Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 72.4% → 81.1%

Time: 18.3s

Alternatives: 22

Speedup: 0.8×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 72.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t - z \cdot y\right) \cdot x - \left(i \cdot a - c \cdot z\right) \cdot b\\ \mathbf{if}\;\left(c \cdot t - i \cdot y\right) \cdot j - t\_1 \leq \infty:\\ \;\;\;\;\frac{j}{\frac{1}{\mathsf{fma}\left(-y, i, c \cdot t\right)}} - t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-x, t, i \cdot b\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* (- (* a t) (* z y)) x) (* (- (* i a) (* c z)) b))))
   (if (<= (- (* (- (* c t) (* i y)) j) t_1) INFINITY)
     (- (/ j (/ 1.0 (fma (- y) i (* c t)))) t_1)
     (* (fma (- x) t (* i b)) a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (((a * t) - (z * y)) * x) - (((i * a) - (c * z)) * b);
	double tmp;
	if (((((c * t) - (i * y)) * j) - t_1) <= ((double) INFINITY)) {
		tmp = (j / (1.0 / fma(-y, i, (c * t)))) - t_1;
	} else {
		tmp = fma(-x, t, (i * b)) * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(Float64(a * t) - Float64(z * y)) * x) - Float64(Float64(Float64(i * a) - Float64(c * z)) * b))
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(c * t) - Float64(i * y)) * j) - t_1) <= Inf)
		tmp = Float64(Float64(j / Float64(1.0 / fma(Float64(-y), i, Float64(c * t)))) - t_1);
	else
		tmp = Float64(fma(Float64(-x), t, Float64(i * b)) * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(N[(a * t), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] - N[(N[(N[(i * a), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision] - t$95$1), $MachinePrecision], Infinity], N[(N[(j / N[(1.0 / N[((-y) * i + N[(c * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.7%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. flip-- N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

      9. lift--.f64 N/A

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

      10. lower-/.f64 91.7

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

      11. lift--.f64 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. distribute-lft-neg-in N/A

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

      17. lower-fma.f64 N/A

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

      18. lower-neg.f64 91.7

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

   4. Applied rewrites 91.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, t, b \cdot i\right) \cdot a \]

      10. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, t, b \cdot i\right) \cdot a \]

      11. lower-*.f64 59.8

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

   5. Applied rewrites 59.8%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot t - i \cdot y\right) \cdot j - \left(\left(a \cdot t - z \cdot y\right) \cdot x - \left(i \cdot a - c \cdot z\right) \cdot b\right) \leq \infty:\\ \;\;\;\;\frac{j}{\frac{1}{\mathsf{fma}\left(-y, i, c \cdot t\right)}} - \left(\left(a \cdot t - z \cdot y\right) \cdot x - \left(i \cdot a - c \cdot z\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-x, t, i \cdot b\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 81.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, t, b \cdot i\right) \cdot a \]

      10. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, t, b \cdot i\right) \cdot a \]

      11. lower-*.f64 59.8

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

   5. Applied rewrites 59.8%

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

4. Final simplification 86.2%

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

Alternative 3: 76.9% accurate, 0.5× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.7%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 84.5%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, t, b \cdot i\right) \cdot a \]

      10. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, t, b \cdot i\right) \cdot a \]

      11. lower-*.f64 59.8

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

   5. Applied rewrites 59.8%

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

4. Final simplification 80.3%

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

Alternative 4: 77.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ t_2 := \mathsf{fma}\left(\mathsf{fma}\left(-b, z, j \cdot t\right), c, t\_1\right) - \mathsf{fma}\left(-b, a, j \cdot y\right) \cdot i\\ \mathbf{if}\;x \leq -4.9 \cdot 10^{-26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-132}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot a\right), b, \mathsf{fma}\left(\mathsf{fma}\left(-x, a, j \cdot c\right), t, \mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+88}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- t) a (* z y)) x))
        (t_2
         (- (fma (fma (- b) z (* j t)) c t_1) (* (fma (- b) a (* j y)) i))))
   (if (<= x -4.9e-26)
     t_2
     (if (<= x 2.75e-132)
       (fma
        (fma (- c) z (* i a))
        b
        (fma (fma (- x) a (* j c)) t (* (fma (- j) i (* z x)) y)))
       (if (<= x 4.2e+88) t_2 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 = fma(-t, a, (z * y)) * x;
	double t_2 = fma(fma(-b, z, (j * t)), c, t_1) - (fma(-b, a, (j * y)) * i);
	double tmp;
	if (x <= -4.9e-26) {
		tmp = t_2;
	} else if (x <= 2.75e-132) {
		tmp = fma(fma(-c, z, (i * a)), b, fma(fma(-x, a, (j * c)), t, (fma(-j, i, (z * x)) * y)));
	} else if (x <= 4.2e+88) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-t), a, Float64(z * y)) * x)
	t_2 = Float64(fma(fma(Float64(-b), z, Float64(j * t)), c, t_1) - Float64(fma(Float64(-b), a, Float64(j * y)) * i))
	tmp = 0.0
	if (x <= -4.9e-26)
		tmp = t_2;
	elseif (x <= 2.75e-132)
		tmp = fma(fma(Float64(-c), z, Float64(i * a)), b, fma(fma(Float64(-x), a, Float64(j * c)), t, Float64(fma(Float64(-j), i, Float64(z * x)) * y)));
	elseif (x <= 4.2e+88)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-t) * a + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[((-b) * z + N[(j * t), $MachinePrecision]), $MachinePrecision] * c + t$95$1), $MachinePrecision] - N[(N[((-b) * a + N[(j * y), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.9e-26], t$95$2, If[LessEqual[x, 2.75e-132], N[(N[((-c) * z + N[(i * a), $MachinePrecision]), $MachinePrecision] * b + N[(N[((-x) * a + N[(j * c), $MachinePrecision]), $MachinePrecision] * t + N[(N[((-j) * i + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e+88], t$95$2, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.8999999999999999e-26 or 2.75e-132 < x < 4.2e88

   1. Initial program 74.8%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 82.7%

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

   if -4.8999999999999999e-26 < x < 2.75e-132

   1. Initial program 79.2%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 89.0%

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

   if 4.2e88 < x

   1. Initial program 71.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. distribute-lft-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, a, y \cdot z\right) \cdot x \]

      10. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, a, y \cdot z\right) \cdot x \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(t\right), a, \color{blue}{z \cdot y}\right) \cdot x \]

      12. lower-*.f64 80.9

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

   5. Applied rewrites 80.9%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{-26}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-b, z, j \cdot t\right), c, \mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\right) - \mathsf{fma}\left(-b, a, j \cdot y\right) \cdot i\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-132}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot a\right), b, \mathsf{fma}\left(\mathsf{fma}\left(-x, a, j \cdot c\right), t, \mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-b, z, j \cdot t\right), c, \mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\right) - \mathsf{fma}\left(-b, a, j \cdot y\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \mathbf{if}\;x \leq -6.6 \cdot 10^{-63}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-j, y, b \cdot a\right), i, t\_1\right)\\ \mathbf{elif}\;x \leq 6.3 \cdot 10^{-136}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot a\right), b, \mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-y, j, b \cdot a\right), i, \mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- t) a (* z y)) x)))
   (if (<= x -6.6e-63)
     (fma (fma (- j) y (* b a)) i t_1)
     (if (<= x 6.3e-136)
       (fma (fma (- c) z (* i a)) b (* (fma (- j) i (* z x)) y))
       (if (<= x 2.2e+38)
         (fma (fma (- y) j (* b a)) i (* (fma (- c) b (* y x)) z))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-t, a, (z * y)) * x;
	double tmp;
	if (x <= -6.6e-63) {
		tmp = fma(fma(-j, y, (b * a)), i, t_1);
	} else if (x <= 6.3e-136) {
		tmp = fma(fma(-c, z, (i * a)), b, (fma(-j, i, (z * x)) * y));
	} else if (x <= 2.2e+38) {
		tmp = fma(fma(-y, j, (b * a)), i, (fma(-c, b, (y * x)) * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-t), a, Float64(z * y)) * x)
	tmp = 0.0
	if (x <= -6.6e-63)
		tmp = fma(fma(Float64(-j), y, Float64(b * a)), i, t_1);
	elseif (x <= 6.3e-136)
		tmp = fma(fma(Float64(-c), z, Float64(i * a)), b, Float64(fma(Float64(-j), i, Float64(z * x)) * y));
	elseif (x <= 2.2e+38)
		tmp = fma(fma(Float64(-y), j, Float64(b * a)), i, Float64(fma(Float64(-c), b, Float64(y * x)) * z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-t) * a + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -6.6e-63], N[(N[((-j) * y + N[(b * a), $MachinePrecision]), $MachinePrecision] * i + t$95$1), $MachinePrecision], If[LessEqual[x, 6.3e-136], N[(N[((-c) * z + N[(i * a), $MachinePrecision]), $MachinePrecision] * b + N[(N[((-j) * i + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e+38], N[(N[((-y) * j + N[(b * a), $MachinePrecision]), $MachinePrecision] * i + N[(N[((-c) * b + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.59999999999999987e-63

   1. Initial program 81.9%

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

   3. Taylor expanded in c around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. cancel-sign-sub N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

      9. distribute-rgt-in N/A

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

      10. cancel-sign-sub N/A

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

      11. mul-1-neg N/A

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

      12. associate-*r* N/A

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

      13. +-commutative N/A

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

   5. Applied rewrites 69.7%

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

   if -6.59999999999999987e-63 < x < 6.3000000000000004e-136

   1. Initial program 77.9%

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

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

   5. Applied rewrites 72.1%

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

   if 6.3000000000000004e-136 < x < 2.20000000000000006e38

   1. Initial program 68.7%

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

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

   5. Applied rewrites 62.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 75.5%

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

   if 2.20000000000000006e38 < x

   1. Initial program 71.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. distribute-lft-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, a, y \cdot z\right) \cdot x \]

      10. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, a, y \cdot z\right) \cdot x \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(t\right), a, \color{blue}{z \cdot y}\right) \cdot x \]

      12. lower-*.f64 77.1

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

   5. Applied rewrites 77.1%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{-63}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-j, y, b \cdot a\right), i, \mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\right)\\ \mathbf{elif}\;x \leq 6.3 \cdot 10^{-136}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot a\right), b, \mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-y, j, b \cdot a\right), i, \mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.3 \cdot 10^{-136}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot a\right), b, \mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-y, j, b \cdot a\right), i, \mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- t) a (* z y)) x)))
   (if (<= x -1.65e+86)
     t_1
     (if (<= x 6.3e-136)
       (fma (fma (- c) z (* i a)) b (* (fma (- j) i (* z x)) y))
       (if (<= x 2.2e+38)
         (fma (fma (- y) j (* b a)) i (* (fma (- c) b (* y x)) z))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-t, a, (z * y)) * x;
	double tmp;
	if (x <= -1.65e+86) {
		tmp = t_1;
	} else if (x <= 6.3e-136) {
		tmp = fma(fma(-c, z, (i * a)), b, (fma(-j, i, (z * x)) * y));
	} else if (x <= 2.2e+38) {
		tmp = fma(fma(-y, j, (b * a)), i, (fma(-c, b, (y * x)) * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-t), a, Float64(z * y)) * x)
	tmp = 0.0
	if (x <= -1.65e+86)
		tmp = t_1;
	elseif (x <= 6.3e-136)
		tmp = fma(fma(Float64(-c), z, Float64(i * a)), b, Float64(fma(Float64(-j), i, Float64(z * x)) * y));
	elseif (x <= 2.2e+38)
		tmp = fma(fma(Float64(-y), j, Float64(b * a)), i, Float64(fma(Float64(-c), b, Float64(y * x)) * z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-t) * a + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.65e+86], t$95$1, If[LessEqual[x, 6.3e-136], N[(N[((-c) * z + N[(i * a), $MachinePrecision]), $MachinePrecision] * b + N[(N[((-j) * i + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e+38], N[(N[((-y) * j + N[(b * a), $MachinePrecision]), $MachinePrecision] * i + N[(N[((-c) * b + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.65e86 or 2.20000000000000006e38 < x

   1. Initial program 75.3%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. distribute-lft-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, a, y \cdot z\right) \cdot x \]

      10. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, a, y \cdot z\right) \cdot x \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(t\right), a, \color{blue}{z \cdot y}\right) \cdot x \]

      12. lower-*.f64 75.3

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

   5. Applied rewrites 75.3%

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

   if -1.65e86 < x < 6.3000000000000004e-136

   1. Initial program 79.1%

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

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

   5. Applied rewrites 69.5%

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

   if 6.3000000000000004e-136 < x < 2.20000000000000006e38

   1. Initial program 68.7%

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

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

   5. Applied rewrites 62.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 75.5%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+86}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq 6.3 \cdot 10^{-136}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot a\right), b, \mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-y, j, b \cdot a\right), i, \mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot a\right), b, \left(y \cdot x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-276}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-x, t, i \cdot b\right), a, \left(j \cdot t\right) \cdot c\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+78}:\\ \;\;\;\;\left(\left(-a\right) \cdot t\right) \cdot x - \left(i \cdot y - c \cdot t\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (fma (fma (- c) z (* i a)) b (* (* y x) z))))
   (if (<= z -3.7e-67)
     t_1
     (if (<= z -2.55e-276)
       (fma (fma (- x) t (* i b)) a (* (* j t) c))
       (if (<= z 4.2e+78)
         (- (* (* (- a) t) x) (* (- (* i y) (* c t)) j))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(fma(-c, z, (i * a)), b, ((y * x) * z));
	double tmp;
	if (z <= -3.7e-67) {
		tmp = t_1;
	} else if (z <= -2.55e-276) {
		tmp = fma(fma(-x, t, (i * b)), a, ((j * t) * c));
	} else if (z <= 4.2e+78) {
		tmp = ((-a * t) * x) - (((i * y) - (c * t)) * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = fma(fma(Float64(-c), z, Float64(i * a)), b, Float64(Float64(y * x) * z))
	tmp = 0.0
	if (z <= -3.7e-67)
		tmp = t_1;
	elseif (z <= -2.55e-276)
		tmp = fma(fma(Float64(-x), t, Float64(i * b)), a, Float64(Float64(j * t) * c));
	elseif (z <= 4.2e+78)
		tmp = Float64(Float64(Float64(Float64(-a) * t) * x) - Float64(Float64(Float64(i * y) - Float64(c * t)) * j));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-c) * z + N[(i * a), $MachinePrecision]), $MachinePrecision] * b + N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.7e-67], t$95$1, If[LessEqual[z, -2.55e-276], N[(N[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a + N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+78], N[(N[(N[((-a) * t), $MachinePrecision] * x), $MachinePrecision] - N[(N[(N[(i * y), $MachinePrecision] - N[(c * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6999999999999999e-67 or 4.2000000000000002e78 < z

   1. Initial program 70.0%

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

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

   5. Applied rewrites 66.3%

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

   6. Taylor expanded in j around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{neg}\left(c\right), z, a \cdot i\right), b, x \cdot \left(y \cdot z\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 70.0%

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

   if -3.6999999999999999e-67 < z < -2.54999999999999984e-276

   1. Initial program 76.2%

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

   3. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. cancel-sign-sub N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. cancel-sign-sub N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. distribute-lft-out-- N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. distribute-lft-out-- N/A

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

      13. +-commutative N/A

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

   5. Applied rewrites 67.4%

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

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{neg}\left(x\right), t, b \cdot i\right), a, c \cdot \left(j \cdot t\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 72.3%

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

   if -2.54999999999999984e-276 < z < 4.2000000000000002e78

   1. Initial program 84.8%

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

   3. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-*.f64 70.5

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

   5. Applied rewrites 70.5%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-67}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot a\right), b, \left(y \cdot x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-276}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-x, t, i \cdot b\right), a, \left(j \cdot t\right) \cdot c\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+78}:\\ \;\;\;\;\left(\left(-a\right) \cdot t\right) \cdot x - \left(i \cdot y - c \cdot t\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot a\right), b, \left(y \cdot x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-75}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-y, j, b \cdot a\right), i, \mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-x, t, i \cdot b\right), a, \mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot a\right), b, \left(y \cdot x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -1.25e-75)
   (fma (fma (- y) j (* b a)) i (* (fma (- c) b (* y x)) z))
   (if (<= z 4.2e+79)
     (fma (fma (- x) t (* i b)) a (* (fma (- i) y (* c t)) j))
     (fma (fma (- c) z (* i a)) b (* (* y x) z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.25e-75) {
		tmp = fma(fma(-y, j, (b * a)), i, (fma(-c, b, (y * x)) * z));
	} else if (z <= 4.2e+79) {
		tmp = fma(fma(-x, t, (i * b)), a, (fma(-i, y, (c * t)) * j));
	} else {
		tmp = fma(fma(-c, z, (i * a)), b, ((y * x) * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -1.25e-75)
		tmp = fma(fma(Float64(-y), j, Float64(b * a)), i, Float64(fma(Float64(-c), b, Float64(y * x)) * z));
	elseif (z <= 4.2e+79)
		tmp = fma(fma(Float64(-x), t, Float64(i * b)), a, Float64(fma(Float64(-i), y, Float64(c * t)) * j));
	else
		tmp = fma(fma(Float64(-c), z, Float64(i * a)), b, Float64(Float64(y * x) * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -1.25e-75], N[(N[((-y) * j + N[(b * a), $MachinePrecision]), $MachinePrecision] * i + N[(N[((-c) * b + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+79], N[(N[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a + N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision], N[(N[((-c) * z + N[(i * a), $MachinePrecision]), $MachinePrecision] * b + N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.24999999999999995e-75

   1. Initial program 71.2%

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

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

   5. Applied rewrites 62.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 69.1%

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

   if -1.24999999999999995e-75 < z < 4.20000000000000016e79

   1. Initial program 83.0%

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

   3. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. cancel-sign-sub N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. cancel-sign-sub N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. distribute-lft-out-- N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. distribute-lft-out-- N/A

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

      13. +-commutative N/A

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

   5. Applied rewrites 74.9%

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

   if 4.20000000000000016e79 < z

   1. Initial program 66.5%

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

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

   5. Applied rewrites 70.8%

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

   6. Taylor expanded in j around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{neg}\left(c\right), z, a \cdot i\right), b, x \cdot \left(y \cdot z\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 76.2%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-75}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-y, j, b \cdot a\right), i, \mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-x, t, i \cdot b\right), a, \mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot a\right), b, \left(y \cdot x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-y, j, b \cdot a\right), i, \mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- t) a (* z y)) x)))
   (if (<= x -1.55e+91)
     t_1
     (if (<= x 2.2e+38)
       (fma (fma (- y) j (* b a)) i (* (fma (- c) b (* y x)) z))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-t, a, (z * y)) * x;
	double tmp;
	if (x <= -1.55e+91) {
		tmp = t_1;
	} else if (x <= 2.2e+38) {
		tmp = fma(fma(-y, j, (b * a)), i, (fma(-c, b, (y * x)) * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-t), a, Float64(z * y)) * x)
	tmp = 0.0
	if (x <= -1.55e+91)
		tmp = t_1;
	elseif (x <= 2.2e+38)
		tmp = fma(fma(Float64(-y), j, Float64(b * a)), i, Float64(fma(Float64(-c), b, Float64(y * x)) * z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-t) * a + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.55e+91], t$95$1, If[LessEqual[x, 2.2e+38], N[(N[((-y) * j + N[(b * a), $MachinePrecision]), $MachinePrecision] * i + N[(N[((-c) * b + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.54999999999999999e91 or 2.20000000000000006e38 < x

   1. Initial program 75.1%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. distribute-lft-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, a, y \cdot z\right) \cdot x \]

      10. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, a, y \cdot z\right) \cdot x \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(t\right), a, \color{blue}{z \cdot y}\right) \cdot x \]

      12. lower-*.f64 76.1

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

   5. Applied rewrites 76.1%

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

   if -1.54999999999999999e91 < x < 2.20000000000000006e38

   1. Initial program 76.5%

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

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

   5. Applied rewrites 67.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 67.0%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+91}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-y, j, b \cdot a\right), i, \mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 29.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(-t\right) \cdot x\right) \cdot a\\ \mathbf{if}\;x \leq -5.4 \cdot 10^{+213}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-224}:\\ \;\;\;\;\left(\left(-z\right) \cdot c\right) \cdot b\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-34}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+33}:\\ \;\;\;\;\left(\left(-b\right) \cdot z\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* (- t) x) a)))
   (if (<= x -5.4e+213)
     (* (* y x) z)
     (if (<= x -6.2e-64)
       t_1
       (if (<= x -2.4e-224)
         (* (* (- z) c) b)
         (if (<= x 3.8e-34)
           (* (* i b) a)
           (if (<= x 3.9e+33) (* (* (- b) 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 = (-t * x) * a;
	double tmp;
	if (x <= -5.4e+213) {
		tmp = (y * x) * z;
	} else if (x <= -6.2e-64) {
		tmp = t_1;
	} else if (x <= -2.4e-224) {
		tmp = (-z * c) * b;
	} else if (x <= 3.8e-34) {
		tmp = (i * b) * a;
	} else if (x <= 3.9e+33) {
		tmp = (-b * 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 = (-t * x) * a
    if (x <= (-5.4d+213)) then
        tmp = (y * x) * z
    else if (x <= (-6.2d-64)) then
        tmp = t_1
    else if (x <= (-2.4d-224)) then
        tmp = (-z * c) * b
    else if (x <= 3.8d-34) then
        tmp = (i * b) * a
    else if (x <= 3.9d+33) then
        tmp = (-b * 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 = (-t * x) * a;
	double tmp;
	if (x <= -5.4e+213) {
		tmp = (y * x) * z;
	} else if (x <= -6.2e-64) {
		tmp = t_1;
	} else if (x <= -2.4e-224) {
		tmp = (-z * c) * b;
	} else if (x <= 3.8e-34) {
		tmp = (i * b) * a;
	} else if (x <= 3.9e+33) {
		tmp = (-b * z) * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (-t * x) * a
	tmp = 0
	if x <= -5.4e+213:
		tmp = (y * x) * z
	elif x <= -6.2e-64:
		tmp = t_1
	elif x <= -2.4e-224:
		tmp = (-z * c) * b
	elif x <= 3.8e-34:
		tmp = (i * b) * a
	elif x <= 3.9e+33:
		tmp = (-b * z) * c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(-t) * x) * a)
	tmp = 0.0
	if (x <= -5.4e+213)
		tmp = Float64(Float64(y * x) * z);
	elseif (x <= -6.2e-64)
		tmp = t_1;
	elseif (x <= -2.4e-224)
		tmp = Float64(Float64(Float64(-z) * c) * b);
	elseif (x <= 3.8e-34)
		tmp = Float64(Float64(i * b) * a);
	elseif (x <= 3.9e+33)
		tmp = Float64(Float64(Float64(-b) * 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 = (-t * x) * a;
	tmp = 0.0;
	if (x <= -5.4e+213)
		tmp = (y * x) * z;
	elseif (x <= -6.2e-64)
		tmp = t_1;
	elseif (x <= -2.4e-224)
		tmp = (-z * c) * b;
	elseif (x <= 3.8e-34)
		tmp = (i * b) * a;
	elseif (x <= 3.9e+33)
		tmp = (-b * 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[(N[((-t) * x), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[x, -5.4e+213], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[x, -6.2e-64], t$95$1, If[LessEqual[x, -2.4e-224], N[(N[((-z) * c), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[x, 3.8e-34], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[x, 3.9e+33], N[(N[((-b) * z), $MachinePrecision] * c), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -5.4000000000000002e213

   1. Initial program 75.5%

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

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

   5. Applied rewrites 56.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 61.5%

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

   if -5.4000000000000002e213 < x < -6.20000000000000049e-64 or 3.9000000000000002e33 < x

   1. Initial program 77.2%

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

   3. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. cancel-sign-sub N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. cancel-sign-sub N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. distribute-lft-out-- N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. distribute-lft-out-- N/A

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

      13. +-commutative N/A

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

   5. Applied rewrites 52.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 40.5%

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

   if -6.20000000000000049e-64 < x < -2.40000000000000014e-224

   1. Initial program 68.5%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot b, z, j \cdot t\right)} \cdot c \]

      8. neg-mul-1 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 53.3

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

   5. Applied rewrites 53.3%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 34.3%

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

   if -2.40000000000000014e-224 < x < 3.8000000000000001e-34

   1. Initial program 82.5%

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

   3. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. cancel-sign-sub N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. cancel-sign-sub N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. distribute-lft-out-- N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. distribute-lft-out-- N/A

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

      13. +-commutative N/A

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

   5. Applied rewrites 72.6%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 42.1%

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

   if 3.8000000000000001e-34 < x < 3.9000000000000002e33

   1. Initial program 59.8%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot b, z, j \cdot t\right)} \cdot c \]

      8. neg-mul-1 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 48.0

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

   5. Applied rewrites 48.0%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 41.9%

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

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+213}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-64}:\\ \;\;\;\;\left(\left(-t\right) \cdot x\right) \cdot a\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-224}:\\ \;\;\;\;\left(\left(-z\right) \cdot c\right) \cdot b\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-34}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+33}:\\ \;\;\;\;\left(\left(-b\right) \cdot z\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-t\right) \cdot x\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 43.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z\\ \mathbf{if}\;c \leq -8 \cdot 10^{+101}:\\ \;\;\;\;\mathsf{fma}\left(t, j, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-258}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 6.7 \cdot 10^{-57}:\\ \;\;\;\;\left(\left(-t\right) \cdot x\right) \cdot a\\ \mathbf{elif}\;c \leq 160000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-b, z, j \cdot t\right) \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- c) b (* y x)) z)))
   (if (<= c -8e+101)
     (* (fma t j (* (- b) z)) c)
     (if (<= c 6e-258)
       t_1
       (if (<= c 6.7e-57)
         (* (* (- t) x) a)
         (if (<= c 160000.0) t_1 (* (fma (- b) z (* j t)) 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 = fma(-c, b, (y * x)) * z;
	double tmp;
	if (c <= -8e+101) {
		tmp = fma(t, j, (-b * z)) * c;
	} else if (c <= 6e-258) {
		tmp = t_1;
	} else if (c <= 6.7e-57) {
		tmp = (-t * x) * a;
	} else if (c <= 160000.0) {
		tmp = t_1;
	} else {
		tmp = fma(-b, z, (j * t)) * c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-c), b, Float64(y * x)) * z)
	tmp = 0.0
	if (c <= -8e+101)
		tmp = Float64(fma(t, j, Float64(Float64(-b) * z)) * c);
	elseif (c <= 6e-258)
		tmp = t_1;
	elseif (c <= 6.7e-57)
		tmp = Float64(Float64(Float64(-t) * x) * a);
	elseif (c <= 160000.0)
		tmp = t_1;
	else
		tmp = Float64(fma(Float64(-b), z, Float64(j * t)) * c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-c) * b + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[c, -8e+101], N[(N[(t * j + N[((-b) * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[c, 6e-258], t$95$1, If[LessEqual[c, 6.7e-57], N[(N[((-t) * x), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[c, 160000.0], t$95$1, N[(N[((-b) * z + N[(j * t), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -7.9999999999999998e101

   1. Initial program 64.7%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot b, z, j \cdot t\right)} \cdot c \]

      8. neg-mul-1 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 70.0

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

   5. Applied rewrites 70.0%

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

   7. Applied rewrites 72.6%

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

   if -7.9999999999999998e101 < c < 6.00000000000000042e-258 or 6.7000000000000006e-57 < c < 1.6e5

   1. Initial program 80.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. neg-mul-1 N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 46.0

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

   5. Applied rewrites 46.0%

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

   if 6.00000000000000042e-258 < c < 6.7000000000000006e-57

   1. Initial program 79.2%

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

   3. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. cancel-sign-sub N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. cancel-sign-sub N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. distribute-lft-out-- N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. distribute-lft-out-- N/A

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

      13. +-commutative N/A

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

   5. Applied rewrites 74.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 45.8%

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

   if 1.6e5 < c

   1. Initial program 71.0%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot b, z, j \cdot t\right)} \cdot c \]

      8. neg-mul-1 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 63.1

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

   5. Applied rewrites 63.1%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8 \cdot 10^{+101}:\\ \;\;\;\;\mathsf{fma}\left(t, j, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-258}:\\ \;\;\;\;\mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z\\ \mathbf{elif}\;c \leq 6.7 \cdot 10^{-57}:\\ \;\;\;\;\left(\left(-t\right) \cdot x\right) \cdot a\\ \mathbf{elif}\;c \leq 160000:\\ \;\;\;\;\mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-b, z, j \cdot t\right) \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot a\right), b, \left(y \cdot x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+77}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-x, t, i \cdot b\right), a, \left(j \cdot t\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (fma (fma (- c) z (* i a)) b (* (* y x) z))))
   (if (<= z -3.7e-67)
     t_1
     (if (<= z 5.4e+77) (fma (fma (- x) t (* i b)) a (* (* j t) 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 = fma(fma(-c, z, (i * a)), b, ((y * x) * z));
	double tmp;
	if (z <= -3.7e-67) {
		tmp = t_1;
	} else if (z <= 5.4e+77) {
		tmp = fma(fma(-x, t, (i * b)), a, ((j * t) * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = fma(fma(Float64(-c), z, Float64(i * a)), b, Float64(Float64(y * x) * z))
	tmp = 0.0
	if (z <= -3.7e-67)
		tmp = t_1;
	elseif (z <= 5.4e+77)
		tmp = fma(fma(Float64(-x), t, Float64(i * b)), a, Float64(Float64(j * t) * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-c) * z + N[(i * a), $MachinePrecision]), $MachinePrecision] * b + N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.7e-67], t$95$1, If[LessEqual[z, 5.4e+77], N[(N[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a + N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6999999999999999e-67 or 5.3999999999999997e77 < z

   1. Initial program 70.0%

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

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

   5. Applied rewrites 66.3%

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

   6. Taylor expanded in j around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{neg}\left(c\right), z, a \cdot i\right), b, x \cdot \left(y \cdot z\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 70.0%

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

   if -3.6999999999999999e-67 < z < 5.3999999999999997e77

   1. Initial program 82.0%

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

   3. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. cancel-sign-sub N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. cancel-sign-sub N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. distribute-lft-out-- N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. distribute-lft-out-- N/A

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

      13. +-commutative N/A

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

   5. Applied rewrites 74.2%

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

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{neg}\left(x\right), t, b \cdot i\right), a, c \cdot \left(j \cdot t\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 67.1%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-x, t, b \cdot i\right), a, \left(j \cdot t\right) \cdot c\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-67}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot a\right), b, \left(y \cdot x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+77}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-x, t, i \cdot b\right), a, \left(j \cdot t\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot a\right), b, \left(y \cdot x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 56.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+57}:\\ \;\;\;\;\mathsf{fma}\left(-x, a, j \cdot c\right) \cdot t\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+102}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot a\right), b, \left(y \cdot x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, b, \left(-t\right) \cdot x\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -7.6e+57)
   (* (fma (- x) a (* j c)) t)
   (if (<= t 9e+102)
     (fma (fma (- c) z (* i a)) b (* (* y x) z))
     (* (fma i b (* (- t) x)) a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -7.6e+57) {
		tmp = fma(-x, a, (j * c)) * t;
	} else if (t <= 9e+102) {
		tmp = fma(fma(-c, z, (i * a)), b, ((y * x) * z));
	} else {
		tmp = fma(i, b, (-t * x)) * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -7.6e+57)
		tmp = Float64(fma(Float64(-x), a, Float64(j * c)) * t);
	elseif (t <= 9e+102)
		tmp = fma(fma(Float64(-c), z, Float64(i * a)), b, Float64(Float64(y * x) * z));
	else
		tmp = Float64(fma(i, b, Float64(Float64(-t) * x)) * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -7.6e+57], N[(N[((-x) * a + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, 9e+102], N[(N[((-c) * z + N[(i * a), $MachinePrecision]), $MachinePrecision] * b + N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(i * b + N[((-t) * x), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.5999999999999997e57

   1. Initial program 67.5%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, a, c \cdot j\right) \cdot t \]

      7. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, a, c \cdot j\right) \cdot t \]

      8. lower-*.f64 70.1

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

   5. Applied rewrites 70.1%

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

   if -7.5999999999999997e57 < t < 9.00000000000000042e102

   1. Initial program 82.9%

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

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

   5. Applied rewrites 68.4%

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

   6. Taylor expanded in j around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{neg}\left(c\right), z, a \cdot i\right), b, x \cdot \left(y \cdot z\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 63.8%

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

   if 9.00000000000000042e102 < t

   1. Initial program 63.8%

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

   4. Applied rewrites 68.3%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, x, b \cdot i\right) \cdot a \]

      6. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, x, b \cdot i\right) \cdot a \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(t\right), x, \color{blue}{i \cdot b}\right) \cdot a \]

      8. lower-*.f64 66.2

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

   7. Applied rewrites 66.2%

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

   9. Applied rewrites 66.3%

      \[\leadsto \mathsf{fma}\left(i, b, \left(-t\right) \cdot x\right) \cdot a \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+57}:\\ \;\;\;\;\mathsf{fma}\left(-x, a, j \cdot c\right) \cdot t\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+102}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot a\right), b, \left(y \cdot x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, b, \left(-t\right) \cdot x\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(-t\right) \cdot x\right) \cdot a\\ \mathbf{if}\;x \leq -5.4 \cdot 10^{+213}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-224}:\\ \;\;\;\;\left(\left(-z\right) \cdot c\right) \cdot b\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-20}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* (- t) x) a)))
   (if (<= x -5.4e+213)
     (* (* y x) z)
     (if (<= x -6.2e-64)
       t_1
       (if (<= x -2.4e-224)
         (* (* (- z) c) b)
         (if (<= x 2.65e-20) (* (* i b) 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 * x) * a;
	double tmp;
	if (x <= -5.4e+213) {
		tmp = (y * x) * z;
	} else if (x <= -6.2e-64) {
		tmp = t_1;
	} else if (x <= -2.4e-224) {
		tmp = (-z * c) * b;
	} else if (x <= 2.65e-20) {
		tmp = (i * b) * 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 * x) * a
    if (x <= (-5.4d+213)) then
        tmp = (y * x) * z
    else if (x <= (-6.2d-64)) then
        tmp = t_1
    else if (x <= (-2.4d-224)) then
        tmp = (-z * c) * b
    else if (x <= 2.65d-20) then
        tmp = (i * b) * 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 * x) * a;
	double tmp;
	if (x <= -5.4e+213) {
		tmp = (y * x) * z;
	} else if (x <= -6.2e-64) {
		tmp = t_1;
	} else if (x <= -2.4e-224) {
		tmp = (-z * c) * b;
	} else if (x <= 2.65e-20) {
		tmp = (i * b) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (-t * x) * a
	tmp = 0
	if x <= -5.4e+213:
		tmp = (y * x) * z
	elif x <= -6.2e-64:
		tmp = t_1
	elif x <= -2.4e-224:
		tmp = (-z * c) * b
	elif x <= 2.65e-20:
		tmp = (i * b) * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(-t) * x) * a)
	tmp = 0.0
	if (x <= -5.4e+213)
		tmp = Float64(Float64(y * x) * z);
	elseif (x <= -6.2e-64)
		tmp = t_1;
	elseif (x <= -2.4e-224)
		tmp = Float64(Float64(Float64(-z) * c) * b);
	elseif (x <= 2.65e-20)
		tmp = Float64(Float64(i * b) * 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 * x) * a;
	tmp = 0.0;
	if (x <= -5.4e+213)
		tmp = (y * x) * z;
	elseif (x <= -6.2e-64)
		tmp = t_1;
	elseif (x <= -2.4e-224)
		tmp = (-z * c) * b;
	elseif (x <= 2.65e-20)
		tmp = (i * b) * 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[(N[((-t) * x), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[x, -5.4e+213], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[x, -6.2e-64], t$95$1, If[LessEqual[x, -2.4e-224], N[(N[((-z) * c), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[x, 2.65e-20], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.4000000000000002e213

   1. Initial program 75.5%

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

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

   5. Applied rewrites 56.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 61.5%

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

   if -5.4000000000000002e213 < x < -6.20000000000000049e-64 or 2.6500000000000001e-20 < x

   1. Initial program 74.3%

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

   3. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. cancel-sign-sub N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. cancel-sign-sub N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. distribute-lft-out-- N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. distribute-lft-out-- N/A

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

      13. +-commutative N/A

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

   5. Applied rewrites 51.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 36.5%

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

   if -6.20000000000000049e-64 < x < -2.40000000000000014e-224

   1. Initial program 68.5%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot b, z, j \cdot t\right)} \cdot c \]

      8. neg-mul-1 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 53.3

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

   5. Applied rewrites 53.3%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 34.3%

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

   if -2.40000000000000014e-224 < x < 2.6500000000000001e-20

   1. Initial program 83.0%

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

   3. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. cancel-sign-sub N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. cancel-sign-sub N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. distribute-lft-out-- N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. distribute-lft-out-- N/A

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

      13. +-commutative N/A

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

   5. Applied rewrites 70.7%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 41.1%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+213}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-64}:\\ \;\;\;\;\left(\left(-t\right) \cdot x\right) \cdot a\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-224}:\\ \;\;\;\;\left(\left(-z\right) \cdot c\right) \cdot b\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-20}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-t\right) \cdot x\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-161}:\\ \;\;\;\;\mathsf{fma}\left(-c, z, i \cdot a\right) \cdot b\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(t, j, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- t) a (* z y)) x)))
   (if (<= x -2.4e+90)
     t_1
     (if (<= x 1.65e-161)
       (* (fma (- c) z (* i a)) b)
       (if (<= x 2e+20) (* (fma t j (* (- b) 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 = fma(-t, a, (z * y)) * x;
	double tmp;
	if (x <= -2.4e+90) {
		tmp = t_1;
	} else if (x <= 1.65e-161) {
		tmp = fma(-c, z, (i * a)) * b;
	} else if (x <= 2e+20) {
		tmp = fma(t, j, (-b * z)) * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-t), a, Float64(z * y)) * x)
	tmp = 0.0
	if (x <= -2.4e+90)
		tmp = t_1;
	elseif (x <= 1.65e-161)
		tmp = Float64(fma(Float64(-c), z, Float64(i * a)) * b);
	elseif (x <= 2e+20)
		tmp = Float64(fma(t, j, Float64(Float64(-b) * z)) * c);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-t) * a + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -2.4e+90], t$95$1, If[LessEqual[x, 1.65e-161], N[(N[((-c) * z + N[(i * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[x, 2e+20], N[(N[(t * j + N[((-b) * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.4000000000000001e90 or 2e20 < x

   1. Initial program 74.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. distribute-lft-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, a, y \cdot z\right) \cdot x \]

      10. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, a, y \cdot z\right) \cdot x \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(t\right), a, \color{blue}{z \cdot y}\right) \cdot x \]

      12. lower-*.f64 75.6

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

   5. Applied rewrites 75.6%

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

   if -2.4000000000000001e90 < x < 1.6499999999999999e-161

   1. Initial program 78.2%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. remove-double-neg N/A

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

      5. distribute-neg-in N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. distribute-neg-in N/A

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

      12. remove-double-neg N/A

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

      13. distribute-lft-neg-in N/A

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

      14. neg-mul-1 N/A

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

      15. lower-fma.f64 N/A

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

      16. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(c\right)}, z, a \cdot i\right) \cdot b \]

      17. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(c\right)}, z, a \cdot i\right) \cdot b \]

      18. lower-*.f64 52.2

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

   5. Applied rewrites 52.2%

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

   if 1.6499999999999999e-161 < x < 2e20

   1. Initial program 73.7%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot b, z, j \cdot t\right)} \cdot c \]

      8. neg-mul-1 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 58.1

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

   5. Applied rewrites 58.1%

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

   7. Applied rewrites 58.1%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+90}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-161}:\\ \;\;\;\;\mathsf{fma}\left(-c, z, i \cdot a\right) \cdot b\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(t, j, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-238}:\\ \;\;\;\;\mathsf{fma}\left(t, j, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(-c, z, i \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- j) i (* z x)) y)))
   (if (<= y -3.2e+34)
     t_1
     (if (<= y 1.3e-238)
       (* (fma t j (* (- b) z)) c)
       (if (<= y 8.8e+109) (* (fma (- c) z (* i a)) 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 = fma(-j, i, (z * x)) * y;
	double tmp;
	if (y <= -3.2e+34) {
		tmp = t_1;
	} else if (y <= 1.3e-238) {
		tmp = fma(t, j, (-b * z)) * c;
	} else if (y <= 8.8e+109) {
		tmp = fma(-c, z, (i * a)) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-j), i, Float64(z * x)) * y)
	tmp = 0.0
	if (y <= -3.2e+34)
		tmp = t_1;
	elseif (y <= 1.3e-238)
		tmp = Float64(fma(t, j, Float64(Float64(-b) * z)) * c);
	elseif (y <= 8.8e+109)
		tmp = Float64(fma(Float64(-c), z, Float64(i * a)) * b);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-j) * i + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -3.2e+34], t$95$1, If[LessEqual[y, 1.3e-238], N[(N[(t * j + N[((-b) * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[y, 8.8e+109], N[(N[((-c) * z + N[(i * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1999999999999998e34 or 8.7999999999999997e109 < y

   1. Initial program 64.4%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. lower-*.f64 64.5

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

   5. Applied rewrites 64.5%

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

   if -3.1999999999999998e34 < y < 1.3000000000000001e-238

   1. Initial program 81.5%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot b, z, j \cdot t\right)} \cdot c \]

      8. neg-mul-1 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 49.1

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

   5. Applied rewrites 49.1%

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

   7. Applied rewrites 49.1%

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

   if 1.3000000000000001e-238 < y < 8.7999999999999997e109

   1. Initial program 84.4%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. remove-double-neg N/A

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

      5. distribute-neg-in N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. distribute-neg-in N/A

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

      12. remove-double-neg N/A

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

      13. distribute-lft-neg-in N/A

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

      14. neg-mul-1 N/A

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

      15. lower-fma.f64 N/A

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

      16. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(c\right)}, z, a \cdot i\right) \cdot b \]

      17. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(c\right)}, z, a \cdot i\right) \cdot b \]

      18. lower-*.f64 52.8

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

   5. Applied rewrites 52.8%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+34}:\\ \;\;\;\;\mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-238}:\\ \;\;\;\;\mathsf{fma}\left(t, j, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(-c, z, i \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 49.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-c, z, i \cdot a\right) \cdot b\\ \mathbf{if}\;b \leq -4.1 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.4 \cdot 10^{-176}:\\ \;\;\;\;\left(\left(-t\right) \cdot x\right) \cdot a\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- c) z (* i a)) b)))
   (if (<= b -4.1e-16)
     t_1
     (if (<= b -5.4e-176)
       (* (* (- t) x) a)
       (if (<= b 2.1e+88) (* (fma (- i) y (* c t)) j) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-c, z, (i * a)) * b;
	double tmp;
	if (b <= -4.1e-16) {
		tmp = t_1;
	} else if (b <= -5.4e-176) {
		tmp = (-t * x) * a;
	} else if (b <= 2.1e+88) {
		tmp = fma(-i, y, (c * t)) * j;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-c), z, Float64(i * a)) * b)
	tmp = 0.0
	if (b <= -4.1e-16)
		tmp = t_1;
	elseif (b <= -5.4e-176)
		tmp = Float64(Float64(Float64(-t) * x) * a);
	elseif (b <= 2.1e+88)
		tmp = Float64(fma(Float64(-i), y, Float64(c * t)) * j);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-c) * z + N[(i * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -4.1e-16], t$95$1, If[LessEqual[b, -5.4e-176], N[(N[((-t) * x), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[b, 2.1e+88], N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.10000000000000006e-16 or 2.1e88 < b

   1. Initial program 77.6%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. remove-double-neg N/A

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

      5. distribute-neg-in N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. distribute-neg-in N/A

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

      12. remove-double-neg N/A

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

      13. distribute-lft-neg-in N/A

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

      14. neg-mul-1 N/A

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

      15. lower-fma.f64 N/A

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

      16. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(c\right)}, z, a \cdot i\right) \cdot b \]

      17. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(c\right)}, z, a \cdot i\right) \cdot b \]

      18. lower-*.f64 69.2

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

   5. Applied rewrites 69.2%

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

   if -4.10000000000000006e-16 < b < -5.3999999999999997e-176

   1. Initial program 69.1%

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

   3. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. cancel-sign-sub N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. cancel-sign-sub N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. distribute-lft-out-- N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. distribute-lft-out-- N/A

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

      13. +-commutative N/A

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

   5. Applied rewrites 59.5%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 44.7%

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

   if -5.3999999999999997e-176 < b < 2.1e88

   1. Initial program 76.5%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. cancel-sign-sub-inv N/A

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

      4. +-commutative N/A

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

      5. neg-mul-1 N/A

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

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot i, y, c \cdot t\right)} \cdot j \]

      7. neg-mul-1 N/A

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

      8. lower-neg.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 46.3

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

   5. Applied rewrites 46.3%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.1 \cdot 10^{-16}:\\ \;\;\;\;\mathsf{fma}\left(-c, z, i \cdot a\right) \cdot b\\ \mathbf{elif}\;b \leq -5.4 \cdot 10^{-176}:\\ \;\;\;\;\left(\left(-t\right) \cdot x\right) \cdot a\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-c, z, i \cdot a\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 42.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, j, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{if}\;c \leq -1.4 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-258}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{-38}:\\ \;\;\;\;\left(\left(-t\right) \cdot x\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma t j (* (- b) z)) c)))
   (if (<= c -1.4e-22)
     t_1
     (if (<= c 5.8e-258)
       (* (* y x) z)
       (if (<= c 3.3e-38) (* (* (- t) x) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(t, j, (-b * z)) * c;
	double tmp;
	if (c <= -1.4e-22) {
		tmp = t_1;
	} else if (c <= 5.8e-258) {
		tmp = (y * x) * z;
	} else if (c <= 3.3e-38) {
		tmp = (-t * x) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(t, j, Float64(Float64(-b) * z)) * c)
	tmp = 0.0
	if (c <= -1.4e-22)
		tmp = t_1;
	elseif (c <= 5.8e-258)
		tmp = Float64(Float64(y * x) * z);
	elseif (c <= 3.3e-38)
		tmp = Float64(Float64(Float64(-t) * x) * a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * j + N[((-b) * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]}, If[LessEqual[c, -1.4e-22], t$95$1, If[LessEqual[c, 5.8e-258], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[c, 3.3e-38], N[(N[((-t) * x), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.39999999999999997e-22 or 3.3000000000000002e-38 < c

   1. Initial program 69.6%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot b, z, j \cdot t\right)} \cdot c \]

      8. neg-mul-1 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 57.0

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

   5. Applied rewrites 57.0%

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

   7. Applied rewrites 58.5%

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

   if -1.39999999999999997e-22 < c < 5.7999999999999999e-258

   1. Initial program 82.1%

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

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

   5. Applied rewrites 63.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 31.8%

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

   if 5.7999999999999999e-258 < c < 3.3000000000000002e-38

   1. Initial program 82.4%

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

   3. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. cancel-sign-sub N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. cancel-sign-sub N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. distribute-lft-out-- N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. distribute-lft-out-- N/A

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

      13. +-commutative N/A

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

   5. Applied rewrites 70.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 42.7%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.4 \cdot 10^{-22}:\\ \;\;\;\;\mathsf{fma}\left(t, j, \left(-b\right) \cdot z\right) \cdot c\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-258}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{-38}:\\ \;\;\;\;\left(\left(-t\right) \cdot x\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, j, \left(-b\right) \cdot z\right) \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+83}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-224}:\\ \;\;\;\;\left(\left(-z\right) \cdot c\right) \cdot b\\ \mathbf{elif}\;x \leq 2.76 \cdot 10^{-14}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -2e+83)
   (* (* y x) z)
   (if (<= x -2.4e-224)
     (* (* (- z) c) b)
     (if (<= x 2.76e-14) (* (* i b) a) (* (* z y) x)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -2e+83) {
		tmp = (y * x) * z;
	} else if (x <= -2.4e-224) {
		tmp = (-z * c) * b;
	} else if (x <= 2.76e-14) {
		tmp = (i * b) * a;
	} else {
		tmp = (z * y) * x;
	}
	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 (x <= (-2d+83)) then
        tmp = (y * x) * z
    else if (x <= (-2.4d-224)) then
        tmp = (-z * c) * b
    else if (x <= 2.76d-14) then
        tmp = (i * b) * a
    else
        tmp = (z * y) * x
    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 (x <= -2e+83) {
		tmp = (y * x) * z;
	} else if (x <= -2.4e-224) {
		tmp = (-z * c) * b;
	} else if (x <= 2.76e-14) {
		tmp = (i * b) * a;
	} else {
		tmp = (z * y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -2e+83:
		tmp = (y * x) * z
	elif x <= -2.4e-224:
		tmp = (-z * c) * b
	elif x <= 2.76e-14:
		tmp = (i * b) * a
	else:
		tmp = (z * y) * x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -2e+83)
		tmp = Float64(Float64(y * x) * z);
	elseif (x <= -2.4e-224)
		tmp = Float64(Float64(Float64(-z) * c) * b);
	elseif (x <= 2.76e-14)
		tmp = Float64(Float64(i * b) * a);
	else
		tmp = Float64(Float64(z * y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -2e+83)
		tmp = (y * x) * z;
	elseif (x <= -2.4e-224)
		tmp = (-z * c) * b;
	elseif (x <= 2.76e-14)
		tmp = (i * b) * a;
	else
		tmp = (z * y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -2e+83], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[x, -2.4e-224], N[(N[((-z) * c), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[x, 2.76e-14], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.00000000000000006e83

   1. Initial program 80.6%

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

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

   5. Applied rewrites 37.3%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 42.8%

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

   if -2.00000000000000006e83 < x < -2.40000000000000014e-224

   1. Initial program 73.7%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot b, z, j \cdot t\right)} \cdot c \]

      8. neg-mul-1 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 46.5

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

   5. Applied rewrites 46.5%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 28.9%

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

   if -2.40000000000000014e-224 < x < 2.76000000000000004e-14

   1. Initial program 82.2%

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

   3. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. cancel-sign-sub N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. cancel-sign-sub N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. distribute-lft-out-- N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. distribute-lft-out-- N/A

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

      13. +-commutative N/A

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

   5. Applied rewrites 70.3%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 40.1%

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

   if 2.76000000000000004e-14 < x

   1. Initial program 67.9%

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

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

   5. Applied rewrites 49.2%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 35.5%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 36.9%

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

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+83}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-224}:\\ \;\;\;\;\left(\left(-z\right) \cdot c\right) \cdot b\\ \mathbf{elif}\;x \leq 2.76 \cdot 10^{-14}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+101}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{elif}\;x \leq 2.76 \cdot 10^{-14}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -2.9e+101)
   (* (* y x) z)
   (if (<= x 2.76e-14) (* (* i b) a) (* (* z y) x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -2.9e+101) {
		tmp = (y * x) * z;
	} else if (x <= 2.76e-14) {
		tmp = (i * b) * a;
	} else {
		tmp = (z * y) * x;
	}
	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 (x <= (-2.9d+101)) then
        tmp = (y * x) * z
    else if (x <= 2.76d-14) then
        tmp = (i * b) * a
    else
        tmp = (z * y) * x
    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 (x <= -2.9e+101) {
		tmp = (y * x) * z;
	} else if (x <= 2.76e-14) {
		tmp = (i * b) * a;
	} else {
		tmp = (z * y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -2.9e+101:
		tmp = (y * x) * z
	elif x <= 2.76e-14:
		tmp = (i * b) * a
	else:
		tmp = (z * y) * x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -2.9e+101)
		tmp = Float64(Float64(y * x) * z);
	elseif (x <= 2.76e-14)
		tmp = Float64(Float64(i * b) * a);
	else
		tmp = Float64(Float64(z * y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -2.9e+101)
		tmp = (y * x) * z;
	elseif (x <= 2.76e-14)
		tmp = (i * b) * a;
	else
		tmp = (z * y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -2.9e+101], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[x, 2.76e-14], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.89999999999999987e101

   1. Initial program 79.2%

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

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

   5. Applied rewrites 39.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 45.7%

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

   if -2.89999999999999987e101 < x < 2.76000000000000004e-14

   1. Initial program 78.8%

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

   3. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. cancel-sign-sub N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(b \cdot i\right)\right)} \]

      6. cancel-sign-sub N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(b \cdot i\right)\right)} \]

      7. associate-*r* N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(b \cdot i\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\left(-1 \cdot a\right) \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot a\right)} \cdot \left(b \cdot i\right)\right) \]

      9. distribute-lft-out-- N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x - b \cdot i\right)} \]

      10. *-commutative N/A

          \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{\left(a \cdot -1\right)} \cdot \left(t \cdot x - b \cdot i\right) \]

      11. associate-*r* N/A

          \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

      12. distribute-lft-out-- N/A

          \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]

      13. +-commutative N/A

          \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \]

   5. Applied rewrites 66.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-x, t, b \cdot i\right), a, \mathsf{fma}\left(-i, y, t \cdot c\right) \cdot j\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 31.2%

      \[\leadsto \left(i \cdot b\right) \cdot \color{blue}{a} \]

   if 2.76000000000000004e-14 < x

   1. Initial program 67.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z - a \cdot i\right) \cdot b}\right)\right) + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right) \cdot b} + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)} \cdot b + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(c \cdot z - a \cdot i\right), b, -1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right)} \]

   5. Applied rewrites 49.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-c, z, a \cdot i\right), b, \mathsf{fma}\left(-j, i, x \cdot z\right) \cdot y\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 35.5%

      \[\leadsto \left(x \cdot y\right) \cdot \color{blue}{z} \]

   9. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 36.9%

       \[\leadsto \left(z \cdot y\right) \cdot \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+101}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{elif}\;x \leq 2.76 \cdot 10^{-14}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+101}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{elif}\;x \leq 2.76 \cdot 10^{-14}:\\ \;\;\;\;\left(i \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -2.9e+101)
   (* (* y x) z)
   (if (<= x 2.76e-14) (* (* i a) b) (* (* z y) x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -2.9e+101) {
		tmp = (y * x) * z;
	} else if (x <= 2.76e-14) {
		tmp = (i * a) * b;
	} else {
		tmp = (z * y) * x;
	}
	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 (x <= (-2.9d+101)) then
        tmp = (y * x) * z
    else if (x <= 2.76d-14) then
        tmp = (i * a) * b
    else
        tmp = (z * y) * x
    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 (x <= -2.9e+101) {
		tmp = (y * x) * z;
	} else if (x <= 2.76e-14) {
		tmp = (i * a) * b;
	} else {
		tmp = (z * y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -2.9e+101:
		tmp = (y * x) * z
	elif x <= 2.76e-14:
		tmp = (i * a) * b
	else:
		tmp = (z * y) * x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -2.9e+101)
		tmp = Float64(Float64(y * x) * z);
	elseif (x <= 2.76e-14)
		tmp = Float64(Float64(i * a) * b);
	else
		tmp = Float64(Float64(z * y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -2.9e+101)
		tmp = (y * x) * z;
	elseif (x <= 2.76e-14)
		tmp = (i * a) * b;
	else
		tmp = (z * y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -2.9e+101], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[x, 2.76e-14], N[(N[(i * a), $MachinePrecision] * b), $MachinePrecision], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.89999999999999987e101

   1. Initial program 79.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z - a \cdot i\right) \cdot b}\right)\right) + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right) \cdot b} + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)} \cdot b + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(c \cdot z - a \cdot i\right), b, -1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right)} \]

   5. Applied rewrites 39.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-c, z, a \cdot i\right), b, \mathsf{fma}\left(-j, i, x \cdot z\right) \cdot y\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 45.7%

      \[\leadsto \left(x \cdot y\right) \cdot \color{blue}{z} \]

   if -2.89999999999999987e101 < x < 2.76000000000000004e-14

   1. Initial program 78.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right) - \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot i\right)} \]

      2. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right) - \color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot \left(b \cdot i\right) \]

      3. cancel-sign-sub N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right) + a \cdot \left(b \cdot i\right)} \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot t - i \cdot y\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} + a \cdot \left(b \cdot i\right) \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(b \cdot i\right)\right)} \]

      6. cancel-sign-sub N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(b \cdot i\right)\right)} \]

      7. associate-*r* N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(b \cdot i\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\left(-1 \cdot a\right) \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot a\right)} \cdot \left(b \cdot i\right)\right) \]

      9. distribute-lft-out-- N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x - b \cdot i\right)} \]

      10. *-commutative N/A

          \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{\left(a \cdot -1\right)} \cdot \left(t \cdot x - b \cdot i\right) \]

      11. associate-*r* N/A

          \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

      12. distribute-lft-out-- N/A

          \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]

      13. +-commutative N/A

          \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \]

   5. Applied rewrites 66.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-x, t, b \cdot i\right), a, \mathsf{fma}\left(-i, y, t \cdot c\right) \cdot j\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 31.2%

      \[\leadsto \left(i \cdot b\right) \cdot \color{blue}{a} \]
   9. Step-by-step derivation

   10. Applied rewrites 30.6%

       \[\leadsto \left(a \cdot i\right) \cdot b \]

   if 2.76000000000000004e-14 < x

   1. Initial program 67.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z - a \cdot i\right) \cdot b}\right)\right) + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right) \cdot b} + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)} \cdot b + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(c \cdot z - a \cdot i\right), b, -1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right)} \]

   5. Applied rewrites 49.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-c, z, a \cdot i\right), b, \mathsf{fma}\left(-j, i, x \cdot z\right) \cdot y\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 35.5%

      \[\leadsto \left(x \cdot y\right) \cdot \color{blue}{z} \]

   9. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 36.9%

       \[\leadsto \left(z \cdot y\right) \cdot \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+101}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{elif}\;x \leq 2.76 \cdot 10^{-14}:\\ \;\;\;\;\left(i \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 21.7% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \left(y \cdot x\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* (* y x) z))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return (y * x) * z;
}

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 = (y * x) * z
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 (y * x) * z;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return (y * x) * z

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(y * x) * z)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = (y * x) * z;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision]

Derivation

1. Initial program 76.0%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Add Preprocessing

3. Taylor expanded in t around 0

   \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
4. Step-by-step derivation

   1. sub-neg N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right)} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right)} \]

   3. *-commutative N/A

      \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z - a \cdot i\right) \cdot b}\right)\right) + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) \]

   4. distribute-lft-neg-in N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right) \cdot b} + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) \]

   5. mul-1-neg N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)} \cdot b + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) \]

   6. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(c \cdot z - a \cdot i\right), b, -1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right)} \]

5. Applied rewrites 57.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-c, z, a \cdot i\right), b, \mathsf{fma}\left(-j, i, x \cdot z\right) \cdot y\right)} \]

6. Taylor expanded in x around inf

   \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
7. Step-by-step derivation

8. Applied rewrites 22.2%

   \[\leadsto \left(x \cdot y\right) \cdot \color{blue}{z} \]

9. Final simplification 22.2%

   \[\leadsto \left(y \cdot x\right) \cdot z \]
10. Add Preprocessing

Developer Target 1: 67.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024235 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -1015122364899489/125000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -942510763643697/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (if (< t -238547917063487/3125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 10535888557455487/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))