Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, E

Percentage Accurate: 85.5% → 90.9%

Time: 42.4s

Alternatives: 30

Speedup: 1.1×

• 50.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (-
  (-
   (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
   (* (* x 4.0) i))
  (* (* j 27.0) k)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    code = (((((((x * 18.0d0) * y) * z) * t) - ((a * 4.0d0) * t)) + (b * c)) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
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 k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]

Initial Program: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (-
  (-
   (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
   (* (* x 4.0) i))
  (* (* j 27.0) k)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    code = (((((((x * 18.0d0) * y) * z) * t) - ((a * 4.0d0) * t)) + (b * c)) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
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 k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]

Alternative 1: 90.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := \left(\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - t_1\\ t_3 := \left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - t_1\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+269}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, -4 \cdot i, b \cdot c\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0)))
        (t_2
         (-
          (-
           (+ (* b c) (* x (- (* 18.0 (* y (* t z))) (* 4.0 i))))
           (* 4.0 (* t a)))
          t_1))
        (t_3
         (-
          (-
           (+ (* b c) (- (* t (* z (* y (* x 18.0)))) (* t (* a 4.0))))
           (* i (* x 4.0)))
          t_1)))
   (if (<= t_3 (- INFINITY))
     t_2
     (if (<= t_3 2e+269)
       t_3
       (if (<= t_3 INFINITY) t_2 (- (fma x (* -4.0 i) (* b c)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double t_2 = (((b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)))) - (4.0 * (t * a))) - t_1;
	double t_3 = (((b * c) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - t_1;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_3 <= 2e+269) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = fma(x, (-4.0 * i), (b * c)) - t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	t_2 = Float64(Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(y * Float64(t * z))) - Float64(4.0 * i)))) - Float64(4.0 * Float64(t * a))) - t_1)
	t_3 = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(t * Float64(z * Float64(y * Float64(x * 18.0)))) - Float64(t * Float64(a * 4.0)))) - Float64(i * Float64(x * 4.0))) - t_1)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_3 <= 2e+269)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(fma(x, Float64(-4.0 * i), Float64(b * c)) - t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$2, If[LessEqual[t$95$3, 2e+269], t$95$3, If[LessEqual[t$95$3, Infinity], t$95$2, N[(N[(x * N[(-4.0 * i), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k)) < -inf.0 or 2.0000000000000001e269 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k)) < +inf.0

   1. Initial program 89.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 96.2%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   if -inf.0 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k)) < 2.0000000000000001e269

   1. Initial program 99.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   if +inf.0 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0 44.3%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in c around 0 44.3%

      \[\leadsto \color{blue}{\left(c \cdot b + -4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. metadata-eval 44.3%

         \[\leadsto \left(c \cdot b + \color{blue}{\left(-4\right)} \cdot \left(i \cdot x\right)\right) - \left(j \cdot 27\right) \cdot k \]

      2. cancel-sign-sub-inv 44.3%

         \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      3. *-commutative 44.3%

         \[\leadsto \left(c \cdot b - \color{blue}{\left(i \cdot x\right) \cdot 4}\right) - \left(j \cdot 27\right) \cdot k \]

      4. associate-*r* 44.3%

         \[\leadsto \left(c \cdot b - \color{blue}{i \cdot \left(x \cdot 4\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      5. *-commutative 44.3%

         \[\leadsto \left(c \cdot b - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k \]

      6. associate-*r* 44.3%

         \[\leadsto \left(c \cdot b - \color{blue}{x \cdot \left(4 \cdot i\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      7. sub-neg 44.3%

         \[\leadsto \color{blue}{\left(c \cdot b + \left(-x \cdot \left(4 \cdot i\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      8. +-commutative 44.3%

         \[\leadsto \color{blue}{\left(\left(-x \cdot \left(4 \cdot i\right)\right) + c \cdot b\right)} - \left(j \cdot 27\right) \cdot k \]

      9. distribute-rgt-neg-in 44.3%

         \[\leadsto \left(\color{blue}{x \cdot \left(-4 \cdot i\right)} + c \cdot b\right) - \left(j \cdot 27\right) \cdot k \]

      10. distribute-lft-neg-in 44.3%

          \[\leadsto \left(x \cdot \color{blue}{\left(\left(-4\right) \cdot i\right)} + c \cdot b\right) - \left(j \cdot 27\right) \cdot k \]

      11. metadata-eval 44.3%

          \[\leadsto \left(x \cdot \left(\color{blue}{-4} \cdot i\right) + c \cdot b\right) - \left(j \cdot 27\right) \cdot k \]

      12. fma-def 52.3%

          \[\leadsto \color{blue}{\mathsf{fma}\left(x, -4 \cdot i, c \cdot b\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Simplified 52.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, -4 \cdot i, c \cdot b\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right) \leq -\infty:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{+269}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right) \leq \infty:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, -4 \cdot i, b \cdot c\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 2: 92.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t_1 \leq 10^{+293}:\\ \;\;\;\;t_1 - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(t, \mathsf{fma}\left(18, y \cdot \left(x \cdot z\right), a \cdot -4\right), -4 \cdot \left(x \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (+ (* b c) (- (* t (* z (* y (* x 18.0)))) (* t (* a 4.0))))
          (* i (* x 4.0)))))
   (if (<= t_1 (- INFINITY))
     (- (+ (* b c) (* x (- (* 18.0 (* y (* t z))) (* 4.0 i)))) (* 4.0 (* t a)))
     (if (<= t_1 1e+293)
       (- t_1 (* k (* j 27.0)))
       (fma
        c
        b
        (fma t (fma 18.0 (* y (* x z)) (* a -4.0)) (* -4.0 (* x i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((b * c) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = ((b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)))) - (4.0 * (t * a));
	} else if (t_1 <= 1e+293) {
		tmp = t_1 - (k * (j * 27.0));
	} else {
		tmp = fma(c, b, fma(t, fma(18.0, (y * (x * z)), (a * -4.0)), (-4.0 * (x * i))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(b * c) + Float64(Float64(t * Float64(z * Float64(y * Float64(x * 18.0)))) - Float64(t * Float64(a * 4.0)))) - Float64(i * Float64(x * 4.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(y * Float64(t * z))) - Float64(4.0 * i)))) - Float64(4.0 * Float64(t * a)));
	elseif (t_1 <= 1e+293)
		tmp = Float64(t_1 - Float64(k * Float64(j * 27.0)));
	else
		tmp = fma(c, b, fma(t, fma(18.0, Float64(y * Float64(x * z)), Float64(a * -4.0)), Float64(-4.0 * Float64(x * i))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+293], N[(t$95$1 - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * b + N[(t * N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) < -inf.0

   1. Initial program 83.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 94.4%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in j around 0 92.7%

      \[\leadsto \color{blue}{\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)} \]

   if -inf.0 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) < 9.9999999999999992e292

   1. Initial program 99.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   if 9.9999999999999992e292 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i))

   1. Initial program 62.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 69.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around 0 68.4%

      \[\leadsto \color{blue}{\left(c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 68.4%

         \[\leadsto \color{blue}{c \cdot b + \left(t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right) - 4 \cdot \left(i \cdot x\right)\right)} \]

      2. fma-def 74.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right) - 4 \cdot \left(i \cdot x\right)\right)} \]

      3. cancel-sign-sub-inv 74.8%

         \[\leadsto \mathsf{fma}\left(c, b, t \cdot \color{blue}{\left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) + \left(-4\right) \cdot a\right)} - 4 \cdot \left(i \cdot x\right)\right) \]

      4. metadata-eval 74.8%

         \[\leadsto \mathsf{fma}\left(c, b, t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) + \color{blue}{-4} \cdot a\right) - 4 \cdot \left(i \cdot x\right)\right) \]

      5. cancel-sign-sub-inv 74.8%

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) + -4 \cdot a\right) + \left(-4\right) \cdot \left(i \cdot x\right)}\right) \]

      6. metadata-eval 74.8%

         \[\leadsto \mathsf{fma}\left(c, b, t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) + -4 \cdot a\right) + \color{blue}{-4} \cdot \left(i \cdot x\right)\right) \]

      7. fma-def 76.1%

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(t, 18 \cdot \left(y \cdot \left(z \cdot x\right)\right) + -4 \cdot a, -4 \cdot \left(i \cdot x\right)\right)}\right) \]

      8. fma-def 76.1%

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(t, \color{blue}{\mathsf{fma}\left(18, y \cdot \left(z \cdot x\right), -4 \cdot a\right)}, -4 \cdot \left(i \cdot x\right)\right)\right) \]

      9. *-commutative 76.1%

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(t, \mathsf{fma}\left(18, y \cdot \left(z \cdot x\right), \color{blue}{a \cdot -4}\right), -4 \cdot \left(i \cdot x\right)\right)\right) \]

      10. *-commutative 76.1%

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(t, \mathsf{fma}\left(18, y \cdot \left(z \cdot x\right), a \cdot -4\right), \color{blue}{\left(i \cdot x\right) \cdot -4}\right)\right) \]

      11. *-commutative 76.1%

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(t, \mathsf{fma}\left(18, y \cdot \left(z \cdot x\right), a \cdot -4\right), \color{blue}{\left(x \cdot i\right)} \cdot -4\right)\right) \]

   6. Simplified 76.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(t, \mathsf{fma}\left(18, y \cdot \left(z \cdot x\right), a \cdot -4\right), \left(x \cdot i\right) \cdot -4\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right) \leq -\infty:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right) \leq 10^{+293}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(t, \mathsf{fma}\left(18, y \cdot \left(x \cdot z\right), a \cdot -4\right), -4 \cdot \left(x \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 3: 93.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t_1 \leq 10^{+293}:\\ \;\;\;\;t_1 - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, -4 \cdot i, \mathsf{fma}\left(c, b, t \cdot \mathsf{fma}\left(18, y \cdot \left(x \cdot z\right), a \cdot -4\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (+ (* b c) (- (* t (* z (* y (* x 18.0)))) (* t (* a 4.0))))
          (* i (* x 4.0)))))
   (if (<= t_1 (- INFINITY))
     (- (+ (* b c) (* x (- (* 18.0 (* y (* t z))) (* 4.0 i)))) (* 4.0 (* t a)))
     (if (<= t_1 1e+293)
       (- t_1 (* k (* j 27.0)))
       (fma
        x
        (* -4.0 i)
        (fma c b (* t (fma 18.0 (* y (* x z)) (* a -4.0)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((b * c) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = ((b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)))) - (4.0 * (t * a));
	} else if (t_1 <= 1e+293) {
		tmp = t_1 - (k * (j * 27.0));
	} else {
		tmp = fma(x, (-4.0 * i), fma(c, b, (t * fma(18.0, (y * (x * z)), (a * -4.0)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(b * c) + Float64(Float64(t * Float64(z * Float64(y * Float64(x * 18.0)))) - Float64(t * Float64(a * 4.0)))) - Float64(i * Float64(x * 4.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(y * Float64(t * z))) - Float64(4.0 * i)))) - Float64(4.0 * Float64(t * a)));
	elseif (t_1 <= 1e+293)
		tmp = Float64(t_1 - Float64(k * Float64(j * 27.0)));
	else
		tmp = fma(x, Float64(-4.0 * i), fma(c, b, Float64(t * fma(18.0, Float64(y * Float64(x * z)), Float64(a * -4.0)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+293], N[(t$95$1 - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(-4.0 * i), $MachinePrecision] + N[(c * b + N[(t * N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) < -inf.0

   1. Initial program 83.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 94.4%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in j around 0 92.7%

      \[\leadsto \color{blue}{\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)} \]

   if -inf.0 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) < 9.9999999999999992e292

   1. Initial program 99.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   if 9.9999999999999992e292 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i))

   1. Initial program 62.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 69.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around 0 68.4%

      \[\leadsto \color{blue}{\left(c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   6. Simplified 76.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(c, b, t \cdot \mathsf{fma}\left(18, y \cdot \left(z \cdot x\right), a \cdot -4\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right) \leq -\infty:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right) \leq 10^{+293}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, -4 \cdot i, \mathsf{fma}\left(c, b, t \cdot \mathsf{fma}\left(18, y \cdot \left(x \cdot z\right), a \cdot -4\right)\right)\right)\\ \end{array} \]

Alternative 4: 92.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+69} \lor \neg \left(t \leq 1.95 \cdot 10^{+99}\right):\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right) - \mathsf{fma}\left(x, 4 \cdot i, j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -5e+69) (not (<= t 1.95e+99)))
   (-
    (fma t (fma x (* 18.0 (* y z)) (* a -4.0)) (* b c))
    (fma x (* 4.0 i) (* j (* 27.0 k))))
   (-
    (- (+ (* b c) (* x (- (* 18.0 (* y (* t z))) (* 4.0 i)))) (* 4.0 (* t a)))
    (* k (* j 27.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -5e+69) || !(t <= 1.95e+99)) {
		tmp = fma(t, fma(x, (18.0 * (y * z)), (a * -4.0)), (b * c)) - fma(x, (4.0 * i), (j * (27.0 * k)));
	} else {
		tmp = (((b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)))) - (4.0 * (t * a))) - (k * (j * 27.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -5e+69) || !(t <= 1.95e+99))
		tmp = Float64(fma(t, fma(x, Float64(18.0 * Float64(y * z)), Float64(a * -4.0)), Float64(b * c)) - fma(x, Float64(4.0 * i), Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(y * Float64(t * z))) - Float64(4.0 * i)))) - Float64(4.0 * Float64(t * a))) - Float64(k * Float64(j * 27.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -5e+69], N[Not[LessEqual[t, 1.95e+99]], $MachinePrecision]], N[(N[(t * N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.00000000000000036e69 or 1.94999999999999997e99 < t

   1. Initial program 80.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l- 80.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 80.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]

   3. Simplified 86.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right) - \mathsf{fma}\left(x, 4 \cdot i, j \cdot \left(27 \cdot k\right)\right)} \]

   if -5.00000000000000036e69 < t < 1.94999999999999997e99

   1. Initial program 87.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 95.6%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+69} \lor \neg \left(t \leq 1.95 \cdot 10^{+99}\right):\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right) - \mathsf{fma}\left(x, 4 \cdot i, j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 5: 92.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := \left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\\ t_3 := \left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 4 \cdot 10^{+227}:\\ \;\;\;\;t_3 - t_1\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_2 - t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0)))
        (t_2
         (-
          (+ (* b c) (* x (- (* 18.0 (* y (* t z))) (* 4.0 i))))
          (* 4.0 (* t a))))
        (t_3
         (-
          (+ (* b c) (- (* t (* z (* y (* x 18.0)))) (* t (* a 4.0))))
          (* i (* x 4.0)))))
   (if (<= t_3 (- INFINITY))
     t_2
     (if (<= t_3 4e+227)
       (- t_3 t_1)
       (if (<= t_3 INFINITY)
         (- t_2 t_1)
         (* t (- (* 18.0 (* y (* x z))) (* a 4.0))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double t_2 = ((b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)))) - (4.0 * (t * a));
	double t_3 = ((b * c) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_3 <= 4e+227) {
		tmp = t_3 - t_1;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2 - t_1;
	} else {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double t_2 = ((b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)))) - (4.0 * (t * a));
	double t_3 = ((b * c) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0));
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_3 <= 4e+227) {
		tmp = t_3 - t_1;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_2 - t_1;
	} else {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	t_2 = ((b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)))) - (4.0 * (t * a))
	t_3 = ((b * c) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0))
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_2
	elif t_3 <= 4e+227:
		tmp = t_3 - t_1
	elif t_3 <= math.inf:
		tmp = t_2 - t_1
	else:
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	t_2 = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(y * Float64(t * z))) - Float64(4.0 * i)))) - Float64(4.0 * Float64(t * a)))
	t_3 = Float64(Float64(Float64(b * c) + Float64(Float64(t * Float64(z * Float64(y * Float64(x * 18.0)))) - Float64(t * Float64(a * 4.0)))) - Float64(i * Float64(x * 4.0)))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_3 <= 4e+227)
		tmp = Float64(t_3 - t_1);
	elseif (t_3 <= Inf)
		tmp = Float64(t_2 - t_1);
	else
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	t_2 = ((b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)))) - (4.0 * (t * a));
	t_3 = ((b * c) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0));
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_2;
	elseif (t_3 <= 4e+227)
		tmp = t_3 - t_1;
	elseif (t_3 <= Inf)
		tmp = t_2 - t_1;
	else
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$2, If[LessEqual[t$95$3, 4e+227], N[(t$95$3 - t$95$1), $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[(t$95$2 - t$95$1), $MachinePrecision], N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) < -inf.0

   1. Initial program 83.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 94.4%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in j around 0 92.7%

      \[\leadsto \color{blue}{\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)} \]

   if -inf.0 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) < 4.0000000000000004e227

   1. Initial program 99.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   if 4.0000000000000004e227 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) < +inf.0

   1. Initial program 87.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 92.1%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   if +inf.0 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i))

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 20.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 60.1%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right) \leq -\infty:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right) \leq 4 \cdot 10^{+227}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right) \leq \infty:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 6: 53.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+87}:\\ \;\;\;\;b \cdot c - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 10^{-69}:\\ \;\;\;\;y \cdot \left(18 \cdot \left(z \cdot \left(t \cdot x\right)\right)\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+48}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+54}:\\ \;\;\;\;b \cdot c - t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-4 \cdot i\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 4.0 (* x i)))) (t_2 (* k (* j 27.0))))
   (if (<= t_2 -1e+87)
     (- (* b c) (* j (* 27.0 k)))
     (if (<= t_2 2e-120)
       t_1
       (if (<= t_2 1e-69)
         (* y (* 18.0 (* z (* t x))))
         (if (<= t_2 5e+15)
           t_1
           (if (<= t_2 2e+48)
             (* t (* a -4.0))
             (if (<= t_2 5e+54)
               (- (* b c) t_2)
               (+ (* x (* -4.0 i)) (* k (* j -27.0)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (x * i));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1e+87) {
		tmp = (b * c) - (j * (27.0 * k));
	} else if (t_2 <= 2e-120) {
		tmp = t_1;
	} else if (t_2 <= 1e-69) {
		tmp = y * (18.0 * (z * (t * x)));
	} else if (t_2 <= 5e+15) {
		tmp = t_1;
	} else if (t_2 <= 2e+48) {
		tmp = t * (a * -4.0);
	} else if (t_2 <= 5e+54) {
		tmp = (b * c) - t_2;
	} else {
		tmp = (x * (-4.0 * i)) + (k * (j * -27.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) - (4.0d0 * (x * i))
    t_2 = k * (j * 27.0d0)
    if (t_2 <= (-1d+87)) then
        tmp = (b * c) - (j * (27.0d0 * k))
    else if (t_2 <= 2d-120) then
        tmp = t_1
    else if (t_2 <= 1d-69) then
        tmp = y * (18.0d0 * (z * (t * x)))
    else if (t_2 <= 5d+15) then
        tmp = t_1
    else if (t_2 <= 2d+48) then
        tmp = t * (a * (-4.0d0))
    else if (t_2 <= 5d+54) then
        tmp = (b * c) - t_2
    else
        tmp = (x * ((-4.0d0) * i)) + (k * (j * (-27.0d0)))
    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 k) {
	double t_1 = (b * c) - (4.0 * (x * i));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1e+87) {
		tmp = (b * c) - (j * (27.0 * k));
	} else if (t_2 <= 2e-120) {
		tmp = t_1;
	} else if (t_2 <= 1e-69) {
		tmp = y * (18.0 * (z * (t * x)));
	} else if (t_2 <= 5e+15) {
		tmp = t_1;
	} else if (t_2 <= 2e+48) {
		tmp = t * (a * -4.0);
	} else if (t_2 <= 5e+54) {
		tmp = (b * c) - t_2;
	} else {
		tmp = (x * (-4.0 * i)) + (k * (j * -27.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (4.0 * (x * i))
	t_2 = k * (j * 27.0)
	tmp = 0
	if t_2 <= -1e+87:
		tmp = (b * c) - (j * (27.0 * k))
	elif t_2 <= 2e-120:
		tmp = t_1
	elif t_2 <= 1e-69:
		tmp = y * (18.0 * (z * (t * x)))
	elif t_2 <= 5e+15:
		tmp = t_1
	elif t_2 <= 2e+48:
		tmp = t * (a * -4.0)
	elif t_2 <= 5e+54:
		tmp = (b * c) - t_2
	else:
		tmp = (x * (-4.0 * i)) + (k * (j * -27.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_2 <= -1e+87)
		tmp = Float64(Float64(b * c) - Float64(j * Float64(27.0 * k)));
	elseif (t_2 <= 2e-120)
		tmp = t_1;
	elseif (t_2 <= 1e-69)
		tmp = Float64(y * Float64(18.0 * Float64(z * Float64(t * x))));
	elseif (t_2 <= 5e+15)
		tmp = t_1;
	elseif (t_2 <= 2e+48)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (t_2 <= 5e+54)
		tmp = Float64(Float64(b * c) - t_2);
	else
		tmp = Float64(Float64(x * Float64(-4.0 * i)) + Float64(k * Float64(j * -27.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (4.0 * (x * i));
	t_2 = k * (j * 27.0);
	tmp = 0.0;
	if (t_2 <= -1e+87)
		tmp = (b * c) - (j * (27.0 * k));
	elseif (t_2 <= 2e-120)
		tmp = t_1;
	elseif (t_2 <= 1e-69)
		tmp = y * (18.0 * (z * (t * x)));
	elseif (t_2 <= 5e+15)
		tmp = t_1;
	elseif (t_2 <= 2e+48)
		tmp = t * (a * -4.0);
	elseif (t_2 <= 5e+54)
		tmp = (b * c) - t_2;
	else
		tmp = (x * (-4.0 * i)) + (k * (j * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+87], N[(N[(b * c), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e-120], t$95$1, If[LessEqual[t$95$2, 1e-69], N[(y * N[(18.0 * N[(z * N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+15], t$95$1, If[LessEqual[t$95$2, 2e+48], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+54], N[(N[(b * c), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 (*.f64 j 27) k) < -9.9999999999999996e86

   1. Initial program 86.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 79.0%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in c around inf 73.1%

      \[\leadsto \color{blue}{c \cdot b} - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. sub-neg 73.1%

         \[\leadsto \color{blue}{c \cdot b + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-*r* 73.2%

         \[\leadsto c \cdot b + \left(-\color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   5. Applied egg-rr 73.2%

      \[\leadsto \color{blue}{c \cdot b + \left(-j \cdot \left(27 \cdot k\right)\right)} \]

   if -9.9999999999999996e86 < (*.f64 (*.f64 j 27) k) < 1.99999999999999996e-120 or 9.9999999999999996e-70 < (*.f64 (*.f64 j 27) k) < 5e15

   1. Initial program 84.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0 57.4%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in j around 0 54.7%

      \[\leadsto \color{blue}{c \cdot b - 4 \cdot \left(i \cdot x\right)} \]

   if 1.99999999999999996e-120 < (*.f64 (*.f64 j 27) k) < 9.9999999999999996e-70

   1. Initial program 86.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 73.0%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in a around 0 46.0%

      \[\leadsto \color{blue}{\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in y around inf 71.8%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 72.0%

         \[\leadsto \color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} \]

      2. *-commutative 72.0%

         \[\leadsto \color{blue}{\left(y \cdot 18\right)} \cdot \left(t \cdot \left(z \cdot x\right)\right) \]

      3. associate-*l* 71.9%

         \[\leadsto \color{blue}{y \cdot \left(18 \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]

      4. associate-*r* 72.3%

         \[\leadsto y \cdot \left(18 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot x\right)}\right) \]

      5. *-commutative 72.3%

         \[\leadsto y \cdot \left(18 \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot x\right)\right) \]

      6. associate-*l* 72.0%

         \[\leadsto y \cdot \left(18 \cdot \color{blue}{\left(z \cdot \left(t \cdot x\right)\right)}\right) \]

   6. Simplified 72.0%

      \[\leadsto \color{blue}{y \cdot \left(18 \cdot \left(z \cdot \left(t \cdot x\right)\right)\right)} \]

   if 5e15 < (*.f64 (*.f64 j 27) k) < 2.00000000000000009e48

   1. Initial program 75.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 87.5%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in a around inf 62.2%

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

      1. *-commutative 62.2%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot -4} \]

      2. *-commutative 62.2%

         \[\leadsto \color{blue}{\left(t \cdot a\right)} \cdot -4 \]

      3. associate-*r* 62.2%

         \[\leadsto \color{blue}{t \cdot \left(a \cdot -4\right)} \]

   6. Simplified 62.2%

      \[\leadsto \color{blue}{t \cdot \left(a \cdot -4\right)} \]

   if 2.00000000000000009e48 < (*.f64 (*.f64 j 27) k) < 5.00000000000000005e54

   1. Initial program 50.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 50.0%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in c around inf 100.0%

      \[\leadsto \color{blue}{c \cdot b} - \left(j \cdot 27\right) \cdot k \]

   if 5.00000000000000005e54 < (*.f64 (*.f64 j 27) k)

   1. Initial program 87.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0 78.9%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in c around 0 76.0%

      \[\leadsto \color{blue}{-1 \cdot \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 76.0%

         \[\leadsto \color{blue}{-\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right)} \]

      2. associate-*r* 76.0%

         \[\leadsto -\left(\color{blue}{\left(4 \cdot i\right) \cdot x} + 27 \cdot \left(k \cdot j\right)\right) \]

      3. *-commutative 76.0%

         \[\leadsto -\left(\color{blue}{x \cdot \left(4 \cdot i\right)} + 27 \cdot \left(k \cdot j\right)\right) \]

      4. associate-*r* 76.0%

         \[\leadsto -\left(x \cdot \left(4 \cdot i\right) + \color{blue}{\left(27 \cdot k\right) \cdot j}\right) \]

      5. *-commutative 76.0%

         \[\leadsto -\left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

      6. distribute-neg-in 76.0%

         \[\leadsto \color{blue}{\left(-x \cdot \left(4 \cdot i\right)\right) + \left(-j \cdot \left(27 \cdot k\right)\right)} \]

      7. distribute-rgt-neg-in 76.0%

         \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} + \left(-j \cdot \left(27 \cdot k\right)\right) \]

      8. distribute-lft-neg-in 76.0%

         \[\leadsto x \cdot \color{blue}{\left(\left(-4\right) \cdot i\right)} + \left(-j \cdot \left(27 \cdot k\right)\right) \]

      9. metadata-eval 76.0%

         \[\leadsto x \cdot \left(\color{blue}{-4} \cdot i\right) + \left(-j \cdot \left(27 \cdot k\right)\right) \]

      10. associate-*r* 76.1%

          \[\leadsto x \cdot \left(-4 \cdot i\right) + \left(-\color{blue}{\left(j \cdot 27\right) \cdot k}\right) \]

      11. distribute-lft-neg-out 76.1%

          \[\leadsto x \cdot \left(-4 \cdot i\right) + \color{blue}{\left(-j \cdot 27\right) \cdot k} \]

      12. *-commutative 76.1%

          \[\leadsto x \cdot \left(-4 \cdot i\right) + \color{blue}{k \cdot \left(-j \cdot 27\right)} \]

      13. distribute-rgt-neg-in 76.1%

          \[\leadsto x \cdot \left(-4 \cdot i\right) + k \cdot \color{blue}{\left(j \cdot \left(-27\right)\right)} \]

      14. metadata-eval 76.1%

          \[\leadsto x \cdot \left(-4 \cdot i\right) + k \cdot \left(j \cdot \color{blue}{-27}\right) \]

   5. Simplified 76.1%

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right) + k \cdot \left(j \cdot -27\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{+87}:\\ \;\;\;\;b \cdot c - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{-120}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 10^{-69}:\\ \;\;\;\;y \cdot \left(18 \cdot \left(z \cdot \left(t \cdot x\right)\right)\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+15}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{+48}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+54}:\\ \;\;\;\;b \cdot c - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-4 \cdot i\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 7: 52.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+87}:\\ \;\;\;\;b \cdot c - t_2\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 10^{-69}:\\ \;\;\;\;y \cdot \left(18 \cdot \left(z \cdot \left(t \cdot x\right)\right)\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;t_2 \leq 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 4.0 (* x i)))) (t_2 (* k (* j 27.0))))
   (if (<= t_2 -1e+87)
     (- (* b c) t_2)
     (if (<= t_2 2e-120)
       t_1
       (if (<= t_2 1e-69)
         (* y (* 18.0 (* z (* t x))))
         (if (<= t_2 5e+15)
           t_1
           (if (<= t_2 2e+50)
             (* t (* a -4.0))
             (if (<= t_2 1e+144) t_1 (* k (* j -27.0))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (x * i));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1e+87) {
		tmp = (b * c) - t_2;
	} else if (t_2 <= 2e-120) {
		tmp = t_1;
	} else if (t_2 <= 1e-69) {
		tmp = y * (18.0 * (z * (t * x)));
	} else if (t_2 <= 5e+15) {
		tmp = t_1;
	} else if (t_2 <= 2e+50) {
		tmp = t * (a * -4.0);
	} else if (t_2 <= 1e+144) {
		tmp = t_1;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) - (4.0d0 * (x * i))
    t_2 = k * (j * 27.0d0)
    if (t_2 <= (-1d+87)) then
        tmp = (b * c) - t_2
    else if (t_2 <= 2d-120) then
        tmp = t_1
    else if (t_2 <= 1d-69) then
        tmp = y * (18.0d0 * (z * (t * x)))
    else if (t_2 <= 5d+15) then
        tmp = t_1
    else if (t_2 <= 2d+50) then
        tmp = t * (a * (-4.0d0))
    else if (t_2 <= 1d+144) then
        tmp = t_1
    else
        tmp = k * (j * (-27.0d0))
    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 k) {
	double t_1 = (b * c) - (4.0 * (x * i));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1e+87) {
		tmp = (b * c) - t_2;
	} else if (t_2 <= 2e-120) {
		tmp = t_1;
	} else if (t_2 <= 1e-69) {
		tmp = y * (18.0 * (z * (t * x)));
	} else if (t_2 <= 5e+15) {
		tmp = t_1;
	} else if (t_2 <= 2e+50) {
		tmp = t * (a * -4.0);
	} else if (t_2 <= 1e+144) {
		tmp = t_1;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (4.0 * (x * i))
	t_2 = k * (j * 27.0)
	tmp = 0
	if t_2 <= -1e+87:
		tmp = (b * c) - t_2
	elif t_2 <= 2e-120:
		tmp = t_1
	elif t_2 <= 1e-69:
		tmp = y * (18.0 * (z * (t * x)))
	elif t_2 <= 5e+15:
		tmp = t_1
	elif t_2 <= 2e+50:
		tmp = t * (a * -4.0)
	elif t_2 <= 1e+144:
		tmp = t_1
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_2 <= -1e+87)
		tmp = Float64(Float64(b * c) - t_2);
	elseif (t_2 <= 2e-120)
		tmp = t_1;
	elseif (t_2 <= 1e-69)
		tmp = Float64(y * Float64(18.0 * Float64(z * Float64(t * x))));
	elseif (t_2 <= 5e+15)
		tmp = t_1;
	elseif (t_2 <= 2e+50)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (t_2 <= 1e+144)
		tmp = t_1;
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (4.0 * (x * i));
	t_2 = k * (j * 27.0);
	tmp = 0.0;
	if (t_2 <= -1e+87)
		tmp = (b * c) - t_2;
	elseif (t_2 <= 2e-120)
		tmp = t_1;
	elseif (t_2 <= 1e-69)
		tmp = y * (18.0 * (z * (t * x)));
	elseif (t_2 <= 5e+15)
		tmp = t_1;
	elseif (t_2 <= 2e+50)
		tmp = t * (a * -4.0);
	elseif (t_2 <= 1e+144)
		tmp = t_1;
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+87], N[(N[(b * c), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t$95$2, 2e-120], t$95$1, If[LessEqual[t$95$2, 1e-69], N[(y * N[(18.0 * N[(z * N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+15], t$95$1, If[LessEqual[t$95$2, 2e+50], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+144], t$95$1, N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 j 27) k) < -9.9999999999999996e86

   1. Initial program 86.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 79.0%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in c around inf 73.1%

      \[\leadsto \color{blue}{c \cdot b} - \left(j \cdot 27\right) \cdot k \]

   if -9.9999999999999996e86 < (*.f64 (*.f64 j 27) k) < 1.99999999999999996e-120 or 9.9999999999999996e-70 < (*.f64 (*.f64 j 27) k) < 5e15 or 2.0000000000000002e50 < (*.f64 (*.f64 j 27) k) < 1.00000000000000002e144

   1. Initial program 84.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0 57.9%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in j around 0 54.2%

      \[\leadsto \color{blue}{c \cdot b - 4 \cdot \left(i \cdot x\right)} \]

   if 1.99999999999999996e-120 < (*.f64 (*.f64 j 27) k) < 9.9999999999999996e-70

   1. Initial program 86.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 73.0%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in a around 0 46.0%

      \[\leadsto \color{blue}{\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in y around inf 71.8%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 72.0%

         \[\leadsto \color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} \]

      2. *-commutative 72.0%

         \[\leadsto \color{blue}{\left(y \cdot 18\right)} \cdot \left(t \cdot \left(z \cdot x\right)\right) \]

      3. associate-*l* 71.9%

         \[\leadsto \color{blue}{y \cdot \left(18 \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]

      4. associate-*r* 72.3%

         \[\leadsto y \cdot \left(18 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot x\right)}\right) \]

      5. *-commutative 72.3%

         \[\leadsto y \cdot \left(18 \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot x\right)\right) \]

      6. associate-*l* 72.0%

         \[\leadsto y \cdot \left(18 \cdot \color{blue}{\left(z \cdot \left(t \cdot x\right)\right)}\right) \]

   6. Simplified 72.0%

      \[\leadsto \color{blue}{y \cdot \left(18 \cdot \left(z \cdot \left(t \cdot x\right)\right)\right)} \]

   if 5e15 < (*.f64 (*.f64 j 27) k) < 2.0000000000000002e50

   1. Initial program 78.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in a around inf 55.5%

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

      1. *-commutative 55.5%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot -4} \]

      2. *-commutative 55.5%

         \[\leadsto \color{blue}{\left(t \cdot a\right)} \cdot -4 \]

      3. associate-*r* 55.5%

         \[\leadsto \color{blue}{t \cdot \left(a \cdot -4\right)} \]

   6. Simplified 55.5%

      \[\leadsto \color{blue}{t \cdot \left(a \cdot -4\right)} \]

   if 1.00000000000000002e144 < (*.f64 (*.f64 j 27) k)

   1. Initial program 86.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around inf 90.2%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. Step-by-step derivation

      1. *-commutative 90.2%

         \[\leadsto \color{blue}{\left(k \cdot j\right) \cdot -27} \]

      2. associate-*l* 90.3%

         \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]

   6. Simplified 90.3%

      \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{+87}:\\ \;\;\;\;b \cdot c - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{-120}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 10^{-69}:\\ \;\;\;\;y \cdot \left(18 \cdot \left(z \cdot \left(t \cdot x\right)\right)\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+15}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 10^{+144}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 8: 52.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+87}:\\ \;\;\;\;b \cdot c - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 10^{-69}:\\ \;\;\;\;y \cdot \left(18 \cdot \left(z \cdot \left(t \cdot x\right)\right)\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;t_2 \leq 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 4.0 (* x i)))) (t_2 (* k (* j 27.0))))
   (if (<= t_2 -1e+87)
     (- (* b c) (* j (* 27.0 k)))
     (if (<= t_2 2e-120)
       t_1
       (if (<= t_2 1e-69)
         (* y (* 18.0 (* z (* t x))))
         (if (<= t_2 5e+15)
           t_1
           (if (<= t_2 2e+50)
             (* t (* a -4.0))
             (if (<= t_2 1e+144) t_1 (* k (* j -27.0))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (x * i));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1e+87) {
		tmp = (b * c) - (j * (27.0 * k));
	} else if (t_2 <= 2e-120) {
		tmp = t_1;
	} else if (t_2 <= 1e-69) {
		tmp = y * (18.0 * (z * (t * x)));
	} else if (t_2 <= 5e+15) {
		tmp = t_1;
	} else if (t_2 <= 2e+50) {
		tmp = t * (a * -4.0);
	} else if (t_2 <= 1e+144) {
		tmp = t_1;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) - (4.0d0 * (x * i))
    t_2 = k * (j * 27.0d0)
    if (t_2 <= (-1d+87)) then
        tmp = (b * c) - (j * (27.0d0 * k))
    else if (t_2 <= 2d-120) then
        tmp = t_1
    else if (t_2 <= 1d-69) then
        tmp = y * (18.0d0 * (z * (t * x)))
    else if (t_2 <= 5d+15) then
        tmp = t_1
    else if (t_2 <= 2d+50) then
        tmp = t * (a * (-4.0d0))
    else if (t_2 <= 1d+144) then
        tmp = t_1
    else
        tmp = k * (j * (-27.0d0))
    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 k) {
	double t_1 = (b * c) - (4.0 * (x * i));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1e+87) {
		tmp = (b * c) - (j * (27.0 * k));
	} else if (t_2 <= 2e-120) {
		tmp = t_1;
	} else if (t_2 <= 1e-69) {
		tmp = y * (18.0 * (z * (t * x)));
	} else if (t_2 <= 5e+15) {
		tmp = t_1;
	} else if (t_2 <= 2e+50) {
		tmp = t * (a * -4.0);
	} else if (t_2 <= 1e+144) {
		tmp = t_1;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (4.0 * (x * i))
	t_2 = k * (j * 27.0)
	tmp = 0
	if t_2 <= -1e+87:
		tmp = (b * c) - (j * (27.0 * k))
	elif t_2 <= 2e-120:
		tmp = t_1
	elif t_2 <= 1e-69:
		tmp = y * (18.0 * (z * (t * x)))
	elif t_2 <= 5e+15:
		tmp = t_1
	elif t_2 <= 2e+50:
		tmp = t * (a * -4.0)
	elif t_2 <= 1e+144:
		tmp = t_1
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_2 <= -1e+87)
		tmp = Float64(Float64(b * c) - Float64(j * Float64(27.0 * k)));
	elseif (t_2 <= 2e-120)
		tmp = t_1;
	elseif (t_2 <= 1e-69)
		tmp = Float64(y * Float64(18.0 * Float64(z * Float64(t * x))));
	elseif (t_2 <= 5e+15)
		tmp = t_1;
	elseif (t_2 <= 2e+50)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (t_2 <= 1e+144)
		tmp = t_1;
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (4.0 * (x * i));
	t_2 = k * (j * 27.0);
	tmp = 0.0;
	if (t_2 <= -1e+87)
		tmp = (b * c) - (j * (27.0 * k));
	elseif (t_2 <= 2e-120)
		tmp = t_1;
	elseif (t_2 <= 1e-69)
		tmp = y * (18.0 * (z * (t * x)));
	elseif (t_2 <= 5e+15)
		tmp = t_1;
	elseif (t_2 <= 2e+50)
		tmp = t * (a * -4.0);
	elseif (t_2 <= 1e+144)
		tmp = t_1;
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+87], N[(N[(b * c), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e-120], t$95$1, If[LessEqual[t$95$2, 1e-69], N[(y * N[(18.0 * N[(z * N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+15], t$95$1, If[LessEqual[t$95$2, 2e+50], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+144], t$95$1, N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 j 27) k) < -9.9999999999999996e86

   1. Initial program 86.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 79.0%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in c around inf 73.1%

      \[\leadsto \color{blue}{c \cdot b} - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. sub-neg 73.1%

         \[\leadsto \color{blue}{c \cdot b + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-*r* 73.2%

         \[\leadsto c \cdot b + \left(-\color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   5. Applied egg-rr 73.2%

      \[\leadsto \color{blue}{c \cdot b + \left(-j \cdot \left(27 \cdot k\right)\right)} \]

   if -9.9999999999999996e86 < (*.f64 (*.f64 j 27) k) < 1.99999999999999996e-120 or 9.9999999999999996e-70 < (*.f64 (*.f64 j 27) k) < 5e15 or 2.0000000000000002e50 < (*.f64 (*.f64 j 27) k) < 1.00000000000000002e144

   1. Initial program 84.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0 57.9%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in j around 0 54.2%

      \[\leadsto \color{blue}{c \cdot b - 4 \cdot \left(i \cdot x\right)} \]

   if 1.99999999999999996e-120 < (*.f64 (*.f64 j 27) k) < 9.9999999999999996e-70

   1. Initial program 86.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 73.0%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in a around 0 46.0%

      \[\leadsto \color{blue}{\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in y around inf 71.8%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 72.0%

         \[\leadsto \color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} \]

      2. *-commutative 72.0%

         \[\leadsto \color{blue}{\left(y \cdot 18\right)} \cdot \left(t \cdot \left(z \cdot x\right)\right) \]

      3. associate-*l* 71.9%

         \[\leadsto \color{blue}{y \cdot \left(18 \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]

      4. associate-*r* 72.3%

         \[\leadsto y \cdot \left(18 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot x\right)}\right) \]

      5. *-commutative 72.3%

         \[\leadsto y \cdot \left(18 \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot x\right)\right) \]

      6. associate-*l* 72.0%

         \[\leadsto y \cdot \left(18 \cdot \color{blue}{\left(z \cdot \left(t \cdot x\right)\right)}\right) \]

   6. Simplified 72.0%

      \[\leadsto \color{blue}{y \cdot \left(18 \cdot \left(z \cdot \left(t \cdot x\right)\right)\right)} \]

   if 5e15 < (*.f64 (*.f64 j 27) k) < 2.0000000000000002e50

   1. Initial program 78.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in a around inf 55.5%

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

      1. *-commutative 55.5%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot -4} \]

      2. *-commutative 55.5%

         \[\leadsto \color{blue}{\left(t \cdot a\right)} \cdot -4 \]

      3. associate-*r* 55.5%

         \[\leadsto \color{blue}{t \cdot \left(a \cdot -4\right)} \]

   6. Simplified 55.5%

      \[\leadsto \color{blue}{t \cdot \left(a \cdot -4\right)} \]

   if 1.00000000000000002e144 < (*.f64 (*.f64 j 27) k)

   1. Initial program 86.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around inf 90.2%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. Step-by-step derivation

      1. *-commutative 90.2%

         \[\leadsto \color{blue}{\left(k \cdot j\right) \cdot -27} \]

      2. associate-*l* 90.3%

         \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]

   6. Simplified 90.3%

      \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{+87}:\\ \;\;\;\;b \cdot c - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{-120}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 10^{-69}:\\ \;\;\;\;y \cdot \left(18 \cdot \left(z \cdot \left(t \cdot x\right)\right)\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+15}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 10^{+144}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 9: 54.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+87}:\\ \;\;\;\;b \cdot c - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 10^{-69}:\\ \;\;\;\;y \cdot \left(18 \cdot \left(z \cdot \left(t \cdot x\right)\right)\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right) - t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 4.0 (* x i)))) (t_2 (* k (* j 27.0))))
   (if (<= t_2 -1e+87)
     (- (* b c) (* j (* 27.0 k)))
     (if (<= t_2 2e-120)
       t_1
       (if (<= t_2 1e-69)
         (* y (* 18.0 (* z (* t x))))
         (if (<= t_2 5e+15) t_1 (- (* a (* t -4.0)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (x * i));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1e+87) {
		tmp = (b * c) - (j * (27.0 * k));
	} else if (t_2 <= 2e-120) {
		tmp = t_1;
	} else if (t_2 <= 1e-69) {
		tmp = y * (18.0 * (z * (t * x)));
	} else if (t_2 <= 5e+15) {
		tmp = t_1;
	} else {
		tmp = (a * (t * -4.0)) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) - (4.0d0 * (x * i))
    t_2 = k * (j * 27.0d0)
    if (t_2 <= (-1d+87)) then
        tmp = (b * c) - (j * (27.0d0 * k))
    else if (t_2 <= 2d-120) then
        tmp = t_1
    else if (t_2 <= 1d-69) then
        tmp = y * (18.0d0 * (z * (t * x)))
    else if (t_2 <= 5d+15) then
        tmp = t_1
    else
        tmp = (a * (t * (-4.0d0))) - 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 k) {
	double t_1 = (b * c) - (4.0 * (x * i));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1e+87) {
		tmp = (b * c) - (j * (27.0 * k));
	} else if (t_2 <= 2e-120) {
		tmp = t_1;
	} else if (t_2 <= 1e-69) {
		tmp = y * (18.0 * (z * (t * x)));
	} else if (t_2 <= 5e+15) {
		tmp = t_1;
	} else {
		tmp = (a * (t * -4.0)) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (4.0 * (x * i))
	t_2 = k * (j * 27.0)
	tmp = 0
	if t_2 <= -1e+87:
		tmp = (b * c) - (j * (27.0 * k))
	elif t_2 <= 2e-120:
		tmp = t_1
	elif t_2 <= 1e-69:
		tmp = y * (18.0 * (z * (t * x)))
	elif t_2 <= 5e+15:
		tmp = t_1
	else:
		tmp = (a * (t * -4.0)) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_2 <= -1e+87)
		tmp = Float64(Float64(b * c) - Float64(j * Float64(27.0 * k)));
	elseif (t_2 <= 2e-120)
		tmp = t_1;
	elseif (t_2 <= 1e-69)
		tmp = Float64(y * Float64(18.0 * Float64(z * Float64(t * x))));
	elseif (t_2 <= 5e+15)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * Float64(t * -4.0)) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (4.0 * (x * i));
	t_2 = k * (j * 27.0);
	tmp = 0.0;
	if (t_2 <= -1e+87)
		tmp = (b * c) - (j * (27.0 * k));
	elseif (t_2 <= 2e-120)
		tmp = t_1;
	elseif (t_2 <= 1e-69)
		tmp = y * (18.0 * (z * (t * x)));
	elseif (t_2 <= 5e+15)
		tmp = t_1;
	else
		tmp = (a * (t * -4.0)) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+87], N[(N[(b * c), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e-120], t$95$1, If[LessEqual[t$95$2, 1e-69], N[(y * N[(18.0 * N[(z * N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+15], t$95$1, N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j 27) k) < -9.9999999999999996e86

   1. Initial program 86.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 79.0%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in c around inf 73.1%

      \[\leadsto \color{blue}{c \cdot b} - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. sub-neg 73.1%

         \[\leadsto \color{blue}{c \cdot b + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-*r* 73.2%

         \[\leadsto c \cdot b + \left(-\color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   5. Applied egg-rr 73.2%

      \[\leadsto \color{blue}{c \cdot b + \left(-j \cdot \left(27 \cdot k\right)\right)} \]

   if -9.9999999999999996e86 < (*.f64 (*.f64 j 27) k) < 1.99999999999999996e-120 or 9.9999999999999996e-70 < (*.f64 (*.f64 j 27) k) < 5e15

   1. Initial program 84.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0 57.4%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in j around 0 54.7%

      \[\leadsto \color{blue}{c \cdot b - 4 \cdot \left(i \cdot x\right)} \]

   if 1.99999999999999996e-120 < (*.f64 (*.f64 j 27) k) < 9.9999999999999996e-70

   1. Initial program 86.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 73.0%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in a around 0 46.0%

      \[\leadsto \color{blue}{\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in y around inf 71.8%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 72.0%

         \[\leadsto \color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} \]

      2. *-commutative 72.0%

         \[\leadsto \color{blue}{\left(y \cdot 18\right)} \cdot \left(t \cdot \left(z \cdot x\right)\right) \]

      3. associate-*l* 71.9%

         \[\leadsto \color{blue}{y \cdot \left(18 \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]

      4. associate-*r* 72.3%

         \[\leadsto y \cdot \left(18 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot x\right)}\right) \]

      5. *-commutative 72.3%

         \[\leadsto y \cdot \left(18 \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot x\right)\right) \]

      6. associate-*l* 72.0%

         \[\leadsto y \cdot \left(18 \cdot \color{blue}{\left(z \cdot \left(t \cdot x\right)\right)}\right) \]

   6. Simplified 72.0%

      \[\leadsto \color{blue}{y \cdot \left(18 \cdot \left(z \cdot \left(t \cdot x\right)\right)\right)} \]

   if 5e15 < (*.f64 (*.f64 j 27) k)

   1. Initial program 84.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 87.6%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in a around inf 71.6%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. *-commutative 71.6%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot a\right)} - \left(j \cdot 27\right) \cdot k \]

      2. associate-*r* 71.6%

         \[\leadsto \color{blue}{\left(-4 \cdot t\right) \cdot a} - \left(j \cdot 27\right) \cdot k \]

   5. Simplified 71.6%

      \[\leadsto \color{blue}{\left(-4 \cdot t\right) \cdot a} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{+87}:\\ \;\;\;\;b \cdot c - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{-120}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 10^{-69}:\\ \;\;\;\;y \cdot \left(18 \cdot \left(z \cdot \left(t \cdot x\right)\right)\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+15}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 10: 82.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+94}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot \left(27 \cdot k\right) + x \cdot \left(4 \cdot i\right)\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-13}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0))))
   (if (<= t_1 -2e+94)
     (- (+ (* b c) (* -4.0 (* t a))) (+ (* j (* 27.0 k)) (* x (* 4.0 i))))
     (if (<= t_1 5e-13)
       (-
        (+ (* b c) (* x (- (* 18.0 (* y (* t z))) (* 4.0 i))))
        (* 4.0 (* t a)))
       (- (- (* b c) (* 4.0 (+ (* t a) (* x 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 k) {
	double t_1 = k * (j * 27.0);
	double tmp;
	if (t_1 <= -2e+94) {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((j * (27.0 * k)) + (x * (4.0 * i)));
	} else if (t_1 <= 5e-13) {
		tmp = ((b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)))) - (4.0 * (t * a));
	} else {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (j * 27.0d0)
    if (t_1 <= (-2d+94)) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - ((j * (27.0d0 * k)) + (x * (4.0d0 * i)))
    else if (t_1 <= 5d-13) then
        tmp = ((b * c) + (x * ((18.0d0 * (y * (t * z))) - (4.0d0 * i)))) - (4.0d0 * (t * a))
    else
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double tmp;
	if (t_1 <= -2e+94) {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((j * (27.0 * k)) + (x * (4.0 * i)));
	} else if (t_1 <= 5e-13) {
		tmp = ((b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)))) - (4.0 * (t * a));
	} else {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	tmp = 0
	if t_1 <= -2e+94:
		tmp = ((b * c) + (-4.0 * (t * a))) - ((j * (27.0 * k)) + (x * (4.0 * i)))
	elif t_1 <= 5e-13:
		tmp = ((b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)))) - (4.0 * (t * a))
	else:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_1 <= -2e+94)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(Float64(j * Float64(27.0 * k)) + Float64(x * Float64(4.0 * i))));
	elseif (t_1 <= 5e-13)
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(y * Float64(t * z))) - Float64(4.0 * i)))) - Float64(4.0 * Float64(t * a)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	tmp = 0.0;
	if (t_1 <= -2e+94)
		tmp = ((b * c) + (-4.0 * (t * a))) - ((j * (27.0 * k)) + (x * (4.0 * i)));
	elseif (t_1 <= 5e-13)
		tmp = ((b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)))) - (4.0 * (t * a));
	else
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+94], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision] + N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-13], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j 27) k) < -2e94

   1. Initial program 87.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 87.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in x around 0 87.5%

      \[\leadsto \color{blue}{\left(c \cdot b + -4 \cdot \left(a \cdot t\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   if -2e94 < (*.f64 (*.f64 j 27) k) < 4.9999999999999999e-13

   1. Initial program 84.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 87.3%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in j around 0 84.3%

      \[\leadsto \color{blue}{\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)} \]

   if 4.9999999999999999e-13 < (*.f64 (*.f64 j 27) k)

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0 86.7%

      \[\leadsto \color{blue}{\left(c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. distribute-lft-out 86.7%

         \[\leadsto \left(c \cdot b - \color{blue}{4 \cdot \left(i \cdot x + a \cdot t\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      2. *-commutative 86.7%

         \[\leadsto \left(c \cdot b - 4 \cdot \left(\color{blue}{x \cdot i} + a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k \]

      3. *-commutative 86.7%

         \[\leadsto \left(c \cdot b - 4 \cdot \left(x \cdot i + \color{blue}{t \cdot a}\right)\right) - \left(j \cdot 27\right) \cdot k \]

   4. Simplified 86.7%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(x \cdot i + t \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -2 \cdot 10^{+94}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot \left(27 \cdot k\right) + x \cdot \left(4 \cdot i\right)\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{-13}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 11: 83.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ t_3 := t_1 - t_2\\ \mathbf{if}\;x \leq -8 \cdot 10^{+117}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{+31}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - t_2\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-92}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+82}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4 + 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - 4 \cdot \left(t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* x (- (* 18.0 (* y (* t z))) (* 4.0 i)))))
        (t_2 (* k (* j 27.0)))
        (t_3 (- t_1 t_2)))
   (if (<= x -8e+117)
     t_3
     (if (<= x -7.8e+31)
       (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) t_2)
       (if (<= x -3.8e-92)
         t_3
         (if (<= x 1.65e+82)
           (-
            (+ (* b c) (* t (+ (* a -4.0) (* 18.0 (* y (* x z))))))
            (* 27.0 (* j k)))
           (- t_1 (* 4.0 (* t a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)));
	double t_2 = k * (j * 27.0);
	double t_3 = t_1 - t_2;
	double tmp;
	if (x <= -8e+117) {
		tmp = t_3;
	} else if (x <= -7.8e+31) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_2;
	} else if (x <= -3.8e-92) {
		tmp = t_3;
	} else if (x <= 1.65e+82) {
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (y * (x * z)))))) - (27.0 * (j * k));
	} else {
		tmp = t_1 - (4.0 * (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (b * c) + (x * ((18.0d0 * (y * (t * z))) - (4.0d0 * i)))
    t_2 = k * (j * 27.0d0)
    t_3 = t_1 - t_2
    if (x <= (-8d+117)) then
        tmp = t_3
    else if (x <= (-7.8d+31)) then
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - t_2
    else if (x <= (-3.8d-92)) then
        tmp = t_3
    else if (x <= 1.65d+82) then
        tmp = ((b * c) + (t * ((a * (-4.0d0)) + (18.0d0 * (y * (x * z)))))) - (27.0d0 * (j * k))
    else
        tmp = t_1 - (4.0d0 * (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)));
	double t_2 = k * (j * 27.0);
	double t_3 = t_1 - t_2;
	double tmp;
	if (x <= -8e+117) {
		tmp = t_3;
	} else if (x <= -7.8e+31) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_2;
	} else if (x <= -3.8e-92) {
		tmp = t_3;
	} else if (x <= 1.65e+82) {
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (y * (x * z)))))) - (27.0 * (j * k));
	} else {
		tmp = t_1 - (4.0 * (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)))
	t_2 = k * (j * 27.0)
	t_3 = t_1 - t_2
	tmp = 0
	if x <= -8e+117:
		tmp = t_3
	elif x <= -7.8e+31:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_2
	elif x <= -3.8e-92:
		tmp = t_3
	elif x <= 1.65e+82:
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (y * (x * z)))))) - (27.0 * (j * k))
	else:
		tmp = t_1 - (4.0 * (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(y * Float64(t * z))) - Float64(4.0 * i))))
	t_2 = Float64(k * Float64(j * 27.0))
	t_3 = Float64(t_1 - t_2)
	tmp = 0.0
	if (x <= -8e+117)
		tmp = t_3;
	elseif (x <= -7.8e+31)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - t_2);
	elseif (x <= -3.8e-92)
		tmp = t_3;
	elseif (x <= 1.65e+82)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(y * Float64(x * z)))))) - Float64(27.0 * Float64(j * k)));
	else
		tmp = Float64(t_1 - Float64(4.0 * Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)));
	t_2 = k * (j * 27.0);
	t_3 = t_1 - t_2;
	tmp = 0.0;
	if (x <= -8e+117)
		tmp = t_3;
	elseif (x <= -7.8e+31)
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_2;
	elseif (x <= -3.8e-92)
		tmp = t_3;
	elseif (x <= 1.65e+82)
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (y * (x * z)))))) - (27.0 * (j * k));
	else
		tmp = t_1 - (4.0 * (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 - t$95$2), $MachinePrecision]}, If[LessEqual[x, -8e+117], t$95$3, If[LessEqual[x, -7.8e+31], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[x, -3.8e-92], t$95$3, If[LessEqual[x, 1.65e+82], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.0000000000000004e117 or -7.79999999999999999e31 < x < -3.8000000000000001e-92

   1. Initial program 75.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 82.4%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in a around 0 86.6%

      \[\leadsto \color{blue}{\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]

   if -8.0000000000000004e117 < x < -7.79999999999999999e31

   1. Initial program 86.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0 95.4%

      \[\leadsto \color{blue}{\left(c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. distribute-lft-out 95.4%

         \[\leadsto \left(c \cdot b - \color{blue}{4 \cdot \left(i \cdot x + a \cdot t\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      2. *-commutative 95.4%

         \[\leadsto \left(c \cdot b - 4 \cdot \left(\color{blue}{x \cdot i} + a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k \]

      3. *-commutative 95.4%

         \[\leadsto \left(c \cdot b - 4 \cdot \left(x \cdot i + \color{blue}{t \cdot a}\right)\right) - \left(j \cdot 27\right) \cdot k \]

   4. Simplified 95.4%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(x \cdot i + t \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   if -3.8000000000000001e-92 < x < 1.6499999999999999e82

   1. Initial program 91.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l- 91.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 91.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]

   3. Simplified 91.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right) - \mathsf{fma}\left(x, 4 \cdot i, j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in i around 0 91.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) + -4 \cdot a\right) + c \cdot b\right) - 27 \cdot \left(k \cdot j\right)} \]

   if 1.6499999999999999e82 < x

   1. Initial program 78.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 97.5%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in j around 0 88.1%

      \[\leadsto \color{blue}{\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+117}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{+31}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-92}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+82}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4 + 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\\ \end{array} \]

Alternative 12: 88.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.6 \cdot 10^{+93}:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4 + 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t 2.6e+93)
   (-
    (- (+ (* b c) (* x (- (* 18.0 (* y (* t z))) (* 4.0 i)))) (* 4.0 (* t a)))
    (* k (* j 27.0)))
   (-
    (+ (* b c) (* t (+ (* a -4.0) (* 18.0 (* y (* x z))))))
    (* 27.0 (* j k)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= 2.6e+93) {
		tmp = (((b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)))) - (4.0 * (t * a))) - (k * (j * 27.0));
	} else {
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (y * (x * z)))))) - (27.0 * (j * k));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: tmp
    if (t <= 2.6d+93) then
        tmp = (((b * c) + (x * ((18.0d0 * (y * (t * z))) - (4.0d0 * i)))) - (4.0d0 * (t * a))) - (k * (j * 27.0d0))
    else
        tmp = ((b * c) + (t * ((a * (-4.0d0)) + (18.0d0 * (y * (x * z)))))) - (27.0d0 * (j * k))
    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 k) {
	double tmp;
	if (t <= 2.6e+93) {
		tmp = (((b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)))) - (4.0 * (t * a))) - (k * (j * 27.0));
	} else {
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (y * (x * z)))))) - (27.0 * (j * k));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= 2.6e+93:
		tmp = (((b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)))) - (4.0 * (t * a))) - (k * (j * 27.0))
	else:
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (y * (x * z)))))) - (27.0 * (j * k))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= 2.6e+93)
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(y * Float64(t * z))) - Float64(4.0 * i)))) - Float64(4.0 * Float64(t * a))) - Float64(k * Float64(j * 27.0)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(y * Float64(x * z)))))) - Float64(27.0 * Float64(j * k)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= 2.6e+93)
		tmp = (((b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)))) - (4.0 * (t * a))) - (k * (j * 27.0));
	else
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (y * (x * z)))))) - (27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, 2.6e+93], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.6e93

   1. Initial program 85.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 91.3%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   if 2.6e93 < t

   1. Initial program 81.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l- 81.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 81.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]

   3. Simplified 85.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right) - \mathsf{fma}\left(x, 4 \cdot i, j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in i around 0 83.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) + -4 \cdot a\right) + c \cdot b\right) - 27 \cdot \left(k \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.6 \cdot 10^{+93}:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4 + 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 13: 66.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ t_3 := \left(b \cdot c + 18 \cdot \left(\left(x \cdot z\right) \cdot \left(t \cdot y\right)\right)\right) - t_2\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+146}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+36}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-104}:\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-103}:\\ \;\;\;\;\left(b \cdot c - t_1\right) - t_2\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+90}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) - t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* x i)))
        (t_2 (* k (* j 27.0)))
        (t_3 (- (+ (* b c) (* 18.0 (* (* x z) (* t y)))) t_2)))
   (if (<= t -2.1e+146)
     t_3
     (if (<= t -2.3e+36)
       (- (+ (* b c) (* -4.0 (* t a))) t_1)
       (if (<= t -2.8e-104)
         (+ (* b c) (* x (- (* 18.0 (* y (* t z))) (* 4.0 i))))
         (if (<= t 1.45e-103)
           (- (- (* b c) t_1) t_2)
           (if (<= t 2.6e+90) t_3 (- (* -4.0 (+ (* t a) (* x i))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = k * (j * 27.0);
	double t_3 = ((b * c) + (18.0 * ((x * z) * (t * y)))) - t_2;
	double tmp;
	if (t <= -2.1e+146) {
		tmp = t_3;
	} else if (t <= -2.3e+36) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} else if (t <= -2.8e-104) {
		tmp = (b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)));
	} else if (t <= 1.45e-103) {
		tmp = ((b * c) - t_1) - t_2;
	} else if (t <= 2.6e+90) {
		tmp = t_3;
	} else {
		tmp = (-4.0 * ((t * a) + (x * i))) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 4.0d0 * (x * i)
    t_2 = k * (j * 27.0d0)
    t_3 = ((b * c) + (18.0d0 * ((x * z) * (t * y)))) - t_2
    if (t <= (-2.1d+146)) then
        tmp = t_3
    else if (t <= (-2.3d+36)) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - t_1
    else if (t <= (-2.8d-104)) then
        tmp = (b * c) + (x * ((18.0d0 * (y * (t * z))) - (4.0d0 * i)))
    else if (t <= 1.45d-103) then
        tmp = ((b * c) - t_1) - t_2
    else if (t <= 2.6d+90) then
        tmp = t_3
    else
        tmp = ((-4.0d0) * ((t * a) + (x * i))) - 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 k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = k * (j * 27.0);
	double t_3 = ((b * c) + (18.0 * ((x * z) * (t * y)))) - t_2;
	double tmp;
	if (t <= -2.1e+146) {
		tmp = t_3;
	} else if (t <= -2.3e+36) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} else if (t <= -2.8e-104) {
		tmp = (b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)));
	} else if (t <= 1.45e-103) {
		tmp = ((b * c) - t_1) - t_2;
	} else if (t <= 2.6e+90) {
		tmp = t_3;
	} else {
		tmp = (-4.0 * ((t * a) + (x * i))) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (x * i)
	t_2 = k * (j * 27.0)
	t_3 = ((b * c) + (18.0 * ((x * z) * (t * y)))) - t_2
	tmp = 0
	if t <= -2.1e+146:
		tmp = t_3
	elif t <= -2.3e+36:
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1
	elif t <= -2.8e-104:
		tmp = (b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)))
	elif t <= 1.45e-103:
		tmp = ((b * c) - t_1) - t_2
	elif t <= 2.6e+90:
		tmp = t_3
	else:
		tmp = (-4.0 * ((t * a) + (x * i))) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(x * i))
	t_2 = Float64(k * Float64(j * 27.0))
	t_3 = Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(Float64(x * z) * Float64(t * y)))) - t_2)
	tmp = 0.0
	if (t <= -2.1e+146)
		tmp = t_3;
	elseif (t <= -2.3e+36)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - t_1);
	elseif (t <= -2.8e-104)
		tmp = Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(y * Float64(t * z))) - Float64(4.0 * i))));
	elseif (t <= 1.45e-103)
		tmp = Float64(Float64(Float64(b * c) - t_1) - t_2);
	elseif (t <= 2.6e+90)
		tmp = t_3;
	else
		tmp = Float64(Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (x * i);
	t_2 = k * (j * 27.0);
	t_3 = ((b * c) + (18.0 * ((x * z) * (t * y)))) - t_2;
	tmp = 0.0;
	if (t <= -2.1e+146)
		tmp = t_3;
	elseif (t <= -2.3e+36)
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	elseif (t <= -2.8e-104)
		tmp = (b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)));
	elseif (t <= 1.45e-103)
		tmp = ((b * c) - t_1) - t_2;
	elseif (t <= 2.6e+90)
		tmp = t_3;
	else
		tmp = (-4.0 * ((t * a) + (x * i))) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(N[(x * z), $MachinePrecision] * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]}, If[LessEqual[t, -2.1e+146], t$95$3, If[LessEqual[t, -2.3e+36], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, -2.8e-104], N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e-103], N[(N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t, 2.6e+90], t$95$3, N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.1000000000000001e146 or 1.4499999999999999e-103 < t < 2.5999999999999998e90

   1. Initial program 82.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 84.0%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in a around 0 84.2%

      \[\leadsto \color{blue}{\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in y around inf 74.4%

      \[\leadsto \left(c \cdot b + \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)}\right) - \left(j \cdot 27\right) \cdot k \]
   5. Step-by-step derivation

      1. associate-*r* 75.7%

         \[\leadsto \left(c \cdot b + 18 \cdot \color{blue}{\left(\left(y \cdot t\right) \cdot \left(z \cdot x\right)\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      2. *-commutative 75.7%

         \[\leadsto \left(c \cdot b + 18 \cdot \left(\left(y \cdot t\right) \cdot \color{blue}{\left(x \cdot z\right)}\right)\right) - \left(j \cdot 27\right) \cdot k \]

   6. Simplified 75.7%

      \[\leadsto \left(c \cdot b + \color{blue}{18 \cdot \left(\left(y \cdot t\right) \cdot \left(x \cdot z\right)\right)}\right) - \left(j \cdot 27\right) \cdot k \]

   if -2.1000000000000001e146 < t < -2.29999999999999996e36

   1. Initial program 85.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 85.5%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in x around 0 82.1%

      \[\leadsto \color{blue}{\left(c \cdot b + -4 \cdot \left(a \cdot t\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. Taylor expanded in j around 0 75.1%

      \[\leadsto \color{blue}{\left(c \cdot b + -4 \cdot \left(a \cdot t\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   if -2.29999999999999996e36 < t < -2.8e-104

   1. Initial program 92.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 96.0%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in a around 0 87.8%

      \[\leadsto \color{blue}{\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 75.5%

      \[\leadsto \color{blue}{c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

   if -2.8e-104 < t < 1.4499999999999999e-103

   1. Initial program 87.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0 86.5%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   if 2.5999999999999998e90 < t

   1. Initial program 79.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in b around 0 70.9%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. associate-*r* 70.9%

         \[\leadsto \left(\color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      2. *-commutative 70.9%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \color{blue}{\left(\left(z \cdot x\right) \cdot t\right)} - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      3. distribute-lft-out 70.9%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - \color{blue}{4 \cdot \left(i \cdot x + a \cdot t\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      4. *-commutative 70.9%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(\color{blue}{x \cdot i} + a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. *-commutative 70.9%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(x \cdot i + \color{blue}{t \cdot a}\right)\right) - \left(j \cdot 27\right) \cdot k \]

   4. Simplified 70.9%

      \[\leadsto \color{blue}{\left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(x \cdot i + t \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in y around 0 80.7%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x + a \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+146}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(\left(x \cdot z\right) \cdot \left(t \cdot y\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+36}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-104}:\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-103}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+90}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(\left(x \cdot z\right) \cdot \left(t \cdot y\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 14: 87.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\right) - \left(j \cdot \left(27 \cdot k\right) + x \cdot \left(4 \cdot i\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (-
  (+ (* b c) (* t (- (* (* y z) (* x 18.0)) (* a 4.0))))
  (+ (* j (* 27.0 k)) (* x (* 4.0 i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((j * (27.0 * k)) + (x * (4.0 * i)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    code = ((b * c) + (t * (((y * z) * (x * 18.0d0)) - (a * 4.0d0)))) - ((j * (27.0d0 * k)) + (x * (4.0d0 * 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, double k) {
	return ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((j * (27.0 * k)) + (x * (4.0 * i)));
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	return ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((j * (27.0 * k)) + (x * (4.0 * i)))

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(y * z) * Float64(x * 18.0)) - Float64(a * 4.0)))) - Float64(Float64(j * Float64(27.0 * k)) + Float64(x * Float64(4.0 * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((j * (27.0 * k)) + (x * (4.0 * i)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision] + N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.9%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

3. Simplified 86.2%

   \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

4. Final simplification 86.2%

   \[\leadsto \left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\right) - \left(j \cdot \left(27 \cdot k\right) + x \cdot \left(4 \cdot i\right)\right) \]

Alternative 15: 69.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ t_3 := b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;t \leq -6 \cdot 10^{+158}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+35}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-107}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-91}:\\ \;\;\;\;\left(b \cdot c - t_1\right) - t_2\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+91}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) - t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* x i)))
        (t_2 (* k (* j 27.0)))
        (t_3 (+ (* b c) (* x (- (* 18.0 (* y (* t z))) (* 4.0 i))))))
   (if (<= t -6e+158)
     (* t (- (* 18.0 (* y (* x z))) (* a 4.0)))
     (if (<= t -6.5e+35)
       (- (+ (* b c) (* -4.0 (* t a))) t_1)
       (if (<= t -5.2e-107)
         t_3
         (if (<= t 2.25e-91)
           (- (- (* b c) t_1) t_2)
           (if (<= t 1.12e+91) t_3 (- (* -4.0 (+ (* t a) (* x i))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = k * (j * 27.0);
	double t_3 = (b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)));
	double tmp;
	if (t <= -6e+158) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else if (t <= -6.5e+35) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} else if (t <= -5.2e-107) {
		tmp = t_3;
	} else if (t <= 2.25e-91) {
		tmp = ((b * c) - t_1) - t_2;
	} else if (t <= 1.12e+91) {
		tmp = t_3;
	} else {
		tmp = (-4.0 * ((t * a) + (x * i))) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 4.0d0 * (x * i)
    t_2 = k * (j * 27.0d0)
    t_3 = (b * c) + (x * ((18.0d0 * (y * (t * z))) - (4.0d0 * i)))
    if (t <= (-6d+158)) then
        tmp = t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0))
    else if (t <= (-6.5d+35)) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - t_1
    else if (t <= (-5.2d-107)) then
        tmp = t_3
    else if (t <= 2.25d-91) then
        tmp = ((b * c) - t_1) - t_2
    else if (t <= 1.12d+91) then
        tmp = t_3
    else
        tmp = ((-4.0d0) * ((t * a) + (x * i))) - 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 k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = k * (j * 27.0);
	double t_3 = (b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)));
	double tmp;
	if (t <= -6e+158) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else if (t <= -6.5e+35) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} else if (t <= -5.2e-107) {
		tmp = t_3;
	} else if (t <= 2.25e-91) {
		tmp = ((b * c) - t_1) - t_2;
	} else if (t <= 1.12e+91) {
		tmp = t_3;
	} else {
		tmp = (-4.0 * ((t * a) + (x * i))) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (x * i)
	t_2 = k * (j * 27.0)
	t_3 = (b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)))
	tmp = 0
	if t <= -6e+158:
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0))
	elif t <= -6.5e+35:
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1
	elif t <= -5.2e-107:
		tmp = t_3
	elif t <= 2.25e-91:
		tmp = ((b * c) - t_1) - t_2
	elif t <= 1.12e+91:
		tmp = t_3
	else:
		tmp = (-4.0 * ((t * a) + (x * i))) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(x * i))
	t_2 = Float64(k * Float64(j * 27.0))
	t_3 = Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(y * Float64(t * z))) - Float64(4.0 * i))))
	tmp = 0.0
	if (t <= -6e+158)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)));
	elseif (t <= -6.5e+35)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - t_1);
	elseif (t <= -5.2e-107)
		tmp = t_3;
	elseif (t <= 2.25e-91)
		tmp = Float64(Float64(Float64(b * c) - t_1) - t_2);
	elseif (t <= 1.12e+91)
		tmp = t_3;
	else
		tmp = Float64(Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (x * i);
	t_2 = k * (j * 27.0);
	t_3 = (b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)));
	tmp = 0.0;
	if (t <= -6e+158)
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	elseif (t <= -6.5e+35)
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	elseif (t <= -5.2e-107)
		tmp = t_3;
	elseif (t <= 2.25e-91)
		tmp = ((b * c) - t_1) - t_2;
	elseif (t <= 1.12e+91)
		tmp = t_3;
	else
		tmp = (-4.0 * ((t * a) + (x * i))) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6e+158], N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.5e+35], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, -5.2e-107], t$95$3, If[LessEqual[t, 2.25e-91], N[(N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t, 1.12e+91], t$95$3, N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -6e158

   1. Initial program 79.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 86.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 69.6%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   if -6e158 < t < -6.5000000000000003e35

   1. Initial program 83.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 83.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in x around 0 80.9%

      \[\leadsto \color{blue}{\left(c \cdot b + -4 \cdot \left(a \cdot t\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. Taylor expanded in j around 0 71.4%

      \[\leadsto \color{blue}{\left(c \cdot b + -4 \cdot \left(a \cdot t\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   if -6.5000000000000003e35 < t < -5.2000000000000001e-107 or 2.24999999999999988e-91 < t < 1.12e91

   1. Initial program 88.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 93.1%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in a around 0 88.1%

      \[\leadsto \color{blue}{\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 76.3%

      \[\leadsto \color{blue}{c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

   if -5.2000000000000001e-107 < t < 2.24999999999999988e-91

   1. Initial program 87.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0 85.9%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   if 1.12e91 < t

   1. Initial program 79.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in b around 0 70.9%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. associate-*r* 70.9%

         \[\leadsto \left(\color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      2. *-commutative 70.9%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \color{blue}{\left(\left(z \cdot x\right) \cdot t\right)} - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      3. distribute-lft-out 70.9%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - \color{blue}{4 \cdot \left(i \cdot x + a \cdot t\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      4. *-commutative 70.9%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(\color{blue}{x \cdot i} + a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. *-commutative 70.9%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(x \cdot i + \color{blue}{t \cdot a}\right)\right) - \left(j \cdot 27\right) \cdot k \]

   4. Simplified 70.9%

      \[\leadsto \color{blue}{\left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(x \cdot i + t \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in y around 0 80.7%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x + a \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+158}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+35}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-107}:\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-91}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+91}:\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 16: 78.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 4 \cdot \left(t \cdot a + x \cdot i\right)\\ t_2 := \left(b \cdot c - t_1\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;y \leq -8 \cdot 10^{+220}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) - t_1\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+123}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+112}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (+ (* t a) (* x i))))
        (t_2 (- (- (* b c) t_1) (* k (* j 27.0)))))
   (if (<= y -8e+220)
     (- (* 18.0 (* y (* t (* x z)))) t_1)
     (if (<= y -8.5e+149)
       t_2
       (if (<= y -4.1e+123)
         (* t (- (* 18.0 (* y (* x z))) (* a 4.0)))
         (if (<= y 2e+112)
           t_2
           (+ (* b c) (* x (- (* 18.0 (* y (* t z))) (* 4.0 i))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * ((t * a) + (x * i));
	double t_2 = ((b * c) - t_1) - (k * (j * 27.0));
	double tmp;
	if (y <= -8e+220) {
		tmp = (18.0 * (y * (t * (x * z)))) - t_1;
	} else if (y <= -8.5e+149) {
		tmp = t_2;
	} else if (y <= -4.1e+123) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else if (y <= 2e+112) {
		tmp = t_2;
	} else {
		tmp = (b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 4.0d0 * ((t * a) + (x * i))
    t_2 = ((b * c) - t_1) - (k * (j * 27.0d0))
    if (y <= (-8d+220)) then
        tmp = (18.0d0 * (y * (t * (x * z)))) - t_1
    else if (y <= (-8.5d+149)) then
        tmp = t_2
    else if (y <= (-4.1d+123)) then
        tmp = t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0))
    else if (y <= 2d+112) then
        tmp = t_2
    else
        tmp = (b * c) + (x * ((18.0d0 * (y * (t * z))) - (4.0d0 * 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 k) {
	double t_1 = 4.0 * ((t * a) + (x * i));
	double t_2 = ((b * c) - t_1) - (k * (j * 27.0));
	double tmp;
	if (y <= -8e+220) {
		tmp = (18.0 * (y * (t * (x * z)))) - t_1;
	} else if (y <= -8.5e+149) {
		tmp = t_2;
	} else if (y <= -4.1e+123) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else if (y <= 2e+112) {
		tmp = t_2;
	} else {
		tmp = (b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * ((t * a) + (x * i))
	t_2 = ((b * c) - t_1) - (k * (j * 27.0))
	tmp = 0
	if y <= -8e+220:
		tmp = (18.0 * (y * (t * (x * z)))) - t_1
	elif y <= -8.5e+149:
		tmp = t_2
	elif y <= -4.1e+123:
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0))
	elif y <= 2e+112:
		tmp = t_2
	else:
		tmp = (b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))
	t_2 = Float64(Float64(Float64(b * c) - t_1) - Float64(k * Float64(j * 27.0)))
	tmp = 0.0
	if (y <= -8e+220)
		tmp = Float64(Float64(18.0 * Float64(y * Float64(t * Float64(x * z)))) - t_1);
	elseif (y <= -8.5e+149)
		tmp = t_2;
	elseif (y <= -4.1e+123)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)));
	elseif (y <= 2e+112)
		tmp = t_2;
	else
		tmp = Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(y * Float64(t * z))) - Float64(4.0 * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * ((t * a) + (x * i));
	t_2 = ((b * c) - t_1) - (k * (j * 27.0));
	tmp = 0.0;
	if (y <= -8e+220)
		tmp = (18.0 * (y * (t * (x * z)))) - t_1;
	elseif (y <= -8.5e+149)
		tmp = t_2;
	elseif (y <= -4.1e+123)
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	elseif (y <= 2e+112)
		tmp = t_2;
	else
		tmp = (b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8e+220], N[(N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[y, -8.5e+149], t$95$2, If[LessEqual[y, -4.1e+123], N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+112], t$95$2, N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8e220

   1. Initial program 54.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in b around 0 76.9%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. associate-*r* 76.8%

         \[\leadsto \left(\color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      2. *-commutative 76.8%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \color{blue}{\left(\left(z \cdot x\right) \cdot t\right)} - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      3. distribute-lft-out 76.8%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - \color{blue}{4 \cdot \left(i \cdot x + a \cdot t\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      4. *-commutative 76.8%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(\color{blue}{x \cdot i} + a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. *-commutative 76.8%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(x \cdot i + \color{blue}{t \cdot a}\right)\right) - \left(j \cdot 27\right) \cdot k \]

   4. Simplified 76.8%

      \[\leadsto \color{blue}{\left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(x \cdot i + t \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in j around 0 76.9%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - 4 \cdot \left(i \cdot x + a \cdot t\right)} \]

   if -8e220 < y < -8.49999999999999956e149 or -4.09999999999999989e123 < y < 1.9999999999999999e112

   1. Initial program 90.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0 87.0%

      \[\leadsto \color{blue}{\left(c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. distribute-lft-out 87.0%

         \[\leadsto \left(c \cdot b - \color{blue}{4 \cdot \left(i \cdot x + a \cdot t\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      2. *-commutative 87.0%

         \[\leadsto \left(c \cdot b - 4 \cdot \left(\color{blue}{x \cdot i} + a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k \]

      3. *-commutative 87.0%

         \[\leadsto \left(c \cdot b - 4 \cdot \left(x \cdot i + \color{blue}{t \cdot a}\right)\right) - \left(j \cdot 27\right) \cdot k \]

   4. Simplified 87.0%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(x \cdot i + t \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   if -8.49999999999999956e149 < y < -4.09999999999999989e123

   1. Initial program 77.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 56.5%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 67.6%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   if 1.9999999999999999e112 < y

   1. Initial program 77.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 78.9%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in a around 0 76.9%

      \[\leadsto \color{blue}{\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 70.6%

      \[\leadsto \color{blue}{c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+220}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+149}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+123}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+112}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]

Alternative 17: 69.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+93}:\\ \;\;\;\;b \cdot c - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+15}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0))))
   (if (<= t_1 -1e+93)
     (- (* b c) (* j (* 27.0 k)))
     (if (<= t_1 5e+15)
       (- (+ (* b c) (* -4.0 (* t a))) (* 4.0 (* x i)))
       (- (* -4.0 (+ (* t a) (* x 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 k) {
	double t_1 = k * (j * 27.0);
	double tmp;
	if (t_1 <= -1e+93) {
		tmp = (b * c) - (j * (27.0 * k));
	} else if (t_1 <= 5e+15) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (4.0 * (x * i));
	} else {
		tmp = (-4.0 * ((t * a) + (x * i))) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (j * 27.0d0)
    if (t_1 <= (-1d+93)) then
        tmp = (b * c) - (j * (27.0d0 * k))
    else if (t_1 <= 5d+15) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - (4.0d0 * (x * i))
    else
        tmp = ((-4.0d0) * ((t * a) + (x * i))) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double tmp;
	if (t_1 <= -1e+93) {
		tmp = (b * c) - (j * (27.0 * k));
	} else if (t_1 <= 5e+15) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (4.0 * (x * i));
	} else {
		tmp = (-4.0 * ((t * a) + (x * i))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	tmp = 0
	if t_1 <= -1e+93:
		tmp = (b * c) - (j * (27.0 * k))
	elif t_1 <= 5e+15:
		tmp = ((b * c) + (-4.0 * (t * a))) - (4.0 * (x * i))
	else:
		tmp = (-4.0 * ((t * a) + (x * i))) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_1 <= -1e+93)
		tmp = Float64(Float64(b * c) - Float64(j * Float64(27.0 * k)));
	elseif (t_1 <= 5e+15)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	tmp = 0.0;
	if (t_1 <= -1e+93)
		tmp = (b * c) - (j * (27.0 * k));
	elseif (t_1 <= 5e+15)
		tmp = ((b * c) + (-4.0 * (t * a))) - (4.0 * (x * i));
	else
		tmp = (-4.0 * ((t * a) + (x * i))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+93], N[(N[(b * c), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+15], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j 27) k) < -1.00000000000000004e93

   1. Initial program 85.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 77.7%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in c around inf 75.4%

      \[\leadsto \color{blue}{c \cdot b} - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. sub-neg 75.4%

         \[\leadsto \color{blue}{c \cdot b + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-*r* 75.5%

         \[\leadsto c \cdot b + \left(-\color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   5. Applied egg-rr 75.5%

      \[\leadsto \color{blue}{c \cdot b + \left(-j \cdot \left(27 \cdot k\right)\right)} \]

   if -1.00000000000000004e93 < (*.f64 (*.f64 j 27) k) < 5e15

   1. Initial program 85.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 85.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in x around 0 72.2%

      \[\leadsto \color{blue}{\left(c \cdot b + -4 \cdot \left(a \cdot t\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. Taylor expanded in j around 0 70.0%

      \[\leadsto \color{blue}{\left(c \cdot b + -4 \cdot \left(a \cdot t\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   if 5e15 < (*.f64 (*.f64 j 27) k)

   1. Initial program 84.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in b around 0 81.9%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. associate-*r* 81.9%

         \[\leadsto \left(\color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      2. *-commutative 81.9%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \color{blue}{\left(\left(z \cdot x\right) \cdot t\right)} - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      3. distribute-lft-out 81.9%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - \color{blue}{4 \cdot \left(i \cdot x + a \cdot t\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      4. *-commutative 81.9%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(\color{blue}{x \cdot i} + a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. *-commutative 81.9%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(x \cdot i + \color{blue}{t \cdot a}\right)\right) - \left(j \cdot 27\right) \cdot k \]

   4. Simplified 81.9%

      \[\leadsto \color{blue}{\left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(x \cdot i + t \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in y around 0 83.4%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x + a \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{+93}:\\ \;\;\;\;b \cdot c - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+15}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 18: 70.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+87}:\\ \;\;\;\;t_1 - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+15}:\\ \;\;\;\;t_1 - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) - t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* -4.0 (* t a)))) (t_2 (* k (* j 27.0))))
   (if (<= t_2 -1e+87)
     (- t_1 (* 27.0 (* j k)))
     (if (<= t_2 5e+15)
       (- t_1 (* 4.0 (* x i)))
       (- (* -4.0 (+ (* t a) (* x i))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1e+87) {
		tmp = t_1 - (27.0 * (j * k));
	} else if (t_2 <= 5e+15) {
		tmp = t_1 - (4.0 * (x * i));
	} else {
		tmp = (-4.0 * ((t * a) + (x * i))) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) + ((-4.0d0) * (t * a))
    t_2 = k * (j * 27.0d0)
    if (t_2 <= (-1d+87)) then
        tmp = t_1 - (27.0d0 * (j * k))
    else if (t_2 <= 5d+15) then
        tmp = t_1 - (4.0d0 * (x * i))
    else
        tmp = ((-4.0d0) * ((t * a) + (x * i))) - 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 k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1e+87) {
		tmp = t_1 - (27.0 * (j * k));
	} else if (t_2 <= 5e+15) {
		tmp = t_1 - (4.0 * (x * i));
	} else {
		tmp = (-4.0 * ((t * a) + (x * i))) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (-4.0 * (t * a))
	t_2 = k * (j * 27.0)
	tmp = 0
	if t_2 <= -1e+87:
		tmp = t_1 - (27.0 * (j * k))
	elif t_2 <= 5e+15:
		tmp = t_1 - (4.0 * (x * i))
	else:
		tmp = (-4.0 * ((t * a) + (x * i))) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_2 <= -1e+87)
		tmp = Float64(t_1 - Float64(27.0 * Float64(j * k)));
	elseif (t_2 <= 5e+15)
		tmp = Float64(t_1 - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (-4.0 * (t * a));
	t_2 = k * (j * 27.0);
	tmp = 0.0;
	if (t_2 <= -1e+87)
		tmp = t_1 - (27.0 * (j * k));
	elseif (t_2 <= 5e+15)
		tmp = t_1 - (4.0 * (x * i));
	else
		tmp = (-4.0 * ((t * a) + (x * i))) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+87], N[(t$95$1 - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+15], N[(t$95$1 - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j 27) k) < -9.9999999999999996e86

   1. Initial program 86.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 86.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in x around 0 82.7%

      \[\leadsto \color{blue}{\left(c \cdot b + -4 \cdot \left(a \cdot t\right)\right) - 27 \cdot \left(k \cdot j\right)} \]

   if -9.9999999999999996e86 < (*.f64 (*.f64 j 27) k) < 5e15

   1. Initial program 84.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 85.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in x around 0 72.3%

      \[\leadsto \color{blue}{\left(c \cdot b + -4 \cdot \left(a \cdot t\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. Taylor expanded in j around 0 70.0%

      \[\leadsto \color{blue}{\left(c \cdot b + -4 \cdot \left(a \cdot t\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   if 5e15 < (*.f64 (*.f64 j 27) k)

   1. Initial program 84.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in b around 0 81.9%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. associate-*r* 81.9%

         \[\leadsto \left(\color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      2. *-commutative 81.9%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \color{blue}{\left(\left(z \cdot x\right) \cdot t\right)} - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      3. distribute-lft-out 81.9%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - \color{blue}{4 \cdot \left(i \cdot x + a \cdot t\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      4. *-commutative 81.9%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(\color{blue}{x \cdot i} + a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. *-commutative 81.9%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(x \cdot i + \color{blue}{t \cdot a}\right)\right) - \left(j \cdot 27\right) \cdot k \]

   4. Simplified 81.9%

      \[\leadsto \color{blue}{\left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(x \cdot i + t \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in y around 0 83.4%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x + a \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{+87}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+15}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 19: 31.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := 18 \cdot \left(\left(x \cdot z\right) \cdot \left(t \cdot y\right)\right)\\ \mathbf{if}\;k \leq -6 \cdot 10^{-47}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 8.1 \cdot 10^{-206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 9 \cdot 10^{-115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 2 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 7.2 \cdot 10^{-75}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 3.1 \cdot 10^{-56}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;k \leq 360000:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.35 \cdot 10^{+105}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* x i))) (t_2 (* 18.0 (* (* x z) (* t y)))))
   (if (<= k -6e-47)
     (* k (* j -27.0))
     (if (<= k 8.1e-206)
       t_1
       (if (<= k 9e-115)
         t_2
         (if (<= k 2e-98)
           t_1
           (if (<= k 7.2e-75)
             (* b c)
             (if (<= k 3.1e-56)
               (* 18.0 (* y (* t (* x z))))
               (if (<= k 360000.0)
                 (* b c)
                 (if (<= k 1.35e+105) t_2 (* j (* k -27.0))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double t_2 = 18.0 * ((x * z) * (t * y));
	double tmp;
	if (k <= -6e-47) {
		tmp = k * (j * -27.0);
	} else if (k <= 8.1e-206) {
		tmp = t_1;
	} else if (k <= 9e-115) {
		tmp = t_2;
	} else if (k <= 2e-98) {
		tmp = t_1;
	} else if (k <= 7.2e-75) {
		tmp = b * c;
	} else if (k <= 3.1e-56) {
		tmp = 18.0 * (y * (t * (x * z)));
	} else if (k <= 360000.0) {
		tmp = b * c;
	} else if (k <= 1.35e+105) {
		tmp = t_2;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-4.0d0) * (x * i)
    t_2 = 18.0d0 * ((x * z) * (t * y))
    if (k <= (-6d-47)) then
        tmp = k * (j * (-27.0d0))
    else if (k <= 8.1d-206) then
        tmp = t_1
    else if (k <= 9d-115) then
        tmp = t_2
    else if (k <= 2d-98) then
        tmp = t_1
    else if (k <= 7.2d-75) then
        tmp = b * c
    else if (k <= 3.1d-56) then
        tmp = 18.0d0 * (y * (t * (x * z)))
    else if (k <= 360000.0d0) then
        tmp = b * c
    else if (k <= 1.35d+105) then
        tmp = t_2
    else
        tmp = j * (k * (-27.0d0))
    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 k) {
	double t_1 = -4.0 * (x * i);
	double t_2 = 18.0 * ((x * z) * (t * y));
	double tmp;
	if (k <= -6e-47) {
		tmp = k * (j * -27.0);
	} else if (k <= 8.1e-206) {
		tmp = t_1;
	} else if (k <= 9e-115) {
		tmp = t_2;
	} else if (k <= 2e-98) {
		tmp = t_1;
	} else if (k <= 7.2e-75) {
		tmp = b * c;
	} else if (k <= 3.1e-56) {
		tmp = 18.0 * (y * (t * (x * z)));
	} else if (k <= 360000.0) {
		tmp = b * c;
	} else if (k <= 1.35e+105) {
		tmp = t_2;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (x * i)
	t_2 = 18.0 * ((x * z) * (t * y))
	tmp = 0
	if k <= -6e-47:
		tmp = k * (j * -27.0)
	elif k <= 8.1e-206:
		tmp = t_1
	elif k <= 9e-115:
		tmp = t_2
	elif k <= 2e-98:
		tmp = t_1
	elif k <= 7.2e-75:
		tmp = b * c
	elif k <= 3.1e-56:
		tmp = 18.0 * (y * (t * (x * z)))
	elif k <= 360000.0:
		tmp = b * c
	elif k <= 1.35e+105:
		tmp = t_2
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(x * i))
	t_2 = Float64(18.0 * Float64(Float64(x * z) * Float64(t * y)))
	tmp = 0.0
	if (k <= -6e-47)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (k <= 8.1e-206)
		tmp = t_1;
	elseif (k <= 9e-115)
		tmp = t_2;
	elseif (k <= 2e-98)
		tmp = t_1;
	elseif (k <= 7.2e-75)
		tmp = Float64(b * c);
	elseif (k <= 3.1e-56)
		tmp = Float64(18.0 * Float64(y * Float64(t * Float64(x * z))));
	elseif (k <= 360000.0)
		tmp = Float64(b * c);
	elseif (k <= 1.35e+105)
		tmp = t_2;
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (x * i);
	t_2 = 18.0 * ((x * z) * (t * y));
	tmp = 0.0;
	if (k <= -6e-47)
		tmp = k * (j * -27.0);
	elseif (k <= 8.1e-206)
		tmp = t_1;
	elseif (k <= 9e-115)
		tmp = t_2;
	elseif (k <= 2e-98)
		tmp = t_1;
	elseif (k <= 7.2e-75)
		tmp = b * c;
	elseif (k <= 3.1e-56)
		tmp = 18.0 * (y * (t * (x * z)));
	elseif (k <= 360000.0)
		tmp = b * c;
	elseif (k <= 1.35e+105)
		tmp = t_2;
	else
		tmp = j * (k * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(18.0 * N[(N[(x * z), $MachinePrecision] * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -6e-47], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 8.1e-206], t$95$1, If[LessEqual[k, 9e-115], t$95$2, If[LessEqual[k, 2e-98], t$95$1, If[LessEqual[k, 7.2e-75], N[(b * c), $MachinePrecision], If[LessEqual[k, 3.1e-56], N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 360000.0], N[(b * c), $MachinePrecision], If[LessEqual[k, 1.35e+105], t$95$2, N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if k < -6.00000000000000033e-47

   1. Initial program 87.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 87.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around inf 41.9%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. Step-by-step derivation

      1. *-commutative 41.9%

         \[\leadsto \color{blue}{\left(k \cdot j\right) \cdot -27} \]

      2. associate-*l* 41.9%

         \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]

   6. Simplified 41.9%

      \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]

   if -6.00000000000000033e-47 < k < 8.1000000000000003e-206 or 9.00000000000000046e-115 < k < 1.99999999999999988e-98

   1. Initial program 86.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in i around inf 24.9%

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

      1. *-commutative 24.9%

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} \]

      2. *-commutative 24.9%

         \[\leadsto \color{blue}{\left(x \cdot i\right)} \cdot -4 \]

   6. Simplified 24.9%

      \[\leadsto \color{blue}{\left(x \cdot i\right) \cdot -4} \]

   if 8.1000000000000003e-206 < k < 9.00000000000000046e-115 or 3.6e5 < k < 1.35000000000000008e105

   1. Initial program 77.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 83.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in x around inf 56.1%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]
   5. Step-by-step derivation

      1. *-commutative 56.1%

         \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)} \]

      2. cancel-sign-sub-inv 56.1%

         \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) + \left(-4\right) \cdot i\right)} \]

      3. associate-*r* 56.1%

         \[\leadsto x \cdot \left(\color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot z\right)} + \left(-4\right) \cdot i\right) \]

      4. metadata-eval 56.1%

         \[\leadsto x \cdot \left(\left(18 \cdot y\right) \cdot \left(t \cdot z\right) + \color{blue}{-4} \cdot i\right) \]

      5. fma-def 56.1%

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(18 \cdot y, t \cdot z, -4 \cdot i\right)} \]

      6. *-commutative 56.1%

         \[\leadsto x \cdot \mathsf{fma}\left(18 \cdot y, \color{blue}{z \cdot t}, -4 \cdot i\right) \]

      7. *-commutative 56.1%

         \[\leadsto x \cdot \mathsf{fma}\left(18 \cdot y, z \cdot t, \color{blue}{i \cdot -4}\right) \]

   6. Simplified 56.1%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(18 \cdot y, z \cdot t, i \cdot -4\right)} \]

   7. Taylor expanded in y around inf 37.9%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 39.8%

         \[\leadsto 18 \cdot \color{blue}{\left(\left(y \cdot t\right) \cdot \left(z \cdot x\right)\right)} \]

      2. *-commutative 39.8%

         \[\leadsto 18 \cdot \left(\left(y \cdot t\right) \cdot \color{blue}{\left(x \cdot z\right)}\right) \]

   9. Simplified 39.8%

      \[\leadsto \color{blue}{18 \cdot \left(\left(y \cdot t\right) \cdot \left(x \cdot z\right)\right)} \]

   if 1.99999999999999988e-98 < k < 7.2000000000000001e-75 or 3.09999999999999987e-56 < k < 3.6e5

   1. Initial program 89.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in b around inf 34.7%

      \[\leadsto \color{blue}{c \cdot b} \]

   if 7.2000000000000001e-75 < k < 3.09999999999999987e-56

   1. Initial program 99.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 71.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in y around inf 44.0%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]

   if 1.35000000000000008e105 < k

   1. Initial program 84.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 81.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around inf 69.9%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. Step-by-step derivation

      1. *-commutative 69.9%

         \[\leadsto \color{blue}{\left(k \cdot j\right) \cdot -27} \]

      2. *-commutative 69.9%

         \[\leadsto \color{blue}{\left(j \cdot k\right)} \cdot -27 \]

      3. associate-*l* 70.0%

         \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]

   6. Simplified 70.0%

      \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -6 \cdot 10^{-47}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 8.1 \cdot 10^{-206}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 9 \cdot 10^{-115}:\\ \;\;\;\;18 \cdot \left(\left(x \cdot z\right) \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;k \leq 2 \cdot 10^{-98}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 7.2 \cdot 10^{-75}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 3.1 \cdot 10^{-56}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;k \leq 360000:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.35 \cdot 10^{+105}:\\ \;\;\;\;18 \cdot \left(\left(x \cdot z\right) \cdot \left(t \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 20: 78.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+220}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+112}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot \left(27 \cdot k\right) + x \cdot \left(4 \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -6e+220)
   (- (* 18.0 (* y (* t (* x z)))) (* 4.0 (+ (* t a) (* x i))))
   (if (<= y 2.3e+112)
     (- (+ (* b c) (* -4.0 (* t a))) (+ (* j (* 27.0 k)) (* x (* 4.0 i))))
     (+ (* b c) (* x (- (* 18.0 (* y (* t z))) (* 4.0 i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -6e+220) {
		tmp = (18.0 * (y * (t * (x * z)))) - (4.0 * ((t * a) + (x * i)));
	} else if (y <= 2.3e+112) {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((j * (27.0 * k)) + (x * (4.0 * i)));
	} else {
		tmp = (b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: tmp
    if (y <= (-6d+220)) then
        tmp = (18.0d0 * (y * (t * (x * z)))) - (4.0d0 * ((t * a) + (x * i)))
    else if (y <= 2.3d+112) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - ((j * (27.0d0 * k)) + (x * (4.0d0 * i)))
    else
        tmp = (b * c) + (x * ((18.0d0 * (y * (t * z))) - (4.0d0 * 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 k) {
	double tmp;
	if (y <= -6e+220) {
		tmp = (18.0 * (y * (t * (x * z)))) - (4.0 * ((t * a) + (x * i)));
	} else if (y <= 2.3e+112) {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((j * (27.0 * k)) + (x * (4.0 * i)));
	} else {
		tmp = (b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if y <= -6e+220:
		tmp = (18.0 * (y * (t * (x * z)))) - (4.0 * ((t * a) + (x * i)))
	elif y <= 2.3e+112:
		tmp = ((b * c) + (-4.0 * (t * a))) - ((j * (27.0 * k)) + (x * (4.0 * i)))
	else:
		tmp = (b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -6e+220)
		tmp = Float64(Float64(18.0 * Float64(y * Float64(t * Float64(x * z)))) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i))));
	elseif (y <= 2.3e+112)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(Float64(j * Float64(27.0 * k)) + Float64(x * Float64(4.0 * i))));
	else
		tmp = Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(y * Float64(t * z))) - Float64(4.0 * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (y <= -6e+220)
		tmp = (18.0 * (y * (t * (x * z)))) - (4.0 * ((t * a) + (x * i)));
	elseif (y <= 2.3e+112)
		tmp = ((b * c) + (-4.0 * (t * a))) - ((j * (27.0 * k)) + (x * (4.0 * i)));
	else
		tmp = (b * c) + (x * ((18.0 * (y * (t * z))) - (4.0 * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -6e+220], N[(N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+112], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision] + N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.00000000000000048e220

   1. Initial program 54.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in b around 0 76.9%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. associate-*r* 76.8%

         \[\leadsto \left(\color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      2. *-commutative 76.8%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \color{blue}{\left(\left(z \cdot x\right) \cdot t\right)} - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      3. distribute-lft-out 76.8%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - \color{blue}{4 \cdot \left(i \cdot x + a \cdot t\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      4. *-commutative 76.8%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(\color{blue}{x \cdot i} + a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. *-commutative 76.8%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(x \cdot i + \color{blue}{t \cdot a}\right)\right) - \left(j \cdot 27\right) \cdot k \]

   4. Simplified 76.8%

      \[\leadsto \color{blue}{\left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(x \cdot i + t \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in j around 0 76.9%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - 4 \cdot \left(i \cdot x + a \cdot t\right)} \]

   if -6.00000000000000048e220 < y < 2.3e112

   1. Initial program 89.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in x around 0 85.1%

      \[\leadsto \color{blue}{\left(c \cdot b + -4 \cdot \left(a \cdot t\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   if 2.3e112 < y

   1. Initial program 77.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 78.9%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in a around 0 76.9%

      \[\leadsto \color{blue}{\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 70.6%

      \[\leadsto \color{blue}{c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+220}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+112}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot \left(27 \cdot k\right) + x \cdot \left(4 \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]

Alternative 21: 50.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ t_3 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{+140}:\\ \;\;\;\;b \cdot c - t_1\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-9}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right) - t_3\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{-68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-89}:\\ \;\;\;\;27 \cdot \left(j \cdot \left(-k\right)\right) - t_1\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-32}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* x i)))
        (t_2 (* t (- (* 18.0 (* y (* x z))) (* a 4.0))))
        (t_3 (* k (* j 27.0))))
   (if (<= b -7.2e+140)
     (- (* b c) t_1)
     (if (<= b -3.1e-9)
       (- (* a (* t -4.0)) t_3)
       (if (<= b -3.7e-68)
         t_2
         (if (<= b 2.7e-89)
           (- (* 27.0 (* j (- k))) t_1)
           (if (<= b 1.8e-32) t_2 (- (* b c) t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	double t_3 = k * (j * 27.0);
	double tmp;
	if (b <= -7.2e+140) {
		tmp = (b * c) - t_1;
	} else if (b <= -3.1e-9) {
		tmp = (a * (t * -4.0)) - t_3;
	} else if (b <= -3.7e-68) {
		tmp = t_2;
	} else if (b <= 2.7e-89) {
		tmp = (27.0 * (j * -k)) - t_1;
	} else if (b <= 1.8e-32) {
		tmp = t_2;
	} else {
		tmp = (b * c) - t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 4.0d0 * (x * i)
    t_2 = t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0))
    t_3 = k * (j * 27.0d0)
    if (b <= (-7.2d+140)) then
        tmp = (b * c) - t_1
    else if (b <= (-3.1d-9)) then
        tmp = (a * (t * (-4.0d0))) - t_3
    else if (b <= (-3.7d-68)) then
        tmp = t_2
    else if (b <= 2.7d-89) then
        tmp = (27.0d0 * (j * -k)) - t_1
    else if (b <= 1.8d-32) then
        tmp = t_2
    else
        tmp = (b * c) - t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	double t_3 = k * (j * 27.0);
	double tmp;
	if (b <= -7.2e+140) {
		tmp = (b * c) - t_1;
	} else if (b <= -3.1e-9) {
		tmp = (a * (t * -4.0)) - t_3;
	} else if (b <= -3.7e-68) {
		tmp = t_2;
	} else if (b <= 2.7e-89) {
		tmp = (27.0 * (j * -k)) - t_1;
	} else if (b <= 1.8e-32) {
		tmp = t_2;
	} else {
		tmp = (b * c) - t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (x * i)
	t_2 = t * ((18.0 * (y * (x * z))) - (a * 4.0))
	t_3 = k * (j * 27.0)
	tmp = 0
	if b <= -7.2e+140:
		tmp = (b * c) - t_1
	elif b <= -3.1e-9:
		tmp = (a * (t * -4.0)) - t_3
	elif b <= -3.7e-68:
		tmp = t_2
	elif b <= 2.7e-89:
		tmp = (27.0 * (j * -k)) - t_1
	elif b <= 1.8e-32:
		tmp = t_2
	else:
		tmp = (b * c) - t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(x * i))
	t_2 = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)))
	t_3 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (b <= -7.2e+140)
		tmp = Float64(Float64(b * c) - t_1);
	elseif (b <= -3.1e-9)
		tmp = Float64(Float64(a * Float64(t * -4.0)) - t_3);
	elseif (b <= -3.7e-68)
		tmp = t_2;
	elseif (b <= 2.7e-89)
		tmp = Float64(Float64(27.0 * Float64(j * Float64(-k))) - t_1);
	elseif (b <= 1.8e-32)
		tmp = t_2;
	else
		tmp = Float64(Float64(b * c) - t_3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (x * i);
	t_2 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	t_3 = k * (j * 27.0);
	tmp = 0.0;
	if (b <= -7.2e+140)
		tmp = (b * c) - t_1;
	elseif (b <= -3.1e-9)
		tmp = (a * (t * -4.0)) - t_3;
	elseif (b <= -3.7e-68)
		tmp = t_2;
	elseif (b <= 2.7e-89)
		tmp = (27.0 * (j * -k)) - t_1;
	elseif (b <= 1.8e-32)
		tmp = t_2;
	else
		tmp = (b * c) - t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.2e+140], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[b, -3.1e-9], N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], If[LessEqual[b, -3.7e-68], t$95$2, If[LessEqual[b, 2.7e-89], N[(N[(27.0 * N[(j * (-k)), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[b, 1.8e-32], t$95$2, N[(N[(b * c), $MachinePrecision] - t$95$3), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -7.1999999999999999e140

   1. Initial program 82.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0 69.7%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in j around 0 59.7%

      \[\leadsto \color{blue}{c \cdot b - 4 \cdot \left(i \cdot x\right)} \]

   if -7.1999999999999999e140 < b < -3.10000000000000005e-9

   1. Initial program 83.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 85.7%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in a around inf 53.0%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. *-commutative 53.0%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot a\right)} - \left(j \cdot 27\right) \cdot k \]

      2. associate-*r* 53.0%

         \[\leadsto \color{blue}{\left(-4 \cdot t\right) \cdot a} - \left(j \cdot 27\right) \cdot k \]

   5. Simplified 53.0%

      \[\leadsto \color{blue}{\left(-4 \cdot t\right) \cdot a} - \left(j \cdot 27\right) \cdot k \]

   if -3.10000000000000005e-9 < b < -3.70000000000000002e-68 or 2.69999999999999988e-89 < b < 1.79999999999999996e-32

   1. Initial program 83.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 80.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 47.3%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   if -3.70000000000000002e-68 < b < 2.69999999999999988e-89

   1. Initial program 88.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in b around 0 83.7%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. associate-*r* 83.7%

         \[\leadsto \left(\color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      2. *-commutative 83.7%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \color{blue}{\left(\left(z \cdot x\right) \cdot t\right)} - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      3. distribute-lft-out 83.7%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - \color{blue}{4 \cdot \left(i \cdot x + a \cdot t\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      4. *-commutative 83.7%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(\color{blue}{x \cdot i} + a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. *-commutative 83.7%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(x \cdot i + \color{blue}{t \cdot a}\right)\right) - \left(j \cdot 27\right) \cdot k \]

   4. Simplified 83.7%

      \[\leadsto \color{blue}{\left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(x \cdot i + t \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in t around 0 50.3%

      \[\leadsto \color{blue}{-1 \cdot \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right)} \]

   if 1.79999999999999996e-32 < b

   1. Initial program 83.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 86.9%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in c around inf 52.8%

      \[\leadsto \color{blue}{c \cdot b} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 5 regimes into one program.

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+140}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-9}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{-68}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-89}:\\ \;\;\;\;27 \cdot \left(j \cdot \left(-k\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-32}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 22: 49.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{+140}:\\ \;\;\;\;b \cdot c - t_1\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-9}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right) - t_2\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-68}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-108}:\\ \;\;\;\;27 \cdot \left(j \cdot \left(-k\right)\right) - t_1\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* x i))) (t_2 (* k (* j 27.0))))
   (if (<= b -6.8e+140)
     (- (* b c) t_1)
     (if (<= b -7.5e-9)
       (- (* a (* t -4.0)) t_2)
       (if (<= b -4e-68)
         (* t (- (* 18.0 (* y (* x z))) (* a 4.0)))
         (if (<= b 1.05e-108)
           (- (* 27.0 (* j (- k))) t_1)
           (if (<= b 1.35e-31)
             (* x (- (* 18.0 (* y (* t z))) (* 4.0 i)))
             (- (* b c) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = k * (j * 27.0);
	double tmp;
	if (b <= -6.8e+140) {
		tmp = (b * c) - t_1;
	} else if (b <= -7.5e-9) {
		tmp = (a * (t * -4.0)) - t_2;
	} else if (b <= -4e-68) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else if (b <= 1.05e-108) {
		tmp = (27.0 * (j * -k)) - t_1;
	} else if (b <= 1.35e-31) {
		tmp = x * ((18.0 * (y * (t * z))) - (4.0 * i));
	} else {
		tmp = (b * c) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 4.0d0 * (x * i)
    t_2 = k * (j * 27.0d0)
    if (b <= (-6.8d+140)) then
        tmp = (b * c) - t_1
    else if (b <= (-7.5d-9)) then
        tmp = (a * (t * (-4.0d0))) - t_2
    else if (b <= (-4d-68)) then
        tmp = t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0))
    else if (b <= 1.05d-108) then
        tmp = (27.0d0 * (j * -k)) - t_1
    else if (b <= 1.35d-31) then
        tmp = x * ((18.0d0 * (y * (t * z))) - (4.0d0 * i))
    else
        tmp = (b * c) - 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 k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = k * (j * 27.0);
	double tmp;
	if (b <= -6.8e+140) {
		tmp = (b * c) - t_1;
	} else if (b <= -7.5e-9) {
		tmp = (a * (t * -4.0)) - t_2;
	} else if (b <= -4e-68) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else if (b <= 1.05e-108) {
		tmp = (27.0 * (j * -k)) - t_1;
	} else if (b <= 1.35e-31) {
		tmp = x * ((18.0 * (y * (t * z))) - (4.0 * i));
	} else {
		tmp = (b * c) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (x * i)
	t_2 = k * (j * 27.0)
	tmp = 0
	if b <= -6.8e+140:
		tmp = (b * c) - t_1
	elif b <= -7.5e-9:
		tmp = (a * (t * -4.0)) - t_2
	elif b <= -4e-68:
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0))
	elif b <= 1.05e-108:
		tmp = (27.0 * (j * -k)) - t_1
	elif b <= 1.35e-31:
		tmp = x * ((18.0 * (y * (t * z))) - (4.0 * i))
	else:
		tmp = (b * c) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(x * i))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (b <= -6.8e+140)
		tmp = Float64(Float64(b * c) - t_1);
	elseif (b <= -7.5e-9)
		tmp = Float64(Float64(a * Float64(t * -4.0)) - t_2);
	elseif (b <= -4e-68)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)));
	elseif (b <= 1.05e-108)
		tmp = Float64(Float64(27.0 * Float64(j * Float64(-k))) - t_1);
	elseif (b <= 1.35e-31)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(t * z))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(b * c) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (x * i);
	t_2 = k * (j * 27.0);
	tmp = 0.0;
	if (b <= -6.8e+140)
		tmp = (b * c) - t_1;
	elseif (b <= -7.5e-9)
		tmp = (a * (t * -4.0)) - t_2;
	elseif (b <= -4e-68)
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	elseif (b <= 1.05e-108)
		tmp = (27.0 * (j * -k)) - t_1;
	elseif (b <= 1.35e-31)
		tmp = x * ((18.0 * (y * (t * z))) - (4.0 * i));
	else
		tmp = (b * c) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.8e+140], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[b, -7.5e-9], N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[b, -4e-68], N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e-108], N[(N[(27.0 * N[(j * (-k)), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[b, 1.35e-31], N[(x * N[(N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -6.8e140

   1. Initial program 82.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0 69.7%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in j around 0 59.7%

      \[\leadsto \color{blue}{c \cdot b - 4 \cdot \left(i \cdot x\right)} \]

   if -6.8e140 < b < -7.49999999999999933e-9

   1. Initial program 83.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 85.7%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in a around inf 53.0%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. *-commutative 53.0%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot a\right)} - \left(j \cdot 27\right) \cdot k \]

      2. associate-*r* 53.0%

         \[\leadsto \color{blue}{\left(-4 \cdot t\right) \cdot a} - \left(j \cdot 27\right) \cdot k \]

   5. Simplified 53.0%

      \[\leadsto \color{blue}{\left(-4 \cdot t\right) \cdot a} - \left(j \cdot 27\right) \cdot k \]

   if -7.49999999999999933e-9 < b < -4.00000000000000027e-68

   1. Initial program 71.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 62.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 61.7%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   if -4.00000000000000027e-68 < b < 1.05e-108

   1. Initial program 87.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in b around 0 84.3%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. associate-*r* 84.3%

         \[\leadsto \left(\color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      2. *-commutative 84.3%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \color{blue}{\left(\left(z \cdot x\right) \cdot t\right)} - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      3. distribute-lft-out 84.3%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - \color{blue}{4 \cdot \left(i \cdot x + a \cdot t\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      4. *-commutative 84.3%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(\color{blue}{x \cdot i} + a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. *-commutative 84.3%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(x \cdot i + \color{blue}{t \cdot a}\right)\right) - \left(j \cdot 27\right) \cdot k \]

   4. Simplified 84.3%

      \[\leadsto \color{blue}{\left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(x \cdot i + t \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in t around 0 48.6%

      \[\leadsto \color{blue}{-1 \cdot \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right)} \]

   if 1.05e-108 < b < 1.35000000000000007e-31

   1. Initial program 94.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 94.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in x around inf 29.7%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

   if 1.35000000000000007e-31 < b

   1. Initial program 82.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 86.7%

      \[\leadsto \color{blue}{\left(\left(c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in c around inf 53.5%

      \[\leadsto \color{blue}{c \cdot b} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 6 regimes into one program.

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+140}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-9}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-68}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-108}:\\ \;\;\;\;27 \cdot \left(j \cdot \left(-k\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 23: 60.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot a + x \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ t_2 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{+143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-67}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* -4.0 (+ (* t a) (* x i))) (* k (* j 27.0))))
        (t_2 (- (* b c) (* 4.0 (* x i)))))
   (if (<= b -3.4e+143)
     t_2
     (if (<= b -8e-11)
       t_1
       (if (<= b -1.8e-67)
         (* t (- (* 18.0 (* y (* x z))) (* a 4.0)))
         (if (<= b 2.6e-15) 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 k) {
	double t_1 = (-4.0 * ((t * a) + (x * i))) - (k * (j * 27.0));
	double t_2 = (b * c) - (4.0 * (x * i));
	double tmp;
	if (b <= -3.4e+143) {
		tmp = t_2;
	} else if (b <= -8e-11) {
		tmp = t_1;
	} else if (b <= -1.8e-67) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else if (b <= 2.6e-15) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((-4.0d0) * ((t * a) + (x * i))) - (k * (j * 27.0d0))
    t_2 = (b * c) - (4.0d0 * (x * i))
    if (b <= (-3.4d+143)) then
        tmp = t_2
    else if (b <= (-8d-11)) then
        tmp = t_1
    else if (b <= (-1.8d-67)) then
        tmp = t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0))
    else if (b <= 2.6d-15) 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 k) {
	double t_1 = (-4.0 * ((t * a) + (x * i))) - (k * (j * 27.0));
	double t_2 = (b * c) - (4.0 * (x * i));
	double tmp;
	if (b <= -3.4e+143) {
		tmp = t_2;
	} else if (b <= -8e-11) {
		tmp = t_1;
	} else if (b <= -1.8e-67) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else if (b <= 2.6e-15) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (-4.0 * ((t * a) + (x * i))) - (k * (j * 27.0))
	t_2 = (b * c) - (4.0 * (x * i))
	tmp = 0
	if b <= -3.4e+143:
		tmp = t_2
	elif b <= -8e-11:
		tmp = t_1
	elif b <= -1.8e-67:
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0))
	elif b <= 2.6e-15:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))) - Float64(k * Float64(j * 27.0)))
	t_2 = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)))
	tmp = 0.0
	if (b <= -3.4e+143)
		tmp = t_2;
	elseif (b <= -8e-11)
		tmp = t_1;
	elseif (b <= -1.8e-67)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)));
	elseif (b <= 2.6e-15)
		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, k)
	t_1 = (-4.0 * ((t * a) + (x * i))) - (k * (j * 27.0));
	t_2 = (b * c) - (4.0 * (x * i));
	tmp = 0.0;
	if (b <= -3.4e+143)
		tmp = t_2;
	elseif (b <= -8e-11)
		tmp = t_1;
	elseif (b <= -1.8e-67)
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	elseif (b <= 2.6e-15)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.4e+143], t$95$2, If[LessEqual[b, -8e-11], t$95$1, If[LessEqual[b, -1.8e-67], N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.6e-15], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.39999999999999982e143 or 2.60000000000000004e-15 < b

   1. Initial program 83.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0 67.9%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in j around 0 54.7%

      \[\leadsto \color{blue}{c \cdot b - 4 \cdot \left(i \cdot x\right)} \]

   if -3.39999999999999982e143 < b < -7.99999999999999952e-11 or -1.8e-67 < b < 2.60000000000000004e-15

   1. Initial program 87.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in b around 0 76.8%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. associate-*r* 76.8%

         \[\leadsto \left(\color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      2. *-commutative 76.8%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \color{blue}{\left(\left(z \cdot x\right) \cdot t\right)} - \left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      3. distribute-lft-out 76.8%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - \color{blue}{4 \cdot \left(i \cdot x + a \cdot t\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      4. *-commutative 76.8%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(\color{blue}{x \cdot i} + a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. *-commutative 76.8%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(x \cdot i + \color{blue}{t \cdot a}\right)\right) - \left(j \cdot 27\right) \cdot k \]

   4. Simplified 76.8%

      \[\leadsto \color{blue}{\left(\left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right) - 4 \cdot \left(x \cdot i + t \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in y around 0 73.6%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x + a \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]

   if -7.99999999999999952e-11 < b < -1.8e-67

   1. Initial program 67.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 57.9%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 68.1%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+143}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-11}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-67}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-15}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 24: 32.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{if}\;k \leq -6 \cdot 10^{-48}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 9.6 \cdot 10^{-206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 2 \cdot 10^{-114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 2.02 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 2.35 \cdot 10^{+35}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 5.4 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 1.5 \cdot 10^{+93}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* x i))) (t_2 (* 18.0 (* y (* t (* x z))))))
   (if (<= k -6e-48)
     (* k (* j -27.0))
     (if (<= k 9.6e-206)
       t_1
       (if (<= k 2e-114)
         t_2
         (if (<= k 2.02e-97)
           t_1
           (if (<= k 2.35e+35)
             (* b c)
             (if (<= k 5.4e+72)
               t_2
               (if (<= k 1.5e+93) (* b c) (* j (* k -27.0)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double t_2 = 18.0 * (y * (t * (x * z)));
	double tmp;
	if (k <= -6e-48) {
		tmp = k * (j * -27.0);
	} else if (k <= 9.6e-206) {
		tmp = t_1;
	} else if (k <= 2e-114) {
		tmp = t_2;
	} else if (k <= 2.02e-97) {
		tmp = t_1;
	} else if (k <= 2.35e+35) {
		tmp = b * c;
	} else if (k <= 5.4e+72) {
		tmp = t_2;
	} else if (k <= 1.5e+93) {
		tmp = b * c;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-4.0d0) * (x * i)
    t_2 = 18.0d0 * (y * (t * (x * z)))
    if (k <= (-6d-48)) then
        tmp = k * (j * (-27.0d0))
    else if (k <= 9.6d-206) then
        tmp = t_1
    else if (k <= 2d-114) then
        tmp = t_2
    else if (k <= 2.02d-97) then
        tmp = t_1
    else if (k <= 2.35d+35) then
        tmp = b * c
    else if (k <= 5.4d+72) then
        tmp = t_2
    else if (k <= 1.5d+93) then
        tmp = b * c
    else
        tmp = j * (k * (-27.0d0))
    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 k) {
	double t_1 = -4.0 * (x * i);
	double t_2 = 18.0 * (y * (t * (x * z)));
	double tmp;
	if (k <= -6e-48) {
		tmp = k * (j * -27.0);
	} else if (k <= 9.6e-206) {
		tmp = t_1;
	} else if (k <= 2e-114) {
		tmp = t_2;
	} else if (k <= 2.02e-97) {
		tmp = t_1;
	} else if (k <= 2.35e+35) {
		tmp = b * c;
	} else if (k <= 5.4e+72) {
		tmp = t_2;
	} else if (k <= 1.5e+93) {
		tmp = b * c;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (x * i)
	t_2 = 18.0 * (y * (t * (x * z)))
	tmp = 0
	if k <= -6e-48:
		tmp = k * (j * -27.0)
	elif k <= 9.6e-206:
		tmp = t_1
	elif k <= 2e-114:
		tmp = t_2
	elif k <= 2.02e-97:
		tmp = t_1
	elif k <= 2.35e+35:
		tmp = b * c
	elif k <= 5.4e+72:
		tmp = t_2
	elif k <= 1.5e+93:
		tmp = b * c
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(x * i))
	t_2 = Float64(18.0 * Float64(y * Float64(t * Float64(x * z))))
	tmp = 0.0
	if (k <= -6e-48)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (k <= 9.6e-206)
		tmp = t_1;
	elseif (k <= 2e-114)
		tmp = t_2;
	elseif (k <= 2.02e-97)
		tmp = t_1;
	elseif (k <= 2.35e+35)
		tmp = Float64(b * c);
	elseif (k <= 5.4e+72)
		tmp = t_2;
	elseif (k <= 1.5e+93)
		tmp = Float64(b * c);
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (x * i);
	t_2 = 18.0 * (y * (t * (x * z)));
	tmp = 0.0;
	if (k <= -6e-48)
		tmp = k * (j * -27.0);
	elseif (k <= 9.6e-206)
		tmp = t_1;
	elseif (k <= 2e-114)
		tmp = t_2;
	elseif (k <= 2.02e-97)
		tmp = t_1;
	elseif (k <= 2.35e+35)
		tmp = b * c;
	elseif (k <= 5.4e+72)
		tmp = t_2;
	elseif (k <= 1.5e+93)
		tmp = b * c;
	else
		tmp = j * (k * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -6e-48], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 9.6e-206], t$95$1, If[LessEqual[k, 2e-114], t$95$2, If[LessEqual[k, 2.02e-97], t$95$1, If[LessEqual[k, 2.35e+35], N[(b * c), $MachinePrecision], If[LessEqual[k, 5.4e+72], t$95$2, If[LessEqual[k, 1.5e+93], N[(b * c), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if k < -5.9999999999999998e-48

   1. Initial program 87.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 87.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around inf 41.9%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. Step-by-step derivation

      1. *-commutative 41.9%

         \[\leadsto \color{blue}{\left(k \cdot j\right) \cdot -27} \]

      2. associate-*l* 41.9%

         \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]

   6. Simplified 41.9%

      \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]

   if -5.9999999999999998e-48 < k < 9.5999999999999998e-206 or 2.0000000000000001e-114 < k < 2.0200000000000001e-97

   1. Initial program 86.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in i around inf 24.6%

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

      1. *-commutative 24.6%

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} \]

      2. *-commutative 24.6%

         \[\leadsto \color{blue}{\left(x \cdot i\right)} \cdot -4 \]

   6. Simplified 24.6%

      \[\leadsto \color{blue}{\left(x \cdot i\right) \cdot -4} \]

   if 9.5999999999999998e-206 < k < 2.0000000000000001e-114 or 2.35000000000000017e35 < k < 5.4000000000000001e72

   1. Initial program 72.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 78.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in y around inf 35.9%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]

   if 2.0200000000000001e-97 < k < 2.35000000000000017e35 or 5.4000000000000001e72 < k < 1.49999999999999989e93

   1. Initial program 90.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 91.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in b around inf 40.2%

      \[\leadsto \color{blue}{c \cdot b} \]

   if 1.49999999999999989e93 < k

   1. Initial program 84.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 82.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around inf 68.1%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. Step-by-step derivation

      1. *-commutative 68.1%

         \[\leadsto \color{blue}{\left(k \cdot j\right) \cdot -27} \]

      2. *-commutative 68.1%

         \[\leadsto \color{blue}{\left(j \cdot k\right)} \cdot -27 \]

      3. associate-*l* 68.3%

         \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]

   6. Simplified 68.3%

      \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -6 \cdot 10^{-48}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 9.6 \cdot 10^{-206}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 2 \cdot 10^{-114}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;k \leq 2.02 \cdot 10^{-97}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 2.35 \cdot 10^{+35}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 5.4 \cdot 10^{+72}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;k \leq 1.5 \cdot 10^{+93}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 25: 42.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;k \leq -3.9 \cdot 10^{-85}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 1.5 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 3.3 \cdot 10^{+72}:\\ \;\;\;\;18 \cdot \left(\left(x \cdot z\right) \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;k \leq 3.2 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 4.0 (* x i)))))
   (if (<= k -3.9e-85)
     (* k (* j -27.0))
     (if (<= k 1.5e+21)
       t_1
       (if (<= k 3.3e+72)
         (* 18.0 (* (* x z) (* t y)))
         (if (<= k 3.2e+92) t_1 (* j (* k -27.0))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (x * i));
	double tmp;
	if (k <= -3.9e-85) {
		tmp = k * (j * -27.0);
	} else if (k <= 1.5e+21) {
		tmp = t_1;
	} else if (k <= 3.3e+72) {
		tmp = 18.0 * ((x * z) * (t * y));
	} else if (k <= 3.2e+92) {
		tmp = t_1;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) - (4.0d0 * (x * i))
    if (k <= (-3.9d-85)) then
        tmp = k * (j * (-27.0d0))
    else if (k <= 1.5d+21) then
        tmp = t_1
    else if (k <= 3.3d+72) then
        tmp = 18.0d0 * ((x * z) * (t * y))
    else if (k <= 3.2d+92) then
        tmp = t_1
    else
        tmp = j * (k * (-27.0d0))
    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 k) {
	double t_1 = (b * c) - (4.0 * (x * i));
	double tmp;
	if (k <= -3.9e-85) {
		tmp = k * (j * -27.0);
	} else if (k <= 1.5e+21) {
		tmp = t_1;
	} else if (k <= 3.3e+72) {
		tmp = 18.0 * ((x * z) * (t * y));
	} else if (k <= 3.2e+92) {
		tmp = t_1;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (4.0 * (x * i))
	tmp = 0
	if k <= -3.9e-85:
		tmp = k * (j * -27.0)
	elif k <= 1.5e+21:
		tmp = t_1
	elif k <= 3.3e+72:
		tmp = 18.0 * ((x * z) * (t * y))
	elif k <= 3.2e+92:
		tmp = t_1
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)))
	tmp = 0.0
	if (k <= -3.9e-85)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (k <= 1.5e+21)
		tmp = t_1;
	elseif (k <= 3.3e+72)
		tmp = Float64(18.0 * Float64(Float64(x * z) * Float64(t * y)));
	elseif (k <= 3.2e+92)
		tmp = t_1;
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (4.0 * (x * i));
	tmp = 0.0;
	if (k <= -3.9e-85)
		tmp = k * (j * -27.0);
	elseif (k <= 1.5e+21)
		tmp = t_1;
	elseif (k <= 3.3e+72)
		tmp = 18.0 * ((x * z) * (t * y));
	elseif (k <= 3.2e+92)
		tmp = t_1;
	else
		tmp = j * (k * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -3.9e-85], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.5e+21], t$95$1, If[LessEqual[k, 3.3e+72], N[(18.0 * N[(N[(x * z), $MachinePrecision] * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.2e+92], t$95$1, N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if k < -3.89999999999999988e-85

   1. Initial program 88.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around inf 41.4%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. Step-by-step derivation

      1. *-commutative 41.4%

         \[\leadsto \color{blue}{\left(k \cdot j\right) \cdot -27} \]

      2. associate-*l* 41.4%

         \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]

   6. Simplified 41.4%

      \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]

   if -3.89999999999999988e-85 < k < 1.5e21 or 3.3e72 < k < 3.20000000000000025e92

   1. Initial program 83.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0 54.4%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in j around 0 48.5%

      \[\leadsto \color{blue}{c \cdot b - 4 \cdot \left(i \cdot x\right)} \]

   if 1.5e21 < k < 3.3e72

   1. Initial program 80.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 81.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in x around inf 49.2%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]
   5. Step-by-step derivation

      1. *-commutative 49.2%

         \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right)} \]

      2. cancel-sign-sub-inv 49.2%

         \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) + \left(-4\right) \cdot i\right)} \]

      3. associate-*r* 49.2%

         \[\leadsto x \cdot \left(\color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot z\right)} + \left(-4\right) \cdot i\right) \]

      4. metadata-eval 49.2%

         \[\leadsto x \cdot \left(\left(18 \cdot y\right) \cdot \left(t \cdot z\right) + \color{blue}{-4} \cdot i\right) \]

      5. fma-def 49.2%

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(18 \cdot y, t \cdot z, -4 \cdot i\right)} \]

      6. *-commutative 49.2%

         \[\leadsto x \cdot \mathsf{fma}\left(18 \cdot y, \color{blue}{z \cdot t}, -4 \cdot i\right) \]

      7. *-commutative 49.2%

         \[\leadsto x \cdot \mathsf{fma}\left(18 \cdot y, z \cdot t, \color{blue}{i \cdot -4}\right) \]

   6. Simplified 49.2%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(18 \cdot y, z \cdot t, i \cdot -4\right)} \]

   7. Taylor expanded in y around inf 48.7%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 61.0%

         \[\leadsto 18 \cdot \color{blue}{\left(\left(y \cdot t\right) \cdot \left(z \cdot x\right)\right)} \]

      2. *-commutative 61.0%

         \[\leadsto 18 \cdot \left(\left(y \cdot t\right) \cdot \color{blue}{\left(x \cdot z\right)}\right) \]

   9. Simplified 61.0%

      \[\leadsto \color{blue}{18 \cdot \left(\left(y \cdot t\right) \cdot \left(x \cdot z\right)\right)} \]

   if 3.20000000000000025e92 < k

   1. Initial program 84.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 82.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around inf 68.1%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. Step-by-step derivation

      1. *-commutative 68.1%

         \[\leadsto \color{blue}{\left(k \cdot j\right) \cdot -27} \]

      2. *-commutative 68.1%

         \[\leadsto \color{blue}{\left(j \cdot k\right)} \cdot -27 \]

      3. associate-*l* 68.3%

         \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]

   6. Simplified 68.3%

      \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3.9 \cdot 10^{-85}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 1.5 \cdot 10^{+21}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 3.3 \cdot 10^{+72}:\\ \;\;\;\;18 \cdot \left(\left(x \cdot z\right) \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;k \leq 3.2 \cdot 10^{+92}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 26: 31.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;k \leq -2.6 \cdot 10^{-93}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 5.5 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 4.2 \cdot 10^{+50}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 4.5 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 2.4 \cdot 10^{+92}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= k -2.6e-93)
     (* k (* j -27.0))
     (if (<= k 5.5e-96)
       t_1
       (if (<= k 4.2e+50)
         (* b c)
         (if (<= k 4.5e+72)
           t_1
           (if (<= k 2.4e+92) (* b c) (* j (* k -27.0)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (k <= -2.6e-93) {
		tmp = k * (j * -27.0);
	} else if (k <= 5.5e-96) {
		tmp = t_1;
	} else if (k <= 4.2e+50) {
		tmp = b * c;
	} else if (k <= 4.5e+72) {
		tmp = t_1;
	} else if (k <= 2.4e+92) {
		tmp = b * c;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    if (k <= (-2.6d-93)) then
        tmp = k * (j * (-27.0d0))
    else if (k <= 5.5d-96) then
        tmp = t_1
    else if (k <= 4.2d+50) then
        tmp = b * c
    else if (k <= 4.5d+72) then
        tmp = t_1
    else if (k <= 2.4d+92) then
        tmp = b * c
    else
        tmp = j * (k * (-27.0d0))
    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 k) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (k <= -2.6e-93) {
		tmp = k * (j * -27.0);
	} else if (k <= 5.5e-96) {
		tmp = t_1;
	} else if (k <= 4.2e+50) {
		tmp = b * c;
	} else if (k <= 4.5e+72) {
		tmp = t_1;
	} else if (k <= 2.4e+92) {
		tmp = b * c;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	tmp = 0
	if k <= -2.6e-93:
		tmp = k * (j * -27.0)
	elif k <= 5.5e-96:
		tmp = t_1
	elif k <= 4.2e+50:
		tmp = b * c
	elif k <= 4.5e+72:
		tmp = t_1
	elif k <= 2.4e+92:
		tmp = b * c
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (k <= -2.6e-93)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (k <= 5.5e-96)
		tmp = t_1;
	elseif (k <= 4.2e+50)
		tmp = Float64(b * c);
	elseif (k <= 4.5e+72)
		tmp = t_1;
	elseif (k <= 2.4e+92)
		tmp = Float64(b * c);
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (k <= -2.6e-93)
		tmp = k * (j * -27.0);
	elseif (k <= 5.5e-96)
		tmp = t_1;
	elseif (k <= 4.2e+50)
		tmp = b * c;
	elseif (k <= 4.5e+72)
		tmp = t_1;
	elseif (k <= 2.4e+92)
		tmp = b * c;
	else
		tmp = j * (k * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -2.6e-93], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 5.5e-96], t$95$1, If[LessEqual[k, 4.2e+50], N[(b * c), $MachinePrecision], If[LessEqual[k, 4.5e+72], t$95$1, If[LessEqual[k, 2.4e+92], N[(b * c), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if k < -2.5999999999999998e-93

   1. Initial program 88.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.6%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around inf 40.4%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. Step-by-step derivation

      1. *-commutative 40.4%

         \[\leadsto \color{blue}{\left(k \cdot j\right) \cdot -27} \]

      2. associate-*l* 40.4%

         \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]

   6. Simplified 40.4%

      \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]

   if -2.5999999999999998e-93 < k < 5.4999999999999997e-96 or 4.1999999999999999e50 < k < 4.4999999999999998e72

   1. Initial program 81.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 85.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in a around inf 32.2%

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

      1. *-commutative 32.2%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot -4} \]

      2. *-commutative 32.2%

         \[\leadsto \color{blue}{\left(t \cdot a\right)} \cdot -4 \]

      3. associate-*r* 32.2%

         \[\leadsto \color{blue}{t \cdot \left(a \cdot -4\right)} \]

   6. Simplified 32.2%

      \[\leadsto \color{blue}{t \cdot \left(a \cdot -4\right)} \]

   if 5.4999999999999997e-96 < k < 4.1999999999999999e50 or 4.4999999999999998e72 < k < 2.40000000000000005e92

   1. Initial program 88.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in b around inf 38.2%

      \[\leadsto \color{blue}{c \cdot b} \]

   if 2.40000000000000005e92 < k

   1. Initial program 84.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 82.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around inf 68.1%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. Step-by-step derivation

      1. *-commutative 68.1%

         \[\leadsto \color{blue}{\left(k \cdot j\right) \cdot -27} \]

      2. *-commutative 68.1%

         \[\leadsto \color{blue}{\left(j \cdot k\right)} \cdot -27 \]

      3. associate-*l* 68.3%

         \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]

   6. Simplified 68.3%

      \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.6 \cdot 10^{-93}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 5.5 \cdot 10^{-96}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;k \leq 4.2 \cdot 10^{+50}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 4.5 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;k \leq 2.4 \cdot 10^{+92}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 27: 31.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -1.8 \cdot 10^{-47}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 1.04 \cdot 10^{-97}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 1.12 \cdot 10^{+51}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 5 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;k \leq 4.1 \cdot 10^{+92}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -1.8e-47)
   (* k (* j -27.0))
   (if (<= k 1.04e-97)
     (* -4.0 (* x i))
     (if (<= k 1.12e+51)
       (* b c)
       (if (<= k 5e+72)
         (* t (* a -4.0))
         (if (<= k 4.1e+92) (* b c) (* j (* k -27.0))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (k <= -1.8e-47) {
		tmp = k * (j * -27.0);
	} else if (k <= 1.04e-97) {
		tmp = -4.0 * (x * i);
	} else if (k <= 1.12e+51) {
		tmp = b * c;
	} else if (k <= 5e+72) {
		tmp = t * (a * -4.0);
	} else if (k <= 4.1e+92) {
		tmp = b * c;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: tmp
    if (k <= (-1.8d-47)) then
        tmp = k * (j * (-27.0d0))
    else if (k <= 1.04d-97) then
        tmp = (-4.0d0) * (x * i)
    else if (k <= 1.12d+51) then
        tmp = b * c
    else if (k <= 5d+72) then
        tmp = t * (a * (-4.0d0))
    else if (k <= 4.1d+92) then
        tmp = b * c
    else
        tmp = j * (k * (-27.0d0))
    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 k) {
	double tmp;
	if (k <= -1.8e-47) {
		tmp = k * (j * -27.0);
	} else if (k <= 1.04e-97) {
		tmp = -4.0 * (x * i);
	} else if (k <= 1.12e+51) {
		tmp = b * c;
	} else if (k <= 5e+72) {
		tmp = t * (a * -4.0);
	} else if (k <= 4.1e+92) {
		tmp = b * c;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -1.8e-47:
		tmp = k * (j * -27.0)
	elif k <= 1.04e-97:
		tmp = -4.0 * (x * i)
	elif k <= 1.12e+51:
		tmp = b * c
	elif k <= 5e+72:
		tmp = t * (a * -4.0)
	elif k <= 4.1e+92:
		tmp = b * c
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -1.8e-47)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (k <= 1.04e-97)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (k <= 1.12e+51)
		tmp = Float64(b * c);
	elseif (k <= 5e+72)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (k <= 4.1e+92)
		tmp = Float64(b * c);
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (k <= -1.8e-47)
		tmp = k * (j * -27.0);
	elseif (k <= 1.04e-97)
		tmp = -4.0 * (x * i);
	elseif (k <= 1.12e+51)
		tmp = b * c;
	elseif (k <= 5e+72)
		tmp = t * (a * -4.0);
	elseif (k <= 4.1e+92)
		tmp = b * c;
	else
		tmp = j * (k * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, -1.8e-47], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.04e-97], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.12e+51], N[(b * c), $MachinePrecision], If[LessEqual[k, 5e+72], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.1e+92], N[(b * c), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if k < -1.79999999999999995e-47

   1. Initial program 87.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 87.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around inf 41.9%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. Step-by-step derivation

      1. *-commutative 41.9%

         \[\leadsto \color{blue}{\left(k \cdot j\right) \cdot -27} \]

      2. associate-*l* 41.9%

         \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]

   6. Simplified 41.9%

      \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]

   if -1.79999999999999995e-47 < k < 1.04000000000000005e-97

   1. Initial program 83.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 87.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in i around inf 27.8%

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

      1. *-commutative 27.8%

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} \]

      2. *-commutative 27.8%

         \[\leadsto \color{blue}{\left(x \cdot i\right)} \cdot -4 \]

   6. Simplified 27.8%

      \[\leadsto \color{blue}{\left(x \cdot i\right) \cdot -4} \]

   if 1.04000000000000005e-97 < k < 1.11999999999999992e51 or 4.99999999999999992e72 < k < 4.10000000000000024e92

   1. Initial program 88.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in b around inf 38.2%

      \[\leadsto \color{blue}{c \cdot b} \]

   if 1.11999999999999992e51 < k < 4.99999999999999992e72

   1. Initial program 67.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 68.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in a around inf 67.3%

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

      1. *-commutative 67.3%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot -4} \]

      2. *-commutative 67.3%

         \[\leadsto \color{blue}{\left(t \cdot a\right)} \cdot -4 \]

      3. associate-*r* 67.3%

         \[\leadsto \color{blue}{t \cdot \left(a \cdot -4\right)} \]

   6. Simplified 67.3%

      \[\leadsto \color{blue}{t \cdot \left(a \cdot -4\right)} \]

   if 4.10000000000000024e92 < k

   1. Initial program 84.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 82.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around inf 68.1%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. Step-by-step derivation

      1. *-commutative 68.1%

         \[\leadsto \color{blue}{\left(k \cdot j\right) \cdot -27} \]

      2. *-commutative 68.1%

         \[\leadsto \color{blue}{\left(j \cdot k\right)} \cdot -27 \]

      3. associate-*l* 68.3%

         \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]

   6. Simplified 68.3%

      \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.8 \cdot 10^{-47}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 1.04 \cdot 10^{-97}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 1.12 \cdot 10^{+51}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 5 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;k \leq 4.1 \cdot 10^{+92}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 28: 32.6% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -3.9 \cdot 10^{-85} \lor \neg \left(k \leq 9.2 \cdot 10^{+91}\right):\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= k -3.9e-85) (not (<= k 9.2e+91))) (* j (* k -27.0)) (* b c)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((k <= -3.9e-85) || !(k <= 9.2e+91)) {
		tmp = j * (k * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: tmp
    if ((k <= (-3.9d-85)) .or. (.not. (k <= 9.2d+91))) then
        tmp = j * (k * (-27.0d0))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((k <= -3.9e-85) || !(k <= 9.2e+91)) {
		tmp = j * (k * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (k <= -3.9e-85) or not (k <= 9.2e+91):
		tmp = j * (k * -27.0)
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((k <= -3.9e-85) || !(k <= 9.2e+91))
		tmp = Float64(j * Float64(k * -27.0));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((k <= -3.9e-85) || ~((k <= 9.2e+91)))
		tmp = j * (k * -27.0);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[k, -3.9e-85], N[Not[LessEqual[k, 9.2e+91]], $MachinePrecision]], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if k < -3.89999999999999988e-85 or 9.19999999999999965e91 < k

   1. Initial program 87.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 86.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around inf 50.5%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. Step-by-step derivation

      1. *-commutative 50.5%

         \[\leadsto \color{blue}{\left(k \cdot j\right) \cdot -27} \]

      2. *-commutative 50.5%

         \[\leadsto \color{blue}{\left(j \cdot k\right)} \cdot -27 \]

      3. associate-*l* 49.7%

         \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]

   6. Simplified 49.7%

      \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]

   if -3.89999999999999988e-85 < k < 9.19999999999999965e91

   1. Initial program 83.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 86.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in b around inf 27.4%

      \[\leadsto \color{blue}{c \cdot b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3.9 \cdot 10^{-85} \lor \neg \left(k \leq 9.2 \cdot 10^{+91}\right):\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 29: 32.6% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -3.9 \cdot 10^{-85}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 10^{+92}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -3.9e-85)
   (* k (* j -27.0))
   (if (<= k 1e+92) (* b c) (* j (* k -27.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (k <= -3.9e-85) {
		tmp = k * (j * -27.0);
	} else if (k <= 1e+92) {
		tmp = b * c;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: tmp
    if (k <= (-3.9d-85)) then
        tmp = k * (j * (-27.0d0))
    else if (k <= 1d+92) then
        tmp = b * c
    else
        tmp = j * (k * (-27.0d0))
    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 k) {
	double tmp;
	if (k <= -3.9e-85) {
		tmp = k * (j * -27.0);
	} else if (k <= 1e+92) {
		tmp = b * c;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -3.9e-85:
		tmp = k * (j * -27.0)
	elif k <= 1e+92:
		tmp = b * c
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -3.9e-85)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (k <= 1e+92)
		tmp = Float64(b * c);
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (k <= -3.9e-85)
		tmp = k * (j * -27.0);
	elseif (k <= 1e+92)
		tmp = b * c;
	else
		tmp = j * (k * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, -3.9e-85], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1e+92], N[(b * c), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if k < -3.89999999999999988e-85

   1. Initial program 88.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around inf 41.4%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. Step-by-step derivation

      1. *-commutative 41.4%

         \[\leadsto \color{blue}{\left(k \cdot j\right) \cdot -27} \]

      2. associate-*l* 41.4%

         \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]

   6. Simplified 41.4%

      \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]

   if -3.89999999999999988e-85 < k < 1e92

   1. Initial program 83.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 86.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in b around inf 27.4%

      \[\leadsto \color{blue}{c \cdot b} \]

   if 1e92 < k

   1. Initial program 84.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 82.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around inf 68.1%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. Step-by-step derivation

      1. *-commutative 68.1%

         \[\leadsto \color{blue}{\left(k \cdot j\right) \cdot -27} \]

      2. *-commutative 68.1%

         \[\leadsto \color{blue}{\left(j \cdot k\right)} \cdot -27 \]

      3. associate-*l* 68.3%

         \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]

   6. Simplified 68.3%

      \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3.9 \cdot 10^{-85}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 10^{+92}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 30: 24.1% accurate, 10.3× speedup

Math

\[\begin{array}{l} \\ b \cdot c \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.9%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

3. Simplified 86.2%

   \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

4. Taylor expanded in b around inf 24.3%

   \[\leadsto \color{blue}{c \cdot b} \]

5. Final simplification 24.3%

   \[\leadsto b \cdot c \]

Developer target: 89.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (+ (* a t) (* i x)) 4.0))
        (t_2
         (-
          (- (* (* 18.0 t) (* (* x y) z)) t_1)
          (- (* (* k j) 27.0) (* c b)))))
   (if (< t -1.6210815397541398e-69)
     t_2
     (if (< t 165.68027943805222)
       (+ (- (* (* 18.0 y) (* x (* z t))) t_1) (- (* c b) (* 27.0 (* k j))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a * t) + (i * x)) * 4.0d0
    t_2 = (((18.0d0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0d0) - (c * b))
    if (t < (-1.6210815397541398d-69)) then
        tmp = t_2
    else if (t < 165.68027943805222d0) then
        tmp = (((18.0d0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0d0 * (k * j)))
    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 k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((a * t) + (i * x)) * 4.0
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b))
	tmp = 0
	if t < -1.6210815397541398e-69:
		tmp = t_2
	elif t < 165.68027943805222:
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(a * t) + Float64(i * x)) * 4.0)
	t_2 = Float64(Float64(Float64(Float64(18.0 * t) * Float64(Float64(x * y) * z)) - t_1) - Float64(Float64(Float64(k * j) * 27.0) - Float64(c * b)))
	tmp = 0.0
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = Float64(Float64(Float64(Float64(18.0 * y) * Float64(x * Float64(z * t))) - t_1) + Float64(Float64(c * b) - Float64(27.0 * Float64(k * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((a * t) + (i * x)) * 4.0;
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	tmp = 0.0;
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] + N[(i * x), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.6210815397541398e-69], t$95$2, If[Less[t, 165.68027943805222], N[(N[(N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023279 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :herbie-target
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18.0 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4.0)) (- (* c b) (* 27.0 (* k j)))) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b)))))

  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))