Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.2% → 83.1%

Time: 13.5s

Alternatives: 19

Speedup: 0.9×

• 58.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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) - (i * a)))) + (j * ((c * t) - (i * y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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) - (i * a)))) + (j * ((c * t) - (i * y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 83.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. fp-cancel-sign-sub N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

      9. *-lft-identity N/A

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

      10. metadata-eval N/A

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

      11. distribute-rgt-in N/A

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

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

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

      13. +-commutative N/A

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

   5. Applied rewrites 49.1%

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

   6. Taylor expanded in j around 0

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

   8. Applied rewrites 50.4%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 51.9%

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

Alternative 2: 78.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -3.2 \cdot 10^{+94}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-y, j, b \cdot a\right), i, \left(\left(-a\right) \cdot t\right) \cdot x\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{+238}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-x, t, i \cdot b\right), a, \mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(j, \frac{y}{b}, -a\right) \cdot \left(-b\right)\right) \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -3.2e+94)
   (fma (fma (- y) j (* b a)) i (* (* (- a) t) x))
   (if (<= i 2.6e+238)
     (fma
      (fma (- x) t (* i b))
      a
      (fma (fma (- i) y (* c t)) j (* (fma (- b) c (* y x)) z)))
     (* (* (fma j (/ y b) (- a)) (- b)) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -3.2e+94) {
		tmp = fma(fma(-y, j, (b * a)), i, ((-a * t) * x));
	} else if (i <= 2.6e+238) {
		tmp = fma(fma(-x, t, (i * b)), a, fma(fma(-i, y, (c * t)), j, (fma(-b, c, (y * x)) * z)));
	} else {
		tmp = (fma(j, (y / b), -a) * -b) * i;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -3.2e+94)
		tmp = fma(fma(Float64(-y), j, Float64(b * a)), i, Float64(Float64(Float64(-a) * t) * x));
	elseif (i <= 2.6e+238)
		tmp = fma(fma(Float64(-x), t, Float64(i * b)), a, fma(fma(Float64(-i), y, Float64(c * t)), j, Float64(fma(Float64(-b), c, Float64(y * x)) * z)));
	else
		tmp = Float64(Float64(fma(j, Float64(y / b), Float64(-a)) * Float64(-b)) * i);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -3.2e+94], N[(N[((-y) * j + N[(b * a), $MachinePrecision]), $MachinePrecision] * i + N[(N[((-a) * t), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.6e+238], N[(N[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a + N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j + N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(j * N[(y / b), $MachinePrecision] + (-a)), $MachinePrecision] * (-b)), $MachinePrecision] * i), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -3.20000000000000014e94

   1. Initial program 60.3%

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

   3. Taylor expanded in c around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. fp-cancel-sign-sub N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

      9. *-lft-identity N/A

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

      10. metadata-eval N/A

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

      11. distribute-rgt-in N/A

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

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

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

      13. +-commutative N/A

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

   5. Applied rewrites 71.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 76.2%

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

   if -3.20000000000000014e94 < i < 2.6e238

   1. Initial program 76.8%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 82.4%

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

   if 2.6e238 < i

   1. Initial program 31.1%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

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

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

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

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

      10. metadata-eval N/A

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

      11. *-lft-identity N/A

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

      12. lower-fma.f64 N/A

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

      13. mul-1-neg N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 92.2

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

   5. Applied rewrites 92.2%

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

   6. Taylor expanded in b around -inf

      \[\leadsto \left(-1 \cdot \left(b \cdot \left(-1 \cdot a + \frac{j \cdot y}{b}\right)\right)\right) \cdot i \]
   7. Step-by-step derivation

   8. Applied rewrites 93.2%

      \[\leadsto \left(\mathsf{fma}\left(j, \frac{y}{b}, -a\right) \cdot \left(-b\right)\right) \cdot i \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 68.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{if}\;c \leq -2.1 \cdot 10^{-116} \lor \neg \left(c \leq 6 \cdot 10^{+174}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-z, b, j \cdot t\right), c, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-y, j, b \cdot a\right), i, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- a) t (* z y)) x)))
   (if (or (<= c -2.1e-116) (not (<= c 6e+174)))
     (fma (fma (- z) b (* j t)) c t_1)
     (fma (fma (- y) j (* b a)) i t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-a, t, (z * y)) * x;
	double tmp;
	if ((c <= -2.1e-116) || !(c <= 6e+174)) {
		tmp = fma(fma(-z, b, (j * t)), c, t_1);
	} else {
		tmp = fma(fma(-y, j, (b * a)), i, t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-a), t, Float64(z * y)) * x)
	tmp = 0.0
	if ((c <= -2.1e-116) || !(c <= 6e+174))
		tmp = fma(fma(Float64(-z), b, Float64(j * t)), c, t_1);
	else
		tmp = fma(fma(Float64(-y), j, Float64(b * a)), i, t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[Or[LessEqual[c, -2.1e-116], N[Not[LessEqual[c, 6e+174]], $MachinePrecision]], N[(N[((-z) * b + N[(j * t), $MachinePrecision]), $MachinePrecision] * c + t$95$1), $MachinePrecision], N[(N[((-y) * j + N[(b * a), $MachinePrecision]), $MachinePrecision] * i + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if c < -2.0999999999999999e-116 or 6e174 < c

   1. Initial program 68.5%

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

   3. Taylor expanded in i around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

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

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-in N/A

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

      10. mul-1-neg N/A

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

      11. *-commutative N/A

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

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

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

      13. cancel-sign-sub-inv N/A

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

      14. *-commutative N/A

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

      15. +-commutative N/A

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

   5. Applied rewrites 74.1%

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

   if -2.0999999999999999e-116 < c < 6e174

   1. Initial program 74.2%

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

   3. Taylor expanded in c around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. fp-cancel-sign-sub N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

      9. *-lft-identity N/A

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

      10. metadata-eval N/A

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

      11. distribute-rgt-in N/A

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

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

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

      13. +-commutative N/A

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

   5. Applied rewrites 77.4%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.1 \cdot 10^{-116} \lor \neg \left(c \leq 6 \cdot 10^{+174}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-z, b, j \cdot t\right), c, \mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-y, j, b \cdot a\right), i, \mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -8.6 \cdot 10^{+181} \lor \neg \left(c \leq 1.05 \cdot 10^{+185}\right):\\ \;\;\;\;\mathsf{fma}\left(-z, b, j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-y, j, b \cdot a\right), i, \mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -8.6e+181) (not (<= c 1.05e+185)))
   (* (fma (- z) b (* j t)) c)
   (fma (fma (- y) j (* b a)) i (* (fma (- a) t (* z y)) x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -8.6e+181) || !(c <= 1.05e+185)) {
		tmp = fma(-z, b, (j * t)) * c;
	} else {
		tmp = fma(fma(-y, j, (b * a)), i, (fma(-a, t, (z * y)) * x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -8.6e+181) || !(c <= 1.05e+185))
		tmp = Float64(fma(Float64(-z), b, Float64(j * t)) * c);
	else
		tmp = fma(fma(Float64(-y), j, Float64(b * a)), i, Float64(fma(Float64(-a), t, Float64(z * y)) * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -8.6e+181], N[Not[LessEqual[c, 1.05e+185]], $MachinePrecision]], N[(N[((-z) * b + N[(j * t), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], N[(N[((-y) * j + N[(b * a), $MachinePrecision]), $MachinePrecision] * i + N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -8.59999999999999943e181 or 1.05e185 < c

   1. Initial program 56.4%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. cancel-sign-sub-inv N/A

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

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

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

      6. *-commutative N/A

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

      7. mul-1-neg N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. lower-fma.f64 N/A

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

      12. mul-1-neg N/A

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

      13. lower-neg.f64 N/A

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

      14. lower-*.f64 73.9

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

   5. Applied rewrites 73.9%

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

   if -8.59999999999999943e181 < c < 1.05e185

   1. Initial program 75.9%

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

   3. Taylor expanded in c around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. fp-cancel-sign-sub N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

      9. *-lft-identity N/A

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

      10. metadata-eval N/A

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

      11. distribute-rgt-in N/A

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

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

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

      13. +-commutative N/A

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

   5. Applied rewrites 72.9%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.6 \cdot 10^{+181} \lor \neg \left(c \leq 1.05 \cdot 10^{+185}\right):\\ \;\;\;\;\mathsf{fma}\left(-z, b, j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-y, j, b \cdot a\right), i, \mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.36 \cdot 10^{+66}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{-73}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot x, z, \mathsf{fma}\left(-t, x, i \cdot b\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.36e+66)
   (* (fma (- i) y (* c t)) j)
   (if (<= j 1.2e-73)
     (fma (* y x) z (* (fma (- t) x (* i b)) a))
     (+ (* (* z x) y) (* j (- (* c t) (* i y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.36e+66) {
		tmp = fma(-i, y, (c * t)) * j;
	} else if (j <= 1.2e-73) {
		tmp = fma((y * x), z, (fma(-t, x, (i * b)) * a));
	} else {
		tmp = ((z * x) * y) + (j * ((c * t) - (i * y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.36e+66)
		tmp = Float64(fma(Float64(-i), y, Float64(c * t)) * j);
	elseif (j <= 1.2e-73)
		tmp = fma(Float64(y * x), z, Float64(fma(Float64(-t), x, Float64(i * b)) * a));
	else
		tmp = Float64(Float64(Float64(z * x) * y) + Float64(j * Float64(Float64(c * t) - Float64(i * y))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1.36e+66], N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[j, 1.2e-73], N[(N[(y * x), $MachinePrecision] * z + N[(N[((-t) * x + N[(i * b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.36e66

   1. Initial program 70.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 67.5%

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

   6. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

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

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

      5. +-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 66.1

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

   8. Applied rewrites 66.1%

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

   if -1.36e66 < j < 1.20000000000000003e-73

   1. Initial program 72.4%

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

   3. Taylor expanded in c around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. fp-cancel-sign-sub N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

      9. *-lft-identity N/A

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

      10. metadata-eval N/A

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

      11. distribute-rgt-in N/A

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

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

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

      13. +-commutative N/A

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

   5. Applied rewrites 71.5%

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

   6. Taylor expanded in j around 0

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

   8. Applied rewrites 71.6%

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

   if 1.20000000000000003e-73 < j

   1. Initial program 70.9%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 68.2

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

   5. Applied rewrites 68.2%

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

Alternative 6: 57.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.36 \cdot 10^{+66}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{-71}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot x, z, \mathsf{fma}\left(-t, x, i \cdot b\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-y, j, b \cdot a\right), i, \left(\left(-a\right) \cdot t\right) \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.36e+66)
   (* (fma (- i) y (* c t)) j)
   (if (<= j 1.9e-71)
     (fma (* y x) z (* (fma (- t) x (* i b)) a))
     (fma (fma (- y) j (* b a)) i (* (* (- 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 tmp;
	if (j <= -1.36e+66) {
		tmp = fma(-i, y, (c * t)) * j;
	} else if (j <= 1.9e-71) {
		tmp = fma((y * x), z, (fma(-t, x, (i * b)) * a));
	} else {
		tmp = fma(fma(-y, j, (b * a)), i, ((-a * t) * x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.36e+66)
		tmp = Float64(fma(Float64(-i), y, Float64(c * t)) * j);
	elseif (j <= 1.9e-71)
		tmp = fma(Float64(y * x), z, Float64(fma(Float64(-t), x, Float64(i * b)) * a));
	else
		tmp = fma(fma(Float64(-y), j, Float64(b * a)), i, Float64(Float64(Float64(-a) * t) * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1.36e+66], N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[j, 1.9e-71], N[(N[(y * x), $MachinePrecision] * z + N[(N[((-t) * x + N[(i * b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[((-y) * j + N[(b * a), $MachinePrecision]), $MachinePrecision] * i + N[(N[((-a) * t), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.36e66

   1. Initial program 70.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 67.5%

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

   6. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

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

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

      5. +-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 66.1

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

   8. Applied rewrites 66.1%

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

   if -1.36e66 < j < 1.89999999999999996e-71

   1. Initial program 72.6%

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

   3. Taylor expanded in c around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. fp-cancel-sign-sub N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

      9. *-lft-identity N/A

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

      10. metadata-eval N/A

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

      11. distribute-rgt-in N/A

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

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

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

      13. +-commutative N/A

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

   5. Applied rewrites 71.7%

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

   6. Taylor expanded in j around 0

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

   8. Applied rewrites 71.2%

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

   if 1.89999999999999996e-71 < j

   1. Initial program 70.5%

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

   3. Taylor expanded in c around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. fp-cancel-sign-sub N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

      9. *-lft-identity N/A

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

      10. metadata-eval N/A

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

      11. distribute-rgt-in N/A

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

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

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

      13. +-commutative N/A

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

   5. Applied rewrites 63.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 62.9%

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

Alternative 7: 58.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \mathbf{if}\;j \leq -1.36 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{-72}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot x, z, \mathsf{fma}\left(-t, x, i \cdot b\right) \cdot a\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+138}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- i) y (* c t)) j)))
   (if (<= j -1.36e+66)
     t_1
     (if (<= j 6.5e-72)
       (fma (* y x) z (* (fma (- t) x (* i b)) a))
       (if (<= j 8.5e+138) (* (fma (- i) j (* z x)) 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 = fma(-i, y, (c * t)) * j;
	double tmp;
	if (j <= -1.36e+66) {
		tmp = t_1;
	} else if (j <= 6.5e-72) {
		tmp = fma((y * x), z, (fma(-t, x, (i * b)) * a));
	} else if (j <= 8.5e+138) {
		tmp = fma(-i, j, (z * x)) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-i), y, Float64(c * t)) * j)
	tmp = 0.0
	if (j <= -1.36e+66)
		tmp = t_1;
	elseif (j <= 6.5e-72)
		tmp = fma(Float64(y * x), z, Float64(fma(Float64(-t), x, Float64(i * b)) * a));
	elseif (j <= 8.5e+138)
		tmp = Float64(fma(Float64(-i), j, Float64(z * x)) * y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]}, If[LessEqual[j, -1.36e+66], t$95$1, If[LessEqual[j, 6.5e-72], N[(N[(y * x), $MachinePrecision] * z + N[(N[((-t) * x + N[(i * b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.5e+138], N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.36e66 or 8.5000000000000006e138 < j

   1. Initial program 67.5%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 74.3%

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

   6. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

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

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

      5. +-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 66.0

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

   8. Applied rewrites 66.0%

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

   if -1.36e66 < j < 6.4999999999999997e-72

   1. Initial program 72.4%

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

   3. Taylor expanded in c around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. fp-cancel-sign-sub N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

      9. *-lft-identity N/A

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

      10. metadata-eval N/A

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

      11. distribute-rgt-in N/A

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

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

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

      13. +-commutative N/A

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

   5. Applied rewrites 71.5%

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

   6. Taylor expanded in j around 0

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

   8. Applied rewrites 71.6%

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

   if 6.4999999999999997e-72 < j < 8.5000000000000006e138

   1. Initial program 76.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 57.7

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

   5. Applied rewrites 57.7%

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

Alternative 8: 29.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot x\\ \mathbf{if}\;t \leq -1.95:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-177}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-219}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+46}:\\ \;\;\;\;\left(b \cdot a\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z y) x)))
   (if (<= t -1.95)
     (* (- a) (* t x))
     (if (<= t -7.8e-177)
       t_1
       (if (<= t 5.6e-219)
         (* (* i b) a)
         (if (<= t 3.5e-30)
           t_1
           (if (<= t 8.8e+46) (* (* b a) i) (* (* j t) c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * y) * x;
	double tmp;
	if (t <= -1.95) {
		tmp = -a * (t * x);
	} else if (t <= -7.8e-177) {
		tmp = t_1;
	} else if (t <= 5.6e-219) {
		tmp = (i * b) * a;
	} else if (t <= 3.5e-30) {
		tmp = t_1;
	} else if (t <= 8.8e+46) {
		tmp = (b * a) * i;
	} else {
		tmp = (j * t) * c;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i, j)
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) * x
    if (t <= (-1.95d0)) then
        tmp = -a * (t * x)
    else if (t <= (-7.8d-177)) then
        tmp = t_1
    else if (t <= 5.6d-219) then
        tmp = (i * b) * a
    else if (t <= 3.5d-30) then
        tmp = t_1
    else if (t <= 8.8d+46) then
        tmp = (b * a) * i
    else
        tmp = (j * t) * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * y) * x;
	double tmp;
	if (t <= -1.95) {
		tmp = -a * (t * x);
	} else if (t <= -7.8e-177) {
		tmp = t_1;
	} else if (t <= 5.6e-219) {
		tmp = (i * b) * a;
	} else if (t <= 3.5e-30) {
		tmp = t_1;
	} else if (t <= 8.8e+46) {
		tmp = (b * a) * i;
	} else {
		tmp = (j * t) * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * y) * x
	tmp = 0
	if t <= -1.95:
		tmp = -a * (t * x)
	elif t <= -7.8e-177:
		tmp = t_1
	elif t <= 5.6e-219:
		tmp = (i * b) * a
	elif t <= 3.5e-30:
		tmp = t_1
	elif t <= 8.8e+46:
		tmp = (b * a) * i
	else:
		tmp = (j * t) * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * y) * x)
	tmp = 0.0
	if (t <= -1.95)
		tmp = Float64(Float64(-a) * Float64(t * x));
	elseif (t <= -7.8e-177)
		tmp = t_1;
	elseif (t <= 5.6e-219)
		tmp = Float64(Float64(i * b) * a);
	elseif (t <= 3.5e-30)
		tmp = t_1;
	elseif (t <= 8.8e+46)
		tmp = Float64(Float64(b * a) * i);
	else
		tmp = Float64(Float64(j * t) * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (z * y) * x;
	tmp = 0.0;
	if (t <= -1.95)
		tmp = -a * (t * x);
	elseif (t <= -7.8e-177)
		tmp = t_1;
	elseif (t <= 5.6e-219)
		tmp = (i * b) * a;
	elseif (t <= 3.5e-30)
		tmp = t_1;
	elseif (t <= 8.8e+46)
		tmp = (b * a) * i;
	else
		tmp = (j * t) * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t, -1.95], N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.8e-177], t$95$1, If[LessEqual[t, 5.6e-219], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t, 3.5e-30], t$95$1, If[LessEqual[t, 8.8e+46], N[(N[(b * a), $MachinePrecision] * i), $MachinePrecision], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.94999999999999996

   1. Initial program 60.1%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 57.2

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

   5. Applied rewrites 57.2%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 41.1%

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

   if -1.94999999999999996 < t < -7.80000000000000028e-177 or 5.5999999999999998e-219 < t < 3.5000000000000003e-30

   1. Initial program 81.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 81.2%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 78.7%

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

   9. Taylor expanded in z around inf

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

       1. *-commutative N/A

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

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

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

       3. mul-1-neg N/A

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

       4. associate-*r* N/A

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

       5. +-commutative N/A

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

       6. lower-*.f64 N/A

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

       7. mul-1-neg N/A

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

       8. *-commutative N/A

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

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

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

       10. lower-fma.f64 N/A

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

       11. lower-neg.f64 N/A

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

       12. *-commutative N/A

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

       13. lower-*.f64 57.9

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

   11. Applied rewrites 57.9%

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

   12. Taylor expanded in x around inf

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

   14. Applied rewrites 45.0%

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

   if -7.80000000000000028e-177 < t < 5.5999999999999998e-219

   1. Initial program 78.0%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

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

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

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

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

      10. metadata-eval N/A

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

      11. *-lft-identity N/A

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

      12. lower-fma.f64 N/A

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

      13. mul-1-neg N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 56.3

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

   5. Applied rewrites 56.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 44.5%

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

   if 3.5000000000000003e-30 < t < 8.8000000000000001e46

   1. Initial program 75.1%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

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

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

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

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

      10. metadata-eval N/A

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

      11. *-lft-identity N/A

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

      12. lower-fma.f64 N/A

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

      13. mul-1-neg N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 55.3

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

   5. Applied rewrites 55.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 38.8%

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

   if 8.8000000000000001e46 < t

   1. Initial program 63.1%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 71.6

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

   5. Applied rewrites 71.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 48.8%

      \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{c} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 9: 29.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot x\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+98}:\\ \;\;\;\;\left(c \cdot t\right) \cdot j\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-177}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-219}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+46}:\\ \;\;\;\;\left(b \cdot a\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z y) x)))
   (if (<= t -4.2e+98)
     (* (* c t) j)
     (if (<= t -7.8e-177)
       t_1
       (if (<= t 5.6e-219)
         (* (* i b) a)
         (if (<= t 3.5e-30)
           t_1
           (if (<= t 8.8e+46) (* (* b a) i) (* (* j t) c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * y) * x;
	double tmp;
	if (t <= -4.2e+98) {
		tmp = (c * t) * j;
	} else if (t <= -7.8e-177) {
		tmp = t_1;
	} else if (t <= 5.6e-219) {
		tmp = (i * b) * a;
	} else if (t <= 3.5e-30) {
		tmp = t_1;
	} else if (t <= 8.8e+46) {
		tmp = (b * a) * i;
	} else {
		tmp = (j * t) * c;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i, j)
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) * x
    if (t <= (-4.2d+98)) then
        tmp = (c * t) * j
    else if (t <= (-7.8d-177)) then
        tmp = t_1
    else if (t <= 5.6d-219) then
        tmp = (i * b) * a
    else if (t <= 3.5d-30) then
        tmp = t_1
    else if (t <= 8.8d+46) then
        tmp = (b * a) * i
    else
        tmp = (j * t) * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * y) * x;
	double tmp;
	if (t <= -4.2e+98) {
		tmp = (c * t) * j;
	} else if (t <= -7.8e-177) {
		tmp = t_1;
	} else if (t <= 5.6e-219) {
		tmp = (i * b) * a;
	} else if (t <= 3.5e-30) {
		tmp = t_1;
	} else if (t <= 8.8e+46) {
		tmp = (b * a) * i;
	} else {
		tmp = (j * t) * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * y) * x
	tmp = 0
	if t <= -4.2e+98:
		tmp = (c * t) * j
	elif t <= -7.8e-177:
		tmp = t_1
	elif t <= 5.6e-219:
		tmp = (i * b) * a
	elif t <= 3.5e-30:
		tmp = t_1
	elif t <= 8.8e+46:
		tmp = (b * a) * i
	else:
		tmp = (j * t) * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * y) * x)
	tmp = 0.0
	if (t <= -4.2e+98)
		tmp = Float64(Float64(c * t) * j);
	elseif (t <= -7.8e-177)
		tmp = t_1;
	elseif (t <= 5.6e-219)
		tmp = Float64(Float64(i * b) * a);
	elseif (t <= 3.5e-30)
		tmp = t_1;
	elseif (t <= 8.8e+46)
		tmp = Float64(Float64(b * a) * i);
	else
		tmp = Float64(Float64(j * t) * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (z * y) * x;
	tmp = 0.0;
	if (t <= -4.2e+98)
		tmp = (c * t) * j;
	elseif (t <= -7.8e-177)
		tmp = t_1;
	elseif (t <= 5.6e-219)
		tmp = (i * b) * a;
	elseif (t <= 3.5e-30)
		tmp = t_1;
	elseif (t <= 8.8e+46)
		tmp = (b * a) * i;
	else
		tmp = (j * t) * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t, -4.2e+98], N[(N[(c * t), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[t, -7.8e-177], t$95$1, If[LessEqual[t, 5.6e-219], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t, 3.5e-30], t$95$1, If[LessEqual[t, 8.8e+46], N[(N[(b * a), $MachinePrecision] * i), $MachinePrecision], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.20000000000000008e98

   1. Initial program 47.2%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 66.4

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

   5. Applied rewrites 66.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 38.6%

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

   10. Applied rewrites 38.7%

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

   if -4.20000000000000008e98 < t < -7.80000000000000028e-177 or 5.5999999999999998e-219 < t < 3.5000000000000003e-30

   1. Initial program 80.3%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 78.5%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 76.6%

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

   9. Taylor expanded in z around inf

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

       1. *-commutative N/A

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

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

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

       3. mul-1-neg N/A

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

       4. associate-*r* N/A

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

       5. +-commutative N/A

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

       6. lower-*.f64 N/A

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

       7. mul-1-neg N/A

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

       8. *-commutative N/A

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

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

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

       10. lower-fma.f64 N/A

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

       11. lower-neg.f64 N/A

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

       12. *-commutative N/A

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

       13. lower-*.f64 52.0

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

   11. Applied rewrites 52.0%

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

   12. Taylor expanded in x around inf

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

   14. Applied rewrites 41.1%

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

   if -7.80000000000000028e-177 < t < 5.5999999999999998e-219

   1. Initial program 78.0%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

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

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

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

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

      10. metadata-eval N/A

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

      11. *-lft-identity N/A

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

      12. lower-fma.f64 N/A

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

      13. mul-1-neg N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 56.3

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

   5. Applied rewrites 56.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 44.5%

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

   if 3.5000000000000003e-30 < t < 8.8000000000000001e46

   1. Initial program 75.1%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

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

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

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

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

      10. metadata-eval N/A

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

      11. *-lft-identity N/A

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

      12. lower-fma.f64 N/A

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

      13. mul-1-neg N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 55.3

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

   5. Applied rewrites 55.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 38.8%

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

   if 8.8000000000000001e46 < t

   1. Initial program 63.1%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 71.6

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

   5. Applied rewrites 71.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 48.8%

      \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{c} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 10: 50.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-178}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+45}:\\ \;\;\;\;\mathsf{fma}\left(-z, c, i \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- a) x (* j c)) t)))
   (if (<= t -4.2e+98)
     t_1
     (if (<= t -4.2e-178)
       (* (fma (- i) j (* z x)) y)
       (if (<= t 4.1e+45) (* (fma (- z) c (* i a)) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-a, x, (j * c)) * t;
	double tmp;
	if (t <= -4.2e+98) {
		tmp = t_1;
	} else if (t <= -4.2e-178) {
		tmp = fma(-i, j, (z * x)) * y;
	} else if (t <= 4.1e+45) {
		tmp = fma(-z, c, (i * a)) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-a), x, Float64(j * c)) * t)
	tmp = 0.0
	if (t <= -4.2e+98)
		tmp = t_1;
	elseif (t <= -4.2e-178)
		tmp = Float64(fma(Float64(-i), j, Float64(z * x)) * y);
	elseif (t <= 4.1e+45)
		tmp = Float64(fma(Float64(-z), c, Float64(i * a)) * b);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -4.2e+98], t$95$1, If[LessEqual[t, -4.2e-178], N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 4.1e+45], N[(N[((-z) * c + N[(i * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.20000000000000008e98 or 4.10000000000000012e45 < t

   1. Initial program 57.4%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 69.7

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

   5. Applied rewrites 69.7%

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

   if -4.20000000000000008e98 < t < -4.2e-178

   1. Initial program 80.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 55.4

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

   5. Applied rewrites 55.4%

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

   if -4.2e-178 < t < 4.10000000000000012e45

   1. Initial program 78.6%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. +-commutative N/A

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

      4. distribute-lft-neg-out N/A

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

      5. *-lft-identity N/A

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

      6. metadata-eval N/A

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

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

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

      8. mul-1-neg N/A

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

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

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

      10. distribute-neg-in N/A

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

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

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

      12. mul-1-neg N/A

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

      13. lower-*.f64 N/A

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

   5. Applied rewrites 60.1%

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

Alternative 11: 52.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{if}\;y \leq -1 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-171}:\\ \;\;\;\;\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(-x, t, i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- i) j (* z x)) y)))
   (if (<= y -1e+85)
     t_1
     (if (<= y -5.2e-171)
       (* (fma (- a) x (* j c)) t)
       (if (<= y 1.42e+65) (* (fma (- x) t (* i b)) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-i, j, (z * x)) * y;
	double tmp;
	if (y <= -1e+85) {
		tmp = t_1;
	} else if (y <= -5.2e-171) {
		tmp = fma(-a, x, (j * c)) * t;
	} else if (y <= 1.42e+65) {
		tmp = fma(-x, t, (i * b)) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-i), j, Float64(z * x)) * y)
	tmp = 0.0
	if (y <= -1e+85)
		tmp = t_1;
	elseif (y <= -5.2e-171)
		tmp = Float64(fma(Float64(-a), x, Float64(j * c)) * t);
	elseif (y <= 1.42e+65)
		tmp = Float64(fma(Float64(-x), t, Float64(i * b)) * a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1e+85], t$95$1, If[LessEqual[y, -5.2e-171], N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 1.42e+65], N[(N[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1e85 or 1.42000000000000012e65 < y

   1. Initial program 58.8%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 66.8

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

   5. Applied rewrites 66.8%

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

   if -1e85 < y < -5.2000000000000001e-171

   1. Initial program 76.8%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 63.1

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

   5. Applied rewrites 63.1%

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

   if -5.2000000000000001e-171 < y < 1.42000000000000012e65

   1. Initial program 84.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. mul-1-neg N/A

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

      7. *-commutative N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 54.2

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

   5. Applied rewrites 54.2%

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

Alternative 12: 51.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-216}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- a) x (* j c)) t)))
   (if (<= t -4.2e+98)
     t_1
     (if (<= t -2.55e-216)
       (* (fma (- i) j (* z x)) y)
       (if (<= t 2.8e-12) (* (fma (- b) c (* y x)) 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 = fma(-a, x, (j * c)) * t;
	double tmp;
	if (t <= -4.2e+98) {
		tmp = t_1;
	} else if (t <= -2.55e-216) {
		tmp = fma(-i, j, (z * x)) * y;
	} else if (t <= 2.8e-12) {
		tmp = fma(-b, c, (y * x)) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-a), x, Float64(j * c)) * t)
	tmp = 0.0
	if (t <= -4.2e+98)
		tmp = t_1;
	elseif (t <= -2.55e-216)
		tmp = Float64(fma(Float64(-i), j, Float64(z * x)) * y);
	elseif (t <= 2.8e-12)
		tmp = Float64(fma(Float64(-b), c, Float64(y * x)) * z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -4.2e+98], t$95$1, If[LessEqual[t, -2.55e-216], N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 2.8e-12], N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.20000000000000008e98 or 2.8000000000000002e-12 < t

   1. Initial program 59.1%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 65.2

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

   5. Applied rewrites 65.2%

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

   if -4.20000000000000008e98 < t < -2.5500000000000001e-216

   1. Initial program 82.2%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 53.7

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

   5. Applied rewrites 53.7%

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

   if -2.5500000000000001e-216 < t < 2.8000000000000002e-12

   1. Initial program 77.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. cancel-sign-sub-inv N/A

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 59.0

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

   5. Applied rewrites 59.0%

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

Alternative 13: 41.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{-197}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-219}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- a) t (* z y)) x)))
   (if (<= t -2.6e-197)
     t_1
     (if (<= t 5.6e-219)
       (* (* i b) a)
       (if (<= t 1.85e+92) t_1 (* (fma (- a) x (* j c)) t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-a, t, (z * y)) * x;
	double tmp;
	if (t <= -2.6e-197) {
		tmp = t_1;
	} else if (t <= 5.6e-219) {
		tmp = (i * b) * a;
	} else if (t <= 1.85e+92) {
		tmp = t_1;
	} else {
		tmp = fma(-a, x, (j * c)) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-a), t, Float64(z * y)) * x)
	tmp = 0.0
	if (t <= -2.6e-197)
		tmp = t_1;
	elseif (t <= 5.6e-219)
		tmp = Float64(Float64(i * b) * a);
	elseif (t <= 1.85e+92)
		tmp = t_1;
	else
		tmp = Float64(fma(Float64(-a), x, Float64(j * c)) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t, -2.6e-197], t$95$1, If[LessEqual[t, 5.6e-219], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t, 1.85e+92], t$95$1, N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.6000000000000001e-197 or 5.5999999999999998e-219 < t < 1.84999999999999999e92

   1. Initial program 73.3%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 75.3%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 73.5%

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

   9. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

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

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

       4. mul-1-neg N/A

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

       5. associate-*r* N/A

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

       6. +-commutative N/A

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

       7. associate-*r* N/A

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

       8. lower-fma.f64 N/A

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

       9. mul-1-neg N/A

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

       10. lower-neg.f64 N/A

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

       11. *-commutative N/A

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

       12. lower-*.f64 51.0

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

   11. Applied rewrites 51.0%

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

   if -2.6000000000000001e-197 < t < 5.5999999999999998e-219

   1. Initial program 76.5%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

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

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

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

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

      10. metadata-eval N/A

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

      11. *-lft-identity N/A

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

      12. lower-fma.f64 N/A

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

      13. mul-1-neg N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 53.5

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

   5. Applied rewrites 53.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 45.2%

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

   if 1.84999999999999999e92 < t

   1. Initial program 60.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 76.3

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

   5. Applied rewrites 76.3%

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

Alternative 14: 29.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot x\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+98}:\\ \;\;\;\;\left(c \cdot t\right) \cdot j\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-177}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-219}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{elif}\;t \leq 6.9 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z y) x)))
   (if (<= t -4.2e+98)
     (* (* c t) j)
     (if (<= t -7.8e-177)
       t_1
       (if (<= t 5.6e-219)
         (* (* i b) a)
         (if (<= t 6.9e+16) t_1 (* (* j t) c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * y) * x;
	double tmp;
	if (t <= -4.2e+98) {
		tmp = (c * t) * j;
	} else if (t <= -7.8e-177) {
		tmp = t_1;
	} else if (t <= 5.6e-219) {
		tmp = (i * b) * a;
	} else if (t <= 6.9e+16) {
		tmp = t_1;
	} else {
		tmp = (j * t) * c;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i, j)
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) * x
    if (t <= (-4.2d+98)) then
        tmp = (c * t) * j
    else if (t <= (-7.8d-177)) then
        tmp = t_1
    else if (t <= 5.6d-219) then
        tmp = (i * b) * a
    else if (t <= 6.9d+16) then
        tmp = t_1
    else
        tmp = (j * t) * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * y) * x;
	double tmp;
	if (t <= -4.2e+98) {
		tmp = (c * t) * j;
	} else if (t <= -7.8e-177) {
		tmp = t_1;
	} else if (t <= 5.6e-219) {
		tmp = (i * b) * a;
	} else if (t <= 6.9e+16) {
		tmp = t_1;
	} else {
		tmp = (j * t) * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * y) * x
	tmp = 0
	if t <= -4.2e+98:
		tmp = (c * t) * j
	elif t <= -7.8e-177:
		tmp = t_1
	elif t <= 5.6e-219:
		tmp = (i * b) * a
	elif t <= 6.9e+16:
		tmp = t_1
	else:
		tmp = (j * t) * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * y) * x)
	tmp = 0.0
	if (t <= -4.2e+98)
		tmp = Float64(Float64(c * t) * j);
	elseif (t <= -7.8e-177)
		tmp = t_1;
	elseif (t <= 5.6e-219)
		tmp = Float64(Float64(i * b) * a);
	elseif (t <= 6.9e+16)
		tmp = t_1;
	else
		tmp = Float64(Float64(j * t) * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (z * y) * x;
	tmp = 0.0;
	if (t <= -4.2e+98)
		tmp = (c * t) * j;
	elseif (t <= -7.8e-177)
		tmp = t_1;
	elseif (t <= 5.6e-219)
		tmp = (i * b) * a;
	elseif (t <= 6.9e+16)
		tmp = t_1;
	else
		tmp = (j * t) * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t, -4.2e+98], N[(N[(c * t), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[t, -7.8e-177], t$95$1, If[LessEqual[t, 5.6e-219], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t, 6.9e+16], t$95$1, N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.20000000000000008e98

   1. Initial program 47.2%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 66.4

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

   5. Applied rewrites 66.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 38.6%

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

   10. Applied rewrites 38.7%

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

   if -4.20000000000000008e98 < t < -7.80000000000000028e-177 or 5.5999999999999998e-219 < t < 6.9e16

   1. Initial program 80.5%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 79.7%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 77.9%

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

   9. Taylor expanded in z around inf

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

       1. *-commutative N/A

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

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

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

       3. mul-1-neg N/A

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

       4. associate-*r* N/A

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

       5. +-commutative N/A

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

       6. lower-*.f64 N/A

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

       7. mul-1-neg N/A

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

       8. *-commutative N/A

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

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

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

       10. lower-fma.f64 N/A

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

       11. lower-neg.f64 N/A

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

       12. *-commutative N/A

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

       13. lower-*.f64 51.1

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

   11. Applied rewrites 51.1%

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

   12. Taylor expanded in x around inf

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

   14. Applied rewrites 39.8%

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

   if -7.80000000000000028e-177 < t < 5.5999999999999998e-219

   1. Initial program 78.0%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

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

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

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

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

      10. metadata-eval N/A

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

      11. *-lft-identity N/A

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

      12. lower-fma.f64 N/A

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

      13. mul-1-neg N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 56.3

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

   5. Applied rewrites 56.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 44.5%

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

   if 6.9e16 < t

   1. Initial program 64.2%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 64.2

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

   5. Applied rewrites 64.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 42.0%

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

Alternative 15: 47.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-30}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -4.2e-30)
   (* (fma (- a) t (* z y)) x)
   (if (<= t 2.8e-12)
     (* (fma (- b) c (* y x)) z)
     (* (fma (- a) x (* j c)) t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -4.2e-30) {
		tmp = fma(-a, t, (z * y)) * x;
	} else if (t <= 2.8e-12) {
		tmp = fma(-b, c, (y * x)) * z;
	} else {
		tmp = fma(-a, x, (j * c)) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -4.2e-30)
		tmp = Float64(fma(Float64(-a), t, Float64(z * y)) * x);
	elseif (t <= 2.8e-12)
		tmp = Float64(fma(Float64(-b), c, Float64(y * x)) * z);
	else
		tmp = Float64(fma(Float64(-a), x, Float64(j * c)) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -4.2e-30], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, 2.8e-12], N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.2000000000000004e-30

   1. Initial program 64.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 67.3%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 67.3%

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

   9. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

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

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

       4. mul-1-neg N/A

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

       5. associate-*r* N/A

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

       6. +-commutative N/A

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

       7. associate-*r* N/A

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

       8. lower-fma.f64 N/A

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

       9. mul-1-neg N/A

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

       10. lower-neg.f64 N/A

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

       11. *-commutative N/A

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

       12. lower-*.f64 55.2

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

   11. Applied rewrites 55.2%

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

   if -4.2000000000000004e-30 < t < 2.8000000000000002e-12

   1. Initial program 78.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. cancel-sign-sub-inv N/A

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 55.4

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

   5. Applied rewrites 55.4%

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

   if 2.8000000000000002e-12 < t

   1. Initial program 64.7%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 64.7

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

   5. Applied rewrites 64.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 16: 40.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2.5 \cdot 10^{+240}:\\ \;\;\;\;\left(\left(-j\right) \cdot y\right) \cdot i\\ \mathbf{elif}\;i \leq 1.45 \cdot 10^{+254}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -2.5e+240)
   (* (* (- j) y) i)
   (if (<= i 1.45e+254) (* (fma (- a) t (* z y)) x) (* (* b a) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -2.5e+240) {
		tmp = (-j * y) * i;
	} else if (i <= 1.45e+254) {
		tmp = fma(-a, t, (z * y)) * x;
	} else {
		tmp = (b * a) * i;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -2.5e+240)
		tmp = Float64(Float64(Float64(-j) * y) * i);
	elseif (i <= 1.45e+254)
		tmp = Float64(fma(Float64(-a), t, Float64(z * y)) * x);
	else
		tmp = Float64(Float64(b * a) * i);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -2.5e+240], N[(N[((-j) * y), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[i, 1.45e+254], N[(N[((-a) * t + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(b * a), $MachinePrecision] * i), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -2.5000000000000001e240

   1. Initial program 67.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]

      3. associate-*r* N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-1 \cdot a\right) \cdot b}\right) \cdot i \]

      4. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot b\right) \cdot i \]

      5. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right) \cdot b\right)} \cdot i \]

      6. *-commutative N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(y \cdot j\right)} + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right) \cdot b\right) \cdot i \]

      7. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot y\right) \cdot j} + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right) \cdot b\right) \cdot i \]

      8. mul-1-neg N/A

         \[\leadsto \left(\left(-1 \cdot y\right) \cdot j + \left(\mathsf{neg}\left(\color{blue}{-1 \cdot a}\right)\right) \cdot b\right) \cdot i \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \left(\left(-1 \cdot y\right) \cdot j + \color{blue}{\left(\left(\mathsf{neg}\left(-1\right)\right) \cdot a\right)} \cdot b\right) \cdot i \]

      10. metadata-eval N/A

          \[\leadsto \left(\left(-1 \cdot y\right) \cdot j + \left(\color{blue}{1} \cdot a\right) \cdot b\right) \cdot i \]

      11. *-lft-identity N/A

          \[\leadsto \left(\left(-1 \cdot y\right) \cdot j + \color{blue}{a} \cdot b\right) \cdot i \]

      12. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot y, j, a \cdot b\right)} \cdot i \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y\right)}, j, a \cdot b\right) \cdot i \]

      14. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-y}, j, a \cdot b\right) \cdot i \]

      15. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-y, j, \color{blue}{b \cdot a}\right) \cdot i \]

      16. lower-*.f64 78.4

          \[\leadsto \mathsf{fma}\left(-y, j, \color{blue}{b \cdot a}\right) \cdot i \]

   5. Applied rewrites 78.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, j, b \cdot a\right) \cdot i} \]

   6. Taylor expanded in y around inf

      \[\leadsto \left(-1 \cdot \left(j \cdot y\right)\right) \cdot i \]
   7. Step-by-step derivation

   8. Applied rewrites 56.5%

      \[\leadsto \left(\left(-j\right) \cdot y\right) \cdot i \]

   if -2.5000000000000001e240 < i < 1.45e254

   1. Initial program 73.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(j \cdot \left(c \cdot t - i \cdot y\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)} \]

   5. Applied rewrites 77.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-x, t, i \cdot b\right), a, \mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(t \cdot \left(-1 \cdot x + \frac{b \cdot i}{t}\right), a, \mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 72.7%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(b, \frac{i}{t}, -x\right) \cdot t, a, \mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\right) \]

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

       2. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

       3. fp-cancel-sub-sign-inv N/A

          \[\leadsto \color{blue}{\left(y \cdot z + \left(\mathsf{neg}\left(a\right)\right) \cdot t\right)} \cdot x \]

       4. mul-1-neg N/A

          \[\leadsto \left(y \cdot z + \color{blue}{\left(-1 \cdot a\right)} \cdot t\right) \cdot x \]

       5. associate-*r* N/A

          \[\leadsto \left(y \cdot z + \color{blue}{-1 \cdot \left(a \cdot t\right)}\right) \cdot x \]

       6. +-commutative N/A

          \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \cdot x \]

       7. associate-*r* N/A

          \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot t} + y \cdot z\right) \cdot x \]

       8. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot a, t, y \cdot z\right)} \cdot x \]

       9. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(a\right)}, t, y \cdot z\right) \cdot x \]

       10. lower-neg.f64 N/A

           \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, t, y \cdot z\right) \cdot x \]

       11. *-commutative N/A

           \[\leadsto \mathsf{fma}\left(-a, t, \color{blue}{z \cdot y}\right) \cdot x \]

       12. lower-*.f64 47.2

           \[\leadsto \mathsf{fma}\left(-a, t, \color{blue}{z \cdot y}\right) \cdot x \]

   11. Applied rewrites 47.2%

       \[\leadsto \color{blue}{\mathsf{fma}\left(-a, t, z \cdot y\right) \cdot x} \]

   if 1.45e254 < i

   1. Initial program 44.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]

      3. associate-*r* N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-1 \cdot a\right) \cdot b}\right) \cdot i \]

      4. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot b\right) \cdot i \]

      5. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right) \cdot b\right)} \cdot i \]

      6. *-commutative N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(y \cdot j\right)} + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right) \cdot b\right) \cdot i \]

      7. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot y\right) \cdot j} + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right) \cdot b\right) \cdot i \]

      8. mul-1-neg N/A

         \[\leadsto \left(\left(-1 \cdot y\right) \cdot j + \left(\mathsf{neg}\left(\color{blue}{-1 \cdot a}\right)\right) \cdot b\right) \cdot i \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \left(\left(-1 \cdot y\right) \cdot j + \color{blue}{\left(\left(\mathsf{neg}\left(-1\right)\right) \cdot a\right)} \cdot b\right) \cdot i \]

      10. metadata-eval N/A

          \[\leadsto \left(\left(-1 \cdot y\right) \cdot j + \left(\color{blue}{1} \cdot a\right) \cdot b\right) \cdot i \]

      11. *-lft-identity N/A

          \[\leadsto \left(\left(-1 \cdot y\right) \cdot j + \color{blue}{a} \cdot b\right) \cdot i \]

      12. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot y, j, a \cdot b\right)} \cdot i \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y\right)}, j, a \cdot b\right) \cdot i \]

      14. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-y}, j, a \cdot b\right) \cdot i \]

      15. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-y, j, \color{blue}{b \cdot a}\right) \cdot i \]

      16. lower-*.f64 100.0

          \[\leadsto \mathsf{fma}\left(-y, j, \color{blue}{b \cdot a}\right) \cdot i \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, j, b \cdot a\right) \cdot i} \]

   6. Taylor expanded in y around 0

      \[\leadsto \left(a \cdot b\right) \cdot i \]
   7. Step-by-step derivation

   8. Applied rewrites 100.0%

      \[\leadsto \left(b \cdot a\right) \cdot i \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 17: 29.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+98}:\\ \;\;\;\;\left(c \cdot t\right) \cdot j\\ \mathbf{elif}\;t \leq 6.9 \cdot 10^{+16}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -4.2e+98)
   (* (* c t) j)
   (if (<= t 6.9e+16) (* (* z y) x) (* (* j t) c))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -4.2e+98) {
		tmp = (c * t) * j;
	} else if (t <= 6.9e+16) {
		tmp = (z * y) * x;
	} else {
		tmp = (j * t) * c;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
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 (t <= (-4.2d+98)) then
        tmp = (c * t) * j
    else if (t <= 6.9d+16) then
        tmp = (z * y) * x
    else
        tmp = (j * t) * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -4.2e+98) {
		tmp = (c * t) * j;
	} else if (t <= 6.9e+16) {
		tmp = (z * y) * x;
	} else {
		tmp = (j * t) * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -4.2e+98:
		tmp = (c * t) * j
	elif t <= 6.9e+16:
		tmp = (z * y) * x
	else:
		tmp = (j * t) * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -4.2e+98)
		tmp = Float64(Float64(c * t) * j);
	elseif (t <= 6.9e+16)
		tmp = Float64(Float64(z * y) * x);
	else
		tmp = Float64(Float64(j * t) * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -4.2e+98)
		tmp = (c * t) * j;
	elseif (t <= 6.9e+16)
		tmp = (z * y) * x;
	else
		tmp = (j * t) * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -4.2e+98], N[(N[(c * t), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[t, 6.9e+16], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.20000000000000008e98

   1. Initial program 47.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

      3. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + c \cdot j\right) \cdot t \]

      4. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + c \cdot j\right) \cdot t \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, c \cdot j\right)} \cdot t \]

      6. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, c \cdot j\right) \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

      8. lower-*.f64 66.4

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

   5. Applied rewrites 66.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]

   6. Taylor expanded in x around 0

      \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 38.6%

      \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{c} \]
   9. Step-by-step derivation

   10. Applied rewrites 38.7%

       \[\leadsto \left(c \cdot t\right) \cdot j \]

   if -4.20000000000000008e98 < t < 6.9e16

   1. Initial program 79.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(j \cdot \left(c \cdot t - i \cdot y\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)} \]

   5. Applied rewrites 79.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-x, t, i \cdot b\right), a, \mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(t \cdot \left(-1 \cdot x + \frac{b \cdot i}{t}\right), a, \mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 72.3%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(b, \frac{i}{t}, -x\right) \cdot t, a, \mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\right) \]

   9. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \color{blue}{\left(x \cdot y - b \cdot c\right) \cdot z} \]

       2. fp-cancel-sub-sign-inv N/A

          \[\leadsto \color{blue}{\left(x \cdot y + \left(\mathsf{neg}\left(b\right)\right) \cdot c\right)} \cdot z \]

       3. mul-1-neg N/A

          \[\leadsto \left(x \cdot y + \color{blue}{\left(-1 \cdot b\right)} \cdot c\right) \cdot z \]

       4. associate-*r* N/A

          \[\leadsto \left(x \cdot y + \color{blue}{-1 \cdot \left(b \cdot c\right)}\right) \cdot z \]

       5. +-commutative N/A

          \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot c\right) + x \cdot y\right)} \cdot z \]

       6. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot c\right) + x \cdot y\right) \cdot z} \]

       7. mul-1-neg N/A

          \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(b \cdot c\right)\right)} + x \cdot y\right) \cdot z \]

       8. *-commutative N/A

          \[\leadsto \left(\left(\mathsf{neg}\left(\color{blue}{c \cdot b}\right)\right) + x \cdot y\right) \cdot z \]

       9. distribute-lft-neg-in N/A

          \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(c\right)\right) \cdot b} + x \cdot y\right) \cdot z \]

       10. lower-fma.f64 N/A

           \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(c\right), b, x \cdot y\right)} \cdot z \]

       11. lower-neg.f64 N/A

           \[\leadsto \mathsf{fma}\left(\color{blue}{-c}, b, x \cdot y\right) \cdot z \]

       12. *-commutative N/A

           \[\leadsto \mathsf{fma}\left(-c, b, \color{blue}{y \cdot x}\right) \cdot z \]

       13. lower-*.f64 50.9

           \[\leadsto \mathsf{fma}\left(-c, b, \color{blue}{y \cdot x}\right) \cdot z \]

   11. Applied rewrites 50.9%

       \[\leadsto \color{blue}{\mathsf{fma}\left(-c, b, y \cdot x\right) \cdot z} \]

   12. Taylor expanded in x around inf

       \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   13. Step-by-step derivation

   14. Applied rewrites 34.4%

       \[\leadsto \left(z \cdot y\right) \cdot \color{blue}{x} \]

   if 6.9e16 < t

   1. Initial program 64.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

      3. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + c \cdot j\right) \cdot t \]

      4. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + c \cdot j\right) \cdot t \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, c \cdot j\right)} \cdot t \]

      6. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, c \cdot j\right) \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

      8. lower-*.f64 64.2

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

   5. Applied rewrites 64.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]

   6. Taylor expanded in x around 0

      \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 42.0%

      \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{c} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 22.1% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{-298}:\\ \;\;\;\;\left(j \cdot t\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot t\right) \cdot j\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1e-298) (* (* j t) c) (* (* c t) j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1e-298) {
		tmp = (j * t) * c;
	} else {
		tmp = (c * t) * j;
	}
	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 (a <= (-1d-298)) then
        tmp = (j * t) * c
    else
        tmp = (c * t) * j
    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 (a <= -1e-298) {
		tmp = (j * t) * c;
	} else {
		tmp = (c * t) * j;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1e-298:
		tmp = (j * t) * c
	else:
		tmp = (c * t) * j
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1e-298)
		tmp = Float64(Float64(j * t) * c);
	else
		tmp = Float64(Float64(c * t) * j);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1e-298)
		tmp = (j * t) * c;
	else
		tmp = (c * t) * j;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1e-298], N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision], N[(N[(c * t), $MachinePrecision] * j), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -9.99999999999999912e-299

   1. Initial program 72.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

      3. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + c \cdot j\right) \cdot t \]

      4. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + c \cdot j\right) \cdot t \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, c \cdot j\right)} \cdot t \]

      6. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, c \cdot j\right) \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

      8. lower-*.f64 38.6

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

   5. Applied rewrites 38.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]

   6. Taylor expanded in x around 0

      \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 22.0%

      \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{c} \]

   if -9.99999999999999912e-299 < a

   1. Initial program 70.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

      3. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + c \cdot j\right) \cdot t \]

      4. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + c \cdot j\right) \cdot t \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, c \cdot j\right)} \cdot t \]

      6. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, c \cdot j\right) \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

      8. lower-*.f64 37.7

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

   5. Applied rewrites 37.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]

   6. Taylor expanded in x around 0

      \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 18.2%

      \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{c} \]
   9. Step-by-step derivation

   10. Applied rewrites 21.7%

       \[\leadsto \left(c \cdot t\right) \cdot j \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 22.3% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \left(c \cdot t\right) \cdot j \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* (* c t) j))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return (c * t) * j;
}

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 = (c * t) * j
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 (c * t) * j;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return (c * t) * j

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(c * t) * j)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = (c * t) * j;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(c * t), $MachinePrecision] * j), $MachinePrecision]

Derivation

1. Initial program 71.6%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Add Preprocessing

3. Taylor expanded in t around inf

   \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

   2. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

   3. associate-*r* N/A

      \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + c \cdot j\right) \cdot t \]

   4. mul-1-neg N/A

      \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + c \cdot j\right) \cdot t \]

   5. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, c \cdot j\right)} \cdot t \]

   6. lower-neg.f64 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, c \cdot j\right) \cdot t \]

   7. *-commutative N/A

      \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

   8. lower-*.f64 38.1

      \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

5. Applied rewrites 38.1%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]

6. Taylor expanded in x around 0

   \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
7. Step-by-step derivation

8. Applied rewrites 20.0%

   \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{c} \]
9. Step-by-step derivation

10. Applied rewrites 20.0%

    \[\leadsto \left(c \cdot t\right) \cdot j \]
11. Add Preprocessing

Developer Target 1: 68.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

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) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024352 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -1015122364899489/125000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -942510763643697/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (if (< t -238547917063487/3125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 10535888557455487/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))