Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 74.5% → 82.5%

Time: 14.5s

Alternatives: 20

Speedup: 0.5×

• 57.3% 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: 74.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.1%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in 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. *-lowering-*.f64 N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. neg-mul-1 N/A

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

      6. neg-lowering-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 58.6

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

   5. Simplified 58.6%

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

4. Final simplification 83.5%

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

Alternative 2: 51.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\\ \mathbf{if}\;b \leq -2.9 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-127}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, -i, x \cdot z\right)\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-272}:\\ \;\;\;\;j \cdot \mathsf{fma}\left(c, t, -y \cdot i\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-191}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+65}:\\ \;\;\;\;-\mathsf{fma}\left(j, y \cdot i, t \cdot \left(x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (fma c (- z) (* a i)))))
   (if (<= b -2.9e+79)
     t_1
     (if (<= b -1.5e-127)
       (* y (fma j (- i) (* x z)))
       (if (<= b -2.15e-272)
         (* j (fma c t (- (* y i))))
         (if (<= b 7e-191)
           (* x (- (* y z) (* t a)))
           (if (<= b 2.1e+65) (- (fma j (* y i) (* t (* x a)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * fma(c, -z, (a * i));
	double tmp;
	if (b <= -2.9e+79) {
		tmp = t_1;
	} else if (b <= -1.5e-127) {
		tmp = y * fma(j, -i, (x * z));
	} else if (b <= -2.15e-272) {
		tmp = j * fma(c, t, -(y * i));
	} else if (b <= 7e-191) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 2.1e+65) {
		tmp = -fma(j, (y * i), (t * (x * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * fma(c, Float64(-z), Float64(a * i)))
	tmp = 0.0
	if (b <= -2.9e+79)
		tmp = t_1;
	elseif (b <= -1.5e-127)
		tmp = Float64(y * fma(j, Float64(-i), Float64(x * z)));
	elseif (b <= -2.15e-272)
		tmp = Float64(j * fma(c, t, Float64(-Float64(y * i))));
	elseif (b <= 7e-191)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (b <= 2.1e+65)
		tmp = Float64(-fma(j, Float64(y * i), Float64(t * Float64(x * a))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(c * (-z) + N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.9e+79], t$95$1, If[LessEqual[b, -1.5e-127], N[(y * N[(j * (-i) + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.15e-272], N[(j * N[(c * t + (-N[(y * i), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e-191], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e+65], (-N[(j * N[(y * i), $MachinePrecision] + N[(t * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.89999999999999992e79 or 2.09999999999999991e65 < b

   1. Initial program 61.7%

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

   3. Taylor expanded in b around inf

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

      4. distribute-neg-in N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. *-lowering-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. distribute-neg-in N/A

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

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

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. mul-1-neg N/A

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

      16. neg-lowering-neg.f64 N/A

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

      17. *-commutative N/A

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

      18. *-lowering-*.f64 74.7

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

   5. Simplified 74.7%

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

   if -2.89999999999999992e79 < b < -1.50000000000000004e-127

   1. Initial program 72.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. 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. *-lowering-*.f64 N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. neg-mul-1 N/A

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

      6. neg-lowering-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 59.2

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

   5. Simplified 59.2%

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

   if -1.50000000000000004e-127 < b < -2.1499999999999999e-272

   1. Initial program 75.3%

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

   3. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

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

      2. sub-neg N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. neg-mul-1 N/A

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

      9. neg-lowering-neg.f64 66.9

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

   5. Simplified 66.9%

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

   if -2.1499999999999999e-272 < b < 7.00000000000000013e-191

   1. Initial program 77.2%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 57.9

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

   5. Simplified 57.9%

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

   if 7.00000000000000013e-191 < b < 2.09999999999999991e65

   1. Initial program 76.5%

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

   3. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 61.7

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

   5. Simplified 61.7%

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

   6. Taylor expanded in c around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. distribute-neg-out N/A

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

      4. neg-lowering-neg.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 N/A

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

      14. *-lowering-*.f64 63.2

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

   8. Simplified 63.2%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-127}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, -i, x \cdot z\right)\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-272}:\\ \;\;\;\;j \cdot \mathsf{fma}\left(c, t, -y \cdot i\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-191}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+65}:\\ \;\;\;\;-\mathsf{fma}\left(j, y \cdot i, t \cdot \left(x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -4 \cdot 10^{+25}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;j \leq 0.235:\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, -i, x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -4e+25)
   (- (* j (- (* t c) (* y i))) (* a (* x t)))
   (if (<= j 0.235)
     (fma x (- (* y z) (* t a)) (* b (fma c (- z) (* a i))))
     (* y (fma j (- i) (* x z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -4e+25) {
		tmp = (j * ((t * c) - (y * i))) - (a * (x * t));
	} else if (j <= 0.235) {
		tmp = fma(x, ((y * z) - (t * a)), (b * fma(c, -z, (a * i))));
	} else {
		tmp = y * fma(j, -i, (x * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -4e+25)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(a * Float64(x * t)));
	elseif (j <= 0.235)
		tmp = fma(x, Float64(Float64(y * z) - Float64(t * a)), Float64(b * fma(c, Float64(-z), Float64(a * i))));
	else
		tmp = Float64(y * fma(j, Float64(-i), Float64(x * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -4e+25], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 0.235], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(b * N[(c * (-z) + N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(j * (-i) + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -4.00000000000000036e25

   1. Initial program 65.7%

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

   3. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 64.5

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

   5. Simplified 64.5%

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

   if -4.00000000000000036e25 < j < 0.23499999999999999

   1. Initial program 70.4%

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

   3. Taylor expanded in j around 0

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

      1. sub-neg N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

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

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

      8. mul-1-neg N/A

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

      9. *-lowering-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. distribute-neg-in N/A

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

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

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. accelerator-lowering-fma.f64 N/A

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

      17. mul-1-neg N/A

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

      18. neg-lowering-neg.f64 N/A

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

      19. *-commutative N/A

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

      20. *-lowering-*.f64 78.2

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

   5. Simplified 78.2%

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

   if 0.23499999999999999 < j

   1. Initial program 72.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. 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. *-lowering-*.f64 N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. neg-mul-1 N/A

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

      6. neg-lowering-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 71.6

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

   5. Simplified 71.6%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4 \cdot 10^{+25}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;j \leq 0.235:\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, -i, x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, y \cdot z, b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\\ \mathbf{if}\;b \leq -4.7 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+62}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (fma x (* y z) (* b (fma c (- z) (* a i))))))
   (if (<= b -4.7e+80)
     t_1
     (if (<= b 6.6e+62) (- (* j (- (* t c) (* y i))) (* a (* x t))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(x, (y * z), (b * fma(c, -z, (a * i))));
	double tmp;
	if (b <= -4.7e+80) {
		tmp = t_1;
	} else if (b <= 6.6e+62) {
		tmp = (j * ((t * c) - (y * i))) - (a * (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = fma(x, Float64(y * z), Float64(b * fma(c, Float64(-z), Float64(a * i))))
	tmp = 0.0
	if (b <= -4.7e+80)
		tmp = t_1;
	elseif (b <= 6.6e+62)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(a * Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision] + N[(b * N[(c * (-z) + N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.7e+80], t$95$1, If[LessEqual[b, 6.6e+62], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -4.70000000000000009e80 or 6.6e62 < b

   1. Initial program 61.7%

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

   3. Taylor expanded in j around 0

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

      1. sub-neg N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

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

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

      8. mul-1-neg N/A

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

      9. *-lowering-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. distribute-neg-in N/A

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

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

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. accelerator-lowering-fma.f64 N/A

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

      17. mul-1-neg N/A

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

      18. neg-lowering-neg.f64 N/A

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

      19. *-commutative N/A

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

      20. *-lowering-*.f64 78.0

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

   5. Simplified 78.0%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 78.1

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

   8. Simplified 78.1%

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

   if -4.70000000000000009e80 < b < 6.6e62

   1. Initial program 75.3%

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

   3. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 61.9

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

   5. Simplified 61.9%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot z, b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+62}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot z, b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.18 \cdot 10^{+47}:\\ \;\;\;\;j \cdot \mathsf{fma}\left(c, t, -y \cdot i\right)\\ \mathbf{elif}\;j \leq 0.155:\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot z, b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, -i, x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.18e+47)
   (* j (fma c t (- (* y i))))
   (if (<= j 0.155)
     (fma x (* y z) (* b (fma c (- z) (* a i))))
     (* y (fma j (- i) (* x z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.18e+47) {
		tmp = j * fma(c, t, -(y * i));
	} else if (j <= 0.155) {
		tmp = fma(x, (y * z), (b * fma(c, -z, (a * i))));
	} else {
		tmp = y * fma(j, -i, (x * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.18e+47)
		tmp = Float64(j * fma(c, t, Float64(-Float64(y * i))));
	elseif (j <= 0.155)
		tmp = fma(x, Float64(y * z), Float64(b * fma(c, Float64(-z), Float64(a * i))));
	else
		tmp = Float64(y * fma(j, Float64(-i), Float64(x * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1.18e+47], N[(j * N[(c * t + (-N[(y * i), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 0.155], N[(x * N[(y * z), $MachinePrecision] + N[(b * N[(c * (-z) + N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(j * (-i) + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.18e47

   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 j around inf

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

      1. *-lowering-*.f64 N/A

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

      2. sub-neg N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. neg-mul-1 N/A

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

      9. neg-lowering-neg.f64 63.6

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

   5. Simplified 63.6%

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

   if -1.18e47 < j < 0.154999999999999999

   1. Initial program 70.1%

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

   3. Taylor expanded in j around 0

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

      1. sub-neg N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

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

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

      8. mul-1-neg N/A

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

      9. *-lowering-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. distribute-neg-in N/A

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

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

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. accelerator-lowering-fma.f64 N/A

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

      17. mul-1-neg N/A

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

      18. neg-lowering-neg.f64 N/A

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

      19. *-commutative N/A

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

      20. *-lowering-*.f64 77.0

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

   5. Simplified 77.0%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 66.7

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

   8. Simplified 66.7%

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

   if 0.154999999999999999 < j

   1. Initial program 72.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. 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. *-lowering-*.f64 N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. neg-mul-1 N/A

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

      6. neg-lowering-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 71.6

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

   5. Simplified 71.6%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.18 \cdot 10^{+47}:\\ \;\;\;\;j \cdot \mathsf{fma}\left(c, t, -y \cdot i\right)\\ \mathbf{elif}\;j \leq 0.155:\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot z, b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, -i, x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -9500000:\\ \;\;\;\;j \cdot \mathsf{fma}\left(c, t, -y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{-255}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 0.115:\\ \;\;\;\;b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, -i, x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -9500000.0)
   (* j (fma c t (- (* y i))))
   (if (<= j -1.1e-255)
     (* x (- (* y z) (* t a)))
     (if (<= j 0.115)
       (* b (fma c (- z) (* a i)))
       (* y (fma j (- i) (* x z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -9500000.0) {
		tmp = j * fma(c, t, -(y * i));
	} else if (j <= -1.1e-255) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 0.115) {
		tmp = b * fma(c, -z, (a * i));
	} else {
		tmp = y * fma(j, -i, (x * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -9500000.0)
		tmp = Float64(j * fma(c, t, Float64(-Float64(y * i))));
	elseif (j <= -1.1e-255)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= 0.115)
		tmp = Float64(b * fma(c, Float64(-z), Float64(a * i)));
	else
		tmp = Float64(y * fma(j, Float64(-i), Float64(x * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -9500000.0], N[(j * N[(c * t + (-N[(y * i), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.1e-255], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 0.115], N[(b * N[(c * (-z) + N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(j * (-i) + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -9.5e6

   1. Initial program 65.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. 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. *-lowering-*.f64 N/A

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

      2. sub-neg N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. neg-mul-1 N/A

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

      9. neg-lowering-neg.f64 62.8

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

   5. Simplified 62.8%

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

   if -9.5e6 < j < -1.1e-255

   1. Initial program 77.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 55.5

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

   5. Simplified 55.5%

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

   if -1.1e-255 < j < 0.115000000000000005

   1. Initial program 66.6%

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

   3. Taylor expanded in b around inf

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

      4. distribute-neg-in N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. *-lowering-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. distribute-neg-in N/A

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

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

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. mul-1-neg N/A

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

      16. neg-lowering-neg.f64 N/A

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

      17. *-commutative N/A

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

      18. *-lowering-*.f64 64.6

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

   5. Simplified 64.6%

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

   if 0.115000000000000005 < j

   1. Initial program 72.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. 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. *-lowering-*.f64 N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. neg-mul-1 N/A

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

      6. neg-lowering-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 71.6

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

   5. Simplified 71.6%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9500000:\\ \;\;\;\;j \cdot \mathsf{fma}\left(c, t, -y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{-255}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 0.115:\\ \;\;\;\;b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, -i, x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 43.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -5.3 \cdot 10^{+57}:\\ \;\;\;\;c \cdot \mathsf{fma}\left(j, t, z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-259}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(t, -x, b \cdot i\right)\\ \mathbf{elif}\;j \leq 2.35 \cdot 10^{+141}:\\ \;\;\;\;b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -5.3e+57)
   (* c (fma j t (* z (- b))))
   (if (<= j -7.5e-259)
     (* a (fma t (- x) (* b i)))
     (if (<= j 2.35e+141) (* b (fma c (- z) (* a i))) (* y (* i (- j)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -5.3e+57) {
		tmp = c * fma(j, t, (z * -b));
	} else if (j <= -7.5e-259) {
		tmp = a * fma(t, -x, (b * i));
	} else if (j <= 2.35e+141) {
		tmp = b * fma(c, -z, (a * i));
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -5.3e+57)
		tmp = Float64(c * fma(j, t, Float64(z * Float64(-b))));
	elseif (j <= -7.5e-259)
		tmp = Float64(a * fma(t, Float64(-x), Float64(b * i)));
	elseif (j <= 2.35e+141)
		tmp = Float64(b * fma(c, Float64(-z), Float64(a * i)));
	else
		tmp = Float64(y * Float64(i * Float64(-j)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -5.3e+57], N[(c * N[(j * t + N[(z * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -7.5e-259], N[(a * N[(t * (-x) + N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.35e+141], N[(b * N[(c * (-z) + N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -5.29999999999999986e57

   1. Initial program 65.7%

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

   3. Taylor expanded in c around inf

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

      1. *-lowering-*.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. mul-1-neg N/A

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

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

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

      7. mul-1-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. neg-lowering-neg.f64 53.8

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

   5. Simplified 53.8%

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

   if -5.29999999999999986e57 < j < -7.50000000000000052e-259

   1. Initial program 76.0%

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

   3. Taylor expanded in 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. *-lowering-*.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. neg-lowering-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 54.2

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

   5. Simplified 54.2%

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

   if -7.50000000000000052e-259 < j < 2.3499999999999999e141

   1. Initial program 68.5%

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

   3. Taylor expanded in b around inf

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

      4. distribute-neg-in N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. *-lowering-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. distribute-neg-in N/A

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

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

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. mul-1-neg N/A

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

      16. neg-lowering-neg.f64 N/A

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

      17. *-commutative N/A

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

      18. *-lowering-*.f64 60.5

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

   5. Simplified 60.5%

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

   if 2.3499999999999999e141 < j

   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 j around inf

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

      1. *-lowering-*.f64 N/A

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

      2. sub-neg N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. neg-mul-1 N/A

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

      9. neg-lowering-neg.f64 67.0

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

   5. Simplified 67.0%

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

   6. Taylor expanded in c around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 N/A

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

      3. *-lowering-*.f64 48.7

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

   8. Simplified 48.7%

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

      1. distribute-rgt-neg-out N/A

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

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

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

      3. associate-*r* N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. neg-lowering-neg.f64 63.7

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

   10. Applied egg-rr 63.7%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.3 \cdot 10^{+57}:\\ \;\;\;\;c \cdot \mathsf{fma}\left(j, t, z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-259}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(t, -x, b \cdot i\right)\\ \mathbf{elif}\;j \leq 2.35 \cdot 10^{+141}:\\ \;\;\;\;b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 42.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{if}\;j \leq -5.4 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -2.3 \cdot 10^{-255}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(t, -x, b \cdot i\right)\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{+137}:\\ \;\;\;\;b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* i (- j)))))
   (if (<= j -5.4e+141)
     t_1
     (if (<= j -2.3e-255)
       (* a (fma t (- x) (* b i)))
       (if (<= j 5.4e+137) (* b (fma c (- z) (* a i))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (i * -j);
	double tmp;
	if (j <= -5.4e+141) {
		tmp = t_1;
	} else if (j <= -2.3e-255) {
		tmp = a * fma(t, -x, (b * i));
	} else if (j <= 5.4e+137) {
		tmp = b * fma(c, -z, (a * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(i * Float64(-j)))
	tmp = 0.0
	if (j <= -5.4e+141)
		tmp = t_1;
	elseif (j <= -2.3e-255)
		tmp = Float64(a * fma(t, Float64(-x), Float64(b * i)));
	elseif (j <= 5.4e+137)
		tmp = Float64(b * fma(c, Float64(-z), Float64(a * i)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5.4e+141], t$95$1, If[LessEqual[j, -2.3e-255], N[(a * N[(t * (-x) + N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.4e+137], N[(b * N[(c * (-z) + N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -5.4000000000000002e141 or 5.40000000000000034e137 < j

   1. Initial program 65.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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. *-lowering-*.f64 N/A

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

      2. sub-neg N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. neg-mul-1 N/A

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

      9. neg-lowering-neg.f64 66.4

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

   5. Simplified 66.4%

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

   6. Taylor expanded in c around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 N/A

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

      3. *-lowering-*.f64 51.9

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

   8. Simplified 51.9%

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

      1. distribute-rgt-neg-out N/A

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

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

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

      3. associate-*r* N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. neg-lowering-neg.f64 61.2

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

   10. Applied egg-rr 61.2%

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

   if -5.4000000000000002e141 < j < -2.2999999999999999e-255

   1. Initial program 76.6%

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

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. neg-lowering-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 49.1

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

   5. Simplified 49.1%

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

   if -2.2999999999999999e-255 < j < 5.40000000000000034e137

   1. Initial program 68.5%

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

   3. Taylor expanded in b around inf

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

      4. distribute-neg-in N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. *-lowering-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. distribute-neg-in N/A

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

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

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. mul-1-neg N/A

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

      16. neg-lowering-neg.f64 N/A

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

      17. *-commutative N/A

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

      18. *-lowering-*.f64 60.5

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

   5. Simplified 60.5%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.4 \cdot 10^{+141}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq -2.3 \cdot 10^{-255}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(t, -x, b \cdot i\right)\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{+137}:\\ \;\;\;\;b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\\ \mathbf{if}\;b \leq -2.45 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+93}:\\ \;\;\;\;j \cdot \mathsf{fma}\left(c, t, -y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (fma c (- z) (* a i)))))
   (if (<= b -2.45e+75)
     t_1
     (if (<= b 6.2e+93) (* j (fma c t (- (* y i)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * fma(c, -z, (a * i));
	double tmp;
	if (b <= -2.45e+75) {
		tmp = t_1;
	} else if (b <= 6.2e+93) {
		tmp = j * fma(c, t, -(y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * fma(c, Float64(-z), Float64(a * i)))
	tmp = 0.0
	if (b <= -2.45e+75)
		tmp = t_1;
	elseif (b <= 6.2e+93)
		tmp = Float64(j * fma(c, t, Float64(-Float64(y * i))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(c * (-z) + N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.45e+75], t$95$1, If[LessEqual[b, 6.2e+93], N[(j * N[(c * t + (-N[(y * i), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.45000000000000005e75 or 6.20000000000000038e93 < b

   1. Initial program 60.1%

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

   3. Taylor expanded in b around inf

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

      4. distribute-neg-in N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. *-lowering-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. distribute-neg-in N/A

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

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

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. mul-1-neg N/A

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

      16. neg-lowering-neg.f64 N/A

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

      17. *-commutative N/A

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

      18. *-lowering-*.f64 76.6

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

   5. Simplified 76.6%

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

   if -2.45000000000000005e75 < b < 6.20000000000000038e93

   1. Initial program 76.0%

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

   3. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

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

      2. sub-neg N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. neg-mul-1 N/A

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

      9. neg-lowering-neg.f64 51.4

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

   5. Simplified 51.4%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.45 \cdot 10^{+75}:\\ \;\;\;\;b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+93}:\\ \;\;\;\;j \cdot \mathsf{fma}\left(c, t, -y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 45.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+66}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(t, -x, b \cdot i\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-21}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(j, -y, a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \mathsf{fma}\left(j, t, z \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -1e+66)
   (* a (fma t (- x) (* b i)))
   (if (<= t 1.55e-21)
     (* i (fma j (- y) (* a b)))
     (* c (fma j t (* z (- b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -1e+66) {
		tmp = a * fma(t, -x, (b * i));
	} else if (t <= 1.55e-21) {
		tmp = i * fma(j, -y, (a * b));
	} else {
		tmp = c * fma(j, t, (z * -b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -1e+66)
		tmp = Float64(a * fma(t, Float64(-x), Float64(b * i)));
	elseif (t <= 1.55e-21)
		tmp = Float64(i * fma(j, Float64(-y), Float64(a * b)));
	else
		tmp = Float64(c * fma(j, t, Float64(z * Float64(-b))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -1e+66], N[(a * N[(t * (-x) + N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e-21], N[(i * N[(j * (-y) + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(j * t + N[(z * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.99999999999999945e65

   1. Initial program 60.9%

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

   3. Taylor expanded in 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. *-lowering-*.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. neg-lowering-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 66.6

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

   5. Simplified 66.6%

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

   if -9.99999999999999945e65 < t < 1.5499999999999999e-21

   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 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. *-lowering-*.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. neg-lowering-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 58.0

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

   5. Simplified 58.0%

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

   if 1.5499999999999999e-21 < t

   1. Initial program 62.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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. *-lowering-*.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. mul-1-neg N/A

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

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

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

      7. mul-1-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. neg-lowering-neg.f64 61.0

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

   5. Simplified 61.0%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+66}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(t, -x, b \cdot i\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-21}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(j, -y, a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \mathsf{fma}\left(j, t, z \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 41.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{if}\;j \leq -1.7 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 0.22:\\ \;\;\;\;a \cdot \mathsf{fma}\left(t, -x, b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* i (- j)))))
   (if (<= j -1.7e+141) t_1 (if (<= j 0.22) (* a (fma t (- x) (* b i))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (i * -j);
	double tmp;
	if (j <= -1.7e+141) {
		tmp = t_1;
	} else if (j <= 0.22) {
		tmp = a * fma(t, -x, (b * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(i * Float64(-j)))
	tmp = 0.0
	if (j <= -1.7e+141)
		tmp = t_1;
	elseif (j <= 0.22)
		tmp = Float64(a * fma(t, Float64(-x), Float64(b * i)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.7e+141], t$95$1, If[LessEqual[j, 0.22], N[(a * N[(t * (-x) + N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if j < -1.6999999999999999e141 or 0.220000000000000001 < j

   1. Initial program 67.6%

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

   3. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

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

      2. sub-neg N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. neg-mul-1 N/A

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

      9. neg-lowering-neg.f64 65.7

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

   5. Simplified 65.7%

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

   6. Taylor expanded in c around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 N/A

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

      3. *-lowering-*.f64 49.7

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

   8. Simplified 49.7%

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

      1. distribute-rgt-neg-out N/A

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

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

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

      3. associate-*r* N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. neg-lowering-neg.f64 57.8

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

   10. Applied egg-rr 57.8%

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

   if -1.6999999999999999e141 < j < 0.220000000000000001

   1. Initial program 71.3%

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

   3. Taylor expanded in 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. *-lowering-*.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. neg-lowering-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 48.5

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

   5. Simplified 48.5%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.7 \cdot 10^{+141}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq 0.22:\\ \;\;\;\;a \cdot \mathsf{fma}\left(t, -x, b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -7.8 \cdot 10^{+155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -4.5 \cdot 10^{+56}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* b i))))
   (if (<= i -7.8e+155)
     t_1
     (if (<= i -4.5e+56)
       (* j (* t c))
       (if (<= i 1.1e-57) (* x (* y z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double tmp;
	if (i <= -7.8e+155) {
		tmp = t_1;
	} else if (i <= -4.5e+56) {
		tmp = j * (t * c);
	} else if (i <= 1.1e-57) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * i)
    if (i <= (-7.8d+155)) then
        tmp = t_1
    else if (i <= (-4.5d+56)) then
        tmp = j * (t * c)
    else if (i <= 1.1d-57) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double tmp;
	if (i <= -7.8e+155) {
		tmp = t_1;
	} else if (i <= -4.5e+56) {
		tmp = j * (t * c);
	} else if (i <= 1.1e-57) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (b * i)
	tmp = 0
	if i <= -7.8e+155:
		tmp = t_1
	elif i <= -4.5e+56:
		tmp = j * (t * c)
	elif i <= 1.1e-57:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (i <= -7.8e+155)
		tmp = t_1;
	elseif (i <= -4.5e+56)
		tmp = Float64(j * Float64(t * c));
	elseif (i <= 1.1e-57)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (b * i);
	tmp = 0.0;
	if (i <= -7.8e+155)
		tmp = t_1;
	elseif (i <= -4.5e+56)
		tmp = j * (t * c);
	elseif (i <= 1.1e-57)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -7.8e+155], t$95$1, If[LessEqual[i, -4.5e+56], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.1e-57], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -7.7999999999999996e155 or 1.09999999999999999e-57 < i

   1. Initial program 62.5%

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

   3. Taylor expanded in j around 0

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

      1. sub-neg N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

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

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

      8. mul-1-neg N/A

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

      9. *-lowering-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. distribute-neg-in N/A

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

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

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. accelerator-lowering-fma.f64 N/A

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

      17. mul-1-neg N/A

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

      18. neg-lowering-neg.f64 N/A

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

      19. *-commutative N/A

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

      20. *-lowering-*.f64 58.7

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

   5. Simplified 58.7%

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

   6. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 41.3

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

   8. Simplified 41.3%

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

   if -7.7999999999999996e155 < i < -4.5000000000000003e56

   1. Initial program 82.7%

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

   3. Taylor expanded in c around inf

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

      1. *-lowering-*.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. mul-1-neg N/A

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

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

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

      7. mul-1-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. neg-lowering-neg.f64 53.5

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

   5. Simplified 53.5%

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

   6. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 49.4

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

   8. Simplified 49.4%

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

   if -4.5000000000000003e56 < i < 1.09999999999999999e-57

   1. Initial program 74.8%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 53.4

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

   5. Simplified 53.4%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 34.4

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

   8. Simplified 34.4%

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

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -7.8 \cdot 10^{+155}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -4.5 \cdot 10^{+56}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 30.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{if}\;j \leq -2.65 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 0.14:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* i (- j)))))
   (if (<= j -2.65e+124) t_1 (if (<= j 0.14) (* 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 = y * (i * -j);
	double tmp;
	if (j <= -2.65e+124) {
		tmp = t_1;
	} else if (j <= 0.14) {
		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 = y * (i * -j)
    if (j <= (-2.65d+124)) then
        tmp = t_1
    else if (j <= 0.14d0) 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 = y * (i * -j);
	double tmp;
	if (j <= -2.65e+124) {
		tmp = t_1;
	} else if (j <= 0.14) {
		tmp = i * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (i * -j)
	tmp = 0
	if j <= -2.65e+124:
		tmp = t_1
	elif j <= 0.14:
		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(y * Float64(i * Float64(-j)))
	tmp = 0.0
	if (j <= -2.65e+124)
		tmp = t_1;
	elseif (j <= 0.14)
		tmp = Float64(i * Float64(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 = y * (i * -j);
	tmp = 0.0;
	if (j <= -2.65e+124)
		tmp = t_1;
	elseif (j <= 0.14)
		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[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.65e+124], t$95$1, If[LessEqual[j, 0.14], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if j < -2.6500000000000001e124 or 0.14000000000000001 < j

   1. Initial program 67.9%

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

   3. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

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

      2. sub-neg N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. neg-mul-1 N/A

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

      9. neg-lowering-neg.f64 66.0

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

   5. Simplified 66.0%

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

   6. Taylor expanded in c around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 N/A

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

      3. *-lowering-*.f64 48.9

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

   8. Simplified 48.9%

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

      1. distribute-rgt-neg-out N/A

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

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

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

      3. associate-*r* N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. neg-lowering-neg.f64 56.7

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

   10. Applied egg-rr 56.7%

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

   if -2.6500000000000001e124 < j < 0.14000000000000001

   1. Initial program 71.2%

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

   3. Taylor expanded in j around 0

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

      1. sub-neg N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

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

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

      8. mul-1-neg N/A

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

      9. *-lowering-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. distribute-neg-in N/A

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

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

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. accelerator-lowering-fma.f64 N/A

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

      17. mul-1-neg N/A

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

      18. neg-lowering-neg.f64 N/A

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

      19. *-commutative N/A

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

      20. *-lowering-*.f64 74.0

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

   5. Simplified 74.0%

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

   6. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 32.3

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

   8. Simplified 32.3%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 35.6

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

   10. Applied egg-rr 35.6%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.65 \cdot 10^{+124}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq 0.14:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 30.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-i\right) \cdot \left(y \cdot j\right)\\ \mathbf{if}\;j \leq -3.2 \cdot 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 0.23:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- i) (* y j))))
   (if (<= j -3.2e+128) t_1 (if (<= j 0.23) (* 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 = -i * (y * j);
	double tmp;
	if (j <= -3.2e+128) {
		tmp = t_1;
	} else if (j <= 0.23) {
		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 = -i * (y * j)
    if (j <= (-3.2d+128)) then
        tmp = t_1
    else if (j <= 0.23d0) 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 = -i * (y * j);
	double tmp;
	if (j <= -3.2e+128) {
		tmp = t_1;
	} else if (j <= 0.23) {
		tmp = i * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = -i * (y * j)
	tmp = 0
	if j <= -3.2e+128:
		tmp = t_1
	elif j <= 0.23:
		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(-i) * Float64(y * j))
	tmp = 0.0
	if (j <= -3.2e+128)
		tmp = t_1;
	elseif (j <= 0.23)
		tmp = Float64(i * Float64(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 = -i * (y * j);
	tmp = 0.0;
	if (j <= -3.2e+128)
		tmp = t_1;
	elseif (j <= 0.23)
		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[((-i) * N[(y * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.2e+128], t$95$1, If[LessEqual[j, 0.23], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if j < -3.19999999999999986e128 or 0.23000000000000001 < j

   1. Initial program 67.9%

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

   3. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

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

      2. sub-neg N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. neg-mul-1 N/A

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

      9. neg-lowering-neg.f64 66.0

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

   5. Simplified 66.0%

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

   6. Taylor expanded in c around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 N/A

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

      3. *-lowering-*.f64 48.9

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

   8. Simplified 48.9%

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

      1. *-commutative N/A

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

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

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

      3. associate-*r* N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. neg-lowering-neg.f64 50.6

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

   10. Applied egg-rr 50.6%

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

   if -3.19999999999999986e128 < j < 0.23000000000000001

   1. Initial program 71.2%

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

   3. Taylor expanded in j around 0

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

      1. sub-neg N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

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

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

      8. mul-1-neg N/A

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

      9. *-lowering-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. distribute-neg-in N/A

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

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

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. accelerator-lowering-fma.f64 N/A

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

      17. mul-1-neg N/A

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

      18. neg-lowering-neg.f64 N/A

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

      19. *-commutative N/A

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

      20. *-lowering-*.f64 74.0

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

   5. Simplified 74.0%

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

   6. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 32.3

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

   8. Simplified 32.3%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 35.6

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

   10. Applied egg-rr 35.6%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.2 \cdot 10^{+128}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;j \leq 0.23:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -j \cdot \left(y \cdot i\right)\\ \mathbf{if}\;j \leq -1.4 \cdot 10^{+126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 0.21:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* j (* y i)))))
   (if (<= j -1.4e+126) t_1 (if (<= j 0.21) (* 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 * (y * i));
	double tmp;
	if (j <= -1.4e+126) {
		tmp = t_1;
	} else if (j <= 0.21) {
		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 * (y * i))
    if (j <= (-1.4d+126)) then
        tmp = t_1
    else if (j <= 0.21d0) 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 * (y * i));
	double tmp;
	if (j <= -1.4e+126) {
		tmp = t_1;
	} else if (j <= 0.21) {
		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 * (y * i))
	tmp = 0
	if j <= -1.4e+126:
		tmp = t_1
	elif j <= 0.21:
		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 * Float64(y * i)))
	tmp = 0.0
	if (j <= -1.4e+126)
		tmp = t_1;
	elseif (j <= 0.21)
		tmp = Float64(i * Float64(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 * (y * i));
	tmp = 0.0;
	if (j <= -1.4e+126)
		tmp = t_1;
	elseif (j <= 0.21)
		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[(j * N[(y * i), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[j, -1.4e+126], t$95$1, If[LessEqual[j, 0.21], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if j < -1.40000000000000005e126 or 0.209999999999999992 < j

   1. Initial program 67.9%

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

   3. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

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

      2. sub-neg N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. neg-mul-1 N/A

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

      9. neg-lowering-neg.f64 66.0

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

   5. Simplified 66.0%

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

   6. Taylor expanded in c around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 N/A

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

      3. *-lowering-*.f64 48.9

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

   8. Simplified 48.9%

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

   if -1.40000000000000005e126 < j < 0.209999999999999992

   1. Initial program 71.2%

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

   3. Taylor expanded in j around 0

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

      1. sub-neg N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

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

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

      8. mul-1-neg N/A

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

      9. *-lowering-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. distribute-neg-in N/A

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

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

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. accelerator-lowering-fma.f64 N/A

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

      17. mul-1-neg N/A

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

      18. neg-lowering-neg.f64 N/A

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

      19. *-commutative N/A

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

      20. *-lowering-*.f64 74.0

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

   5. Simplified 74.0%

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

   6. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 32.3

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

   8. Simplified 32.3%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 35.6

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

   10. Applied egg-rr 35.6%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.4 \cdot 10^{+126}:\\ \;\;\;\;-j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;j \leq 0.21:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-j \cdot \left(y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -20:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -20.0)
   (* i (* a b))
   (if (<= i 1.15e-57) (* y (* x z)) (* a (* b i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -20.0) {
		tmp = i * (a * b);
	} else if (i <= 1.15e-57) {
		tmp = y * (x * z);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-20.0d0)) then
        tmp = i * (a * b)
    else if (i <= 1.15d-57) then
        tmp = y * (x * z)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -20.0) {
		tmp = i * (a * b);
	} else if (i <= 1.15e-57) {
		tmp = y * (x * z);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -20.0:
		tmp = i * (a * b)
	elif i <= 1.15e-57:
		tmp = y * (x * z)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -20.0)
		tmp = Float64(i * Float64(a * b));
	elseif (i <= 1.15e-57)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -20.0)
		tmp = i * (a * b);
	elseif (i <= 1.15e-57)
		tmp = y * (x * z);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -20.0], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.15e-57], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -20

   1. Initial program 63.9%

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

   3. Taylor expanded in j around 0

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

      1. sub-neg N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

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

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

      8. mul-1-neg N/A

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

      9. *-lowering-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. distribute-neg-in N/A

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

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

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. accelerator-lowering-fma.f64 N/A

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

      17. mul-1-neg N/A

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

      18. neg-lowering-neg.f64 N/A

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

      19. *-commutative N/A

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

      20. *-lowering-*.f64 60.6

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

   5. Simplified 60.6%

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

   6. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 32.1

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

   8. Simplified 32.1%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 37.7

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot i \]

   10. Applied egg-rr 37.7%

       \[\leadsto \color{blue}{\left(b \cdot a\right) \cdot i} \]

   if -20 < i < 1.15e-57

   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 x around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \left(\color{blue}{y \cdot z} - a \cdot t\right) \]

      4. *-commutative N/A

         \[\leadsto x \cdot \left(y \cdot z - \color{blue}{t \cdot a}\right) \]

      5. *-lowering-*.f64 53.9

         \[\leadsto x \cdot \left(y \cdot z - \color{blue}{t \cdot a}\right) \]

   5. Simplified 53.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

      2. *-lowering-*.f64 35.7

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   8. Simplified 35.7%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]
   9. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(x \cdot z\right) \cdot y} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot z\right) \cdot y} \]

      3. *-lowering-*.f64 36.6

         \[\leadsto \color{blue}{\left(x \cdot z\right)} \cdot y \]

   10. Applied egg-rr 36.6%

       \[\leadsto \color{blue}{\left(x \cdot z\right) \cdot y} \]

   if 1.15e-57 < i

   1. Initial program 63.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around 0

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right)} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - a \cdot t, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right)} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{y \cdot z - a \cdot t}, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{y \cdot z} - a \cdot t, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - \color{blue}{t \cdot a}, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - \color{blue}{t \cdot a}, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{b \cdot \left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)}\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)}\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right)}\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z + \left(\mathsf{neg}\left(a \cdot i\right)\right)\right)}\right)\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \color{blue}{\left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot i\right)\right)\right)\right)\right)}\right) \]

      13. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \left(\color{blue}{c \cdot \left(\mathsf{neg}\left(z\right)\right)} + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot i\right)\right)\right)\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \left(c \cdot \color{blue}{\left(-1 \cdot z\right)} + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot i\right)\right)\right)\right)\right)\right) \]

      15. remove-double-neg N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \left(c \cdot \left(-1 \cdot z\right) + \color{blue}{a \cdot i}\right)\right) \]

      16. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \color{blue}{\mathsf{fma}\left(c, -1 \cdot z, a \cdot i\right)}\right) \]

      17. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(z\right)}, a \cdot i\right)\right) \]

      18. neg-lowering-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(z\right)}, a \cdot i\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, \mathsf{neg}\left(z\right), \color{blue}{i \cdot a}\right)\right) \]

      20. *-lowering-*.f64 57.7

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, -z, \color{blue}{i \cdot a}\right)\right) \]

   5. Simplified 57.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, -z, i \cdot a\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

      2. *-lowering-*.f64 43.3

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]

   8. Simplified 43.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -20:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 30.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -5 \cdot 10^{+17}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;i \leq 2.25 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -5e+17)
   (* i (* a b))
   (if (<= i 2.25e-57) (* x (* y z)) (* a (* b i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -5e+17) {
		tmp = i * (a * b);
	} else if (i <= 2.25e-57) {
		tmp = x * (y * z);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-5d+17)) then
        tmp = i * (a * b)
    else if (i <= 2.25d-57) then
        tmp = x * (y * z)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -5e+17) {
		tmp = i * (a * b);
	} else if (i <= 2.25e-57) {
		tmp = x * (y * z);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -5e+17:
		tmp = i * (a * b)
	elif i <= 2.25e-57:
		tmp = x * (y * z)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -5e+17)
		tmp = Float64(i * Float64(a * b));
	elseif (i <= 2.25e-57)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -5e+17)
		tmp = i * (a * b);
	elseif (i <= 2.25e-57)
		tmp = x * (y * z);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -5e+17], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.25e-57], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -5e17

   1. Initial program 65.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around 0

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right)} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - a \cdot t, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right)} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{y \cdot z - a \cdot t}, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{y \cdot z} - a \cdot t, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - \color{blue}{t \cdot a}, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - \color{blue}{t \cdot a}, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{b \cdot \left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)}\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)}\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right)}\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z + \left(\mathsf{neg}\left(a \cdot i\right)\right)\right)}\right)\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \color{blue}{\left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot i\right)\right)\right)\right)\right)}\right) \]

      13. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \left(\color{blue}{c \cdot \left(\mathsf{neg}\left(z\right)\right)} + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot i\right)\right)\right)\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \left(c \cdot \color{blue}{\left(-1 \cdot z\right)} + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot i\right)\right)\right)\right)\right)\right) \]

      15. remove-double-neg N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \left(c \cdot \left(-1 \cdot z\right) + \color{blue}{a \cdot i}\right)\right) \]

      16. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \color{blue}{\mathsf{fma}\left(c, -1 \cdot z, a \cdot i\right)}\right) \]

      17. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(z\right)}, a \cdot i\right)\right) \]

      18. neg-lowering-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(z\right)}, a \cdot i\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, \mathsf{neg}\left(z\right), \color{blue}{i \cdot a}\right)\right) \]

      20. *-lowering-*.f64 61.1

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, -z, \color{blue}{i \cdot a}\right)\right) \]

   5. Simplified 61.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, -z, i \cdot a\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

      2. *-lowering-*.f64 31.1

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]

   8. Simplified 31.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   9. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot i \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot a\right) \cdot i} \]

      4. *-lowering-*.f64 37.1

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot i \]

   10. Applied egg-rr 37.1%

       \[\leadsto \color{blue}{\left(b \cdot a\right) \cdot i} \]

   if -5e17 < i < 2.24999999999999986e-57

   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. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \left(\color{blue}{y \cdot z} - a \cdot t\right) \]

      4. *-commutative N/A

         \[\leadsto x \cdot \left(y \cdot z - \color{blue}{t \cdot a}\right) \]

      5. *-lowering-*.f64 53.8

         \[\leadsto x \cdot \left(y \cdot z - \color{blue}{t \cdot a}\right) \]

   5. Simplified 53.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

      2. *-lowering-*.f64 36.4

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   8. Simplified 36.4%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   if 2.24999999999999986e-57 < i

   1. Initial program 63.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around 0

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right)} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - a \cdot t, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right)} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{y \cdot z - a \cdot t}, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{y \cdot z} - a \cdot t, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - \color{blue}{t \cdot a}, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - \color{blue}{t \cdot a}, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{b \cdot \left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)}\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)}\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right)}\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z + \left(\mathsf{neg}\left(a \cdot i\right)\right)\right)}\right)\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \color{blue}{\left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot i\right)\right)\right)\right)\right)}\right) \]

      13. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \left(\color{blue}{c \cdot \left(\mathsf{neg}\left(z\right)\right)} + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot i\right)\right)\right)\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \left(c \cdot \color{blue}{\left(-1 \cdot z\right)} + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot i\right)\right)\right)\right)\right)\right) \]

      15. remove-double-neg N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \left(c \cdot \left(-1 \cdot z\right) + \color{blue}{a \cdot i}\right)\right) \]

      16. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \color{blue}{\mathsf{fma}\left(c, -1 \cdot z, a \cdot i\right)}\right) \]

      17. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(z\right)}, a \cdot i\right)\right) \]

      18. neg-lowering-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(z\right)}, a \cdot i\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, \mathsf{neg}\left(z\right), \color{blue}{i \cdot a}\right)\right) \]

      20. *-lowering-*.f64 57.7

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, -z, \color{blue}{i \cdot a}\right)\right) \]

   5. Simplified 57.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, -z, i \cdot a\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

      2. *-lowering-*.f64 43.3

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]

   8. Simplified 43.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5 \cdot 10^{+17}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;i \leq 2.25 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c\right)\\ \mathbf{if}\;c \leq -2.55 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-47}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* t c))))
   (if (<= c -2.55e+141) t_1 (if (<= c 2.9e-47) (* a (* b i)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (t * c);
	double tmp;
	if (c <= -2.55e+141) {
		tmp = t_1;
	} else if (c <= 2.9e-47) {
		tmp = a * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (t * c)
    if (c <= (-2.55d+141)) then
        tmp = t_1
    else if (c <= 2.9d-47) then
        tmp = a * (b * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (t * c);
	double tmp;
	if (c <= -2.55e+141) {
		tmp = t_1;
	} else if (c <= 2.9e-47) {
		tmp = a * (b * i);
	} 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 c <= -2.55e+141:
		tmp = t_1
	elif c <= 2.9e-47:
		tmp = a * (b * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(t * c))
	tmp = 0.0
	if (c <= -2.55e+141)
		tmp = t_1;
	elseif (c <= 2.9e-47)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (t * c);
	tmp = 0.0;
	if (c <= -2.55e+141)
		tmp = t_1;
	elseif (c <= 2.9e-47)
		tmp = a * (b * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.55e+141], t$95$1, If[LessEqual[c, 2.9e-47], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if c < -2.5499999999999999e141 or 2.9e-47 < c

   1. Initial program 64.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

      2. sub-neg N/A

         \[\leadsto c \cdot \color{blue}{\left(j \cdot t + \left(\mathsf{neg}\left(b \cdot z\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto c \cdot \left(j \cdot t + \color{blue}{-1 \cdot \left(b \cdot z\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto c \cdot \color{blue}{\mathsf{fma}\left(j, t, -1 \cdot \left(b \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, \color{blue}{\mathsf{neg}\left(b \cdot z\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, \color{blue}{b \cdot \left(\mathsf{neg}\left(z\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, b \cdot \color{blue}{\left(-1 \cdot z\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, \color{blue}{b \cdot \left(-1 \cdot z\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, b \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right) \]

      10. neg-lowering-neg.f64 58.5

          \[\leadsto c \cdot \mathsf{fma}\left(j, t, b \cdot \color{blue}{\left(-z\right)}\right) \]

   5. Simplified 58.5%

      \[\leadsto \color{blue}{c \cdot \mathsf{fma}\left(j, t, b \cdot \left(-z\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot t} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(j \cdot c\right)} \cdot t \]

      3. associate-*r* N/A

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t\right)} \]

      5. *-lowering-*.f64 42.0

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t\right)} \]

   8. Simplified 42.0%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t\right)} \]

   if -2.5499999999999999e141 < c < 2.9e-47

   1. Initial program 73.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around 0

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right)} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - a \cdot t, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right)} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{y \cdot z - a \cdot t}, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{y \cdot z} - a \cdot t, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - \color{blue}{t \cdot a}, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - \color{blue}{t \cdot a}, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{b \cdot \left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)}\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)}\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right)}\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z + \left(\mathsf{neg}\left(a \cdot i\right)\right)\right)}\right)\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \color{blue}{\left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot i\right)\right)\right)\right)\right)}\right) \]

      13. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \left(\color{blue}{c \cdot \left(\mathsf{neg}\left(z\right)\right)} + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot i\right)\right)\right)\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \left(c \cdot \color{blue}{\left(-1 \cdot z\right)} + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot i\right)\right)\right)\right)\right)\right) \]

      15. remove-double-neg N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \left(c \cdot \left(-1 \cdot z\right) + \color{blue}{a \cdot i}\right)\right) \]

      16. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \color{blue}{\mathsf{fma}\left(c, -1 \cdot z, a \cdot i\right)}\right) \]

      17. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(z\right)}, a \cdot i\right)\right) \]

      18. neg-lowering-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(z\right)}, a \cdot i\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, \mathsf{neg}\left(z\right), \color{blue}{i \cdot a}\right)\right) \]

      20. *-lowering-*.f64 66.0

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, -z, \color{blue}{i \cdot a}\right)\right) \]

   5. Simplified 66.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, -z, i \cdot a\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

      2. *-lowering-*.f64 32.7

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]

   8. Simplified 32.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.55 \cdot 10^{+141}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-47}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 28.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;a \leq -2.05 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.56 \cdot 10^{-34}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* b i))))
   (if (<= a -2.05e-36) t_1 (if (<= a 1.56e-34) (* 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 = a * (b * i);
	double tmp;
	if (a <= -2.05e-36) {
		tmp = t_1;
	} else if (a <= 1.56e-34) {
		tmp = c * (t * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * i)
    if (a <= (-2.05d-36)) then
        tmp = t_1
    else if (a <= 1.56d-34) then
        tmp = c * (t * j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double tmp;
	if (a <= -2.05e-36) {
		tmp = t_1;
	} else if (a <= 1.56e-34) {
		tmp = c * (t * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (b * i)
	tmp = 0
	if a <= -2.05e-36:
		tmp = t_1
	elif a <= 1.56e-34:
		tmp = c * (t * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (a <= -2.05e-36)
		tmp = t_1;
	elseif (a <= 1.56e-34)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (b * i);
	tmp = 0.0;
	if (a <= -2.05e-36)
		tmp = t_1;
	elseif (a <= 1.56e-34)
		tmp = c * (t * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.05e-36], t$95$1, If[LessEqual[a, 1.56e-34], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.05000000000000006e-36 or 1.55999999999999992e-34 < a

   1. Initial program 61.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around 0

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right)} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - a \cdot t, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right)} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{y \cdot z - a \cdot t}, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{y \cdot z} - a \cdot t, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - \color{blue}{t \cdot a}, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - \color{blue}{t \cdot a}, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{b \cdot \left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)}\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)}\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right)}\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z + \left(\mathsf{neg}\left(a \cdot i\right)\right)\right)}\right)\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \color{blue}{\left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot i\right)\right)\right)\right)\right)}\right) \]

      13. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \left(\color{blue}{c \cdot \left(\mathsf{neg}\left(z\right)\right)} + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot i\right)\right)\right)\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \left(c \cdot \color{blue}{\left(-1 \cdot z\right)} + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot i\right)\right)\right)\right)\right)\right) \]

      15. remove-double-neg N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \left(c \cdot \left(-1 \cdot z\right) + \color{blue}{a \cdot i}\right)\right) \]

      16. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \color{blue}{\mathsf{fma}\left(c, -1 \cdot z, a \cdot i\right)}\right) \]

      17. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(z\right)}, a \cdot i\right)\right) \]

      18. neg-lowering-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(z\right)}, a \cdot i\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, \mathsf{neg}\left(z\right), \color{blue}{i \cdot a}\right)\right) \]

      20. *-lowering-*.f64 66.6

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, -z, \color{blue}{i \cdot a}\right)\right) \]

   5. Simplified 66.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, -z, i \cdot a\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

      2. *-lowering-*.f64 42.5

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]

   8. Simplified 42.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if -2.05000000000000006e-36 < a < 1.55999999999999992e-34

   1. Initial program 79.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

      2. sub-neg N/A

         \[\leadsto c \cdot \color{blue}{\left(j \cdot t + \left(\mathsf{neg}\left(b \cdot z\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto c \cdot \left(j \cdot t + \color{blue}{-1 \cdot \left(b \cdot z\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto c \cdot \color{blue}{\mathsf{fma}\left(j, t, -1 \cdot \left(b \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, \color{blue}{\mathsf{neg}\left(b \cdot z\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, \color{blue}{b \cdot \left(\mathsf{neg}\left(z\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, b \cdot \color{blue}{\left(-1 \cdot z\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, \color{blue}{b \cdot \left(-1 \cdot z\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, b \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right) \]

      10. neg-lowering-neg.f64 48.5

          \[\leadsto c \cdot \mathsf{fma}\left(j, t, b \cdot \color{blue}{\left(-z\right)}\right) \]

   5. Simplified 48.5%

      \[\leadsto \color{blue}{c \cdot \mathsf{fma}\left(j, t, b \cdot \left(-z\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

      2. *-lowering-*.f64 26.4

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   8. Simplified 26.4%

      \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 22.1% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* b i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (b * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (b * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(b * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (b * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.8%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Add Preprocessing

3. Taylor expanded in j around 0

   \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
4. Step-by-step derivation

   1. sub-neg N/A

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right)} \]

   2. accelerator-lowering-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - a \cdot t, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right)} \]

   3. --lowering--.f64 N/A

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{y \cdot z - a \cdot t}, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{y \cdot z} - a \cdot t, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

   5. *-commutative N/A

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - \color{blue}{t \cdot a}, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

   6. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - \color{blue}{t \cdot a}, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

   7. distribute-rgt-neg-in N/A

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{b \cdot \left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right)}\right) \]

   8. mul-1-neg N/A

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)}\right) \]

   9. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)}\right) \]

   10. mul-1-neg N/A

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right)}\right) \]

   11. sub-neg N/A

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z + \left(\mathsf{neg}\left(a \cdot i\right)\right)\right)}\right)\right)\right) \]

   12. distribute-neg-in N/A

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \color{blue}{\left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot i\right)\right)\right)\right)\right)}\right) \]

   13. distribute-rgt-neg-in N/A

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \left(\color{blue}{c \cdot \left(\mathsf{neg}\left(z\right)\right)} + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot i\right)\right)\right)\right)\right)\right) \]

   14. mul-1-neg N/A

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \left(c \cdot \color{blue}{\left(-1 \cdot z\right)} + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot i\right)\right)\right)\right)\right)\right) \]

   15. remove-double-neg N/A

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \left(c \cdot \left(-1 \cdot z\right) + \color{blue}{a \cdot i}\right)\right) \]

   16. accelerator-lowering-fma.f64 N/A

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \color{blue}{\mathsf{fma}\left(c, -1 \cdot z, a \cdot i\right)}\right) \]

   17. mul-1-neg N/A

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(z\right)}, a \cdot i\right)\right) \]

   18. neg-lowering-neg.f64 N/A

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(z\right)}, a \cdot i\right)\right) \]

   19. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, \mathsf{neg}\left(z\right), \color{blue}{i \cdot a}\right)\right) \]

   20. *-lowering-*.f64 62.8

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, -z, \color{blue}{i \cdot a}\right)\right) \]

5. Simplified 62.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, b \cdot \mathsf{fma}\left(c, -z, i \cdot a\right)\right)} \]

6. Taylor expanded in i around inf

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
7. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   2. *-lowering-*.f64 27.1

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]

8. Simplified 27.1%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
9. Add Preprocessing

Developer Target 1: 70.0% 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 2024199 
(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)))))