Data.Colour.Matrix:determinant from colour-2.3.3, A

Percentage Accurate: 73.0% → 81.2%

Time: 6.2s

Alternatives: 17

Speedup: 0.5×

• 58.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = ((z * y) - (a * t)) * x;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.1%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 41.2

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

   4. Applied rewrites 41.2%

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

Alternative 2: 68.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b\\ \mathbf{if}\;j \leq -1.04 \cdot 10^{-85}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x + t\_1\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{-81}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(-t, x, j \cdot c\right) \cdot a\\ \mathbf{elif}\;j \leq 10^{+81}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2 (- (* (- (* z y) (* a t)) x) (* (- (* c z) (* i t)) b))))
   (if (<= j -1.04e-85)
     (+ (* (* z y) x) t_1)
     (if (<= j 3.7e-81)
       t_2
       (if (<= j 2.2e-5)
         (* (fma (- t) x (* j c)) a)
         (if (<= j 1e+81) t_2 (+ (* (- a) (* t x)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = (((z * y) - (a * t)) * x) - (((c * z) - (i * t)) * b);
	double tmp;
	if (j <= -1.04e-85) {
		tmp = ((z * y) * x) + t_1;
	} else if (j <= 3.7e-81) {
		tmp = t_2;
	} else if (j <= 2.2e-5) {
		tmp = fma(-t, x, (j * c)) * a;
	} else if (j <= 1e+81) {
		tmp = t_2;
	} else {
		tmp = (-a * (t * x)) + t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(Float64(z * y) - Float64(a * t)) * x) - Float64(Float64(Float64(c * z) - Float64(i * t)) * b))
	tmp = 0.0
	if (j <= -1.04e-85)
		tmp = Float64(Float64(Float64(z * y) * x) + t_1);
	elseif (j <= 3.7e-81)
		tmp = t_2;
	elseif (j <= 2.2e-5)
		tmp = Float64(fma(Float64(-t), x, Float64(j * c)) * a);
	elseif (j <= 1e+81)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(-a) * Float64(t * x)) + t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] - N[(N[(N[(c * z), $MachinePrecision] - N[(i * t), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.04e-85], N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[j, 3.7e-81], t$95$2, If[LessEqual[j, 2.2e-5], N[(N[((-t) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[j, 1e+81], t$95$2, N[(N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.04e-85

   1. Initial program 73.4%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

         \[\leadsto \left(z \cdot y\right) \cdot x + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. lower-*.f64 57.2

         \[\leadsto \left(z \cdot y\right) \cdot x + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied rewrites 57.2%

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

   if -1.04e-85 < j < 3.69999999999999986e-81 or 2.1999999999999999e-5 < j < 9.99999999999999921e80

   1. Initial program 72.3%

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

   2. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

         \[\leadsto \left(y \cdot z - t \cdot a\right) \cdot x - b \cdot \left(c \cdot z - i \cdot t\right) \]

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

         \[\leadsto \left(y \cdot z - t \cdot a\right) \cdot x - b \cdot \left(c \cdot z - i \cdot t\right) \]

      6. *-commutative N/A

         \[\leadsto \left(z \cdot y - t \cdot a\right) \cdot x - b \cdot \left(c \cdot z - i \cdot t\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \left(z \cdot y - t \cdot a\right) \cdot x - b \cdot \left(c \cdot z - i \cdot t\right) \]

      8. *-commutative N/A

         \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - b \cdot \left(c \cdot z - i \cdot t\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - b \cdot \left(c \cdot z - i \cdot t\right) \]

      10. *-commutative N/A

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

      11. *-commutative N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - t \cdot i\right) \cdot b \]

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - t \cdot i\right) \cdot b \]

      14. lift-*.f64 N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - t \cdot i\right) \cdot b \]

      15. *-commutative N/A

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b \]

      16. lower-*.f64 71.4

          \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b \]

   4. Applied rewrites 71.4%

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

   if 3.69999999999999986e-81 < j < 2.1999999999999999e-5

   1. Initial program 79.2%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 35.8

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

   4. Applied rewrites 35.8%

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

   if 9.99999999999999921e80 < j

   1. Initial program 71.9%

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

   2. Taylor expanded in a around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-*.f64 67.2

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

   4. Applied rewrites 67.2%

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

Alternative 3: 66.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+108}:\\ \;\;\;\;\left(y \cdot x - c \cdot b\right) \cdot z\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+123}:\\ \;\;\;\;\left(-t\right) \cdot \left(a \cdot x - i \cdot b\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(\left(\frac{\left(-a\right) \cdot t}{y} + z\right) \cdot y\right) - b \cdot \left(c \cdot z\right)\right) + j \cdot \left(c \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -1.55e+108)
   (* (- (* y x) (* c b)) z)
   (if (<= z 4.1e+123)
     (+ (* (- t) (- (* a x) (* i b))) (* j (- (* c a) (* y i))))
     (+ (- (* x (* (+ (/ (* (- a) t) y) z) y)) (* b (* c z))) (* j (* c a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.55e+108) {
		tmp = ((y * x) - (c * b)) * z;
	} else if (z <= 4.1e+123) {
		tmp = (-t * ((a * x) - (i * b))) + (j * ((c * a) - (y * i)));
	} else {
		tmp = ((x * ((((-a * t) / y) + z) * y)) - (b * (c * z))) + (j * (c * a));
	}
	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)
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) :: tmp
    if (z <= (-1.55d+108)) then
        tmp = ((y * x) - (c * b)) * z
    else if (z <= 4.1d+123) then
        tmp = (-t * ((a * x) - (i * b))) + (j * ((c * a) - (y * i)))
    else
        tmp = ((x * ((((-a * t) / y) + z) * y)) - (b * (c * z))) + (j * (c * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.55e+108) {
		tmp = ((y * x) - (c * b)) * z;
	} else if (z <= 4.1e+123) {
		tmp = (-t * ((a * x) - (i * b))) + (j * ((c * a) - (y * i)));
	} else {
		tmp = ((x * ((((-a * t) / y) + z) * y)) - (b * (c * z))) + (j * (c * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -1.55e+108:
		tmp = ((y * x) - (c * b)) * z
	elif z <= 4.1e+123:
		tmp = (-t * ((a * x) - (i * b))) + (j * ((c * a) - (y * i)))
	else:
		tmp = ((x * ((((-a * t) / y) + z) * y)) - (b * (c * z))) + (j * (c * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -1.55e+108)
		tmp = Float64(Float64(Float64(y * x) - Float64(c * b)) * z);
	elseif (z <= 4.1e+123)
		tmp = Float64(Float64(Float64(-t) * Float64(Float64(a * x) - Float64(i * b))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))));
	else
		tmp = Float64(Float64(Float64(x * Float64(Float64(Float64(Float64(Float64(-a) * t) / y) + z) * y)) - Float64(b * Float64(c * z))) + Float64(j * Float64(c * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -1.55e+108)
		tmp = ((y * x) - (c * b)) * z;
	elseif (z <= 4.1e+123)
		tmp = (-t * ((a * x) - (i * b))) + (j * ((c * a) - (y * i)));
	else
		tmp = ((x * ((((-a * t) / y) + z) * y)) - (b * (c * z))) + (j * (c * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -1.55e+108], N[(N[(N[(y * x), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 4.1e+123], N[(N[((-t) * N[(N[(a * x), $MachinePrecision] - N[(i * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * N[(N[(N[(N[((-a) * t), $MachinePrecision] / y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] - N[(b * N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5500000000000001e108

   1. Initial program 60.0%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 66.4

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

   4. Applied rewrites 66.4%

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

   if -1.5500000000000001e108 < z < 4.09999999999999989e123

   1. Initial program 78.6%

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

   2. Taylor expanded in t around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 65.9

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

   4. Applied rewrites 65.9%

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

   if 4.09999999999999989e123 < z

   1. Initial program 61.3%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 59.2

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

   4. Applied rewrites 59.2%

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

   5. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lift-*.f64 60.0

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

   7. Applied rewrites 60.0%

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

   8. Taylor expanded in z around inf

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

      1. lift-*.f64 58.0

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

   10. Applied rewrites 58.0%

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

Alternative 4: 64.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((c * z) - (t * i));
	tmp = 0.0;
	if ((((x * ((y * z) - (t * a))) - t_1) + (j * ((c * a) - (y * i)))) <= Inf)
		tmp = ((x * ((((-a * t) / y) + z) * y)) - t_1) + (j * (c * a));
	else
		tmp = ((z * y) - (a * t)) * x;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.1%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 86.9

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

   4. Applied rewrites 86.9%

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

   5. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lift-*.f64 75.4

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

   7. Applied rewrites 75.4%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 41.2

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

   4. Applied rewrites 41.2%

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

Alternative 5: 63.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot x - c \cdot b\right) \cdot z\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+124}:\\ \;\;\;\;\left(-t\right) \cdot \left(a \cdot x - i \cdot b\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- (* y x) (* c b)) z)))
   (if (<= z -1.55e+108)
     t_1
     (if (<= z 1.35e+124)
       (+ (* (- t) (- (* a x) (* i b))) (* j (- (* c a) (* y i))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((y * x) - (c * b)) * z;
	double tmp;
	if (z <= -1.55e+108) {
		tmp = t_1;
	} else if (z <= 1.35e+124) {
		tmp = (-t * ((a * x) - (i * b))) + (j * ((c * a) - (y * i)));
	} 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)
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) :: t_1
    real(8) :: tmp
    t_1 = ((y * x) - (c * b)) * z
    if (z <= (-1.55d+108)) then
        tmp = t_1
    else if (z <= 1.35d+124) then
        tmp = (-t * ((a * x) - (i * b))) + (j * ((c * a) - (y * i)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((y * x) - (c * b)) * z;
	double tmp;
	if (z <= -1.55e+108) {
		tmp = t_1;
	} else if (z <= 1.35e+124) {
		tmp = (-t * ((a * x) - (i * b))) + (j * ((c * a) - (y * i)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((y * x) - (c * b)) * z
	tmp = 0
	if z <= -1.55e+108:
		tmp = t_1
	elif z <= 1.35e+124:
		tmp = (-t * ((a * x) - (i * b))) + (j * ((c * a) - (y * i)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(y * x) - Float64(c * b)) * z)
	tmp = 0.0
	if (z <= -1.55e+108)
		tmp = t_1;
	elseif (z <= 1.35e+124)
		tmp = Float64(Float64(Float64(-t) * Float64(Float64(a * x) - Float64(i * b))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((y * x) - (c * b)) * z;
	tmp = 0.0;
	if (z <= -1.55e+108)
		tmp = t_1;
	elseif (z <= 1.35e+124)
		tmp = (-t * ((a * x) - (i * b))) + (j * ((c * a) - (y * i)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(y * x), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -1.55e+108], t$95$1, If[LessEqual[z, 1.35e+124], N[(N[((-t) * N[(N[(a * x), $MachinePrecision] - N[(i * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5500000000000001e108 or 1.34999999999999989e124 < z

   1. Initial program 60.6%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 67.9

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

   4. Applied rewrites 67.9%

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

   if -1.5500000000000001e108 < z < 1.34999999999999989e124

   1. Initial program 78.6%

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

   2. Taylor expanded in t around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 65.9

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

   4. Applied rewrites 65.9%

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

Alternative 6: 58.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -7.2 \cdot 10^{-25}:\\ \;\;\;\;\left(j \cdot a - b \cdot z\right) \cdot c\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{-48}:\\ \;\;\;\;\left(-t\right) \cdot \left(a \cdot x - i \cdot b\right) + j \cdot \left(\left(-i\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x + j \cdot \left(c \cdot a - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -7.2e-25)
   (* (- (* j a) (* b z)) c)
   (if (<= c 2.05e-48)
     (+ (* (- t) (- (* a x) (* i b))) (* j (* (- i) y)))
     (+ (* (* z y) x) (* j (- (* c a) (* y i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -7.2e-25) {
		tmp = ((j * a) - (b * z)) * c;
	} else if (c <= 2.05e-48) {
		tmp = (-t * ((a * x) - (i * b))) + (j * (-i * y));
	} else {
		tmp = ((z * y) * x) + (j * ((c * a) - (y * i)));
	}
	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)
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) :: tmp
    if (c <= (-7.2d-25)) then
        tmp = ((j * a) - (b * z)) * c
    else if (c <= 2.05d-48) then
        tmp = (-t * ((a * x) - (i * b))) + (j * (-i * y))
    else
        tmp = ((z * y) * x) + (j * ((c * a) - (y * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -7.2e-25) {
		tmp = ((j * a) - (b * z)) * c;
	} else if (c <= 2.05e-48) {
		tmp = (-t * ((a * x) - (i * b))) + (j * (-i * y));
	} else {
		tmp = ((z * y) * x) + (j * ((c * a) - (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -7.2e-25:
		tmp = ((j * a) - (b * z)) * c
	elif c <= 2.05e-48:
		tmp = (-t * ((a * x) - (i * b))) + (j * (-i * y))
	else:
		tmp = ((z * y) * x) + (j * ((c * a) - (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -7.2e-25)
		tmp = Float64(Float64(Float64(j * a) - Float64(b * z)) * c);
	elseif (c <= 2.05e-48)
		tmp = Float64(Float64(Float64(-t) * Float64(Float64(a * x) - Float64(i * b))) + Float64(j * Float64(Float64(-i) * y)));
	else
		tmp = Float64(Float64(Float64(z * y) * x) + Float64(j * Float64(Float64(c * a) - Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -7.2e-25)
		tmp = ((j * a) - (b * z)) * c;
	elseif (c <= 2.05e-48)
		tmp = (-t * ((a * x) - (i * b))) + (j * (-i * y));
	else
		tmp = ((z * y) * x) + (j * ((c * a) - (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -7.2e-25], N[(N[(N[(j * a), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[c, 2.05e-48], N[(N[((-t) * N[(N[(a * x), $MachinePrecision] - N[(i * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[((-i) * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -7.1999999999999998e-25

   1. Initial program 66.9%

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

   2. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto \left(a \cdot j - b \cdot z\right) \cdot c \]

      4. *-commutative N/A

         \[\leadsto \left(j \cdot a - b \cdot z\right) \cdot c \]

      5. lower-*.f64 N/A

         \[\leadsto \left(j \cdot a - b \cdot z\right) \cdot c \]

      6. lower-*.f64 57.7

         \[\leadsto \left(j \cdot a - b \cdot z\right) \cdot c \]

   4. Applied rewrites 57.7%

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

   if -7.1999999999999998e-25 < c < 2.05000000000000007e-48

   1. Initial program 80.9%

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

   2. Taylor expanded in t around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 64.8

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

   4. Applied rewrites 64.8%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 60.3

         \[\leadsto \left(-t\right) \cdot \left(a \cdot x - i \cdot b\right) + j \cdot \left(\left(-i\right) \cdot y\right) \]

   7. Applied rewrites 60.3%

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

   if 2.05000000000000007e-48 < c

   1. Initial program 66.5%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

         \[\leadsto \left(z \cdot y\right) \cdot x + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. lower-*.f64 49.6

         \[\leadsto \left(z \cdot y\right) \cdot x + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied rewrites 49.6%

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

Alternative 7: 56.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-t\right) \cdot \left(\left(-a\right) \cdot \mathsf{fma}\left(b, \frac{i}{a}, -x\right)\right)\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+96}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- t) (* (- a) (fma b (/ i a) (- x))))))
   (if (<= t -4.6e+142)
     t_1
     (if (<= t 4.1e+96) (+ (* (* z y) x) (* j (- (* c a) (* y i)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -t * (-a * fma(b, (i / a), -x));
	double tmp;
	if (t <= -4.6e+142) {
		tmp = t_1;
	} else if (t <= 4.1e+96) {
		tmp = ((z * y) * x) + (j * ((c * a) - (y * i)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(-t) * Float64(Float64(-a) * fma(b, Float64(i / a), Float64(-x))))
	tmp = 0.0
	if (t <= -4.6e+142)
		tmp = t_1;
	elseif (t <= 4.1e+96)
		tmp = Float64(Float64(Float64(z * y) * x) + Float64(j * Float64(Float64(c * a) - Float64(y * i))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-t) * N[((-a) * N[(b * N[(i / a), $MachinePrecision] + (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.6e+142], t$95$1, If[LessEqual[t, 4.1e+96], N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.60000000000000004e142 or 4.09999999999999998e96 < t

   1. Initial program 60.7%

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

   2. Taylor expanded in t around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 68.5

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

   4. Applied rewrites 68.5%

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

   5. Taylor expanded in a around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lift-neg.f64 N/A

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-neg.f64 68.1

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

   7. Applied rewrites 68.1%

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

   if -4.60000000000000004e142 < t < 4.09999999999999998e96

   1. Initial program 78.4%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

         \[\leadsto \left(z \cdot y\right) \cdot x + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. lower-*.f64 54.7

         \[\leadsto \left(z \cdot y\right) \cdot x + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied rewrites 54.7%

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

Alternative 8: 51.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot y - a \cdot t\right) \cdot x\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-152}:\\ \;\;\;\;\left(-i\right) \cdot \left(j \cdot y - b \cdot t\right)\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+52}:\\ \;\;\;\;\left(j \cdot a - b \cdot z\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- (* z y) (* a t)) x)))
   (if (<= x -1.35e+132)
     t_1
     (if (<= x -4.9e-152)
       (* (- i) (- (* j y) (* b t)))
       (if (<= x 4.1e+52) (* (- (* j a) (* b z)) c) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((z * y) - (a * t)) * x;
	double tmp;
	if (x <= -1.35e+132) {
		tmp = t_1;
	} else if (x <= -4.9e-152) {
		tmp = -i * ((j * y) - (b * t));
	} else if (x <= 4.1e+52) {
		tmp = ((j * a) - (b * z)) * 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)
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) :: t_1
    real(8) :: tmp
    t_1 = ((z * y) - (a * t)) * x
    if (x <= (-1.35d+132)) then
        tmp = t_1
    else if (x <= (-4.9d-152)) then
        tmp = -i * ((j * y) - (b * t))
    else if (x <= 4.1d+52) then
        tmp = ((j * a) - (b * z)) * c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((z * y) - (a * t)) * x;
	double tmp;
	if (x <= -1.35e+132) {
		tmp = t_1;
	} else if (x <= -4.9e-152) {
		tmp = -i * ((j * y) - (b * t));
	} else if (x <= 4.1e+52) {
		tmp = ((j * a) - (b * z)) * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((z * y) - (a * t)) * x
	tmp = 0
	if x <= -1.35e+132:
		tmp = t_1
	elif x <= -4.9e-152:
		tmp = -i * ((j * y) - (b * t))
	elif x <= 4.1e+52:
		tmp = ((j * a) - (b * z)) * c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(z * y) - Float64(a * t)) * x)
	tmp = 0.0
	if (x <= -1.35e+132)
		tmp = t_1;
	elseif (x <= -4.9e-152)
		tmp = Float64(Float64(-i) * Float64(Float64(j * y) - Float64(b * t)));
	elseif (x <= 4.1e+52)
		tmp = Float64(Float64(Float64(j * a) - Float64(b * z)) * c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((z * y) - (a * t)) * x;
	tmp = 0.0;
	if (x <= -1.35e+132)
		tmp = t_1;
	elseif (x <= -4.9e-152)
		tmp = -i * ((j * y) - (b * t));
	elseif (x <= 4.1e+52)
		tmp = ((j * a) - (b * z)) * c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.35e+132], t$95$1, If[LessEqual[x, -4.9e-152], N[((-i) * N[(N[(j * y), $MachinePrecision] - N[(b * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.1e+52], N[(N[(N[(j * a), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.35e132 or 4.1e52 < x

   1. Initial program 72.3%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 65.5

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

   4. Applied rewrites 65.5%

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

   if -1.35e132 < x < -4.89999999999999983e-152

   1. Initial program 75.4%

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

   2. Taylor expanded in i around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 40.4

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

   4. Applied rewrites 40.4%

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

   if -4.89999999999999983e-152 < x < 4.1e52

   1. Initial program 72.2%

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

   2. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto \left(a \cdot j - b \cdot z\right) \cdot c \]

      4. *-commutative N/A

         \[\leadsto \left(j \cdot a - b \cdot z\right) \cdot c \]

      5. lower-*.f64 N/A

         \[\leadsto \left(j \cdot a - b \cdot z\right) \cdot c \]

      6. lower-*.f64 44.9

         \[\leadsto \left(j \cdot a - b \cdot z\right) \cdot c \]

   4. Applied rewrites 44.9%

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

Alternative 9: 51.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot y - a \cdot t\right) \cdot x\\ \mathbf{if}\;x \leq -3.3 \cdot 10^{+135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-303}:\\ \;\;\;\;\left(c \cdot a - i \cdot y\right) \cdot j\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+52}:\\ \;\;\;\;\left(j \cdot a - b \cdot z\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- (* z y) (* a t)) x)))
   (if (<= x -3.3e+135)
     t_1
     (if (<= x 9.2e-303)
       (* (- (* c a) (* i y)) j)
       (if (<= x 4.1e+52) (* (- (* j a) (* b z)) c) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((z * y) - (a * t)) * x;
	double tmp;
	if (x <= -3.3e+135) {
		tmp = t_1;
	} else if (x <= 9.2e-303) {
		tmp = ((c * a) - (i * y)) * j;
	} else if (x <= 4.1e+52) {
		tmp = ((j * a) - (b * z)) * 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)
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) :: t_1
    real(8) :: tmp
    t_1 = ((z * y) - (a * t)) * x
    if (x <= (-3.3d+135)) then
        tmp = t_1
    else if (x <= 9.2d-303) then
        tmp = ((c * a) - (i * y)) * j
    else if (x <= 4.1d+52) then
        tmp = ((j * a) - (b * z)) * c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((z * y) - (a * t)) * x;
	double tmp;
	if (x <= -3.3e+135) {
		tmp = t_1;
	} else if (x <= 9.2e-303) {
		tmp = ((c * a) - (i * y)) * j;
	} else if (x <= 4.1e+52) {
		tmp = ((j * a) - (b * z)) * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((z * y) - (a * t)) * x
	tmp = 0
	if x <= -3.3e+135:
		tmp = t_1
	elif x <= 9.2e-303:
		tmp = ((c * a) - (i * y)) * j
	elif x <= 4.1e+52:
		tmp = ((j * a) - (b * z)) * c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(z * y) - Float64(a * t)) * x)
	tmp = 0.0
	if (x <= -3.3e+135)
		tmp = t_1;
	elseif (x <= 9.2e-303)
		tmp = Float64(Float64(Float64(c * a) - Float64(i * y)) * j);
	elseif (x <= 4.1e+52)
		tmp = Float64(Float64(Float64(j * a) - Float64(b * z)) * c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((z * y) - (a * t)) * x;
	tmp = 0.0;
	if (x <= -3.3e+135)
		tmp = t_1;
	elseif (x <= 9.2e-303)
		tmp = ((c * a) - (i * y)) * j;
	elseif (x <= 4.1e+52)
		tmp = ((j * a) - (b * z)) * c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -3.3e+135], t$95$1, If[LessEqual[x, 9.2e-303], N[(N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[x, 4.1e+52], N[(N[(N[(j * a), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.2999999999999999e135 or 4.1e52 < x

   1. Initial program 72.3%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 65.5

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

   4. Applied rewrites 65.5%

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

   if -3.2999999999999999e135 < x < 9.19999999999999981e-303

   1. Initial program 73.7%

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

   2. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 41.3

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

   4. Applied rewrites 41.3%

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

   if 9.19999999999999981e-303 < x < 4.1e52

   1. Initial program 73.0%

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

   2. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto \left(a \cdot j - b \cdot z\right) \cdot c \]

      4. *-commutative N/A

         \[\leadsto \left(j \cdot a - b \cdot z\right) \cdot c \]

      5. lower-*.f64 N/A

         \[\leadsto \left(j \cdot a - b \cdot z\right) \cdot c \]

      6. lower-*.f64 44.4

         \[\leadsto \left(j \cdot a - b \cdot z\right) \cdot c \]

   4. Applied rewrites 44.4%

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

Alternative 10: 50.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot a - i \cdot y\right) \cdot j\\ \mathbf{if}\;j \leq -5.4 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 5 \cdot 10^{-67}:\\ \;\;\;\;\left(y \cdot x - c \cdot b\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- (* c a) (* i y)) j)))
   (if (<= j -5.4e+68) t_1 (if (<= j 5e-67) (* (- (* y x) (* c b)) z) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((c * a) - (i * y)) * j;
	double tmp;
	if (j <= -5.4e+68) {
		tmp = t_1;
	} else if (j <= 5e-67) {
		tmp = ((y * x) - (c * b)) * z;
	} 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)
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) :: t_1
    real(8) :: tmp
    t_1 = ((c * a) - (i * y)) * j
    if (j <= (-5.4d+68)) then
        tmp = t_1
    else if (j <= 5d-67) then
        tmp = ((y * x) - (c * b)) * z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((c * a) - (i * y)) * j;
	double tmp;
	if (j <= -5.4e+68) {
		tmp = t_1;
	} else if (j <= 5e-67) {
		tmp = ((y * x) - (c * b)) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((c * a) - (i * y)) * j
	tmp = 0
	if j <= -5.4e+68:
		tmp = t_1
	elif j <= 5e-67:
		tmp = ((y * x) - (c * b)) * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(c * a) - Float64(i * y)) * j)
	tmp = 0.0
	if (j <= -5.4e+68)
		tmp = t_1;
	elseif (j <= 5e-67)
		tmp = Float64(Float64(Float64(y * x) - Float64(c * b)) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((c * a) - (i * y)) * j;
	tmp = 0.0;
	if (j <= -5.4e+68)
		tmp = t_1;
	elseif (j <= 5e-67)
		tmp = ((y * x) - (c * b)) * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]}, If[LessEqual[j, -5.4e+68], t$95$1, If[LessEqual[j, 5e-67], N[(N[(N[(y * x), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if j < -5.39999999999999982e68 or 4.9999999999999999e-67 < j

   1. Initial program 73.7%

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

   2. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 57.2

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

   4. Applied rewrites 57.2%

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

   if -5.39999999999999982e68 < j < 4.9999999999999999e-67

   1. Initial program 72.3%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 45.8

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

   4. Applied rewrites 45.8%

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

Alternative 11: 50.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot a - i \cdot y\right) \cdot j\\ \mathbf{if}\;j \leq -1.6 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{-81}:\\ \;\;\;\;\left(i \cdot t - c \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- (* c a) (* i y)) j)))
   (if (<= j -1.6e-25) t_1 (if (<= j 3.7e-81) (* (- (* i t) (* c z)) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((c * a) - (i * y)) * j;
	double tmp;
	if (j <= -1.6e-25) {
		tmp = t_1;
	} else if (j <= 3.7e-81) {
		tmp = ((i * t) - (c * z)) * b;
	} 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)
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) :: t_1
    real(8) :: tmp
    t_1 = ((c * a) - (i * y)) * j
    if (j <= (-1.6d-25)) then
        tmp = t_1
    else if (j <= 3.7d-81) then
        tmp = ((i * t) - (c * z)) * b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((c * a) - (i * y)) * j;
	double tmp;
	if (j <= -1.6e-25) {
		tmp = t_1;
	} else if (j <= 3.7e-81) {
		tmp = ((i * t) - (c * z)) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((c * a) - (i * y)) * j
	tmp = 0
	if j <= -1.6e-25:
		tmp = t_1
	elif j <= 3.7e-81:
		tmp = ((i * t) - (c * z)) * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(c * a) - Float64(i * y)) * j)
	tmp = 0.0
	if (j <= -1.6e-25)
		tmp = t_1;
	elseif (j <= 3.7e-81)
		tmp = Float64(Float64(Float64(i * t) - Float64(c * z)) * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((c * a) - (i * y)) * j;
	tmp = 0.0;
	if (j <= -1.6e-25)
		tmp = t_1;
	elseif (j <= 3.7e-81)
		tmp = ((i * t) - (c * z)) * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]}, If[LessEqual[j, -1.6e-25], t$95$1, If[LessEqual[j, 3.7e-81], N[(N[(N[(i * t), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if j < -1.6000000000000001e-25 or 3.69999999999999986e-81 < j

   1. Initial program 74.0%

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

   2. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 53.9

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

   4. Applied rewrites 53.9%

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

   if -1.6000000000000001e-25 < j < 3.69999999999999986e-81

   1. Initial program 71.6%

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

   2. Taylor expanded in b around inf

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

      1. negate-sub2 N/A

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

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. negate-sub2 N/A

         \[\leadsto \left(i \cdot t - c \cdot z\right) \cdot b \]

      7. lower--.f64 N/A

         \[\leadsto \left(i \cdot t - c \cdot z\right) \cdot b \]

      8. lower-*.f64 N/A

         \[\leadsto \left(i \cdot t - c \cdot z\right) \cdot b \]

      9. lift-*.f64 45.7

         \[\leadsto \left(i \cdot t - c \cdot z\right) \cdot b \]

   4. Applied rewrites 45.7%

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

Alternative 12: 40.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-t\right) \cdot \left(a \cdot x\right)\\ \mathbf{if}\;x \leq -6.3 \cdot 10^{+168}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+55}:\\ \;\;\;\;\left(c \cdot a - i \cdot y\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- t) (* a x))))
   (if (<= x -6.3e+168)
     t_1
     (if (<= x 3.4e+55) (* (- (* c a) (* i y)) j) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -t * (a * x);
	double tmp;
	if (x <= -6.3e+168) {
		tmp = t_1;
	} else if (x <= 3.4e+55) {
		tmp = ((c * a) - (i * y)) * 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)
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) :: t_1
    real(8) :: tmp
    t_1 = -t * (a * x)
    if (x <= (-6.3d+168)) then
        tmp = t_1
    else if (x <= 3.4d+55) then
        tmp = ((c * a) - (i * y)) * j
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -t * (a * x);
	double tmp;
	if (x <= -6.3e+168) {
		tmp = t_1;
	} else if (x <= 3.4e+55) {
		tmp = ((c * a) - (i * y)) * j;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = -t * (a * x)
	tmp = 0
	if x <= -6.3e+168:
		tmp = t_1
	elif x <= 3.4e+55:
		tmp = ((c * a) - (i * y)) * j
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(-t) * Float64(a * x))
	tmp = 0.0
	if (x <= -6.3e+168)
		tmp = t_1;
	elseif (x <= 3.4e+55)
		tmp = Float64(Float64(Float64(c * a) - Float64(i * y)) * j);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = -t * (a * x);
	tmp = 0.0;
	if (x <= -6.3e+168)
		tmp = t_1;
	elseif (x <= 3.4e+55)
		tmp = ((c * a) - (i * y)) * j;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-t) * N[(a * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.3e+168], t$95$1, If[LessEqual[x, 3.4e+55], N[(N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.2999999999999997e168 or 3.3999999999999998e55 < x

   1. Initial program 72.2%

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

   2. Taylor expanded in t around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 46.2

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

   4. Applied rewrites 46.2%

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

   5. Taylor expanded in x around inf

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

      1. lift-*.f64 37.9

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

   7. Applied rewrites 37.9%

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

   if -6.2999999999999997e168 < x < 3.3999999999999998e55

   1. Initial program 73.4%

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

   2. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 41.4

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

   4. Applied rewrites 41.4%

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

Alternative 13: 29.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot j\right) \cdot a\\ \mathbf{if}\;c \leq -3.1 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -3.9 \cdot 10^{-218}:\\ \;\;\;\;\left(-t\right) \cdot \left(a \cdot x\right)\\ \mathbf{elif}\;c \leq 5.2 \cdot 10^{-69}:\\ \;\;\;\;\left(-i\right) \cdot \left(j \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* c j) a)))
   (if (<= c -3.1e-9)
     t_1
     (if (<= c -3.9e-218)
       (* (- t) (* a x))
       (if (<= c 5.2e-69) (* (- i) (* j y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (c * j) * a;
	double tmp;
	if (c <= -3.1e-9) {
		tmp = t_1;
	} else if (c <= -3.9e-218) {
		tmp = -t * (a * x);
	} else if (c <= 5.2e-69) {
		tmp = -i * (j * y);
	} 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)
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) :: t_1
    real(8) :: tmp
    t_1 = (c * j) * a
    if (c <= (-3.1d-9)) then
        tmp = t_1
    else if (c <= (-3.9d-218)) then
        tmp = -t * (a * x)
    else if (c <= 5.2d-69) then
        tmp = -i * (j * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (c * j) * a;
	double tmp;
	if (c <= -3.1e-9) {
		tmp = t_1;
	} else if (c <= -3.9e-218) {
		tmp = -t * (a * x);
	} else if (c <= 5.2e-69) {
		tmp = -i * (j * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (c * j) * a
	tmp = 0
	if c <= -3.1e-9:
		tmp = t_1
	elif c <= -3.9e-218:
		tmp = -t * (a * x)
	elif c <= 5.2e-69:
		tmp = -i * (j * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(c * j) * a)
	tmp = 0.0
	if (c <= -3.1e-9)
		tmp = t_1;
	elseif (c <= -3.9e-218)
		tmp = Float64(Float64(-t) * Float64(a * x));
	elseif (c <= 5.2e-69)
		tmp = Float64(Float64(-i) * Float64(j * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (c * j) * a;
	tmp = 0.0;
	if (c <= -3.1e-9)
		tmp = t_1;
	elseif (c <= -3.9e-218)
		tmp = -t * (a * x);
	elseif (c <= 5.2e-69)
		tmp = -i * (j * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(c * j), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[c, -3.1e-9], t$95$1, If[LessEqual[c, -3.9e-218], N[((-t) * N[(a * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.2e-69], N[((-i) * N[(j * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.10000000000000005e-9 or 5.2000000000000004e-69 < c

   1. Initial program 66.7%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 44.0

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

   4. Applied rewrites 44.0%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 32.0

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

   7. Applied rewrites 32.0%

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

   if -3.10000000000000005e-9 < c < -3.9e-218

   1. Initial program 81.6%

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

   2. Taylor expanded in t around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 45.0

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

   4. Applied rewrites 45.0%

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

   5. Taylor expanded in x around inf

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

      1. lift-*.f64 24.6

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

   7. Applied rewrites 24.6%

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

   if -3.9e-218 < c < 5.2000000000000004e-69

   1. Initial program 80.6%

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

   2. Taylor expanded in i around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 48.7

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

   4. Applied rewrites 48.7%

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

   5. Taylor expanded in y around inf

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

      1. lift-*.f64 28.3

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

   7. Applied rewrites 28.3%

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

Alternative 14: 29.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot j\right) \cdot a\\ \mathbf{if}\;c \leq -2.6 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -4.3 \cdot 10^{-218}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;c \leq 5.2 \cdot 10^{-69}:\\ \;\;\;\;\left(-i\right) \cdot \left(j \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* c j) a)))
   (if (<= c -2.6e-9)
     t_1
     (if (<= c -4.3e-218)
       (* (- a) (* t x))
       (if (<= c 5.2e-69) (* (- i) (* j y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (c * j) * a;
	double tmp;
	if (c <= -2.6e-9) {
		tmp = t_1;
	} else if (c <= -4.3e-218) {
		tmp = -a * (t * x);
	} else if (c <= 5.2e-69) {
		tmp = -i * (j * y);
	} 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)
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) :: t_1
    real(8) :: tmp
    t_1 = (c * j) * a
    if (c <= (-2.6d-9)) then
        tmp = t_1
    else if (c <= (-4.3d-218)) then
        tmp = -a * (t * x)
    else if (c <= 5.2d-69) then
        tmp = -i * (j * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (c * j) * a;
	double tmp;
	if (c <= -2.6e-9) {
		tmp = t_1;
	} else if (c <= -4.3e-218) {
		tmp = -a * (t * x);
	} else if (c <= 5.2e-69) {
		tmp = -i * (j * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (c * j) * a
	tmp = 0
	if c <= -2.6e-9:
		tmp = t_1
	elif c <= -4.3e-218:
		tmp = -a * (t * x)
	elif c <= 5.2e-69:
		tmp = -i * (j * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(c * j) * a)
	tmp = 0.0
	if (c <= -2.6e-9)
		tmp = t_1;
	elseif (c <= -4.3e-218)
		tmp = Float64(Float64(-a) * Float64(t * x));
	elseif (c <= 5.2e-69)
		tmp = Float64(Float64(-i) * Float64(j * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (c * j) * a;
	tmp = 0.0;
	if (c <= -2.6e-9)
		tmp = t_1;
	elseif (c <= -4.3e-218)
		tmp = -a * (t * x);
	elseif (c <= 5.2e-69)
		tmp = -i * (j * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(c * j), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[c, -2.6e-9], t$95$1, If[LessEqual[c, -4.3e-218], N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.2e-69], N[((-i) * N[(j * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.6000000000000001e-9 or 5.2000000000000004e-69 < c

   1. Initial program 66.7%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 44.0

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

   4. Applied rewrites 44.0%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 32.0

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

   7. Applied rewrites 32.0%

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

   if -2.6000000000000001e-9 < c < -4.3e-218

   1. Initial program 81.6%

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

   2. Taylor expanded in t around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 45.0

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

   4. Applied rewrites 45.0%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t \cdot x\right) \]

      4. lift-neg.f64 N/A

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

      5. lower-*.f64 25.2

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

   7. Applied rewrites 25.2%

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

   if -4.3e-218 < c < 5.2000000000000004e-69

   1. Initial program 80.6%

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

   2. Taylor expanded in i around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 48.7

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

   4. Applied rewrites 48.7%

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

   5. Taylor expanded in y around inf

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

      1. lift-*.f64 28.3

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

   7. Applied rewrites 28.3%

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

Alternative 15: 29.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot j\right) \cdot a\\ \mathbf{if}\;c \leq -2.6 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-227}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{-43}:\\ \;\;\;\;\left(i \cdot t\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* c j) a)))
   (if (<= c -2.6e-9)
     t_1
     (if (<= c -1.25e-227)
       (* (- a) (* t x))
       (if (<= c 5.4e-43) (* (* i t) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (c * j) * a;
	double tmp;
	if (c <= -2.6e-9) {
		tmp = t_1;
	} else if (c <= -1.25e-227) {
		tmp = -a * (t * x);
	} else if (c <= 5.4e-43) {
		tmp = (i * t) * b;
	} 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)
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) :: t_1
    real(8) :: tmp
    t_1 = (c * j) * a
    if (c <= (-2.6d-9)) then
        tmp = t_1
    else if (c <= (-1.25d-227)) then
        tmp = -a * (t * x)
    else if (c <= 5.4d-43) then
        tmp = (i * t) * b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (c * j) * a;
	double tmp;
	if (c <= -2.6e-9) {
		tmp = t_1;
	} else if (c <= -1.25e-227) {
		tmp = -a * (t * x);
	} else if (c <= 5.4e-43) {
		tmp = (i * t) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (c * j) * a
	tmp = 0
	if c <= -2.6e-9:
		tmp = t_1
	elif c <= -1.25e-227:
		tmp = -a * (t * x)
	elif c <= 5.4e-43:
		tmp = (i * t) * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(c * j) * a)
	tmp = 0.0
	if (c <= -2.6e-9)
		tmp = t_1;
	elseif (c <= -1.25e-227)
		tmp = Float64(Float64(-a) * Float64(t * x));
	elseif (c <= 5.4e-43)
		tmp = Float64(Float64(i * t) * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (c * j) * a;
	tmp = 0.0;
	if (c <= -2.6e-9)
		tmp = t_1;
	elseif (c <= -1.25e-227)
		tmp = -a * (t * x);
	elseif (c <= 5.4e-43)
		tmp = (i * t) * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(c * j), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[c, -2.6e-9], t$95$1, If[LessEqual[c, -1.25e-227], N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.4e-43], N[(N[(i * t), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.6000000000000001e-9 or 5.39999999999999982e-43 < c

   1. Initial program 66.1%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 44.3

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

   4. Applied rewrites 44.3%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 32.6

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

   7. Applied rewrites 32.6%

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

   if -2.6000000000000001e-9 < c < -1.2499999999999999e-227

   1. Initial program 81.3%

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

   2. Taylor expanded in t around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 45.6

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t \cdot x\right) \]

      4. lift-neg.f64 N/A

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

      5. lower-*.f64 25.5

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

   7. Applied rewrites 25.5%

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

   if -1.2499999999999999e-227 < c < 5.39999999999999982e-43

   1. Initial program 80.9%

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

   2. Taylor expanded in t around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 46.2

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

   4. Applied rewrites 46.2%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

         \[\leadsto \left(i \cdot t\right) \cdot b \]

      2. lower-*.f64 N/A

         \[\leadsto \left(i \cdot t\right) \cdot b \]

      3. lower-*.f64 25.5

         \[\leadsto \left(i \cdot t\right) \cdot b \]

   7. Applied rewrites 25.5%

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

Alternative 16: 29.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot j\right) \cdot a\\ \mathbf{if}\;j \leq -1.7 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{-81}:\\ \;\;\;\;\left(i \cdot t\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* c j) a)))
   (if (<= j -1.7e+64) t_1 (if (<= j 3.4e-81) (* (* i t) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (c * j) * a;
	double tmp;
	if (j <= -1.7e+64) {
		tmp = t_1;
	} else if (j <= 3.4e-81) {
		tmp = (i * t) * b;
	} 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)
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) :: t_1
    real(8) :: tmp
    t_1 = (c * j) * a
    if (j <= (-1.7d+64)) then
        tmp = t_1
    else if (j <= 3.4d-81) then
        tmp = (i * t) * b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (c * j) * a;
	double tmp;
	if (j <= -1.7e+64) {
		tmp = t_1;
	} else if (j <= 3.4e-81) {
		tmp = (i * t) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (c * j) * a
	tmp = 0
	if j <= -1.7e+64:
		tmp = t_1
	elif j <= 3.4e-81:
		tmp = (i * t) * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(c * j) * a)
	tmp = 0.0
	if (j <= -1.7e+64)
		tmp = t_1;
	elseif (j <= 3.4e-81)
		tmp = Float64(Float64(i * t) * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (c * j) * a;
	tmp = 0.0;
	if (j <= -1.7e+64)
		tmp = t_1;
	elseif (j <= 3.4e-81)
		tmp = (i * t) * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(c * j), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[j, -1.7e+64], t$95$1, If[LessEqual[j, 3.4e-81], N[(N[(i * t), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if j < -1.7000000000000001e64 or 3.3999999999999999e-81 < j

   1. Initial program 74.0%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 44.5

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

   4. Applied rewrites 44.5%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 33.1

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

   7. Applied rewrites 33.1%

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

   if -1.7000000000000001e64 < j < 3.3999999999999999e-81

   1. Initial program 72.0%

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

   2. Taylor expanded in t around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 45.6

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

         \[\leadsto \left(i \cdot t\right) \cdot b \]

      2. lower-*.f64 N/A

         \[\leadsto \left(i \cdot t\right) \cdot b \]

      3. lower-*.f64 25.1

         \[\leadsto \left(i \cdot t\right) \cdot b \]

   7. Applied rewrites 25.1%

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

Alternative 17: 22.3% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \left(i \cdot t\right) \cdot b \end{array} \]

FPCore

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

C

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

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)
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
    code = (i * t) * b
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.0%

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

2. Taylor expanded in t around -inf

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

   1. associate-*r* N/A

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

   2. lower-*.f64 N/A

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

   3. mul-1-neg N/A

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

   4. lower-neg.f64 N/A

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

   5. lower--.f64 N/A

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

   6. lower-*.f64 N/A

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

   7. *-commutative N/A

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

   8. lower-*.f64 39.3

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

4. Applied rewrites 39.3%

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

5. Taylor expanded in x around 0

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

   1. *-commutative N/A

      \[\leadsto \left(i \cdot t\right) \cdot b \]

   2. lower-*.f64 N/A

      \[\leadsto \left(i \cdot t\right) \cdot b \]

   3. lower-*.f64 22.3

      \[\leadsto \left(i \cdot t\right) \cdot b \]

7. Applied rewrites 22.3%

   \[\leadsto \left(i \cdot t\right) \cdot \color{blue}{b} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025110 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64
  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))