{c}\right)}\right) \]

   10. Simplified 46.2%

       \[\leadsto \color{blue}{c \cdot \left(j \cdot a - a \cdot \left(t \cdot \frac{x}{c}\right)\right)} \]

   11. Taylor expanded in c around inf 35.0%

       \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   12. Step-by-step derivation

       1. *-commutative 35.0%

          \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

       2. associate-*l* 36.7%

          \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c} \]

       3. *-commutative 36.7%

          \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   13. Simplified 36.7%

       \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   if -7.1e19 < c < 8.80000000000000001e-16

   1. Initial program 79.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 79.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 80.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 80.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 80.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 80.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 80.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(a \cdot \left(c \cdot j\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   7. Simplified 80.8%

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j - t \cdot x\right) + y \cdot \left(z \cdot x - i \cdot j\right)\right) + b \cdot \left(t \cdot i - c \cdot z\right)} \]

   8. Taylor expanded in i around inf 44.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   9. Step-by-step derivation

      1. +-commutative 44.0%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 44.0%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 44.0%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      4. *-commutative 44.0%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} - j \cdot y\right) \]

      5. *-commutative 44.0%

         \[\leadsto i \cdot \left(t \cdot b - \color{blue}{y \cdot j}\right) \]

   10. Simplified 44.0%

       \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   11. Taylor expanded in t around inf 25.7%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.1 \cdot 10^{+19} \lor \neg \left(c \leq 8.8 \cdot 10^{-16}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 30.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -8 \cdot 10^{+21} \lor \neg \left(c \leq 3.4 \cdot 10^{-16}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -8e+21) (not (<= c 3.4e-16))) (* a (* c j)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -8e+21) || !(c <= 3.4e-16)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-8d+21)) .or. (.not. (c <= 3.4d-16))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -8e+21) || !(c <= 3.4e-16)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -8e+21) or not (c <= 3.4e-16):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -8e+21) || !(c <= 3.4e-16))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -8e+21) || ~((c <= 3.4e-16)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -8e+21], N[Not[LessEqual[c, 3.4e-16]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -8e21 or 3.4e-16 < c

   1. Initial program 69.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 69.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 70.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 70.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 70.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 70.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 47.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 47.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 47.6%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 47.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   7. Simplified 47.6%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   8. Taylor expanded in c around inf 35.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   9. Step-by-step derivation

      1. *-commutative 62.8%

         \[\leadsto \left(a \cdot \color{blue}{\left(j \cdot c\right)} + y \cdot \left(j \cdot \left(x \cdot \frac{z}{j} - i\right)\right)\right) + b \cdot \left(t \cdot i - c \cdot z\right) \]

   10. Simplified 35.0%

       \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

   if -8e21 < c < 3.4e-16

   1. Initial program 79.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 79.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 80.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 80.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 80.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 80.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 80.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(a \cdot \left(c \cdot j\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   7. Simplified 80.8%

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j - t \cdot x\right) + y \cdot \left(z \cdot x - i \cdot j\right)\right) + b \cdot \left(t \cdot i - c \cdot z\right)} \]

   8. Taylor expanded in i around inf 44.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   9. Step-by-step derivation

      1. +-commutative 44.0%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 44.0%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 44.0%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      4. *-commutative 44.0%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} - j \cdot y\right) \]

      5. *-commutative 44.0%

         \[\leadsto i \cdot \left(t \cdot b - \color{blue}{y \cdot j}\right) \]

   10. Simplified 44.0%

       \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   11. Taylor expanded in t around inf 25.7%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8 \cdot 10^{+21} \lor \neg \left(c \leq 3.4 \cdot 10^{-16}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 23.1% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (c * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 74.4%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Step-by-step derivation

   1. +-commutative 74.4%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

   2. fma-define 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

   3. *-commutative 76.0%

      \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

   4. *-commutative 76.0%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

3. Simplified 76.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in a around inf 39.2%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
6. Step-by-step derivation

   1. +-commutative 39.2%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 39.2%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 39.2%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

7. Simplified 39.2%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

8. Taylor expanded in c around inf 20.3%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
9. Step-by-step derivation

   1. *-commutative 65.2%

      \[\leadsto \left(a \cdot \color{blue}{\left(j \cdot c\right)} + y \cdot \left(j \cdot \left(x \cdot \frac{z}{j} - i\right)\right)\right) + b \cdot \left(t \cdot i - c \cdot z\right) \]

10. Simplified 20.3%

    \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

11. Final simplification 20.3%

    \[\leadsto a \cdot \left(c \cdot j\right) \]
12. Add Preprocessing

Developer Target 1: 59.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024139 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -293938859355541/2000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 32113527362226803/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))