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

Percentage Accurate: 85.4% → 89.0%

Time: 6.6s

Alternatives: 16

Speedup: 0.9×

• 49.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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: 85.4% accurate, 1.0× speedup

Math

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

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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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: 89.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := \left(x \cdot 4\right) \cdot i\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - t\_1\right) - t\_2 \leq \infty:\\ \;\;\;\;\left(\left(c \cdot b - \left(4 \cdot a - z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right) \cdot t\right) - t\_1\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(i \cdot x\right) - t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (let* ((t_1 (* (* x 4.0) i)) (t_2 (* (* j 27.0) k)))
  (if (<=
       (-
        (-
         (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
         t_1)
        t_2)
       INFINITY)
    (-
     (- (- (* c b) (* (- (* 4.0 a) (* z (* y (* 18.0 x)))) t)) t_1)
     t_2)
    (- (* -4.0 (* i x)) 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 = (x * 4.0) * i;
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (((((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - t_1) - t_2) <= ((double) INFINITY)) {
		tmp = (((c * b) - (((4.0 * a) - (z * (y * (18.0 * x)))) * t)) - t_1) - t_2;
	} else {
		tmp = (-4.0 * (i * x)) - t_2;
	}
	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 = (x * 4.0) * i;
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (((((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - t_1) - t_2) <= Double.POSITIVE_INFINITY) {
		tmp = (((c * b) - (((4.0 * a) - (z * (y * (18.0 * x)))) * t)) - t_1) - t_2;
	} else {
		tmp = (-4.0 * (i * x)) - t_2;
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (x * 4.0) * i;
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (((((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - t_1) - t_2) <= Inf)
		tmp = (((c * b) - (((4.0 * a) - (z * (y * (18.0 * x)))) * t)) - t_1) - t_2;
	else
		tmp = (-4.0 * (i * x)) - 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[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[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] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], Infinity], N[(N[(N[(N[(c * b), $MachinePrecision] - N[(N[(N[(4.0 * a), $MachinePrecision] - N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(-4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < +inf.0

   1. Initial program 85.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-negate-rev N/A

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

      5. sub-flip-reverse N/A

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

      6. lower--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

   3. Applied rewrites 87.2%

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

   if +inf.0 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k))

   1. Initial program 85.4%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 41.7%

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

   4. Applied rewrites 41.7%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 87.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;b \cdot c \leq 10^{+306}:\\ \;\;\;\;\left(c \cdot b - \left(x \cdot \left(i \cdot 4 - \left(\left(y \cdot 18\right) \cdot t\right) \cdot z\right) - \left(-4 \cdot a\right) \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(-1 \cdot \left(b \cdot c\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (if (<= (* b c) 1e+306)
  (-
   (-
    (* c b)
    (- (* x (- (* i 4.0) (* (* (* y 18.0) t) z))) (* (* -4.0 a) t)))
   (* (* j 27.0) k))
  (* -1.0 (* -1.0 (* 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 ((b * c) <= 1e+306) {
		tmp = ((c * b) - ((x * ((i * 4.0) - (((y * 18.0) * t) * z))) - ((-4.0 * a) * t))) - ((j * 27.0) * k);
	} else {
		tmp = -1.0 * (-1.0 * (b * c));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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 ((b * c) <= 1d+306) then
        tmp = ((c * b) - ((x * ((i * 4.0d0) - (((y * 18.0d0) * t) * z))) - (((-4.0d0) * a) * t))) - ((j * 27.0d0) * k)
    else
        tmp = (-1.0d0) * ((-1.0d0) * (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 ((b * c) <= 1e+306) {
		tmp = ((c * b) - ((x * ((i * 4.0) - (((y * 18.0) * t) * z))) - ((-4.0 * a) * t))) - ((j * 27.0) * k);
	} else {
		tmp = -1.0 * (-1.0 * (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= 1e+306:
		tmp = ((c * b) - ((x * ((i * 4.0) - (((y * 18.0) * t) * z))) - ((-4.0 * a) * t))) - ((j * 27.0) * k)
	else:
		tmp = -1.0 * (-1.0 * (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= 1e+306)
		tmp = Float64(Float64(Float64(c * b) - Float64(Float64(x * Float64(Float64(i * 4.0) - Float64(Float64(Float64(y * 18.0) * t) * z))) - Float64(Float64(-4.0 * a) * t))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(-1.0 * Float64(-1.0 * 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 ((b * c) <= 1e+306)
		tmp = ((c * b) - ((x * ((i * 4.0) - (((y * 18.0) * t) * z))) - ((-4.0 * a) * t))) - ((j * 27.0) * k);
	else
		tmp = -1.0 * (-1.0 * (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], 1e+306], N[(N[(N[(c * b), $MachinePrecision] - N[(N[(x * N[(N[(i * 4.0), $MachinePrecision] - N[(N[(N[(y * 18.0), $MachinePrecision] * t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(-4.0 * a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(-1.0 * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < 1e306

   1. Initial program 85.4%

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

      1. lift--.f64 N/A

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

      2. sub-negate-rev N/A

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

      3. lift-+.f64 N/A

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

      4. associate--r+ N/A

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

      5. sub-negate N/A

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

      6. lower--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. fp-cancel-sub-sign-inv N/A

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

      13. associate--r+ N/A

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

   3. Applied rewrites 86.9%

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

   if 1e306 < (*.f64 b c)

   1. Initial program 85.4%

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

   2. Taylor expanded in k around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(-1 \cdot \frac{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}{k} - -27 \cdot j\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \frac{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}{k} - -27 \cdot j\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(k \cdot \color{blue}{\left(-1 \cdot \frac{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}{k} - -27 \cdot j\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(k \cdot \left(-1 \cdot \frac{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}{k} - \color{blue}{-27 \cdot j}\right)\right) \]

   4. Applied rewrites 75.9%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(-1 \cdot \frac{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}{k} - -27 \cdot j\right)\right)} \]

   5. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 23.5%

         \[\leadsto -1 \cdot \left(-1 \cdot \left(b \cdot c\right)\right) \]

   7. Applied rewrites 23.5%

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{\left(b \cdot c\right)}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 82.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := \left(\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;i \leq -4.3 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 0.00345:\\ \;\;\;\;\left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z - 4 \cdot a\right) \cdot t + c \cdot b\right) - k \cdot \left(27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (let* ((t_1
        (-
         (- (+ (* -4.0 (* a t)) (* b c)) (* (* x 4.0) i))
         (* (* j 27.0) k))))
  (if (<= i -4.3e-27)
    t_1
    (if (<= i 0.00345)
      (-
       (+ (* (- (* (* y (* x 18.0)) z) (* 4.0 a)) t) (* c b))
       (* k (* 27.0 j)))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (((-4.0 * (a * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (i <= -4.3e-27) {
		tmp = t_1;
	} else if (i <= 0.00345) {
		tmp = (((((y * (x * 18.0)) * z) - (4.0 * a)) * t) + (c * b)) - (k * (27.0 * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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 = ((((-4.0d0) * (a * t)) + (b * c)) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
    if (i <= (-4.3d-27)) then
        tmp = t_1
    else if (i <= 0.00345d0) then
        tmp = (((((y * (x * 18.0d0)) * z) - (4.0d0 * a)) * t) + (c * b)) - (k * (27.0d0 * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (((-4.0 * (a * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (i <= -4.3e-27) {
		tmp = t_1;
	} else if (i <= 0.00345) {
		tmp = (((((y * (x * 18.0)) * z) - (4.0 * a)) * t) + (c * b)) - (k * (27.0 * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (((-4.0 * (a * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	tmp = 0
	if i <= -4.3e-27:
		tmp = t_1
	elif i <= 0.00345:
		tmp = (((((y * (x * 18.0)) * z) - (4.0 * a)) * t) + (c * b)) - (k * (27.0 * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (i <= -4.3e-27)
		tmp = t_1;
	elseif (i <= 0.00345)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(y * Float64(x * 18.0)) * z) - Float64(4.0 * a)) * t) + Float64(c * b)) - Float64(k * Float64(27.0 * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (((-4.0 * (a * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	tmp = 0.0;
	if (i <= -4.3e-27)
		tmp = t_1;
	elseif (i <= 0.00345)
		tmp = (((((y * (x * 18.0)) * z) - (4.0 * a)) * t) + (c * b)) - (k * (27.0 * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(-4.0 * N[(a * 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]}, If[LessEqual[i, -4.3e-27], t$95$1, If[LessEqual[i, 0.00345], N[(N[(N[(N[(N[(N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] - N[(4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision] - N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if i < -4.3e-27 or 0.0034499999999999999 < i

   1. Initial program 85.4%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 76.0%

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

   4. Applied rewrites 76.0%

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

   if -4.3e-27 < i < 0.0034499999999999999

   1. Initial program 85.4%

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

   2. Taylor expanded in i around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

   6. Applied rewrites 77.3%

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

Alternative 4: 79.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)\\ \mathbf{if}\;x \leq -2 \cdot 10^{+201}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+198}:\\ \;\;\;\;\left(\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (let* ((t_1 (* -1.0 (* x (- (* -18.0 (* t (* y z))) (* -4.0 i))))))
  (if (<= x -2e+201)
    t_1
    (if (<= x 1.85e+198)
      (-
       (- (+ (* -4.0 (* a t)) (* b c)) (* (* x 4.0) i))
       (* (* j 27.0) k))
      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 = -1.0 * (x * ((-18.0 * (t * (y * z))) - (-4.0 * i)));
	double tmp;
	if (x <= -2e+201) {
		tmp = t_1;
	} else if (x <= 1.85e+198) {
		tmp = (((-4.0 * (a * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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 = (-1.0d0) * (x * (((-18.0d0) * (t * (y * z))) - ((-4.0d0) * i)))
    if (x <= (-2d+201)) then
        tmp = t_1
    else if (x <= 1.85d+198) then
        tmp = ((((-4.0d0) * (a * t)) + (b * c)) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -1.0 * (x * ((-18.0 * (t * (y * z))) - (-4.0 * i)));
	double tmp;
	if (x <= -2e+201) {
		tmp = t_1;
	} else if (x <= 1.85e+198) {
		tmp = (((-4.0 * (a * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -1.0 * (x * ((-18.0 * (t * (y * z))) - (-4.0 * i)))
	tmp = 0
	if x <= -2e+201:
		tmp = t_1
	elif x <= 1.85e+198:
		tmp = (((-4.0 * (a * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-1.0 * Float64(x * Float64(Float64(-18.0 * Float64(t * Float64(y * z))) - Float64(-4.0 * i))))
	tmp = 0.0
	if (x <= -2e+201)
		tmp = t_1;
	elseif (x <= 1.85e+198)
		tmp = Float64(Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -1.0 * (x * ((-18.0 * (t * (y * z))) - (-4.0 * i)));
	tmp = 0.0;
	if (x <= -2e+201)
		tmp = t_1;
	elseif (x <= 1.85e+198)
		tmp = (((-4.0 * (a * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-1.0 * N[(x * N[(N[(-18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2e+201], t$95$1, If[LessEqual[x, 1.85e+198], N[(N[(N[(N[(-4.0 * N[(a * 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], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.0000000000000001e201 or 1.8499999999999999e198 < x

   1. Initial program 85.4%

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

   2. Taylor expanded in k around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(-1 \cdot \frac{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}{k} - -27 \cdot j\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \frac{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}{k} - -27 \cdot j\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(k \cdot \color{blue}{\left(-1 \cdot \frac{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}{k} - -27 \cdot j\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(k \cdot \left(-1 \cdot \frac{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}{k} - \color{blue}{-27 \cdot j}\right)\right) \]

   4. Applied rewrites 75.9%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(-1 \cdot \frac{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}{k} - -27 \cdot j\right)\right)} \]

   5. Taylor expanded in x around -inf

      \[\leadsto -1 \cdot \left(x \cdot \color{blue}{\left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - \color{blue}{-4 \cdot i}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot \color{blue}{i}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right) \]

      6. lower-*.f64 42.6%

         \[\leadsto -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right) \]

   7. Applied rewrites 42.6%

      \[\leadsto -1 \cdot \left(x \cdot \color{blue}{\left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)}\right) \]

   if -2.0000000000000001e201 < x < 1.8499999999999999e198

   1. Initial program 85.4%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 76.0%

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

   4. Applied rewrites 76.0%

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

Alternative 5: 70.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := 27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;i \leq -2.6 \cdot 10^{+66}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) - t\_1\\ \mathbf{elif}\;i \leq -1.25 \cdot 10^{-290}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(a \cdot t\right) + t\_2\right)\\ \mathbf{elif}\;i \leq 0.0062:\\ \;\;\;\;\left(18 \cdot \left(\left(\left(x \cdot t\right) \cdot y\right) \cdot z\right) + b \cdot c\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (let* ((t_1 (* (* j 27.0) k)) (t_2 (* 27.0 (* j k))))
  (if (<= i -2.6e+66)
    (- (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))) t_1)
    (if (<= i -1.25e-290)
      (- (* b c) (+ (* 4.0 (* a t)) t_2))
      (if (<= i 0.0062)
        (- (+ (* 18.0 (* (* (* x t) y) z)) (* b c)) t_2)
        (- (- (* b c) (* (* x 4.0) 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 = (j * 27.0) * k;
	double t_2 = 27.0 * (j * k);
	double tmp;
	if (i <= -2.6e+66) {
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - t_1;
	} else if (i <= -1.25e-290) {
		tmp = (b * c) - ((4.0 * (a * t)) + t_2);
	} else if (i <= 0.0062) {
		tmp = ((18.0 * (((x * t) * y) * z)) + (b * c)) - t_2;
	} else {
		tmp = ((b * c) - ((x * 4.0) * i)) - t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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 = (j * 27.0d0) * k
    t_2 = 27.0d0 * (j * k)
    if (i <= (-2.6d+66)) then
        tmp = (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))) - t_1
    else if (i <= (-1.25d-290)) then
        tmp = (b * c) - ((4.0d0 * (a * t)) + t_2)
    else if (i <= 0.0062d0) then
        tmp = ((18.0d0 * (((x * t) * y) * z)) + (b * c)) - t_2
    else
        tmp = ((b * c) - ((x * 4.0d0) * 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 = (j * 27.0) * k;
	double t_2 = 27.0 * (j * k);
	double tmp;
	if (i <= -2.6e+66) {
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - t_1;
	} else if (i <= -1.25e-290) {
		tmp = (b * c) - ((4.0 * (a * t)) + t_2);
	} else if (i <= 0.0062) {
		tmp = ((18.0 * (((x * t) * y) * z)) + (b * c)) - t_2;
	} else {
		tmp = ((b * c) - ((x * 4.0) * i)) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = 27.0 * (j * k)
	tmp = 0
	if i <= -2.6e+66:
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - t_1
	elif i <= -1.25e-290:
		tmp = (b * c) - ((4.0 * (a * t)) + t_2)
	elif i <= 0.0062:
		tmp = ((18.0 * (((x * t) * y) * z)) + (b * c)) - t_2
	else:
		tmp = ((b * c) - ((x * 4.0) * i)) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(27.0 * Float64(j * k))
	tmp = 0.0
	if (i <= -2.6e+66)
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i))) - t_1);
	elseif (i <= -1.25e-290)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(a * t)) + t_2));
	elseif (i <= 0.0062)
		tmp = Float64(Float64(Float64(18.0 * Float64(Float64(Float64(x * t) * y) * z)) + Float64(b * c)) - t_2);
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(x * 4.0) * i)) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = 27.0 * (j * k);
	tmp = 0.0;
	if (i <= -2.6e+66)
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - t_1;
	elseif (i <= -1.25e-290)
		tmp = (b * c) - ((4.0 * (a * t)) + t_2);
	elseif (i <= 0.0062)
		tmp = ((18.0 * (((x * t) * y) * z)) + (b * c)) - t_2;
	else
		tmp = ((b * c) - ((x * 4.0) * 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[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.6e+66], N[(N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[i, -1.25e-290], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 0.0062], N[(N[(N[(18.0 * N[(N[(N[(x * t), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -2.6000000000000001e66

   1. Initial program 85.4%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 59.4%

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

   4. Applied rewrites 59.4%

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

   if -2.6000000000000001e66 < i < -1.25e-290

   1. Initial program 85.4%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 76.0%

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

   4. Applied rewrites 76.0%

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

   5. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 60.9%

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

   7. Applied rewrites 60.9%

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

   if -1.25e-290 < i < 0.0061999999999999998

   1. Initial program 85.4%

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

   2. Taylor expanded in i around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 74.6%

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

   6. Applied rewrites 74.6%

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

   7. Taylor expanded in t around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 63.2%

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

   9. Applied rewrites 63.2%

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

   if 0.0061999999999999998 < i

   1. Initial program 85.4%

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

   2. Taylor expanded in t around 0

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

      1. lower-*.f64 60.4%

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

   4. Applied rewrites 60.4%

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

Alternative 6: 68.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)\\ t_2 := \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{+198}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-133}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-44}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+197}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (let* ((t_1 (* -1.0 (* x (- (* -18.0 (* t (* y z))) (* -4.0 i)))))
       (t_2 (- (- (* b c) (* (* x 4.0) i)) (* (* j 27.0) k))))
  (if (<= x -1.45e+198)
    t_1
    (if (<= x -5.8e-133)
      t_2
      (if (<= x 3e-44)
        (- (* b c) (+ (* 4.0 (* a t)) (* 27.0 (* j k))))
        (if (<= x 2.35e+197) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -1.0 * (x * ((-18.0 * (t * (y * z))) - (-4.0 * i)));
	double t_2 = ((b * c) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (x <= -1.45e+198) {
		tmp = t_1;
	} else if (x <= -5.8e-133) {
		tmp = t_2;
	} else if (x <= 3e-44) {
		tmp = (b * c) - ((4.0 * (a * t)) + (27.0 * (j * k)));
	} else if (x <= 2.35e+197) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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 = (-1.0d0) * (x * (((-18.0d0) * (t * (y * z))) - ((-4.0d0) * i)))
    t_2 = ((b * c) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
    if (x <= (-1.45d+198)) then
        tmp = t_1
    else if (x <= (-5.8d-133)) then
        tmp = t_2
    else if (x <= 3d-44) then
        tmp = (b * c) - ((4.0d0 * (a * t)) + (27.0d0 * (j * k)))
    else if (x <= 2.35d+197) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -1.0 * (x * ((-18.0 * (t * (y * z))) - (-4.0 * i)));
	double t_2 = ((b * c) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (x <= -1.45e+198) {
		tmp = t_1;
	} else if (x <= -5.8e-133) {
		tmp = t_2;
	} else if (x <= 3e-44) {
		tmp = (b * c) - ((4.0 * (a * t)) + (27.0 * (j * k)));
	} else if (x <= 2.35e+197) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -1.0 * (x * ((-18.0 * (t * (y * z))) - (-4.0 * i)))
	t_2 = ((b * c) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	tmp = 0
	if x <= -1.45e+198:
		tmp = t_1
	elif x <= -5.8e-133:
		tmp = t_2
	elif x <= 3e-44:
		tmp = (b * c) - ((4.0 * (a * t)) + (27.0 * (j * k)))
	elif x <= 2.35e+197:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-1.0 * Float64(x * Float64(Float64(-18.0 * Float64(t * Float64(y * z))) - Float64(-4.0 * i))))
	t_2 = Float64(Float64(Float64(b * c) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (x <= -1.45e+198)
		tmp = t_1;
	elseif (x <= -5.8e-133)
		tmp = t_2;
	elseif (x <= 3e-44)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(a * t)) + Float64(27.0 * Float64(j * k))));
	elseif (x <= 2.35e+197)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -1.0 * (x * ((-18.0 * (t * (y * z))) - (-4.0 * i)));
	t_2 = ((b * c) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	tmp = 0.0;
	if (x <= -1.45e+198)
		tmp = t_1;
	elseif (x <= -5.8e-133)
		tmp = t_2;
	elseif (x <= 3e-44)
		tmp = (b * c) - ((4.0 * (a * t)) + (27.0 * (j * k)));
	elseif (x <= 2.35e+197)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-1.0 * N[(x * N[(N[(-18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * c), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.45e+198], t$95$1, If[LessEqual[x, -5.8e-133], t$95$2, If[LessEqual[x, 3e-44], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.35e+197], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.45e198 or 2.35e197 < x

   1. Initial program 85.4%

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

   2. Taylor expanded in k around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(-1 \cdot \frac{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}{k} - -27 \cdot j\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \frac{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}{k} - -27 \cdot j\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(k \cdot \color{blue}{\left(-1 \cdot \frac{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}{k} - -27 \cdot j\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(k \cdot \left(-1 \cdot \frac{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}{k} - \color{blue}{-27 \cdot j}\right)\right) \]

   4. Applied rewrites 75.9%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(-1 \cdot \frac{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}{k} - -27 \cdot j\right)\right)} \]

   5. Taylor expanded in x around -inf

      \[\leadsto -1 \cdot \left(x \cdot \color{blue}{\left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - \color{blue}{-4 \cdot i}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot \color{blue}{i}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right) \]

      6. lower-*.f64 42.6%

         \[\leadsto -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right) \]

   7. Applied rewrites 42.6%

      \[\leadsto -1 \cdot \left(x \cdot \color{blue}{\left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)}\right) \]

   if -1.45e198 < x < -5.7999999999999997e-133 or 3.0000000000000002e-44 < x < 2.35e197

   1. Initial program 85.4%

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

   2. Taylor expanded in t around 0

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

      1. lower-*.f64 60.4%

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

   4. Applied rewrites 60.4%

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

   if -5.7999999999999997e-133 < x < 3.0000000000000002e-44

   1. Initial program 85.4%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 76.0%

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

   4. Applied rewrites 76.0%

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

   5. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 60.9%

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

   7. Applied rewrites 60.9%

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

Alternative 7: 68.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := 27 \cdot \left(j \cdot k\right)\\ t_2 := \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;i \leq -2.6 \cdot 10^{+66}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -1.25 \cdot 10^{-290}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(a \cdot t\right) + t\_1\right)\\ \mathbf{elif}\;i \leq 0.0062:\\ \;\;\;\;\left(18 \cdot \left(\left(\left(x \cdot t\right) \cdot y\right) \cdot z\right) + b \cdot c\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (let* ((t_1 (* 27.0 (* j k)))
       (t_2 (- (- (* b c) (* (* x 4.0) i)) (* (* j 27.0) k))))
  (if (<= i -2.6e+66)
    t_2
    (if (<= i -1.25e-290)
      (- (* b c) (+ (* 4.0 (* a t)) t_1))
      (if (<= i 0.0062)
        (- (+ (* 18.0 (* (* (* x t) y) z)) (* b c)) 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 = 27.0 * (j * k);
	double t_2 = ((b * c) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (i <= -2.6e+66) {
		tmp = t_2;
	} else if (i <= -1.25e-290) {
		tmp = (b * c) - ((4.0 * (a * t)) + t_1);
	} else if (i <= 0.0062) {
		tmp = ((18.0 * (((x * t) * y) * z)) + (b * c)) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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 = 27.0d0 * (j * k)
    t_2 = ((b * c) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
    if (i <= (-2.6d+66)) then
        tmp = t_2
    else if (i <= (-1.25d-290)) then
        tmp = (b * c) - ((4.0d0 * (a * t)) + t_1)
    else if (i <= 0.0062d0) then
        tmp = ((18.0d0 * (((x * t) * y) * z)) + (b * c)) - 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 = 27.0 * (j * k);
	double t_2 = ((b * c) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (i <= -2.6e+66) {
		tmp = t_2;
	} else if (i <= -1.25e-290) {
		tmp = (b * c) - ((4.0 * (a * t)) + t_1);
	} else if (i <= 0.0062) {
		tmp = ((18.0 * (((x * t) * y) * z)) + (b * c)) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 27.0 * (j * k)
	t_2 = ((b * c) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	tmp = 0
	if i <= -2.6e+66:
		tmp = t_2
	elif i <= -1.25e-290:
		tmp = (b * c) - ((4.0 * (a * t)) + t_1)
	elif i <= 0.0062:
		tmp = ((18.0 * (((x * t) * y) * z)) + (b * c)) - t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(27.0 * Float64(j * k))
	t_2 = Float64(Float64(Float64(b * c) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (i <= -2.6e+66)
		tmp = t_2;
	elseif (i <= -1.25e-290)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(a * t)) + t_1));
	elseif (i <= 0.0062)
		tmp = Float64(Float64(Float64(18.0 * Float64(Float64(Float64(x * t) * y) * z)) + Float64(b * c)) - 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 = 27.0 * (j * k);
	t_2 = ((b * c) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	tmp = 0.0;
	if (i <= -2.6e+66)
		tmp = t_2;
	elseif (i <= -1.25e-290)
		tmp = (b * c) - ((4.0 * (a * t)) + t_1);
	elseif (i <= 0.0062)
		tmp = ((18.0 * (((x * t) * y) * z)) + (b * c)) - 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[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * c), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.6e+66], t$95$2, If[LessEqual[i, -1.25e-290], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 0.0062], N[(N[(N[(18.0 * N[(N[(N[(x * t), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -2.6000000000000001e66 or 0.0061999999999999998 < i

   1. Initial program 85.4%

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

   2. Taylor expanded in t around 0

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

      1. lower-*.f64 60.4%

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

   4. Applied rewrites 60.4%

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

   if -2.6000000000000001e66 < i < -1.25e-290

   1. Initial program 85.4%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 76.0%

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

   4. Applied rewrites 76.0%

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

   5. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 60.9%

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

   7. Applied rewrites 60.9%

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

   if -1.25e-290 < i < 0.0061999999999999998

   1. Initial program 85.4%

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

   2. Taylor expanded in i around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 74.6%

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

   6. Applied rewrites 74.6%

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

   7. Taylor expanded in t around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 63.2%

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

   9. Applied rewrites 63.2%

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

Alternative 8: 68.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} t_1 := \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;i \leq -2.6 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+30}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (let* ((t_1 (- (- (* b c) (* (* x 4.0) i)) (* (* j 27.0) k))))
  (if (<= i -2.6e+66)
    t_1
    (if (<= i 2.5e+30)
      (- (* b c) (+ (* 4.0 (* a t)) (* 27.0 (* j k))))
      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 = ((b * c) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (i <= -2.6e+66) {
		tmp = t_1;
	} else if (i <= 2.5e+30) {
		tmp = (b * c) - ((4.0 * (a * t)) + (27.0 * (j * k)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
    if (i <= (-2.6d+66)) then
        tmp = t_1
    else if (i <= 2.5d+30) then
        tmp = (b * c) - ((4.0d0 * (a * t)) + (27.0d0 * (j * k)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((b * c) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (i <= -2.6e+66) {
		tmp = t_1;
	} else if (i <= 2.5e+30) {
		tmp = (b * c) - ((4.0 * (a * t)) + (27.0 * (j * k)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((b * c) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	tmp = 0
	if i <= -2.6e+66:
		tmp = t_1
	elif i <= 2.5e+30:
		tmp = (b * c) - ((4.0 * (a * t)) + (27.0 * (j * k)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(b * c) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (i <= -2.6e+66)
		tmp = t_1;
	elseif (i <= 2.5e+30)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(a * t)) + Float64(27.0 * Float64(j * k))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((b * c) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	tmp = 0.0;
	if (i <= -2.6e+66)
		tmp = t_1;
	elseif (i <= 2.5e+30)
		tmp = (b * c) - ((4.0 * (a * t)) + (27.0 * (j * k)));
	else
		tmp = t_1;
	end
	tmp_2 = 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[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.6e+66], t$95$1, If[LessEqual[i, 2.5e+30], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if i < -2.6000000000000001e66 or 2.4999999999999999e30 < i

   1. Initial program 85.4%

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

   2. Taylor expanded in t around 0

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

      1. lower-*.f64 60.4%

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

   4. Applied rewrites 60.4%

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

   if -2.6000000000000001e66 < i < 2.4999999999999999e30

   1. Initial program 85.4%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 76.0%

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

   4. Applied rewrites 76.0%

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

   5. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 60.9%

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

   7. Applied rewrites 60.9%

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

Alternative 9: 64.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} t_1 := -4 \cdot \left(i \cdot x\right)\\ \mathbf{if}\;i \leq -1.2 \cdot 10^{+214}:\\ \;\;\;\;t\_1 - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;i \leq 3.3 \cdot 10^{+167}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - \left(k \cdot j\right) \cdot 27\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (let* ((t_1 (* -4.0 (* i x))))
  (if (<= i -1.2e+214)
    (- t_1 (* (* j 27.0) k))
    (if (<= i 3.3e+167)
      (- (* b c) (+ (* 4.0 (* a t)) (* 27.0 (* j k))))
      (- 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 = -4.0 * (i * x);
	double tmp;
	if (i <= -1.2e+214) {
		tmp = t_1 - ((j * 27.0) * k);
	} else if (i <= 3.3e+167) {
		tmp = (b * c) - ((4.0 * (a * t)) + (27.0 * (j * k)));
	} else {
		tmp = t_1 - ((k * j) * 27.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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 = (-4.0d0) * (i * x)
    if (i <= (-1.2d+214)) then
        tmp = t_1 - ((j * 27.0d0) * k)
    else if (i <= 3.3d+167) then
        tmp = (b * c) - ((4.0d0 * (a * t)) + (27.0d0 * (j * k)))
    else
        tmp = t_1 - ((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 = -4.0 * (i * x);
	double tmp;
	if (i <= -1.2e+214) {
		tmp = t_1 - ((j * 27.0) * k);
	} else if (i <= 3.3e+167) {
		tmp = (b * c) - ((4.0 * (a * t)) + (27.0 * (j * k)));
	} else {
		tmp = t_1 - ((k * j) * 27.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (i * x)
	tmp = 0
	if i <= -1.2e+214:
		tmp = t_1 - ((j * 27.0) * k)
	elif i <= 3.3e+167:
		tmp = (b * c) - ((4.0 * (a * t)) + (27.0 * (j * k)))
	else:
		tmp = t_1 - ((k * j) * 27.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(i * x))
	tmp = 0.0
	if (i <= -1.2e+214)
		tmp = Float64(t_1 - Float64(Float64(j * 27.0) * k));
	elseif (i <= 3.3e+167)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(a * t)) + Float64(27.0 * Float64(j * k))));
	else
		tmp = Float64(t_1 - Float64(Float64(k * j) * 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 * (i * x);
	tmp = 0.0;
	if (i <= -1.2e+214)
		tmp = t_1 - ((j * 27.0) * k);
	elseif (i <= 3.3e+167)
		tmp = (b * c) - ((4.0 * (a * t)) + (27.0 * (j * k)));
	else
		tmp = t_1 - ((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[(-4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.2e+214], N[(t$95$1 - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.3e+167], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.2e214

   1. Initial program 85.4%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 41.7%

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

   4. Applied rewrites 41.7%

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

   if -1.2e214 < i < 3.3000000000000002e167

   1. Initial program 85.4%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 76.0%

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

   4. Applied rewrites 76.0%

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

   5. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 60.9%

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

   7. Applied rewrites 60.9%

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

   if 3.3000000000000002e167 < i

   1. Initial program 85.4%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 41.7%

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

   4. Applied rewrites 41.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 41.8%

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 41.8%

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

   6. Applied rewrites 41.8%

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

Alternative 10: 57.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} t_1 := t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-219}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-83}:\\ \;\;\;\;-4 \cdot \left(i \cdot x\right) - \left(k \cdot j\right) \cdot 27\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (let* ((t_1 (* t (+ (* -4.0 a) (* 18.0 (* x (* y z)))))))
  (if (<= t -5.5e+104)
    t_1
    (if (<= t -1.4e-219)
      (- (* b c) (* 27.0 (* j k)))
      (if (<= t 5.8e-83) (- (* -4.0 (* i x)) (* (* k j) 27.0)) 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 = t * ((-4.0 * a) + (18.0 * (x * (y * z))));
	double tmp;
	if (t <= -5.5e+104) {
		tmp = t_1;
	} else if (t <= -1.4e-219) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t <= 5.8e-83) {
		tmp = (-4.0 * (i * x)) - ((k * j) * 27.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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 * (((-4.0d0) * a) + (18.0d0 * (x * (y * z))))
    if (t <= (-5.5d+104)) then
        tmp = t_1
    else if (t <= (-1.4d-219)) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (t <= 5.8d-83) then
        tmp = ((-4.0d0) * (i * x)) - ((k * j) * 27.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((-4.0 * a) + (18.0 * (x * (y * z))));
	double tmp;
	if (t <= -5.5e+104) {
		tmp = t_1;
	} else if (t <= -1.4e-219) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t <= 5.8e-83) {
		tmp = (-4.0 * (i * x)) - ((k * j) * 27.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * ((-4.0 * a) + (18.0 * (x * (y * z))))
	tmp = 0
	if t <= -5.5e+104:
		tmp = t_1
	elif t <= -1.4e-219:
		tmp = (b * c) - (27.0 * (j * k))
	elif t <= 5.8e-83:
		tmp = (-4.0 * (i * x)) - ((k * j) * 27.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(Float64(-4.0 * a) + Float64(18.0 * Float64(x * Float64(y * z)))))
	tmp = 0.0
	if (t <= -5.5e+104)
		tmp = t_1;
	elseif (t <= -1.4e-219)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (t <= 5.8e-83)
		tmp = Float64(Float64(-4.0 * Float64(i * x)) - Float64(Float64(k * j) * 27.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * ((-4.0 * a) + (18.0 * (x * (y * z))));
	tmp = 0.0;
	if (t <= -5.5e+104)
		tmp = t_1;
	elseif (t <= -1.4e-219)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (t <= 5.8e-83)
		tmp = (-4.0 * (i * x)) - ((k * j) * 27.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(N[(-4.0 * a), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.5e+104], t$95$1, If[LessEqual[t, -1.4e-219], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e-83], N[(N[(-4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision] - N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.5000000000000002e104 or 5.7999999999999998e-83 < t

   1. Initial program 85.4%

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

   2. Taylor expanded in i around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. fp-cancel-sign-sub-inv N/A

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

      7. lower--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 N/A

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

      13. lower-*.f64 73.9%

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 73.9%

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

      17. lift-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lift-*.f64 73.9%

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

   6. Applied rewrites 73.9%

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

   7. Taylor expanded in t around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 42.9%

         \[\leadsto t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

   9. Applied rewrites 42.9%

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

   if -5.5000000000000002e104 < t < -1.4e-219

   1. Initial program 85.4%

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

   2. Taylor expanded in i around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

   5. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 44.2%

         \[\leadsto b \cdot c - 27 \cdot \left(j \cdot k\right) \]

   7. Applied rewrites 44.2%

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

   if -1.4e-219 < t < 5.7999999999999998e-83

   1. Initial program 85.4%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 41.7%

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

   4. Applied rewrites 41.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 41.8%

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 41.8%

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

   6. Applied rewrites 41.8%

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

Alternative 11: 51.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} t_1 := -4 \cdot \left(i \cdot x\right)\\ \mathbf{if}\;i \leq -2.6 \cdot 10^{+66}:\\ \;\;\;\;t\_1 - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{+26}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - \left(k \cdot j\right) \cdot 27\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (let* ((t_1 (* -4.0 (* i x))))
  (if (<= i -2.6e+66)
    (- t_1 (* (* j 27.0) k))
    (if (<= i 1.65e+26)
      (- (* b c) (* 27.0 (* j k)))
      (- 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 = -4.0 * (i * x);
	double tmp;
	if (i <= -2.6e+66) {
		tmp = t_1 - ((j * 27.0) * k);
	} else if (i <= 1.65e+26) {
		tmp = (b * c) - (27.0 * (j * k));
	} else {
		tmp = t_1 - ((k * j) * 27.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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 = (-4.0d0) * (i * x)
    if (i <= (-2.6d+66)) then
        tmp = t_1 - ((j * 27.0d0) * k)
    else if (i <= 1.65d+26) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else
        tmp = t_1 - ((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 = -4.0 * (i * x);
	double tmp;
	if (i <= -2.6e+66) {
		tmp = t_1 - ((j * 27.0) * k);
	} else if (i <= 1.65e+26) {
		tmp = (b * c) - (27.0 * (j * k));
	} else {
		tmp = t_1 - ((k * j) * 27.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (i * x)
	tmp = 0
	if i <= -2.6e+66:
		tmp = t_1 - ((j * 27.0) * k)
	elif i <= 1.65e+26:
		tmp = (b * c) - (27.0 * (j * k))
	else:
		tmp = t_1 - ((k * j) * 27.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(i * x))
	tmp = 0.0
	if (i <= -2.6e+66)
		tmp = Float64(t_1 - Float64(Float64(j * 27.0) * k));
	elseif (i <= 1.65e+26)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	else
		tmp = Float64(t_1 - Float64(Float64(k * j) * 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 * (i * x);
	tmp = 0.0;
	if (i <= -2.6e+66)
		tmp = t_1 - ((j * 27.0) * k);
	elseif (i <= 1.65e+26)
		tmp = (b * c) - (27.0 * (j * k));
	else
		tmp = t_1 - ((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[(-4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.6e+66], N[(t$95$1 - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.65e+26], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if i < -2.6000000000000001e66

   1. Initial program 85.4%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 41.7%

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

   4. Applied rewrites 41.7%

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

   if -2.6000000000000001e66 < i < 1.65e26

   1. Initial program 85.4%

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

   2. Taylor expanded in i around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

   5. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 44.2%

         \[\leadsto b \cdot c - 27 \cdot \left(j \cdot k\right) \]

   7. Applied rewrites 44.2%

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

   if 1.65e26 < i

   1. Initial program 85.4%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 41.7%

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

   4. Applied rewrites 41.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 41.8%

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 41.8%

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

   6. Applied rewrites 41.8%

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

Alternative 12: 51.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} t_1 := -4 \cdot \left(i \cdot x\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;i \leq -2.6 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{+26}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (let* ((t_1 (- (* -4.0 (* i x)) (* (* j 27.0) k))))
  (if (<= i -2.6e+66)
    t_1
    (if (<= i 1.65e+26) (- (* b c) (* 27.0 (* j k))) 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 = (-4.0 * (i * x)) - ((j * 27.0) * k);
	double tmp;
	if (i <= -2.6e+66) {
		tmp = t_1;
	} else if (i <= 1.65e+26) {
		tmp = (b * c) - (27.0 * (j * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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 = ((-4.0d0) * (i * x)) - ((j * 27.0d0) * k)
    if (i <= (-2.6d+66)) then
        tmp = t_1
    else if (i <= 1.65d+26) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (-4.0 * (i * x)) - ((j * 27.0) * k);
	double tmp;
	if (i <= -2.6e+66) {
		tmp = t_1;
	} else if (i <= 1.65e+26) {
		tmp = (b * c) - (27.0 * (j * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (-4.0 * (i * x)) - ((j * 27.0) * k)
	tmp = 0
	if i <= -2.6e+66:
		tmp = t_1
	elif i <= 1.65e+26:
		tmp = (b * c) - (27.0 * (j * k))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(-4.0 * Float64(i * x)) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (i <= -2.6e+66)
		tmp = t_1;
	elseif (i <= 1.65e+26)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (-4.0 * (i * x)) - ((j * 27.0) * k);
	tmp = 0.0;
	if (i <= -2.6e+66)
		tmp = t_1;
	elseif (i <= 1.65e+26)
		tmp = (b * c) - (27.0 * (j * k));
	else
		tmp = t_1;
	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[(i * x), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.6e+66], t$95$1, If[LessEqual[i, 1.65e+26], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if i < -2.6000000000000001e66 or 1.65e26 < i

   1. Initial program 85.4%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 41.7%

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

   4. Applied rewrites 41.7%

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

   if -2.6000000000000001e66 < i < 1.65e26

   1. Initial program 85.4%

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

   2. Taylor expanded in i around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

   5. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 44.2%

         \[\leadsto b \cdot c - 27 \cdot \left(j \cdot k\right) \]

   7. Applied rewrites 44.2%

      \[\leadsto b \cdot c - \color{blue}{27 \cdot \left(j \cdot k\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 48.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+221}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+140}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (let* ((t_1 (* -4.0 (* a t))))
  (if (<= a -1.8e+221)
    t_1
    (if (<= a 6.4e+140) (- (* b c) (* 27.0 (* j k))) 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 = -4.0 * (a * t);
	double tmp;
	if (a <= -1.8e+221) {
		tmp = t_1;
	} else if (a <= 6.4e+140) {
		tmp = (b * c) - (27.0 * (j * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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 = (-4.0d0) * (a * t)
    if (a <= (-1.8d+221)) then
        tmp = t_1
    else if (a <= 6.4d+140) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (a * t);
	double tmp;
	if (a <= -1.8e+221) {
		tmp = t_1;
	} else if (a <= 6.4e+140) {
		tmp = (b * c) - (27.0 * (j * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (a * t)
	tmp = 0
	if a <= -1.8e+221:
		tmp = t_1
	elif a <= 6.4e+140:
		tmp = (b * c) - (27.0 * (j * k))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(a * t))
	tmp = 0.0
	if (a <= -1.8e+221)
		tmp = t_1;
	elseif (a <= 6.4e+140)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (a * t);
	tmp = 0.0;
	if (a <= -1.8e+221)
		tmp = t_1;
	elseif (a <= 6.4e+140)
		tmp = (b * c) - (27.0 * (j * k));
	else
		tmp = t_1;
	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[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8e+221], t$95$1, If[LessEqual[a, 6.4e+140], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.8e221 or 6.4000000000000002e140 < a

   1. Initial program 85.4%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 76.0%

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

   4. Applied rewrites 76.0%

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

   5. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 60.9%

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

   7. Applied rewrites 60.9%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 21.5%

         \[\leadsto -4 \cdot \left(a \cdot t\right) \]

   10. Applied rewrites 21.5%

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

   if -1.8e221 < a < 6.4000000000000002e140

   1. Initial program 85.4%

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

   2. Taylor expanded in i around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 74.0%

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

   4. Applied rewrites 74.0%

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

   5. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 44.2%

         \[\leadsto b \cdot c - 27 \cdot \left(j \cdot k\right) \]

   7. Applied rewrites 44.2%

      \[\leadsto b \cdot c - \color{blue}{27 \cdot \left(j \cdot k\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 35.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-61}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+73}:\\ \;\;\;\;-1 \cdot \left(-1 \cdot \left(b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (let* ((t_1 (* -27.0 (* j k))) (t_2 (* (* j 27.0) k)))
  (if (<= t_2 -4e+207)
    t_1
    (if (<= t_2 -2e-61)
      (* -4.0 (* a t))
      (if (<= t_2 2e+73) (* -1.0 (* -1.0 (* 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 = -27.0 * (j * k);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -4e+207) {
		tmp = t_1;
	} else if (t_2 <= -2e-61) {
		tmp = -4.0 * (a * t);
	} else if (t_2 <= 2e+73) {
		tmp = -1.0 * (-1.0 * (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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 = (-27.0d0) * (j * k)
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-4d+207)) then
        tmp = t_1
    else if (t_2 <= (-2d-61)) then
        tmp = (-4.0d0) * (a * t)
    else if (t_2 <= 2d+73) then
        tmp = (-1.0d0) * ((-1.0d0) * (b * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -4e+207) {
		tmp = t_1;
	} else if (t_2 <= -2e-61) {
		tmp = -4.0 * (a * t);
	} else if (t_2 <= 2e+73) {
		tmp = -1.0 * (-1.0 * (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (j * k)
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -4e+207:
		tmp = t_1
	elif t_2 <= -2e-61:
		tmp = -4.0 * (a * t)
	elif t_2 <= 2e+73:
		tmp = -1.0 * (-1.0 * (b * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(j * k))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -4e+207)
		tmp = t_1;
	elseif (t_2 <= -2e-61)
		tmp = Float64(-4.0 * Float64(a * t));
	elseif (t_2 <= 2e+73)
		tmp = Float64(-1.0 * Float64(-1.0 * Float64(b * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (j * k);
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -4e+207)
		tmp = t_1;
	elseif (t_2 <= -2e-61)
		tmp = -4.0 * (a * t);
	elseif (t_2 <= 2e+73)
		tmp = -1.0 * (-1.0 * (b * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+207], t$95$1, If[LessEqual[t$95$2, -2e-61], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+73], N[(-1.0 * N[(-1.0 * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.0000000000000002e207 or 2e73 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.4%

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

   2. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 24.3%

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

   4. Applied rewrites 24.3%

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

   if -4.0000000000000002e207 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.0000000000000001e-61

   1. Initial program 85.4%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 76.0%

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

   4. Applied rewrites 76.0%

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

   5. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 60.9%

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

   7. Applied rewrites 60.9%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 21.5%

         \[\leadsto -4 \cdot \left(a \cdot t\right) \]

   10. Applied rewrites 21.5%

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

   if -2.0000000000000001e-61 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2e73

   1. Initial program 85.4%

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

   2. Taylor expanded in k around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(-1 \cdot \frac{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}{k} - -27 \cdot j\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \frac{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}{k} - -27 \cdot j\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(k \cdot \color{blue}{\left(-1 \cdot \frac{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}{k} - -27 \cdot j\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(k \cdot \left(-1 \cdot \frac{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}{k} - \color{blue}{-27 \cdot j}\right)\right) \]

   4. Applied rewrites 75.9%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(-1 \cdot \frac{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}{k} - -27 \cdot j\right)\right)} \]

   5. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 23.5%

         \[\leadsto -1 \cdot \left(-1 \cdot \left(b \cdot c\right)\right) \]

   7. Applied rewrites 23.5%

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{\left(b \cdot c\right)}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 34.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+73}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
  :precision binary64
  (let* ((t_1 (* -27.0 (* j k))) (t_2 (* (* j 27.0) k)))
  (if (<= t_2 -4e+207) t_1 (if (<= t_2 2e+73) (* -4.0 (* a t)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -4e+207) {
		tmp = t_1;
	} else if (t_2 <= 2e+73) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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 = (-27.0d0) * (j * k)
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-4d+207)) then
        tmp = t_1
    else if (t_2 <= 2d+73) then
        tmp = (-4.0d0) * (a * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -4e+207) {
		tmp = t_1;
	} else if (t_2 <= 2e+73) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (j * k)
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -4e+207:
		tmp = t_1
	elif t_2 <= 2e+73:
		tmp = -4.0 * (a * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(j * k))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -4e+207)
		tmp = t_1;
	elseif (t_2 <= 2e+73)
		tmp = Float64(-4.0 * Float64(a * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (j * k);
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -4e+207)
		tmp = t_1;
	elseif (t_2 <= 2e+73)
		tmp = -4.0 * (a * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+207], t$95$1, If[LessEqual[t$95$2, 2e+73], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.0000000000000002e207 or 2e73 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.4%

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

   2. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 24.3%

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

   4. Applied rewrites 24.3%

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

   if -4.0000000000000002e207 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2e73

   1. Initial program 85.4%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 76.0%

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

   4. Applied rewrites 76.0%

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

   5. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 60.9%

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

   7. Applied rewrites 60.9%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 21.5%

         \[\leadsto -4 \cdot \left(a \cdot t\right) \]

   10. Applied rewrites 21.5%

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

Alternative 16: 21.5% accurate, 6.2× speedup

Math

\[-4 \cdot \left(a \cdot t\right) \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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 = (-4.0d0) * (a * t)
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 -4.0 * (a * t);
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 85.4%

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

2. Taylor expanded in x around 0

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

   1. lower-*.f64 N/A

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

   2. lower-*.f64 76.0%

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

4. Applied rewrites 76.0%

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

5. Taylor expanded in x around 0

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

   1. lower--.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower-+.f64 N/A

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

   4. lower-*.f64 N/A

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

   5. lower-*.f64 N/A

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

   6. lower-*.f64 N/A

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

   7. lower-*.f64 60.9%

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

7. Applied rewrites 60.9%

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

8. Taylor expanded in t around inf

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

   1. lower-*.f64 N/A

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

   2. lower-*.f64 21.5%

      \[\leadsto -4 \cdot \left(a \cdot t\right) \]

10. Applied rewrites 21.5%

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

Reproduce

herbie shell --seed 2025258 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64
  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))