Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.6% → 82.0%

Time: 15.2s

Alternatives: 19

Speedup: 0.5×

• 57.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.6% 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: 82.0% accurate, 0.5× speedup

Math

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

FPCore

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

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-a), t, Float64(z * y)) * x)
	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(-y), i, Float64(c * t)), j, fma(Float64(-b), fma(Float64(-a), i, Float64(c * z)), t_1));
	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[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, 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[((-y) * i + N[(c * t), $MachinePrecision]), $MachinePrecision] * j + N[((-b) * N[((-a) * i + N[(c * z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], t$95$1]]

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 91.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 91.2

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

      6. lift--.f64 N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

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

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

      12. lower-fma.f64 N/A

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

      13. lower-neg.f64 91.2

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

      14. lift--.f64 N/A

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

      15. sub-neg N/A

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

      16. +-commutative N/A

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

   4. Applied rewrites 91.2%

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

   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 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. mul-1-neg N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 63.0

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

   5. Applied rewrites 63.0%

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

4. Final simplification 85.9%

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

Alternative 2: 43.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ t_2 := \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+162}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-218}:\\ \;\;\;\;\left(\left(-i\right) \cdot j\right) \cdot y\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-271}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-22}:\\ \;\;\;\;\left(\left(-i\right) \cdot y\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- a) t (* z y)) x)) (t_2 (* (fma (- b) c (* y x)) z)))
   (if (<= z -2.4e+162)
     t_2
     (if (<= z -5.2e-96)
       t_1
       (if (<= z -3.2e-218)
         (* (* (- i) j) y)
         (if (<= z 4.1e-271)
           (* (* i b) a)
           (if (<= z 5.2e-121)
             t_1
             (if (<= z 1.1e-22) (* (* (- i) y) j) 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 = fma(-a, t, (z * y)) * x;
	double t_2 = fma(-b, c, (y * x)) * z;
	double tmp;
	if (z <= -2.4e+162) {
		tmp = t_2;
	} else if (z <= -5.2e-96) {
		tmp = t_1;
	} else if (z <= -3.2e-218) {
		tmp = (-i * j) * y;
	} else if (z <= 4.1e-271) {
		tmp = (i * b) * a;
	} else if (z <= 5.2e-121) {
		tmp = t_1;
	} else if (z <= 1.1e-22) {
		tmp = (-i * y) * j;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-a), t, Float64(z * y)) * x)
	t_2 = Float64(fma(Float64(-b), c, Float64(y * x)) * z)
	tmp = 0.0
	if (z <= -2.4e+162)
		tmp = t_2;
	elseif (z <= -5.2e-96)
		tmp = t_1;
	elseif (z <= -3.2e-218)
		tmp = Float64(Float64(Float64(-i) * j) * y);
	elseif (z <= 4.1e-271)
		tmp = Float64(Float64(i * b) * a);
	elseif (z <= 5.2e-121)
		tmp = t_1;
	elseif (z <= 1.1e-22)
		tmp = Float64(Float64(Float64(-i) * y) * j);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -2.4e+162], t$95$2, If[LessEqual[z, -5.2e-96], t$95$1, If[LessEqual[z, -3.2e-218], N[(N[((-i) * j), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, 4.1e-271], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[z, 5.2e-121], t$95$1, If[LessEqual[z, 1.1e-22], N[(N[((-i) * y), $MachinePrecision] * j), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.40000000000000009e162 or 1.1e-22 < z

   1. Initial program 66.2%

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

   3. Taylor expanded in z around 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. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. neg-mul-1 N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 65.5

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

   5. Applied rewrites 65.5%

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

   if -2.40000000000000009e162 < z < -5.2000000000000003e-96 or 4.1000000000000003e-271 < z < 5.19999999999999972e-121

   1. Initial program 77.4%

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

   3. Taylor expanded in x around 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. mul-1-neg N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 50.4

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

   5. Applied rewrites 50.4%

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

   if -5.2000000000000003e-96 < z < -3.2000000000000001e-218

   1. Initial program 79.6%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 66.2

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

   5. Applied rewrites 66.2%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 52.9%

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

   if -3.2000000000000001e-218 < z < 4.1000000000000003e-271

   1. Initial program 80.1%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 56.6

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

   5. Applied rewrites 56.6%

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

   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 51.2%

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

   if 5.19999999999999972e-121 < z < 1.1e-22

   1. Initial program 84.0%

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

   3. Taylor expanded in j around inf

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

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

      9. lower-*.f64 73.8

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

   5. Applied rewrites 73.8%

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

   6. Taylor expanded in c around 0

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

   8. Applied rewrites 51.7%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+162}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-96}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-218}:\\ \;\;\;\;\left(\left(-i\right) \cdot j\right) \cdot y\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-271}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-121}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-22}:\\ \;\;\;\;\left(\left(-i\right) \cdot y\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+197}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-x, t, i \cdot b\right), a, \mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- j) i (* z x)) y)))
   (if (<= y -4.4e+33)
     t_1
     (if (<= y 1.25e+197)
       (fma (fma (- x) t (* i b)) a (* (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(-j, i, (z * x)) * y;
	double tmp;
	if (y <= -4.4e+33) {
		tmp = t_1;
	} else if (y <= 1.25e+197) {
		tmp = fma(fma(-x, t, (i * b)), a, (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(-j), i, Float64(z * x)) * y)
	tmp = 0.0
	if (y <= -4.4e+33)
		tmp = t_1;
	elseif (y <= 1.25e+197)
		tmp = fma(fma(Float64(-x), t, Float64(i * b)), a, 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[((-j) * i + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -4.4e+33], t$95$1, If[LessEqual[y, 1.25e+197], N[(N[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a + N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.39999999999999988e33 or 1.25000000000000002e197 < y

   1. Initial program 56.7%

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

   3. Taylor expanded in 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

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

      8. *-commutative N/A

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

      9. lower-*.f64 76.9

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

   5. Applied rewrites 76.9%

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

   if -4.39999999999999988e33 < y < 1.25000000000000002e197

   1. Initial program 83.1%

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

   3. Taylor expanded in 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. mul-1-neg N/A

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

      7. distribute-rgt-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. distribute-lft-in N/A

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

      10. *-lft-identity N/A

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

      11. metadata-eval N/A

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

      12. cancel-sign-sub-inv 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 66.8%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+197}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-x, t, i \cdot b\right), a, \mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 56.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(-y, i, c \cdot t\right), j, \left(\left(-c\right) \cdot z\right) \cdot b\right)\\ \mathbf{if}\;j \leq -8.8 \cdot 10^{-83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.95 \cdot 10^{-44}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (fma (fma (- y) i (* c t)) j (* (* (- c) z) b))))
   (if (<= j -8.8e-83)
     t_1
     (if (<= j 1.95e-44) (* (fma (- a) t (* z y)) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(fma(-y, i, (c * t)), j, ((-c * z) * b));
	double tmp;
	if (j <= -8.8e-83) {
		tmp = t_1;
	} else if (j <= 1.95e-44) {
		tmp = fma(-a, t, (z * y)) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = fma(fma(Float64(-y), i, Float64(c * t)), j, Float64(Float64(Float64(-c) * z) * b))
	tmp = 0.0
	if (j <= -8.8e-83)
		tmp = t_1;
	elseif (j <= 1.95e-44)
		tmp = Float64(fma(Float64(-a), t, Float64(z * y)) * x);
	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[((-y) * i + N[(c * t), $MachinePrecision]), $MachinePrecision] * j + N[(N[((-c) * z), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -8.8e-83], t$95$1, If[LessEqual[j, 1.95e-44], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if j < -8.8000000000000003e-83 or 1.9500000000000001e-44 < j

   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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 79.3

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

      6. lift--.f64 N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

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

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

      12. lower-fma.f64 N/A

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

      13. lower-neg.f64 80.0

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

      14. lift--.f64 N/A

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

      15. sub-neg N/A

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

      16. +-commutative N/A

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

   4. Applied rewrites 80.7%

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

   5. Taylor expanded in c around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-y, i, c \cdot t\right), j, \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. associate-*r* N/A

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

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

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

      4. mul-1-neg N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. *-commutative N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-*.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 69.8

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

   7. Applied rewrites 69.8%

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

   9. Applied rewrites 71.3%

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

   if -8.8000000000000003e-83 < j < 1.9500000000000001e-44

   1. Initial program 71.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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. mul-1-neg N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 59.0

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

   5. Applied rewrites 59.0%

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

Alternative 5: 56.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(-y, i, c \cdot t\right), j, \left(\left(-c\right) \cdot b\right) \cdot z\right)\\ \mathbf{if}\;j \leq -9.8 \cdot 10^{-83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{-44}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (fma (fma (- y) i (* c t)) j (* (* (- c) b) z))))
   (if (<= j -9.8e-83)
     t_1
     (if (<= j 1.15e-44) (* (fma (- a) t (* z y)) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(fma(-y, i, (c * t)), j, ((-c * b) * z));
	double tmp;
	if (j <= -9.8e-83) {
		tmp = t_1;
	} else if (j <= 1.15e-44) {
		tmp = fma(-a, t, (z * y)) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = fma(fma(Float64(-y), i, Float64(c * t)), j, Float64(Float64(Float64(-c) * b) * z))
	tmp = 0.0
	if (j <= -9.8e-83)
		tmp = t_1;
	elseif (j <= 1.15e-44)
		tmp = Float64(fma(Float64(-a), t, Float64(z * y)) * x);
	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[((-y) * i + N[(c * t), $MachinePrecision]), $MachinePrecision] * j + N[(N[((-c) * b), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -9.8e-83], t$95$1, If[LessEqual[j, 1.15e-44], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if j < -9.8e-83 or 1.14999999999999999e-44 < j

   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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 79.3

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

      6. lift--.f64 N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

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

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

      12. lower-fma.f64 N/A

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

      13. lower-neg.f64 80.0

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

      14. lift--.f64 N/A

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

      15. sub-neg N/A

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

      16. +-commutative N/A

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

   4. Applied rewrites 80.7%

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

   5. Taylor expanded in c around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-y, i, c \cdot t\right), j, \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. associate-*r* N/A

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

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

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

      4. mul-1-neg N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. *-commutative N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-*.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 69.8

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

   7. Applied rewrites 69.8%

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

   if -9.8e-83 < j < 1.14999999999999999e-44

   1. Initial program 71.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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. mul-1-neg N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 59.0

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

   5. Applied rewrites 59.0%

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

Alternative 6: 52.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-54}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-228}:\\ \;\;\;\;\mathsf{fma}\left(-x, t, i \cdot b\right) \cdot a\\ \mathbf{elif}\;y \leq 4.25 \cdot 10^{-41}:\\ \;\;\;\;\mathsf{fma}\left(-b, z, j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- j) i (* z x)) y)))
   (if (<= y -6.4e+19)
     t_1
     (if (<= y -3.9e-54)
       (* (fma (- i) y (* c t)) j)
       (if (<= y 3.1e-228)
         (* (fma (- x) t (* i b)) a)
         (if (<= y 4.25e-41) (* (fma (- b) z (* 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(-j, i, (z * x)) * y;
	double tmp;
	if (y <= -6.4e+19) {
		tmp = t_1;
	} else if (y <= -3.9e-54) {
		tmp = fma(-i, y, (c * t)) * j;
	} else if (y <= 3.1e-228) {
		tmp = fma(-x, t, (i * b)) * a;
	} else if (y <= 4.25e-41) {
		tmp = fma(-b, z, (j * t)) * c;
	} 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 <= -6.4e+19)
		tmp = t_1;
	elseif (y <= -3.9e-54)
		tmp = Float64(fma(Float64(-i), y, Float64(c * t)) * j);
	elseif (y <= 3.1e-228)
		tmp = Float64(fma(Float64(-x), t, Float64(i * b)) * a);
	elseif (y <= 4.25e-41)
		tmp = Float64(fma(Float64(-b), z, 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[((-j) * i + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -6.4e+19], t$95$1, If[LessEqual[y, -3.9e-54], N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[y, 3.1e-228], N[(N[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[y, 4.25e-41], N[(N[((-b) * z + N[(j * t), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.4e19 or 4.2499999999999998e-41 < y

   1. Initial program 67.2%

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

   3. Taylor expanded in y around 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

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

      8. *-commutative N/A

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

      9. lower-*.f64 67.7

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

   5. Applied rewrites 67.7%

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

   if -6.4e19 < y < -3.9e-54

   1. Initial program 77.3%

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

   3. Taylor expanded in j around 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

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

      9. lower-*.f64 65.6

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

   5. Applied rewrites 65.6%

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

   if -3.9e-54 < y < 3.0999999999999998e-228

   1. Initial program 83.8%

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

   3. Taylor expanded in 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

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

      11. lower-*.f64 62.8

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

   5. Applied rewrites 62.8%

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

   if 3.0999999999999998e-228 < y < 4.2499999999999998e-41

   1. Initial program 81.3%

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

   3. Taylor expanded in c around 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

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

      10. *-commutative N/A

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

      11. lower-*.f64 54.5

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

   5. Applied rewrites 54.5%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-54}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-228}:\\ \;\;\;\;\mathsf{fma}\left(-x, t, i \cdot b\right) \cdot a\\ \mathbf{elif}\;y \leq 4.25 \cdot 10^{-41}:\\ \;\;\;\;\mathsf{fma}\left(-b, z, j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-109}:\\ \;\;\;\;\mathsf{fma}\left(-c, z, i \cdot a\right) \cdot b\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(-b, z, j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- a) t (* z y)) x)))
   (if (<= x -1.5e-43)
     t_1
     (if (<= x 1.1e-109)
       (* (fma (- c) z (* i a)) b)
       (if (<= x 3.9e+78) (* (fma (- b) z (* 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(-a, t, (z * y)) * x;
	double tmp;
	if (x <= -1.5e-43) {
		tmp = t_1;
	} else if (x <= 1.1e-109) {
		tmp = fma(-c, z, (i * a)) * b;
	} else if (x <= 3.9e+78) {
		tmp = fma(-b, z, (j * t)) * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-a), t, Float64(z * y)) * x)
	tmp = 0.0
	if (x <= -1.5e-43)
		tmp = t_1;
	elseif (x <= 1.1e-109)
		tmp = Float64(fma(Float64(-c), z, Float64(i * a)) * b);
	elseif (x <= 3.9e+78)
		tmp = Float64(fma(Float64(-b), z, 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[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.5e-43], t$95$1, If[LessEqual[x, 1.1e-109], N[(N[((-c) * z + N[(i * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[x, 3.9e+78], N[(N[((-b) * z + N[(j * t), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.50000000000000002e-43 or 3.9000000000000004e78 < x

   1. Initial program 68.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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. mul-1-neg N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 62.4

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

   5. Applied rewrites 62.4%

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

   if -1.50000000000000002e-43 < x < 1.1e-109

   1. Initial program 81.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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. distribute-lft-neg-in N/A

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

      13. remove-double-neg N/A

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

      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

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

      18. lower-*.f64 50.7

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

   5. Applied rewrites 50.7%

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

   if 1.1e-109 < x < 3.9000000000000004e78

   1. Initial program 75.2%

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

   3. Taylor expanded in 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

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

      10. *-commutative N/A

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

      11. lower-*.f64 47.5

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

   5. Applied rewrites 47.5%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-43}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-109}:\\ \;\;\;\;\mathsf{fma}\left(-c, z, i \cdot a\right) \cdot b\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(-b, z, j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 29.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.075:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-48}:\\ \;\;\;\;\left(c \cdot t\right) \cdot j\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-242}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-17}:\\ \;\;\;\;\left(j \cdot c\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -0.075)
   (* (* z x) y)
   (if (<= y -1.45e-48)
     (* (* c t) j)
     (if (<= y 2.25e-242)
       (* (* i b) a)
       (if (<= y 1.55e-17) (* (* j c) t) (* (* 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 (y <= -0.075) {
		tmp = (z * x) * y;
	} else if (y <= -1.45e-48) {
		tmp = (c * t) * j;
	} else if (y <= 2.25e-242) {
		tmp = (i * b) * a;
	} else if (y <= 1.55e-17) {
		tmp = (j * c) * t;
	} 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 (y <= (-0.075d0)) then
        tmp = (z * x) * y
    else if (y <= (-1.45d-48)) then
        tmp = (c * t) * j
    else if (y <= 2.25d-242) then
        tmp = (i * b) * a
    else if (y <= 1.55d-17) then
        tmp = (j * c) * t
    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 (y <= -0.075) {
		tmp = (z * x) * y;
	} else if (y <= -1.45e-48) {
		tmp = (c * t) * j;
	} else if (y <= 2.25e-242) {
		tmp = (i * b) * a;
	} else if (y <= 1.55e-17) {
		tmp = (j * c) * t;
	} else {
		tmp = (z * y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -0.075:
		tmp = (z * x) * y
	elif y <= -1.45e-48:
		tmp = (c * t) * j
	elif y <= 2.25e-242:
		tmp = (i * b) * a
	elif y <= 1.55e-17:
		tmp = (j * c) * t
	else:
		tmp = (z * y) * x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -0.075)
		tmp = Float64(Float64(z * x) * y);
	elseif (y <= -1.45e-48)
		tmp = Float64(Float64(c * t) * j);
	elseif (y <= 2.25e-242)
		tmp = Float64(Float64(i * b) * a);
	elseif (y <= 1.55e-17)
		tmp = Float64(Float64(j * c) * t);
	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 (y <= -0.075)
		tmp = (z * x) * y;
	elseif (y <= -1.45e-48)
		tmp = (c * t) * j;
	elseif (y <= 2.25e-242)
		tmp = (i * b) * a;
	elseif (y <= 1.55e-17)
		tmp = (j * c) * t;
	else
		tmp = (z * y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -0.075], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, -1.45e-48], N[(N[(c * t), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[y, 2.25e-242], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[y, 1.55e-17], N[(N[(j * c), $MachinePrecision] * t), $MachinePrecision], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -0.0749999999999999972

   1. Initial program 56.6%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 72.9%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 52.0%

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

   9. Taylor expanded in c around 0

      \[\leadsto \left(x \cdot z\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 44.7%

       \[\leadsto \left(z \cdot x\right) \cdot y \]

   if -0.0749999999999999972 < y < -1.4500000000000001e-48

   1. Initial program 76.3%

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

   3. Taylor expanded in j around 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

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

      9. lower-*.f64 75.9

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

   5. Applied rewrites 75.9%

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

   6. Taylor expanded in c around inf

      \[\leadsto \left(c \cdot t\right) \cdot j \]
   7. Step-by-step derivation

   8. Applied rewrites 67.6%

      \[\leadsto \left(c \cdot t\right) \cdot j \]

   if -1.4500000000000001e-48 < y < 2.2499999999999999e-242

   1. Initial program 83.8%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 52.9

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

   5. Applied rewrites 52.9%

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

   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 46.9%

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

   if 2.2499999999999999e-242 < y < 1.5499999999999999e-17

   1. Initial program 83.2%

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

   3. Taylor expanded in t around inf

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

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

      8. lower-*.f64 48.4

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

   5. Applied rewrites 48.4%

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

   6. Taylor expanded in c around inf

      \[\leadsto \left(c \cdot j\right) \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 27.4%

      \[\leadsto \left(c \cdot j\right) \cdot t \]

   if 1.5499999999999999e-17 < y

   1. Initial program 75.7%

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

   3. Taylor expanded in 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. mul-1-neg N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 51.6

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

   5. Applied rewrites 51.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 38.8%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.075:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-48}:\\ \;\;\;\;\left(c \cdot t\right) \cdot j\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-242}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-17}:\\ \;\;\;\;\left(j \cdot c\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 29.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot x\\ \mathbf{if}\;y \leq -0.075:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-48}:\\ \;\;\;\;\left(c \cdot t\right) \cdot j\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-242}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-17}:\\ \;\;\;\;\left(j \cdot c\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z y) x)))
   (if (<= y -0.075)
     t_1
     (if (<= y -1.45e-48)
       (* (* c t) j)
       (if (<= y 2.25e-242)
         (* (* i b) a)
         (if (<= y 1.55e-17) (* (* j c) t) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * y) * x;
	double tmp;
	if (y <= -0.075) {
		tmp = t_1;
	} else if (y <= -1.45e-48) {
		tmp = (c * t) * j;
	} else if (y <= 2.25e-242) {
		tmp = (i * b) * a;
	} else if (y <= 1.55e-17) {
		tmp = (j * c) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * y) * x
    if (y <= (-0.075d0)) then
        tmp = t_1
    else if (y <= (-1.45d-48)) then
        tmp = (c * t) * j
    else if (y <= 2.25d-242) then
        tmp = (i * b) * a
    else if (y <= 1.55d-17) then
        tmp = (j * c) * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * y) * x;
	double tmp;
	if (y <= -0.075) {
		tmp = t_1;
	} else if (y <= -1.45e-48) {
		tmp = (c * t) * j;
	} else if (y <= 2.25e-242) {
		tmp = (i * b) * a;
	} else if (y <= 1.55e-17) {
		tmp = (j * c) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * y) * x
	tmp = 0
	if y <= -0.075:
		tmp = t_1
	elif y <= -1.45e-48:
		tmp = (c * t) * j
	elif y <= 2.25e-242:
		tmp = (i * b) * a
	elif y <= 1.55e-17:
		tmp = (j * c) * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * y) * x)
	tmp = 0.0
	if (y <= -0.075)
		tmp = t_1;
	elseif (y <= -1.45e-48)
		tmp = Float64(Float64(c * t) * j);
	elseif (y <= 2.25e-242)
		tmp = Float64(Float64(i * b) * a);
	elseif (y <= 1.55e-17)
		tmp = Float64(Float64(j * c) * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (z * y) * x;
	tmp = 0.0;
	if (y <= -0.075)
		tmp = t_1;
	elseif (y <= -1.45e-48)
		tmp = (c * t) * j;
	elseif (y <= 2.25e-242)
		tmp = (i * b) * a;
	elseif (y <= 1.55e-17)
		tmp = (j * c) * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -0.075], t$95$1, If[LessEqual[y, -1.45e-48], N[(N[(c * t), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[y, 2.25e-242], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[y, 1.55e-17], N[(N[(j * c), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -0.0749999999999999972 or 1.5499999999999999e-17 < y

   1. Initial program 66.4%

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

   3. Taylor expanded in x around 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. mul-1-neg N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 52.2

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

   5. Applied rewrites 52.2%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 41.0%

      \[\leadsto \left(z \cdot y\right) \cdot x \]

   if -0.0749999999999999972 < y < -1.4500000000000001e-48

   1. Initial program 76.3%

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

   3. Taylor expanded in j around 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

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

      9. lower-*.f64 75.9

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

   5. Applied rewrites 75.9%

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

   6. Taylor expanded in c around inf

      \[\leadsto \left(c \cdot t\right) \cdot j \]
   7. Step-by-step derivation

   8. Applied rewrites 67.6%

      \[\leadsto \left(c \cdot t\right) \cdot j \]

   if -1.4500000000000001e-48 < y < 2.2499999999999999e-242

   1. Initial program 83.8%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 52.9

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

   5. Applied rewrites 52.9%

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

   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 46.9%

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

   if 2.2499999999999999e-242 < y < 1.5499999999999999e-17

   1. Initial program 83.2%

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

   3. Taylor expanded in t around inf

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

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

      8. lower-*.f64 48.4

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

   5. Applied rewrites 48.4%

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

   6. Taylor expanded in c around inf

      \[\leadsto \left(c \cdot j\right) \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 27.4%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.075:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-48}:\\ \;\;\;\;\left(c \cdot t\right) \cdot j\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-242}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-17}:\\ \;\;\;\;\left(j \cdot c\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \mathbf{if}\;j \leq -8.6 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 7 \cdot 10^{-49}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- i) y (* c t)) j)))
   (if (<= j -8.6e+87) t_1 (if (<= j 7e-49) (* (fma (- a) t (* z y)) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-i, y, (c * t)) * j;
	double tmp;
	if (j <= -8.6e+87) {
		tmp = t_1;
	} else if (j <= 7e-49) {
		tmp = fma(-a, t, (z * y)) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-i), y, Float64(c * t)) * j)
	tmp = 0.0
	if (j <= -8.6e+87)
		tmp = t_1;
	elseif (j <= 7e-49)
		tmp = Float64(fma(Float64(-a), t, Float64(z * y)) * x);
	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[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]}, If[LessEqual[j, -8.6e+87], t$95$1, If[LessEqual[j, 7e-49], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if j < -8.6000000000000002e87 or 7.00000000000000012e-49 < j

   1. Initial program 79.4%

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

   3. Taylor expanded in j around inf

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

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

      9. lower-*.f64 65.0

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

   5. Applied rewrites 65.0%

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

   if -8.6000000000000002e87 < j < 7.00000000000000012e-49

   1. Initial program 69.4%

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

   3. Taylor expanded in x around 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. mul-1-neg N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 56.6

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

   5. Applied rewrites 56.6%

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

Alternative 11: 51.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(-b, z, j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- a) t (* z y)) x)))
   (if (<= x -5.5e-43)
     t_1
     (if (<= x 3.9e+78) (* (fma (- b) z (* 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(-a, t, (z * y)) * x;
	double tmp;
	if (x <= -5.5e-43) {
		tmp = t_1;
	} else if (x <= 3.9e+78) {
		tmp = fma(-b, z, (j * t)) * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-a), t, Float64(z * y)) * x)
	tmp = 0.0
	if (x <= -5.5e-43)
		tmp = t_1;
	elseif (x <= 3.9e+78)
		tmp = Float64(fma(Float64(-b), z, 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[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -5.5e-43], t$95$1, If[LessEqual[x, 3.9e+78], N[(N[((-b) * z + N[(j * t), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.50000000000000013e-43 or 3.9000000000000004e78 < x

   1. Initial program 68.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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. mul-1-neg N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 62.4

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

   5. Applied rewrites 62.4%

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

   if -5.50000000000000013e-43 < x < 3.9000000000000004e78

   1. Initial program 79.5%

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

   3. Taylor expanded in 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

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

      10. *-commutative N/A

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

      11. lower-*.f64 44.7

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

   5. Applied rewrites 44.7%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-43}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(-b, z, j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 40.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.8 \cdot 10^{+88}:\\ \;\;\;\;\left(\left(-i\right) \cdot y\right) \cdot j\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{-28}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot c\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.8e+88)
   (* (* (- i) y) j)
   (if (<= j 1.05e-28) (* (fma (- a) t (* z y)) x) (* (* j c) t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.8e+88) {
		tmp = (-i * y) * j;
	} else if (j <= 1.05e-28) {
		tmp = fma(-a, t, (z * y)) * x;
	} else {
		tmp = (j * c) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.8e+88)
		tmp = Float64(Float64(Float64(-i) * y) * j);
	elseif (j <= 1.05e-28)
		tmp = Float64(fma(Float64(-a), t, Float64(z * y)) * x);
	else
		tmp = Float64(Float64(j * c) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1.8e+88], N[(N[((-i) * y), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[j, 1.05e-28], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(j * c), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.8000000000000001e88

   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 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

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

      9. lower-*.f64 70.9

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

   5. Applied rewrites 70.9%

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

   6. Taylor expanded in c around 0

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

   8. Applied rewrites 45.6%

      \[\leadsto \left(\left(-i\right) \cdot y\right) \cdot j \]

   if -1.8000000000000001e88 < j < 1.05000000000000003e-28

   1. Initial program 69.5%

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

   3. Taylor expanded in 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. mul-1-neg N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 55.5

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

   5. Applied rewrites 55.5%

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

   if 1.05000000000000003e-28 < j

   1. Initial program 77.3%

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

   3. Taylor expanded in 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

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

      8. lower-*.f64 52.7

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

   5. Applied rewrites 52.7%

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

   6. Taylor expanded in c around inf

      \[\leadsto \left(c \cdot j\right) \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 41.9%

      \[\leadsto \left(c \cdot j\right) \cdot t \]
3. Recombined 3 regimes into one program.

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.8 \cdot 10^{+88}:\\ \;\;\;\;\left(\left(-i\right) \cdot y\right) \cdot j\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{-28}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot c\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 30.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot x\\ \mathbf{if}\;y \leq -0.075:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-48}:\\ \;\;\;\;\left(c \cdot t\right) \cdot j\\ \mathbf{elif}\;y \leq 0.000125:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z y) x)))
   (if (<= y -0.075)
     t_1
     (if (<= y -1.45e-48)
       (* (* c t) j)
       (if (<= y 0.000125) (* (* 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 = (z * y) * x;
	double tmp;
	if (y <= -0.075) {
		tmp = t_1;
	} else if (y <= -1.45e-48) {
		tmp = (c * t) * j;
	} else if (y <= 0.000125) {
		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 = (z * y) * x
    if (y <= (-0.075d0)) then
        tmp = t_1
    else if (y <= (-1.45d-48)) then
        tmp = (c * t) * j
    else if (y <= 0.000125d0) 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 = (z * y) * x;
	double tmp;
	if (y <= -0.075) {
		tmp = t_1;
	} else if (y <= -1.45e-48) {
		tmp = (c * t) * j;
	} else if (y <= 0.000125) {
		tmp = (i * b) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * y) * x
	tmp = 0
	if y <= -0.075:
		tmp = t_1
	elif y <= -1.45e-48:
		tmp = (c * t) * j
	elif y <= 0.000125:
		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(z * y) * x)
	tmp = 0.0
	if (y <= -0.075)
		tmp = t_1;
	elseif (y <= -1.45e-48)
		tmp = Float64(Float64(c * t) * j);
	elseif (y <= 0.000125)
		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 = (z * y) * x;
	tmp = 0.0;
	if (y <= -0.075)
		tmp = t_1;
	elseif (y <= -1.45e-48)
		tmp = (c * t) * j;
	elseif (y <= 0.000125)
		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[(z * y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -0.075], t$95$1, If[LessEqual[y, -1.45e-48], N[(N[(c * t), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[y, 0.000125], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.0749999999999999972 or 1.25e-4 < y

   1. Initial program 65.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. 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. mul-1-neg N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 53.3

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

   5. Applied rewrites 53.3%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 41.7%

      \[\leadsto \left(z \cdot y\right) \cdot x \]

   if -0.0749999999999999972 < y < -1.4500000000000001e-48

   1. Initial program 76.3%

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

   3. Taylor expanded in j around 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

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

      9. lower-*.f64 75.9

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

   5. Applied rewrites 75.9%

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

   6. Taylor expanded in c around inf

      \[\leadsto \left(c \cdot t\right) \cdot j \]
   7. Step-by-step derivation

   8. Applied rewrites 67.6%

      \[\leadsto \left(c \cdot t\right) \cdot j \]

   if -1.4500000000000001e-48 < y < 1.25e-4

   1. Initial program 84.3%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 42.5

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

   5. Applied rewrites 42.5%

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

   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 34.0%

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

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.075:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-48}:\\ \;\;\;\;\left(c \cdot t\right) \cdot j\\ \mathbf{elif}\;y \leq 0.000125:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 30.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot x\\ \mathbf{if}\;y \leq -0.075:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-48}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;y \leq 0.000125:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z y) x)))
   (if (<= y -0.075)
     t_1
     (if (<= y -1.4e-48)
       (* (* j t) c)
       (if (<= y 0.000125) (* (* 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 = (z * y) * x;
	double tmp;
	if (y <= -0.075) {
		tmp = t_1;
	} else if (y <= -1.4e-48) {
		tmp = (j * t) * c;
	} else if (y <= 0.000125) {
		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 = (z * y) * x
    if (y <= (-0.075d0)) then
        tmp = t_1
    else if (y <= (-1.4d-48)) then
        tmp = (j * t) * c
    else if (y <= 0.000125d0) 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 = (z * y) * x;
	double tmp;
	if (y <= -0.075) {
		tmp = t_1;
	} else if (y <= -1.4e-48) {
		tmp = (j * t) * c;
	} else if (y <= 0.000125) {
		tmp = (i * b) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * y) * x
	tmp = 0
	if y <= -0.075:
		tmp = t_1
	elif y <= -1.4e-48:
		tmp = (j * t) * c
	elif y <= 0.000125:
		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(z * y) * x)
	tmp = 0.0
	if (y <= -0.075)
		tmp = t_1;
	elseif (y <= -1.4e-48)
		tmp = Float64(Float64(j * t) * c);
	elseif (y <= 0.000125)
		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 = (z * y) * x;
	tmp = 0.0;
	if (y <= -0.075)
		tmp = t_1;
	elseif (y <= -1.4e-48)
		tmp = (j * t) * c;
	elseif (y <= 0.000125)
		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[(z * y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -0.075], t$95$1, If[LessEqual[y, -1.4e-48], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[y, 0.000125], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.0749999999999999972 or 1.25e-4 < y

   1. Initial program 65.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. 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. mul-1-neg N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 53.3

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

   5. Applied rewrites 53.3%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 41.7%

      \[\leadsto \left(z \cdot y\right) \cdot x \]

   if -0.0749999999999999972 < y < -1.40000000000000002e-48

   1. Initial program 76.3%

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

   3. Taylor expanded in j around 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

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

      9. lower-*.f64 75.9

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

   5. Applied rewrites 75.9%

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

   6. Taylor expanded in c around inf

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

   8. Applied rewrites 59.5%

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

   if -1.40000000000000002e-48 < y < 1.25e-4

   1. Initial program 84.3%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 42.5

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

   5. Applied rewrites 42.5%

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

   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 34.0%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.075:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-48}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;y \leq 0.000125:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.05 \cdot 10^{-22}:\\ \;\;\;\;\left(\left(-i\right) \cdot y\right) \cdot j\\ \mathbf{elif}\;j \leq 9.4 \cdot 10^{-29}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot c\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -2.05e-22)
   (* (* (- i) y) j)
   (if (<= j 9.4e-29) (* (* z y) x) (* (* j c) t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2.05e-22) {
		tmp = (-i * y) * j;
	} else if (j <= 9.4e-29) {
		tmp = (z * y) * x;
	} else {
		tmp = (j * c) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-2.05d-22)) then
        tmp = (-i * y) * j
    else if (j <= 9.4d-29) then
        tmp = (z * y) * x
    else
        tmp = (j * c) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2.05e-22) {
		tmp = (-i * y) * j;
	} else if (j <= 9.4e-29) {
		tmp = (z * y) * x;
	} else {
		tmp = (j * c) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -2.05e-22:
		tmp = (-i * y) * j
	elif j <= 9.4e-29:
		tmp = (z * y) * x
	else:
		tmp = (j * c) * t
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -2.05e-22)
		tmp = Float64(Float64(Float64(-i) * y) * j);
	elseif (j <= 9.4e-29)
		tmp = Float64(Float64(z * y) * x);
	else
		tmp = Float64(Float64(j * c) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -2.05e-22)
		tmp = (-i * y) * j;
	elseif (j <= 9.4e-29)
		tmp = (z * y) * x;
	else
		tmp = (j * c) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -2.05e-22], N[(N[((-i) * y), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[j, 9.4e-29], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], N[(N[(j * c), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.05e-22

   1. Initial program 80.0%

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

   3. Taylor expanded in j around inf

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

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

      9. lower-*.f64 67.2

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

   5. Applied rewrites 67.2%

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

   6. Taylor expanded in c around 0

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

   8. Applied rewrites 44.2%

      \[\leadsto \left(\left(-i\right) \cdot y\right) \cdot j \]

   if -2.05e-22 < j < 9.3999999999999997e-29

   1. Initial program 69.5%

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

   3. Taylor expanded in 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. mul-1-neg N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 55.6

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

   5. Applied rewrites 55.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 38.2%

      \[\leadsto \left(z \cdot y\right) \cdot x \]

   if 9.3999999999999997e-29 < j

   1. Initial program 77.3%

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

   3. Taylor expanded in 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

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

      8. lower-*.f64 52.7

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

   5. Applied rewrites 52.7%

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

   6. Taylor expanded in c around inf

      \[\leadsto \left(c \cdot j\right) \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 41.9%

      \[\leadsto \left(c \cdot j\right) \cdot t \]
3. Recombined 3 regimes into one program.

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.05 \cdot 10^{-22}:\\ \;\;\;\;\left(\left(-i\right) \cdot y\right) \cdot j\\ \mathbf{elif}\;j \leq 9.4 \cdot 10^{-29}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot c\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.05 \cdot 10^{-22}:\\ \;\;\;\;\left(\left(-i\right) \cdot j\right) \cdot y\\ \mathbf{elif}\;j \leq 9.4 \cdot 10^{-29}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot c\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -2.05e-22)
   (* (* (- i) j) y)
   (if (<= j 9.4e-29) (* (* z y) x) (* (* j c) t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2.05e-22) {
		tmp = (-i * j) * y;
	} else if (j <= 9.4e-29) {
		tmp = (z * y) * x;
	} else {
		tmp = (j * c) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-2.05d-22)) then
        tmp = (-i * j) * y
    else if (j <= 9.4d-29) then
        tmp = (z * y) * x
    else
        tmp = (j * c) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2.05e-22) {
		tmp = (-i * j) * y;
	} else if (j <= 9.4e-29) {
		tmp = (z * y) * x;
	} else {
		tmp = (j * c) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -2.05e-22:
		tmp = (-i * j) * y
	elif j <= 9.4e-29:
		tmp = (z * y) * x
	else:
		tmp = (j * c) * t
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -2.05e-22)
		tmp = Float64(Float64(Float64(-i) * j) * y);
	elseif (j <= 9.4e-29)
		tmp = Float64(Float64(z * y) * x);
	else
		tmp = Float64(Float64(j * c) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -2.05e-22)
		tmp = (-i * j) * y;
	elseif (j <= 9.4e-29)
		tmp = (z * y) * x;
	else
		tmp = (j * c) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -2.05e-22], N[(N[((-i) * j), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[j, 9.4e-29], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], N[(N[(j * c), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.05e-22

   1. Initial program 80.0%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 47.7

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

   5. Applied rewrites 47.7%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 39.5%

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

   if -2.05e-22 < j < 9.3999999999999997e-29

   1. Initial program 69.5%

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

   3. Taylor expanded in 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. mul-1-neg N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 55.6

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

   5. Applied rewrites 55.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 38.2%

      \[\leadsto \left(z \cdot y\right) \cdot x \]

   if 9.3999999999999997e-29 < j

   1. Initial program 77.3%

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

   3. Taylor expanded in 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

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

      8. lower-*.f64 52.7

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

   5. Applied rewrites 52.7%

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

   6. Taylor expanded in c around inf

      \[\leadsto \left(c \cdot j\right) \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 41.9%

      \[\leadsto \left(c \cdot j\right) \cdot t \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.05 \cdot 10^{-22}:\\ \;\;\;\;\left(\left(-i\right) \cdot j\right) \cdot y\\ \mathbf{elif}\;j \leq 9.4 \cdot 10^{-29}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot c\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot t\right) \cdot c\\ \mathbf{if}\;j \leq -1.15 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{-35}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* j t) c)))
   (if (<= j -1.15e-52) t_1 (if (<= j 1.65e-35) (* (* 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 = (j * t) * c;
	double tmp;
	if (j <= -1.15e-52) {
		tmp = t_1;
	} else if (j <= 1.65e-35) {
		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 = (j * t) * c
    if (j <= (-1.15d-52)) then
        tmp = t_1
    else if (j <= 1.65d-35) 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 = (j * t) * c;
	double tmp;
	if (j <= -1.15e-52) {
		tmp = t_1;
	} else if (j <= 1.65e-35) {
		tmp = (i * b) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * t) * c
	tmp = 0
	if j <= -1.15e-52:
		tmp = t_1
	elif j <= 1.65e-35:
		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(j * t) * c)
	tmp = 0.0
	if (j <= -1.15e-52)
		tmp = t_1;
	elseif (j <= 1.65e-35)
		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 = (j * t) * c;
	tmp = 0.0;
	if (j <= -1.15e-52)
		tmp = t_1;
	elseif (j <= 1.65e-35)
		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[(j * t), $MachinePrecision] * c), $MachinePrecision]}, If[LessEqual[j, -1.15e-52], t$95$1, If[LessEqual[j, 1.65e-35], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if j < -1.14999999999999997e-52 or 1.65e-35 < j

   1. Initial program 77.0%

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

   3. Taylor expanded in j around inf

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

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

      9. lower-*.f64 62.1

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

   5. Applied rewrites 62.1%

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

   6. Taylor expanded in c around inf

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

   8. Applied rewrites 32.5%

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

   if -1.14999999999999997e-52 < j < 1.65e-35

   1. Initial program 70.8%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 34.9

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

   5. Applied rewrites 34.9%

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

   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 34.1%

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

4. Final simplification 33.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.15 \cdot 10^{-52}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{-35}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot t\right) \cdot c\\ \mathbf{if}\;j \leq -1.15 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.12 \cdot 10^{-35}:\\ \;\;\;\;\left(i \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* j t) c)))
   (if (<= j -1.15e-52) t_1 (if (<= j 1.12e-35) (* (* 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 = (j * t) * c;
	double tmp;
	if (j <= -1.15e-52) {
		tmp = t_1;
	} else if (j <= 1.12e-35) {
		tmp = (i * a) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * t) * c
    if (j <= (-1.15d-52)) then
        tmp = t_1
    else if (j <= 1.12d-35) then
        tmp = (i * a) * b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * t) * c;
	double tmp;
	if (j <= -1.15e-52) {
		tmp = t_1;
	} else if (j <= 1.12e-35) {
		tmp = (i * a) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * t) * c
	tmp = 0
	if j <= -1.15e-52:
		tmp = t_1
	elif j <= 1.12e-35:
		tmp = (i * a) * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * t) * c)
	tmp = 0.0
	if (j <= -1.15e-52)
		tmp = t_1;
	elseif (j <= 1.12e-35)
		tmp = Float64(Float64(i * a) * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * t) * c;
	tmp = 0.0;
	if (j <= -1.15e-52)
		tmp = t_1;
	elseif (j <= 1.12e-35)
		tmp = (i * a) * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision]}, If[LessEqual[j, -1.15e-52], t$95$1, If[LessEqual[j, 1.12e-35], N[(N[(i * a), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if j < -1.14999999999999997e-52 or 1.12e-35 < j

   1. Initial program 77.0%

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

   3. Taylor expanded in j around inf

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

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

      9. lower-*.f64 62.1

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

   5. Applied rewrites 62.1%

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

   6. Taylor expanded in c around inf

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

   8. Applied rewrites 32.5%

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

   if -1.14999999999999997e-52 < j < 1.12e-35

   1. Initial program 70.8%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 34.9

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

   5. Applied rewrites 34.9%

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

   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 34.1%

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

   10. Applied rewrites 33.7%

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

4. Final simplification 33.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.15 \cdot 10^{-52}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{elif}\;j \leq 1.12 \cdot 10^{-35}:\\ \;\;\;\;\left(i \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 22.0% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \left(j \cdot t\right) \cdot c \end{array} \]

FPCore

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

C

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

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 = (j * t) * c
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 (j * t) * c;
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision]

Derivation

1. Initial program 74.1%

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

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

   9. lower-*.f64 39.3

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

5. Applied rewrites 39.3%

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

6. Taylor expanded in c around inf

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

8. Applied rewrites 19.9%

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

9. Final simplification 19.9%

   \[\leadsto \left(j \cdot t\right) \cdot c \]
10. Add Preprocessing

Developer Target 1: 68.9% 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 2024270 
(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)))))