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

Percentage Accurate: 73.9% → 84.0%

Time: 58.5s

Alternatives: 25

Speedup: 0.5×

• 41.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 84.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{if}\;\left(t\_1 - b \cdot \left(c \cdot z - t \cdot i\right)\right) + t\_2 \leq \infty:\\ \;\;\;\;\left(t\_1 - \mathsf{134\_z0z1z2z3z4}\left(b, z, c, t, i\right)\right) + t\_2\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (let* ((t_1 (* x (- (* y z) (* t a))))
       (t_2 (* j (- (* c a) (* y i)))))
  (if (<= (+ (- t_1 (* b (- (* c z) (* t i)))) t_2) INFINITY)
    (+ (- t_1 (134-z0z1z2z3z4 b z c t i)) t_2)
    (* j (- (* a c) (* i y))))))

Derivation

1. Split input into 2 regimes

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

   1. Initial program 73.9%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

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

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

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

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

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

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

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

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

      10. remove-double-neg N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. lower-134-z0z1z2z3z4 78.1%

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, t, i\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   3. Applied rewrites 78.1%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, t, i\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

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

   1. Initial program 73.9%

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

   2. Taylor expanded in b around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 59.8%

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

   4. Applied rewrites 59.8%

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

   5. Taylor expanded in i around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 51.3%

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

   7. Applied rewrites 51.3%

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

   8. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 39.6%

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

   10. Applied rewrites 39.6%

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

Alternative 2: 84.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\\ \mathbf{if}\;t\_1 + j \cdot \left(c \cdot a - y \cdot i\right) \leq \infty:\\ \;\;\;\;t\_1 + \mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (let* ((t_1 (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i))))))
  (if (<= (+ t_1 (* j (- (* c a) (* y i)))) INFINITY)
    (+ t_1 (134-z0z1z2z3z4 j c a y i))
    (* j (- (* a c) (* i y))))))

Derivation

1. Split input into 2 regimes

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

   1. Initial program 73.9%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

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

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

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

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

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

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

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

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

      10. remove-double-neg N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lower-134-z0z1z2z3z4 78.1%

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right)} \]

   3. Applied rewrites 78.1%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right)} \]

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

   1. Initial program 73.9%

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

   2. Taylor expanded in b around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 59.8%

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

   4. Applied rewrites 59.8%

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

   5. Taylor expanded in i around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 51.3%

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

   7. Applied rewrites 51.3%

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

   8. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 39.6%

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

   10. Applied rewrites 39.6%

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

Alternative 3: 81.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 73.9%

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

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

   1. Initial program 73.9%

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

   2. Taylor expanded in b around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 59.8%

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

   4. Applied rewrites 59.8%

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

   5. Taylor expanded in i around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 51.3%

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

   7. Applied rewrites 51.3%

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

   8. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 39.6%

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

   10. Applied rewrites 39.6%

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

Alternative 4: 66.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{if}\;j \leq \frac{-2561194933379311}{26959946667150639794667015087019630673637144422540572481103610249216}:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(t, i, b, x, a\right) + t\_1\\ \mathbf{elif}\;j \leq \frac{1210964111994553}{6210072369202835740595917953850010221027544068466786444556208152104203810745507545323513635314585911801950922788524292824686320176459257565777149100164724556817819904083399622201061142526393779301051996774865875003571387415264231424}:\\ \;\;\;\;\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)\\ \mathbf{elif}\;j \leq \frac{1725436586697641}{6901746346790563787434755862277025452451108972170386555162524223799296}:\\ \;\;\;\;-1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right) + \mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (let* ((t_1 (* j (- (* c a) (* y i)))))
  (if (<=
       j
       -2561194933379311/26959946667150639794667015087019630673637144422540572481103610249216)
    (+ (134-z0z1z2z3z4 t i b x a) t_1)
    (if (<=
         j
         1210964111994553/6210072369202835740595917953850010221027544068466786444556208152104203810745507545323513635314585911801950922788524292824686320176459257565777149100164724556817819904083399622201061142526393779301051996774865875003571387415264231424)
      (-
       (+ (* -1 (* a (* t x))) (* a (* c j)))
       (* b (- (* c z) (* i t))))
      (if (<=
           j
           1725436586697641/6901746346790563787434755862277025452451108972170386555162524223799296)
        (+
         (* -1 (* t (- (* a x) (* b i))))
         (134-z0z1z2z3z4 j c a y i))
        (+ (* z (- (* x y) (* b c))) t_1))))))

Derivation

1. Split input into 4 regimes

2. if j < -9.5000000000000008e-53

   1. Initial program 73.9%

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

   2. Taylor expanded in t around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 59.3%

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

   4. Applied rewrites 59.3%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

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

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

      8. add-flip N/A

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

      9. sub-negate N/A

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

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

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

      11. lift-*.f64 N/A

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

      12. remove-double-neg N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-134-z0z1z2z3z4 62.8%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(t, \color{blue}{i}, b, x, a\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Applied rewrites 62.8%

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(t, \color{blue}{i}, b, x, a\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   if -9.5000000000000008e-53 < j < 1.95e-217

   1. Initial program 73.9%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 58.6%

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

   4. Applied rewrites 58.6%

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

   if 1.95e-217 < j < 2.5000000000000001e-55

   1. Initial program 73.9%

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

   2. Taylor expanded in t around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 59.3%

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

   4. Applied rewrites 59.3%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lower-134-z0z1z2z3z4 62.7%

         \[\leadsto -1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right) + \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right)} \]

   6. Applied rewrites 62.7%

      \[\leadsto -1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right) + \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right)} \]

   if 2.5000000000000001e-55 < j

   1. Initial program 73.9%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 59.4%

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

   4. Applied rewrites 59.4%

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

Alternative 5: 66.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right) + t\_1\\ \mathbf{if}\;c \leq \frac{-1968499104217263}{803469022129495137770981046170581301261101496891396417650688}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 82000000000000000000:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(t, i, b, x, a\right) + t\_1\\ \mathbf{elif}\;c \leq 69999999999999996580030472474645924373724123228303516896266087234014582066249714282948715224206381596671128141369967796948637772753867451648450151483935177956392565768613975005440655767603603570688:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(c, j, a, z, b\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (let* ((t_1 (* j (- (* c a) (* y i))))
       (t_2 (+ (* z (- (* x y) (* b c))) t_1)))
  (if (<=
       c
       -1968499104217263/803469022129495137770981046170581301261101496891396417650688)
    t_2
    (if (<= c 82000000000000000000)
      (+ (134-z0z1z2z3z4 t i b x a) t_1)
      (if (<=
           c
           69999999999999996580030472474645924373724123228303516896266087234014582066249714282948715224206381596671128141369967796948637772753867451648450151483935177956392565768613975005440655767603603570688)
        t_2
        (134-z0z1z2z3z4 c j a z b))))))

Derivation

1. Split input into 3 regimes

2. if c < -2.4499999999999999e-45 or 8.2e19 < c < 6.9999999999999997e196

   1. Initial program 73.9%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 59.4%

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

   4. Applied rewrites 59.4%

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

   if -2.4499999999999999e-45 < c < 8.2e19

   1. Initial program 73.9%

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

   2. Taylor expanded in t around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 59.3%

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

   4. Applied rewrites 59.3%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

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

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

      8. add-flip N/A

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

      9. sub-negate N/A

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

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

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

      11. lift-*.f64 N/A

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

      12. remove-double-neg N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-134-z0z1z2z3z4 62.8%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(t, \color{blue}{i}, b, x, a\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Applied rewrites 62.8%

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(t, \color{blue}{i}, b, x, a\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   if 6.9999999999999997e196 < c

   1. Initial program 73.9%

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

   2. Taylor expanded in c around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 39.7%

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

   4. Applied rewrites 39.7%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

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

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

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

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

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

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

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

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

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

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. remove-double-neg N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-134-z0z1z2z3z4 39.5%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(c, \color{blue}{j}, a, z, b\right) \]

   6. Applied rewrites 39.5%

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(c, \color{blue}{j}, a, z, b\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 63.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;j \leq \frac{1725436586697641}{6901746346790563787434755862277025452451108972170386555162524223799296}:\\ \;\;\;\;-1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right) + \mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (if (<=
     j
     1725436586697641/6901746346790563787434755862277025452451108972170386555162524223799296)
  (+ (* -1 (* t (- (* a x) (* b i)))) (134-z0z1z2z3z4 j c a y i))
  (+ (* z (- (* x y) (* b c))) (* j (- (* c a) (* y i))))))

Derivation

1. Split input into 2 regimes

2. if j < 2.5000000000000001e-55

   1. Initial program 73.9%

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

   2. Taylor expanded in t around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 59.3%

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

   4. Applied rewrites 59.3%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lower-134-z0z1z2z3z4 62.7%

         \[\leadsto -1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right) + \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right)} \]

   6. Applied rewrites 62.7%

      \[\leadsto -1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right) + \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right)} \]

   if 2.5000000000000001e-55 < j

   1. Initial program 73.9%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 59.4%

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

   4. Applied rewrites 59.4%

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

Alternative 7: 63.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := b \cdot \left(i \cdot t\right) + \mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right)\\ \mathbf{if}\;i \leq -6600000000000000170498070795170432660144950935994891604555722343977806925614311324299607146496:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 749999999999999941246189568:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + t\_1\\ \mathbf{elif}\;i \leq 27000000000000000922834500647727241045210369510666415635740567789841827394974450876641813549004880291063176848469465534841235627977264177678370097423367893744448087470656798904802291653415713371904815015478794649600:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(b \cdot \left(c \cdot z\right)\right) + t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (let* ((t_1 (* j (- (* c a) (* y i))))
       (t_2 (+ (* b (* i t)) (134-z0z1z2z3z4 j c a y i))))
  (if (<=
       i
       -6600000000000000170498070795170432660144950935994891604555722343977806925614311324299607146496)
    t_2
    (if (<= i 749999999999999941246189568)
      (+ (* z (- (* x y) (* b c))) t_1)
      (if (<=
           i
           27000000000000000922834500647727241045210369510666415635740567789841827394974450876641813549004880291063176848469465534841235627977264177678370097423367893744448087470656798904802291653415713371904815015478794649600)
        t_2
        (+ (* -1 (* b (* c z))) t_1))))))

Derivation

1. Split input into 3 regimes

2. if i < -6.6000000000000002e93 or 7.4999999999999994e26 < i < 2.7000000000000001e214

   1. Initial program 73.9%

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

   2. Taylor expanded in t around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 59.3%

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

   4. Applied rewrites 59.3%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lower-134-z0z1z2z3z4 62.7%

         \[\leadsto -1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right) + \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right)} \]

   6. Applied rewrites 62.7%

      \[\leadsto -1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right) + \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right)} \]

   7. Taylor expanded in x around 0

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} + \mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right) \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(i \cdot \color{blue}{t}\right) + \mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right) \]

      2. lower-*.f64 51.7%

         \[\leadsto b \cdot \left(i \cdot t\right) + \mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right) \]

   9. Applied rewrites 51.7%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} + \mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right) \]

   if -6.6000000000000002e93 < i < 7.4999999999999994e26

   1. Initial program 73.9%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 59.4%

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

   4. Applied rewrites 59.4%

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

   if 2.7000000000000001e214 < i

   1. Initial program 73.9%

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

   2. Taylor expanded in c around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 50.0%

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

   4. Applied rewrites 50.0%

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

Alternative 8: 62.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := b \cdot \left(i \cdot t\right) + \mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right)\\ \mathbf{if}\;i \leq -55000000000000000981369353015810551861615715402103866681329908659147537121280:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq \frac{8620287417370625}{11972621413014756705924586149611790497021399392059392}:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\\ \mathbf{elif}\;i \leq 27000000000000000922834500647727241045210369510666415635740567789841827394974450876641813549004880291063176848469465534841235627977264177678370097423367893744448087470656798904802291653415713371904815015478794649600:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(b \cdot \left(c \cdot z\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (let* ((t_1 (+ (* b (* i t)) (134-z0z1z2z3z4 j c a y i))))
  (if (<=
       i
       -55000000000000000981369353015810551861615715402103866681329908659147537121280)
    t_1
    (if (<=
         i
         8620287417370625/11972621413014756705924586149611790497021399392059392)
      (+ (* j (- (* a c) (* i y))) (* x (- (* y z) (* a t))))
      (if (<=
           i
           27000000000000000922834500647727241045210369510666415635740567789841827394974450876641813549004880291063176848469465534841235627977264177678370097423367893744448087470656798904802291653415713371904815015478794649600)
        t_1
        (+ (* -1 (* b (* c z))) (* j (- (* c a) (* y i)))))))))

Derivation

1. Split input into 3 regimes

2. if i < -5.5000000000000001e76 or 7.2000000000000001e-37 < i < 2.7000000000000001e214

   1. Initial program 73.9%

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

   2. Taylor expanded in t around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 59.3%

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

   4. Applied rewrites 59.3%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lower-134-z0z1z2z3z4 62.7%

         \[\leadsto -1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right) + \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right)} \]

   6. Applied rewrites 62.7%

      \[\leadsto -1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right) + \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right)} \]

   7. Taylor expanded in x around 0

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} + \mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right) \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(i \cdot \color{blue}{t}\right) + \mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right) \]

      2. lower-*.f64 51.7%

         \[\leadsto b \cdot \left(i \cdot t\right) + \mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right) \]

   9. Applied rewrites 51.7%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} + \mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right) \]

   if -5.5000000000000001e76 < i < 7.2000000000000001e-37

   1. Initial program 73.9%

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

   2. Taylor expanded in b around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 59.8%

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

   4. Applied rewrites 59.8%

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

   if 2.7000000000000001e214 < i

   1. Initial program 73.9%

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

   2. Taylor expanded in c around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 50.0%

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

   4. Applied rewrites 50.0%

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

Alternative 9: 61.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := b \cdot \left(i \cdot t\right) + \mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right)\\ \mathbf{if}\;i \leq -749999999999999992703876120785120969834346383151554625536:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq \frac{8612299728833109}{273406340597876490546562778389702670669146178861651554553221325801244124899921990402939147127881728}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + \mathsf{134\_z0z1z2z3z4}\left(x, z, y, t, a\right)\\ \mathbf{elif}\;i \leq 27000000000000000922834500647727241045210369510666415635740567789841827394974450876641813549004880291063176848469465534841235627977264177678370097423367893744448087470656798904802291653415713371904815015478794649600:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(b \cdot \left(c \cdot z\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (let* ((t_1 (+ (* b (* i t)) (134-z0z1z2z3z4 j c a y i))))
  (if (<=
       i
       -749999999999999992703876120785120969834346383151554625536)
    t_1
    (if (<=
         i
         8612299728833109/273406340597876490546562778389702670669146178861651554553221325801244124899921990402939147127881728)
      (+ (* a (* c j)) (134-z0z1z2z3z4 x z y t a))
      (if (<=
           i
           27000000000000000922834500647727241045210369510666415635740567789841827394974450876641813549004880291063176848469465534841235627977264177678370097423367893744448087470656798904802291653415713371904815015478794649600)
        t_1
        (+ (* -1 (* b (* c z))) (* j (- (* c a) (* y i)))))))))

Derivation

1. Split input into 3 regimes

2. if i < -7.4999999999999999e56 or 3.1499999999999998e-83 < i < 2.7000000000000001e214

   1. Initial program 73.9%

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

   2. Taylor expanded in t around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 59.3%

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

   4. Applied rewrites 59.3%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lower-134-z0z1z2z3z4 62.7%

         \[\leadsto -1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right) + \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right)} \]

   6. Applied rewrites 62.7%

      \[\leadsto -1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right) + \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right)} \]

   7. Taylor expanded in x around 0

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} + \mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right) \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(i \cdot \color{blue}{t}\right) + \mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right) \]

      2. lower-*.f64 51.7%

         \[\leadsto b \cdot \left(i \cdot t\right) + \mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right) \]

   9. Applied rewrites 51.7%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} + \mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right) \]

   if -7.4999999999999999e56 < i < 3.1499999999999998e-83

   1. Initial program 73.9%

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

   2. Taylor expanded in b around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 59.8%

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

   4. Applied rewrites 59.8%

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

   5. Taylor expanded in i around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 51.3%

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

   7. Applied rewrites 51.3%

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

      1. remove-double-neg N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

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

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

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

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. *-commutative N/A

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

      9. sub-negate-rev N/A

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

      10. lift--.f64 N/A

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

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

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

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

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

      13. remove-double-neg N/A

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

      14. lift--.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lift-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-134-z0z1z2z3z4 53.4%

          \[\leadsto a \cdot \left(c \cdot j\right) + \mathsf{134\_z0z1z2z3z4}\left(x, z, y, t, a\right) \]

   9. Applied rewrites 53.4%

      \[\leadsto a \cdot \left(c \cdot j\right) + \mathsf{134\_z0z1z2z3z4}\left(x, z, y, t, a\right) \]

   if 2.7000000000000001e214 < i

   1. Initial program 73.9%

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

   2. Taylor expanded in c around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 50.0%

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

   4. Applied rewrites 50.0%

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

Alternative 10: 61.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := b \cdot \left(i \cdot t\right) + \mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right)\\ \mathbf{if}\;i \leq -749999999999999992703876120785120969834346383151554625536:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq \frac{8612299728833109}{273406340597876490546562778389702670669146178861651554553221325801244124899921990402939147127881728}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + \mathsf{134\_z0z1z2z3z4}\left(x, z, y, t, a\right)\\ \mathbf{elif}\;i \leq 36000000000000001230446000863636321393613826014221887514320757053122436526632601168855751398673173721417569131292620713121647503969685570237826796564490524992597449960875731873069722204554284495873086687305059532800:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (let* ((t_1 (+ (* b (* i t)) (134-z0z1z2z3z4 j c a y i))))
  (if (<=
       i
       -749999999999999992703876120785120969834346383151554625536)
    t_1
    (if (<=
         i
         8612299728833109/273406340597876490546562778389702670669146178861651554553221325801244124899921990402939147127881728)
      (+ (* a (* c j)) (134-z0z1z2z3z4 x z y t a))
      (if (<=
           i
           36000000000000001230446000863636321393613826014221887514320757053122436526632601168855751398673173721417569131292620713121647503969685570237826796564490524992597449960875731873069722204554284495873086687305059532800)
        t_1
        (* j (- (* a c) (* i y))))))))

Derivation

1. Split input into 3 regimes

2. if i < -7.4999999999999999e56 or 3.1499999999999998e-83 < i < 3.6000000000000001e214

   1. Initial program 73.9%

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

   2. Taylor expanded in t around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 59.3%

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

   4. Applied rewrites 59.3%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lower-134-z0z1z2z3z4 62.7%

         \[\leadsto -1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right) + \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right)} \]

   6. Applied rewrites 62.7%

      \[\leadsto -1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right) + \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right)} \]

   7. Taylor expanded in x around 0

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} + \mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right) \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(i \cdot \color{blue}{t}\right) + \mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right) \]

      2. lower-*.f64 51.7%

         \[\leadsto b \cdot \left(i \cdot t\right) + \mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right) \]

   9. Applied rewrites 51.7%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} + \mathsf{134\_z0z1z2z3z4}\left(j, c, a, y, i\right) \]

   if -7.4999999999999999e56 < i < 3.1499999999999998e-83

   1. Initial program 73.9%

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

   2. Taylor expanded in b around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 59.8%

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

   4. Applied rewrites 59.8%

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

   5. Taylor expanded in i around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 51.3%

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

   7. Applied rewrites 51.3%

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

      1. remove-double-neg N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

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

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

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

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. *-commutative N/A

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

      9. sub-negate-rev N/A

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

      10. lift--.f64 N/A

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

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

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

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

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

      13. remove-double-neg N/A

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

      14. lift--.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lift-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-134-z0z1z2z3z4 53.4%

          \[\leadsto a \cdot \left(c \cdot j\right) + \mathsf{134\_z0z1z2z3z4}\left(x, z, y, t, a\right) \]

   9. Applied rewrites 53.4%

      \[\leadsto a \cdot \left(c \cdot j\right) + \mathsf{134\_z0z1z2z3z4}\left(x, z, y, t, a\right) \]

   if 3.6000000000000001e214 < i

   1. Initial program 73.9%

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

   2. Taylor expanded in b around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 59.8%

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

   4. Applied rewrites 59.8%

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

   5. Taylor expanded in i around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 51.3%

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

   7. Applied rewrites 51.3%

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

   8. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 39.6%

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

   10. Applied rewrites 39.6%

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

Alternative 11: 55.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;c \leq \frac{-8021834716940879}{102844034832575377634685573909834406561420991602098741459288064}:\\ \;\;\;\;-1 \cdot \left(b \cdot \left(c \cdot z\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;c \leq 11500000000000001048576:\\ \;\;\;\;-1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right) + j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(c, j, a, z, b\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (if (<=
     c
     -8021834716940879/102844034832575377634685573909834406561420991602098741459288064)
  (+ (* -1 (* b (* c z))) (* j (- (* c a) (* y i))))
  (if (<= c 11500000000000001048576)
    (+ (* -1 (* t (- (* a x) (* b i)))) (* j (* a c)))
    (134-z0z1z2z3z4 c j a z b))))

Derivation

1. Split input into 3 regimes

2. if c < -7.7999999999999996e-47

   1. Initial program 73.9%

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

   2. Taylor expanded in c around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 50.0%

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

   4. Applied rewrites 50.0%

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

   if -7.7999999999999996e-47 < c < 1.1500000000000001e22

   1. Initial program 73.9%

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

   2. Taylor expanded in t around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 59.3%

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

   4. Applied rewrites 59.3%

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

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 49.4%

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

   7. Applied rewrites 49.4%

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

   if 1.1500000000000001e22 < c

   1. Initial program 73.9%

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

   2. Taylor expanded in c around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 39.7%

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

   4. Applied rewrites 39.7%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

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

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

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

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

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

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

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

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

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

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. remove-double-neg N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-134-z0z1z2z3z4 39.5%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(c, \color{blue}{j}, a, z, b\right) \]

   6. Applied rewrites 39.5%

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(c, \color{blue}{j}, a, z, b\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 53.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;c \leq -3399999999999999831186108956068229205858928944848587501332570464514623530847100049246365002819165417460259049247034162670765820368522630572013466729871336663874751765025393289173714528632832:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;c \leq \frac{-2639280756911205}{3105036184601417870297958976925005110513772034233393222278104076052101905372753772661756817657292955900975461394262146412343160088229628782888574550082362278408909952041699811100530571263196889650525998387432937501785693707632115712}:\\ \;\;\;\;b \cdot \left(i \cdot t\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;c \leq 1720000000:\\ \;\;\;\;-1 \cdot \left(i \cdot \left(j \cdot y - b \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(c, j, a, z, b\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (if (<=
     c
     -3399999999999999831186108956068229205858928944848587501332570464514623530847100049246365002819165417460259049247034162670765820368522630572013466729871336663874751765025393289173714528632832)
  (* c (- (* a j) (* b z)))
  (if (<=
       c
       -2639280756911205/3105036184601417870297958976925005110513772034233393222278104076052101905372753772661756817657292955900975461394262146412343160088229628782888574550082362278408909952041699811100530571263196889650525998387432937501785693707632115712)
    (+ (* b (* i t)) (* j (- (* c a) (* y i))))
    (if (<= c 1720000000)
      (* -1 (* i (- (* j y) (* b t))))
      (134-z0z1z2z3z4 c j a z b)))))

Derivation

1. Split input into 4 regimes

2. if c < -3.3999999999999998e189

   1. Initial program 73.9%

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

   2. Taylor expanded in c around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 39.7%

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

   4. Applied rewrites 39.7%

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

   if -3.3999999999999998e189 < c < -8.4999999999999994e-217

   1. Initial program 73.9%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 49.8%

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

   4. Applied rewrites 49.8%

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

   if -8.4999999999999994e-217 < c < 1.72e9

   1. Initial program 73.9%

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

   2. Taylor expanded in i around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 39.6%

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

   4. Applied rewrites 39.6%

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

   if 1.72e9 < c

   1. Initial program 73.9%

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

   2. Taylor expanded in c around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 39.7%

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

   4. Applied rewrites 39.7%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

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

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

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

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

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

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

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

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

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

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. remove-double-neg N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-134-z0z1z2z3z4 39.5%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(c, \color{blue}{j}, a, z, b\right) \]

   6. Applied rewrites 39.5%

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(c, \color{blue}{j}, a, z, b\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 13: 52.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;c \leq -1220000000000000007013907797317579868768389929320174277104788231821610384184081590843392043250260152214957873851109129026390557322570104832:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;c \leq 1720000000:\\ \;\;\;\;-1 \cdot \left(i \cdot \left(j \cdot y - b \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(c, j, a, z, b\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (if (<=
     c
     -1220000000000000007013907797317579868768389929320174277104788231821610384184081590843392043250260152214957873851109129026390557322570104832)
  (* c (- (* a j) (* b z)))
  (if (<= c 1720000000)
    (* -1 (* i (- (* j y) (* b t))))
    (134-z0z1z2z3z4 c j a z b))))

Derivation

1. Split input into 3 regimes

2. if c < -1.22e138

   1. Initial program 73.9%

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

   2. Taylor expanded in c around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 39.7%

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

   4. Applied rewrites 39.7%

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

   if -1.22e138 < c < 1.72e9

   1. Initial program 73.9%

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

   2. Taylor expanded in i around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 39.6%

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

   4. Applied rewrites 39.6%

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

   if 1.72e9 < c

   1. Initial program 73.9%

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

   2. Taylor expanded in c around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 39.7%

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

   4. Applied rewrites 39.7%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

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

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

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

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

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

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

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

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

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

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. remove-double-neg N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-134-z0z1z2z3z4 39.5%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(c, \color{blue}{j}, a, z, b\right) \]

   6. Applied rewrites 39.5%

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(c, \color{blue}{j}, a, z, b\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 52.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;c \leq -3399999999999999831186108956068229205858928944848587501332570464514623530847100049246365002819165417460259049247034162670765820368522630572013466729871336663874751765025393289173714528632832:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;c \leq -2149999999999999937085440:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right)\\ \mathbf{elif}\;c \leq 1720000000:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(y, z, x, j, i\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(c, j, a, z, b\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (if (<=
     c
     -3399999999999999831186108956068229205858928944848587501332570464514623530847100049246365002819165417460259049247034162670765820368522630572013466729871336663874751765025393289173714528632832)
  (* c (- (* a j) (* b z)))
  (if (<= c -2149999999999999937085440)
    (* j (- (* a c) (* i y)))
    (if (<= c 1720000000)
      (134-z0z1z2z3z4 y z x j i)
      (134-z0z1z2z3z4 c j a z b)))))

Derivation

1. Split input into 4 regimes

2. if c < -3.3999999999999998e189

   1. Initial program 73.9%

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

   2. Taylor expanded in c around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 39.7%

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

   4. Applied rewrites 39.7%

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

   if -3.3999999999999998e189 < c < -2.1499999999999999e24

   1. Initial program 73.9%

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

   2. Taylor expanded in b around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 59.8%

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

   4. Applied rewrites 59.8%

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

   5. Taylor expanded in i around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 51.3%

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

   7. Applied rewrites 51.3%

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

   8. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 39.6%

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

   10. Applied rewrites 39.6%

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

   if -2.1499999999999999e24 < c < 1.72e9

   1. Initial program 73.9%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 39.6%

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

   4. Applied rewrites 39.6%

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

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lift-*.f64 N/A

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

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

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

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

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

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

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

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

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

      13. lift-*.f64 N/A

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

      14. mul-1-neg N/A

          \[\leadsto y \cdot \left(z \cdot x - \left(\mathsf{neg}\left(-1 \cdot \left(i \cdot j\right)\right)\right)\right) \]

      15. lift-*.f64 N/A

          \[\leadsto y \cdot \left(z \cdot x - \left(\mathsf{neg}\left(-1 \cdot \left(i \cdot j\right)\right)\right)\right) \]

      16. lift-*.f64 N/A

          \[\leadsto y \cdot \left(z \cdot x - \left(\mathsf{neg}\left(-1 \cdot \left(i \cdot j\right)\right)\right)\right) \]

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

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. lower-134-z0z1z2z3z4 39.0%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(y, \color{blue}{z}, x, j, i\right) \]

   6. Applied rewrites 39.0%

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(y, \color{blue}{z}, x, j, i\right) \]

   if 1.72e9 < c

   1. Initial program 73.9%

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

   2. Taylor expanded in c around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 39.7%

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

   4. Applied rewrites 39.7%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

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

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

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

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

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

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

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

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

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

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. remove-double-neg N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-134-z0z1z2z3z4 39.5%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(c, \color{blue}{j}, a, z, b\right) \]

   6. Applied rewrites 39.5%

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(c, \color{blue}{j}, a, z, b\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 15: 50.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;c \leq -3399999999999999831186108956068229205858928944848587501332570464514623530847100049246365002819165417460259049247034162670765820368522630572013466729871336663874751765025393289173714528632832:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;c \leq \frac{-4099067742394941}{17822033662586700072817076584766762987864173856439687228824970773044043621908896041038721919208482030385321521771853153557377752817872804680674458280164899172859354196719784961261227313463296}:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right)\\ \mathbf{elif}\;c \leq \frac{872305872233851}{20769187434139310514121985316880384}:\\ \;\;\;\;\left(z \cdot x - j \cdot i\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(c, j, a, z, b\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (if (<=
     c
     -3399999999999999831186108956068229205858928944848587501332570464514623530847100049246365002819165417460259049247034162670765820368522630572013466729871336663874751765025393289173714528632832)
  (* c (- (* a j) (* b z)))
  (if (<=
       c
       -4099067742394941/17822033662586700072817076584766762987864173856439687228824970773044043621908896041038721919208482030385321521771853153557377752817872804680674458280164899172859354196719784961261227313463296)
    (* j (- (* a c) (* i y)))
    (if (<= c 872305872233851/20769187434139310514121985316880384)
      (* (- (* z x) (* j i)) y)
      (134-z0z1z2z3z4 c j a z b)))))

Derivation

1. Split input into 4 regimes

2. if c < -3.3999999999999998e189

   1. Initial program 73.9%

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

   2. Taylor expanded in c around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 39.7%

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

   4. Applied rewrites 39.7%

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

   if -3.3999999999999998e189 < c < -2.3e-175

   1. Initial program 73.9%

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

   2. Taylor expanded in b around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 59.8%

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

   4. Applied rewrites 59.8%

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

   5. Taylor expanded in i around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 51.3%

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

   7. Applied rewrites 51.3%

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

   8. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 39.6%

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

   10. Applied rewrites 39.6%

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

   if -2.3e-175 < c < 4.1999999999999998e-20

   1. Initial program 73.9%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 39.6%

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

   4. Applied rewrites 39.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 39.6%

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. add-flip N/A

         \[\leadsto \left(x \cdot z - \left(\mathsf{neg}\left(-1 \cdot \left(i \cdot j\right)\right)\right)\right) \cdot y \]

      7. lower--.f64 N/A

         \[\leadsto \left(x \cdot z - \left(\mathsf{neg}\left(-1 \cdot \left(i \cdot j\right)\right)\right)\right) \cdot y \]

      8. lift-*.f64 N/A

         \[\leadsto \left(x \cdot z - \left(\mathsf{neg}\left(-1 \cdot \left(i \cdot j\right)\right)\right)\right) \cdot y \]

      9. *-commutative N/A

         \[\leadsto \left(z \cdot x - \left(\mathsf{neg}\left(-1 \cdot \left(i \cdot j\right)\right)\right)\right) \cdot y \]

      10. lower-*.f64 N/A

          \[\leadsto \left(z \cdot x - \left(\mathsf{neg}\left(-1 \cdot \left(i \cdot j\right)\right)\right)\right) \cdot y \]

      11. lift-*.f64 N/A

          \[\leadsto \left(z \cdot x - \left(\mathsf{neg}\left(-1 \cdot \left(i \cdot j\right)\right)\right)\right) \cdot y \]

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

          \[\leadsto \left(z \cdot x - \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(i \cdot j\right)\right) \cdot y \]

      13. metadata-eval N/A

          \[\leadsto \left(z \cdot x - 1 \cdot \left(i \cdot j\right)\right) \cdot y \]

      14. *-lft-identity 39.6%

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 39.6%

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

   6. Applied rewrites 39.6%

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

   if 4.1999999999999998e-20 < c

   1. Initial program 73.9%

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

   2. Taylor expanded in c around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 39.7%

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

   4. Applied rewrites 39.7%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

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

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

      7. distribute-rgt-neg-in N/A

         \[\leadsto c \cdot \left(a \cdot j + z \cdot \color{blue}{\left(\mathsf{neg}\left(b\right)\right)}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot \left(\mathsf{neg}\left(b\right)\right)}\right) \]

      9. lift-*.f64 N/A

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot \left(\mathsf{neg}\left(b\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto c \cdot \left(j \cdot a - \color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot \left(\mathsf{neg}\left(b\right)\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto c \cdot \left(j \cdot a - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right) \cdot b\right)\right)\right) \]

      12. distribute-lft-neg-in N/A

          \[\leadsto c \cdot \left(j \cdot a - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z \cdot b\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto c \cdot \left(j \cdot a - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b \cdot z\right)\right)\right)\right)\right) \]

      14. lift-*.f64 N/A

          \[\leadsto c \cdot \left(j \cdot a - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b \cdot z\right)\right)\right)\right)\right) \]

      15. remove-double-neg N/A

          \[\leadsto c \cdot \left(j \cdot a - b \cdot \color{blue}{z}\right) \]

      16. lift-*.f64 N/A

          \[\leadsto c \cdot \left(j \cdot a - b \cdot \color{blue}{z}\right) \]

      17. *-commutative N/A

          \[\leadsto c \cdot \left(j \cdot a - z \cdot \color{blue}{b}\right) \]

      18. lower-134-z0z1z2z3z4 39.5%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(c, \color{blue}{j}, a, z, b\right) \]

   6. Applied rewrites 39.5%

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(c, \color{blue}{j}, a, z, b\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 16: 49.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{if}\;c \leq -3399999999999999831186108956068229205858928944848587501332570464514623530847100049246365002819165417460259049247034162670765820368522630572013466729871336663874751765025393289173714528632832:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq \frac{-4099067742394941}{17822033662586700072817076584766762987864173856439687228824970773044043621908896041038721919208482030385321521771853153557377752817872804680674458280164899172859354196719784961261227313463296}:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right)\\ \mathbf{elif}\;c \leq \frac{872305872233851}{20769187434139310514121985316880384}:\\ \;\;\;\;\left(z \cdot x - j \cdot i\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (let* ((t_1 (* c (- (* a j) (* b z)))))
  (if (<=
       c
       -3399999999999999831186108956068229205858928944848587501332570464514623530847100049246365002819165417460259049247034162670765820368522630572013466729871336663874751765025393289173714528632832)
    t_1
    (if (<=
         c
         -4099067742394941/17822033662586700072817076584766762987864173856439687228824970773044043621908896041038721919208482030385321521771853153557377752817872804680674458280164899172859354196719784961261227313463296)
      (* j (- (* a c) (* i y)))
      (if (<= c 872305872233851/20769187434139310514121985316880384)
        (* (- (* z x) (* j i)) y)
        t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (b * z));
	double tmp;
	if (c <= -3.4e+189) {
		tmp = t_1;
	} else if (c <= -2.3e-175) {
		tmp = j * ((a * c) - (i * y));
	} else if (c <= 4.2e-20) {
		tmp = ((z * x) - (j * i)) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a * j) - (b * z))
    if (c <= (-3.4d+189)) then
        tmp = t_1
    else if (c <= (-2.3d-175)) then
        tmp = j * ((a * c) - (i * y))
    else if (c <= 4.2d-20) then
        tmp = ((z * x) - (j * i)) * y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (b * z));
	double tmp;
	if (c <= -3.4e+189) {
		tmp = t_1;
	} else if (c <= -2.3e-175) {
		tmp = j * ((a * c) - (i * y));
	} else if (c <= 4.2e-20) {
		tmp = ((z * x) - (j * i)) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (b * z))
	tmp = 0
	if c <= -3.4e+189:
		tmp = t_1
	elif c <= -2.3e-175:
		tmp = j * ((a * c) - (i * y))
	elif c <= 4.2e-20:
		tmp = ((z * x) - (j * i)) * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(b * z)))
	tmp = 0.0
	if (c <= -3.4e+189)
		tmp = t_1;
	elseif (c <= -2.3e-175)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(i * y)));
	elseif (c <= 4.2e-20)
		tmp = Float64(Float64(Float64(z * x) - Float64(j * i)) * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (b * z));
	tmp = 0.0;
	if (c <= -3.4e+189)
		tmp = t_1;
	elseif (c <= -2.3e-175)
		tmp = j * ((a * c) - (i * y));
	elseif (c <= 4.2e-20)
		tmp = ((z * x) - (j * i)) * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3399999999999999831186108956068229205858928944848587501332570464514623530847100049246365002819165417460259049247034162670765820368522630572013466729871336663874751765025393289173714528632832], t$95$1, If[LessEqual[c, -4099067742394941/17822033662586700072817076584766762987864173856439687228824970773044043621908896041038721919208482030385321521771853153557377752817872804680674458280164899172859354196719784961261227313463296], N[(j * N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 872305872233851/20769187434139310514121985316880384], N[(N[(N[(z * x), $MachinePrecision] - N[(j * i), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.3999999999999998e189 or 4.1999999999999998e-20 < c

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(a \cdot j - b \cdot z\right)} \]

      2. lower--.f64 N/A

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{b \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{b} \cdot z\right) \]

      4. lower-*.f64 39.7%

         \[\leadsto c \cdot \left(a \cdot j - b \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 39.7%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   if -3.3999999999999998e189 < c < -2.3e-175

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around 0

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{x} \cdot \left(y \cdot z - a \cdot t\right) \]

      3. lower--.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      4. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      5. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      6. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      7. lower--.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - \color{blue}{a} \cdot t\right) \]

      9. lower-*.f64 59.8%

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot \color{blue}{t}\right) \]

   4. Applied rewrites 59.8%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in i around 0

      \[\leadsto a \cdot \left(c \cdot j\right) + \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   6. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(\color{blue}{y \cdot z} - a \cdot t\right) \]

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot \color{blue}{z} - a \cdot t\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) \]

      5. lower--.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot \color{blue}{t}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      7. lower-*.f64 51.3%

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

   7. Applied rewrites 51.3%

      \[\leadsto a \cdot \left(c \cdot j\right) + \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

   8. Taylor expanded in x around 0

      \[\leadsto j \cdot \color{blue}{\left(a \cdot c - i \cdot y\right)} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - \color{blue}{i \cdot y}\right) \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot \color{blue}{y}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) \]

      4. lower-*.f64 39.6%

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) \]

   10. Applied rewrites 39.6%

       \[\leadsto j \cdot \color{blue}{\left(a \cdot c - i \cdot y\right)} \]

   if -2.3e-175 < c < 4.1999999999999998e-20

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + \color{blue}{x \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + \color{blue}{x} \cdot z\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right) \]

      5. lower-*.f64 39.6%

         \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 39.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right) \cdot \color{blue}{y} \]

      3. lower-*.f64 39.6%

         \[\leadsto \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right) \cdot \color{blue}{y} \]

      4. lift-+.f64 N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right) \cdot y \]

      5. +-commutative N/A

         \[\leadsto \left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right) \cdot y \]

      6. add-flip N/A

         \[\leadsto \left(x \cdot z - \left(\mathsf{neg}\left(-1 \cdot \left(i \cdot j\right)\right)\right)\right) \cdot y \]

      7. lower--.f64 N/A

         \[\leadsto \left(x \cdot z - \left(\mathsf{neg}\left(-1 \cdot \left(i \cdot j\right)\right)\right)\right) \cdot y \]

      8. lift-*.f64 N/A

         \[\leadsto \left(x \cdot z - \left(\mathsf{neg}\left(-1 \cdot \left(i \cdot j\right)\right)\right)\right) \cdot y \]

      9. *-commutative N/A

         \[\leadsto \left(z \cdot x - \left(\mathsf{neg}\left(-1 \cdot \left(i \cdot j\right)\right)\right)\right) \cdot y \]

      10. lower-*.f64 N/A

          \[\leadsto \left(z \cdot x - \left(\mathsf{neg}\left(-1 \cdot \left(i \cdot j\right)\right)\right)\right) \cdot y \]

      11. lift-*.f64 N/A

          \[\leadsto \left(z \cdot x - \left(\mathsf{neg}\left(-1 \cdot \left(i \cdot j\right)\right)\right)\right) \cdot y \]

      12. distribute-lft-neg-out N/A

          \[\leadsto \left(z \cdot x - \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(i \cdot j\right)\right) \cdot y \]

      13. metadata-eval N/A

          \[\leadsto \left(z \cdot x - 1 \cdot \left(i \cdot j\right)\right) \cdot y \]

      14. *-lft-identity 39.6%

          \[\leadsto \left(z \cdot x - i \cdot j\right) \cdot y \]

      15. lift-*.f64 N/A

          \[\leadsto \left(z \cdot x - i \cdot j\right) \cdot y \]

      16. *-commutative N/A

          \[\leadsto \left(z \cdot x - j \cdot i\right) \cdot y \]

      17. lower-*.f64 39.6%

          \[\leadsto \left(z \cdot x - j \cdot i\right) \cdot y \]

   6. Applied rewrites 39.6%

      \[\leadsto \left(z \cdot x - j \cdot i\right) \cdot \color{blue}{y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 17: 45.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} t_1 := c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{if}\;c \leq -3399999999999999831186108956068229205858928944848587501332570464514623530847100049246365002819165417460259049247034162670765820368522630572013466729871336663874751765025393289173714528632832:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1720000000:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (let* ((t_1 (* c (- (* a j) (* b z)))))
  (if (<=
       c
       -3399999999999999831186108956068229205858928944848587501332570464514623530847100049246365002819165417460259049247034162670765820368522630572013466729871336663874751765025393289173714528632832)
    t_1
    (if (<= c 1720000000) (* j (- (* a c) (* i y))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (b * z));
	double tmp;
	if (c <= -3.4e+189) {
		tmp = t_1;
	} else if (c <= 1720000000.0) {
		tmp = j * ((a * c) - (i * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a * j) - (b * z))
    if (c <= (-3.4d+189)) then
        tmp = t_1
    else if (c <= 1720000000.0d0) then
        tmp = j * ((a * c) - (i * y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (b * z));
	double tmp;
	if (c <= -3.4e+189) {
		tmp = t_1;
	} else if (c <= 1720000000.0) {
		tmp = j * ((a * c) - (i * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (b * z))
	tmp = 0
	if c <= -3.4e+189:
		tmp = t_1
	elif c <= 1720000000.0:
		tmp = j * ((a * c) - (i * y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(b * z)))
	tmp = 0.0
	if (c <= -3.4e+189)
		tmp = t_1;
	elseif (c <= 1720000000.0)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(i * y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (b * z));
	tmp = 0.0;
	if (c <= -3.4e+189)
		tmp = t_1;
	elseif (c <= 1720000000.0)
		tmp = j * ((a * c) - (i * y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3399999999999999831186108956068229205858928944848587501332570464514623530847100049246365002819165417460259049247034162670765820368522630572013466729871336663874751765025393289173714528632832], t$95$1, If[LessEqual[c, 1720000000], N[(j * N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if c < -3.3999999999999998e189 or 1.72e9 < c

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(a \cdot j - b \cdot z\right)} \]

      2. lower--.f64 N/A

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{b \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{b} \cdot z\right) \]

      4. lower-*.f64 39.7%

         \[\leadsto c \cdot \left(a \cdot j - b \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 39.7%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   if -3.3999999999999998e189 < c < 1.72e9

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around 0

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{x} \cdot \left(y \cdot z - a \cdot t\right) \]

      3. lower--.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      4. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      5. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      6. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      7. lower--.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - \color{blue}{a} \cdot t\right) \]

      9. lower-*.f64 59.8%

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot \color{blue}{t}\right) \]

   4. Applied rewrites 59.8%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in i around 0

      \[\leadsto a \cdot \left(c \cdot j\right) + \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   6. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(\color{blue}{y \cdot z} - a \cdot t\right) \]

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot \color{blue}{z} - a \cdot t\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) \]

      5. lower--.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot \color{blue}{t}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      7. lower-*.f64 51.3%

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

   7. Applied rewrites 51.3%

      \[\leadsto a \cdot \left(c \cdot j\right) + \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

   8. Taylor expanded in x around 0

      \[\leadsto j \cdot \color{blue}{\left(a \cdot c - i \cdot y\right)} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - \color{blue}{i \cdot y}\right) \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot \color{blue}{y}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) \]

      4. lower-*.f64 39.6%

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) \]

   10. Applied rewrites 39.6%

       \[\leadsto j \cdot \color{blue}{\left(a \cdot c - i \cdot y\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 40.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq 16000000000000001252664646473539901476885764798177869824:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-z\right) \cdot b\right) \cdot c\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (if (<= z 16000000000000001252664646473539901476885764798177869824)
  (* j (- (* a c) (* i y)))
  (* (* (- z) b) 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 (z <= 1.6e+55) {
		tmp = j * ((a * c) - (i * y));
	} else {
		tmp = (-z * b) * c;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= 1.6d+55) then
        tmp = j * ((a * c) - (i * y))
    else
        tmp = (-z * b) * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= 1.6e+55) {
		tmp = j * ((a * c) - (i * y));
	} else {
		tmp = (-z * b) * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= 1.6e+55:
		tmp = j * ((a * c) - (i * y))
	else:
		tmp = (-z * b) * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= 1.6e+55)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(i * y)));
	else
		tmp = Float64(Float64(Float64(-z) * b) * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= 1.6e+55)
		tmp = j * ((a * c) - (i * y));
	else
		tmp = (-z * b) * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, 16000000000000001252664646473539901476885764798177869824], N[(j * N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-z) * b), $MachinePrecision] * c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.6000000000000001e55

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around 0

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{x} \cdot \left(y \cdot z - a \cdot t\right) \]

      3. lower--.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      4. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      5. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      6. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      7. lower--.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - \color{blue}{a} \cdot t\right) \]

      9. lower-*.f64 59.8%

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot \color{blue}{t}\right) \]

   4. Applied rewrites 59.8%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in i around 0

      \[\leadsto a \cdot \left(c \cdot j\right) + \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   6. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(\color{blue}{y \cdot z} - a \cdot t\right) \]

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot \color{blue}{z} - a \cdot t\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) \]

      5. lower--.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot \color{blue}{t}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      7. lower-*.f64 51.3%

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

   7. Applied rewrites 51.3%

      \[\leadsto a \cdot \left(c \cdot j\right) + \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

   8. Taylor expanded in x around 0

      \[\leadsto j \cdot \color{blue}{\left(a \cdot c - i \cdot y\right)} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - \color{blue}{i \cdot y}\right) \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot \color{blue}{y}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) \]

      4. lower-*.f64 39.6%

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) \]

   10. Applied rewrites 39.6%

       \[\leadsto j \cdot \color{blue}{\left(a \cdot c - i \cdot y\right)} \]

   if 1.6000000000000001e55 < z

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(a \cdot j - b \cdot z\right)} \]

      2. lower--.f64 N/A

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{b \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{b} \cdot z\right) \]

      4. lower-*.f64 39.7%

         \[\leadsto c \cdot \left(a \cdot j - b \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 39.7%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   5. Taylor expanded in z around inf

      \[\leadsto c \cdot \left(-1 \cdot \color{blue}{\left(b \cdot z\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \left(-1 \cdot \left(b \cdot \color{blue}{z}\right)\right) \]

      2. lower-*.f64 22.6%

         \[\leadsto c \cdot \left(-1 \cdot \left(b \cdot z\right)\right) \]

   7. Applied rewrites 22.6%

      \[\leadsto c \cdot \left(-1 \cdot \color{blue}{\left(b \cdot z\right)}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(b \cdot z\right)\right) \cdot \color{blue}{c} \]

      3. lower-*.f64 22.6%

         \[\leadsto \left(-1 \cdot \left(b \cdot z\right)\right) \cdot \color{blue}{c} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(b \cdot z\right)\right) \cdot c \]

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(b \cdot z\right)\right) \cdot c \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(b \cdot z\right)\right) \cdot c \]

      7. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(z \cdot b\right)\right) \cdot c \]

      8. distribute-lft-neg-out N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(z\right)\right) \cdot b\right) \cdot c \]

      9. lower-*.f64 N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(z\right)\right) \cdot b\right) \cdot c \]

      10. lower-neg.f64 22.6%

          \[\leadsto \left(\left(-z\right) \cdot b\right) \cdot c \]

   9. Applied rewrites 22.6%

      \[\leadsto \left(\left(-z\right) \cdot b\right) \cdot \color{blue}{c} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 30.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;c \leq -519999999999999984024814054874131613477481132868446090246168833440487479354929993962591122310850963336193220502083424121336613878622060544:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;c \leq 1720000000:\\ \;\;\;\;-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-z\right) \cdot b\right) \cdot c\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (if (<=
     c
     -519999999999999984024814054874131613477481132868446090246168833440487479354929993962591122310850963336193220502083424121336613878622060544)
  (* c (* a j))
  (if (<= c 1720000000) (* -1 (* i (* j y))) (* (* (- z) b) 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 (c <= -5.2e+137) {
		tmp = c * (a * j);
	} else if (c <= 1720000000.0) {
		tmp = -1.0 * (i * (j * y));
	} else {
		tmp = (-z * b) * c;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-5.2d+137)) then
        tmp = c * (a * j)
    else if (c <= 1720000000.0d0) then
        tmp = (-1.0d0) * (i * (j * y))
    else
        tmp = (-z * b) * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -5.2e+137) {
		tmp = c * (a * j);
	} else if (c <= 1720000000.0) {
		tmp = -1.0 * (i * (j * y));
	} else {
		tmp = (-z * b) * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -5.2e+137:
		tmp = c * (a * j)
	elif c <= 1720000000.0:
		tmp = -1.0 * (i * (j * y))
	else:
		tmp = (-z * b) * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -5.2e+137)
		tmp = Float64(c * Float64(a * j));
	elseif (c <= 1720000000.0)
		tmp = Float64(-1.0 * Float64(i * Float64(j * y)));
	else
		tmp = Float64(Float64(Float64(-z) * b) * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -5.2e+137)
		tmp = c * (a * j);
	elseif (c <= 1720000000.0)
		tmp = -1.0 * (i * (j * y));
	else
		tmp = (-z * b) * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -519999999999999984024814054874131613477481132868446090246168833440487479354929993962591122310850963336193220502083424121336613878622060544], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1720000000], N[(-1 * N[(i * N[(j * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-z) * b), $MachinePrecision] * c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -5.1999999999999998e137

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(a \cdot j - b \cdot z\right)} \]

      2. lower--.f64 N/A

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{b \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{b} \cdot z\right) \]

      4. lower-*.f64 39.7%

         \[\leadsto c \cdot \left(a \cdot j - b \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 39.7%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto c \cdot \left(a \cdot \color{blue}{j}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 23.0%

         \[\leadsto c \cdot \left(a \cdot j\right) \]

   7. Applied rewrites 23.0%

      \[\leadsto c \cdot \left(a \cdot \color{blue}{j}\right) \]

   if -5.1999999999999998e137 < c < 1.72e9

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + \color{blue}{x \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + \color{blue}{x} \cdot z\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right) \]

      5. lower-*.f64 39.6%

         \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 39.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \color{blue}{z}\right) \]

      2. lower-*.f64 22.9%

         \[\leadsto x \cdot \left(y \cdot z\right) \]

   7. Applied rewrites 22.9%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]

   8. Taylor expanded in x around 0

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y\right)\right)} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(j \cdot y\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot \color{blue}{y}\right)\right) \]

      3. lower-*.f64 22.2%

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y\right)\right) \]

   10. Applied rewrites 22.2%

       \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y\right)\right)} \]

   if 1.72e9 < c

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(a \cdot j - b \cdot z\right)} \]

      2. lower--.f64 N/A

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{b \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{b} \cdot z\right) \]

      4. lower-*.f64 39.7%

         \[\leadsto c \cdot \left(a \cdot j - b \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 39.7%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   5. Taylor expanded in z around inf

      \[\leadsto c \cdot \left(-1 \cdot \color{blue}{\left(b \cdot z\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \left(-1 \cdot \left(b \cdot \color{blue}{z}\right)\right) \]

      2. lower-*.f64 22.6%

         \[\leadsto c \cdot \left(-1 \cdot \left(b \cdot z\right)\right) \]

   7. Applied rewrites 22.6%

      \[\leadsto c \cdot \left(-1 \cdot \color{blue}{\left(b \cdot z\right)}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(b \cdot z\right)\right) \cdot \color{blue}{c} \]

      3. lower-*.f64 22.6%

         \[\leadsto \left(-1 \cdot \left(b \cdot z\right)\right) \cdot \color{blue}{c} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(b \cdot z\right)\right) \cdot c \]

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(b \cdot z\right)\right) \cdot c \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(b \cdot z\right)\right) \cdot c \]

      7. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(z \cdot b\right)\right) \cdot c \]

      8. distribute-lft-neg-out N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(z\right)\right) \cdot b\right) \cdot c \]

      9. lower-*.f64 N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(z\right)\right) \cdot b\right) \cdot c \]

      10. lower-neg.f64 22.6%

          \[\leadsto \left(\left(-z\right) \cdot b\right) \cdot c \]

   9. Applied rewrites 22.6%

      \[\leadsto \left(\left(-z\right) \cdot b\right) \cdot \color{blue}{c} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 20: 30.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;j \leq \frac{-5499829120098731}{53919893334301279589334030174039261347274288845081144962207220498432}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;j \leq 38000000000000001390623291328167936:\\ \;\;\;\;\left(\left(-z\right) \cdot b\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (if (<=
     j
     -5499829120098731/53919893334301279589334030174039261347274288845081144962207220498432)
  (* c (* a j))
  (if (<= j 38000000000000001390623291328167936)
    (* (* (- z) b) c)
    (* a (* c j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.02e-52) {
		tmp = c * (a * j);
	} else if (j <= 3.8e+34) {
		tmp = (-z * b) * c;
	} else {
		tmp = a * (c * 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 (j <= (-1.02d-52)) then
        tmp = c * (a * j)
    else if (j <= 3.8d+34) then
        tmp = (-z * b) * c
    else
        tmp = a * (c * 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 (j <= -1.02e-52) {
		tmp = c * (a * j);
	} else if (j <= 3.8e+34) {
		tmp = (-z * b) * c;
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -1.02e-52:
		tmp = c * (a * j)
	elif j <= 3.8e+34:
		tmp = (-z * b) * c
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.02e-52)
		tmp = Float64(c * Float64(a * j));
	elseif (j <= 3.8e+34)
		tmp = Float64(Float64(Float64(-z) * b) * c);
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -1.02e-52)
		tmp = c * (a * j);
	elseif (j <= 3.8e+34)
		tmp = (-z * b) * c;
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -5499829120098731/53919893334301279589334030174039261347274288845081144962207220498432], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 38000000000000001390623291328167936], N[(N[((-z) * b), $MachinePrecision] * c), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.0200000000000001e-52

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(a \cdot j - b \cdot z\right)} \]

      2. lower--.f64 N/A

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{b \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{b} \cdot z\right) \]

      4. lower-*.f64 39.7%

         \[\leadsto c \cdot \left(a \cdot j - b \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 39.7%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto c \cdot \left(a \cdot \color{blue}{j}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 23.0%

         \[\leadsto c \cdot \left(a \cdot j\right) \]

   7. Applied rewrites 23.0%

      \[\leadsto c \cdot \left(a \cdot \color{blue}{j}\right) \]

   if -1.0200000000000001e-52 < j < 3.8000000000000001e34

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(a \cdot j - b \cdot z\right)} \]

      2. lower--.f64 N/A

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{b \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{b} \cdot z\right) \]

      4. lower-*.f64 39.7%

         \[\leadsto c \cdot \left(a \cdot j - b \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 39.7%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   5. Taylor expanded in z around inf

      \[\leadsto c \cdot \left(-1 \cdot \color{blue}{\left(b \cdot z\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \left(-1 \cdot \left(b \cdot \color{blue}{z}\right)\right) \]

      2. lower-*.f64 22.6%

         \[\leadsto c \cdot \left(-1 \cdot \left(b \cdot z\right)\right) \]

   7. Applied rewrites 22.6%

      \[\leadsto c \cdot \left(-1 \cdot \color{blue}{\left(b \cdot z\right)}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(b \cdot z\right)\right) \cdot \color{blue}{c} \]

      3. lower-*.f64 22.6%

         \[\leadsto \left(-1 \cdot \left(b \cdot z\right)\right) \cdot \color{blue}{c} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(b \cdot z\right)\right) \cdot c \]

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(b \cdot z\right)\right) \cdot c \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(b \cdot z\right)\right) \cdot c \]

      7. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(z \cdot b\right)\right) \cdot c \]

      8. distribute-lft-neg-out N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(z\right)\right) \cdot b\right) \cdot c \]

      9. lower-*.f64 N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(z\right)\right) \cdot b\right) \cdot c \]

      10. lower-neg.f64 22.6%

          \[\leadsto \left(\left(-z\right) \cdot b\right) \cdot c \]

   9. Applied rewrites 22.6%

      \[\leadsto \left(\left(-z\right) \cdot b\right) \cdot \color{blue}{c} \]

   if 3.8000000000000001e34 < j

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around 0

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{x} \cdot \left(y \cdot z - a \cdot t\right) \]

      3. lower--.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      4. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      5. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      6. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      7. lower--.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - \color{blue}{a} \cdot t\right) \]

      9. lower-*.f64 59.8%

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot \color{blue}{t}\right) \]

   4. Applied rewrites 59.8%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in i around 0

      \[\leadsto a \cdot \left(c \cdot j\right) + \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   6. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(\color{blue}{y \cdot z} - a \cdot t\right) \]

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot \color{blue}{z} - a \cdot t\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) \]

      5. lower--.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot \color{blue}{t}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      7. lower-*.f64 51.3%

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

   7. Applied rewrites 51.3%

      \[\leadsto a \cdot \left(c \cdot j\right) + \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

   8. Taylor expanded in x around 0

      \[\leadsto a \cdot \left(c \cdot \color{blue}{j}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) \]

      2. lower-*.f64 23.0%

         \[\leadsto a \cdot \left(c \cdot j\right) \]

   10. Applied rewrites 23.0%

       \[\leadsto a \cdot \left(c \cdot \color{blue}{j}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 21: 28.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;j \leq \frac{-5499829120098731}{53919893334301279589334030174039261347274288845081144962207220498432}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;j \leq 38000000000000001390623291328167936:\\ \;\;\;\;\left(\left(-c\right) \cdot b\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (if (<=
     j
     -5499829120098731/53919893334301279589334030174039261347274288845081144962207220498432)
  (* c (* a j))
  (if (<= j 38000000000000001390623291328167936)
    (* (* (- c) b) z)
    (* a (* c j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.02e-52) {
		tmp = c * (a * j);
	} else if (j <= 3.8e+34) {
		tmp = (-c * b) * z;
	} else {
		tmp = a * (c * 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 (j <= (-1.02d-52)) then
        tmp = c * (a * j)
    else if (j <= 3.8d+34) then
        tmp = (-c * b) * z
    else
        tmp = a * (c * 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 (j <= -1.02e-52) {
		tmp = c * (a * j);
	} else if (j <= 3.8e+34) {
		tmp = (-c * b) * z;
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -1.02e-52:
		tmp = c * (a * j)
	elif j <= 3.8e+34:
		tmp = (-c * b) * z
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.02e-52)
		tmp = Float64(c * Float64(a * j));
	elseif (j <= 3.8e+34)
		tmp = Float64(Float64(Float64(-c) * b) * z);
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -1.02e-52)
		tmp = c * (a * j);
	elseif (j <= 3.8e+34)
		tmp = (-c * b) * z;
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -5499829120098731/53919893334301279589334030174039261347274288845081144962207220498432], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 38000000000000001390623291328167936], N[(N[((-c) * b), $MachinePrecision] * z), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.0200000000000001e-52

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(a \cdot j - b \cdot z\right)} \]

      2. lower--.f64 N/A

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{b \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{b} \cdot z\right) \]

      4. lower-*.f64 39.7%

         \[\leadsto c \cdot \left(a \cdot j - b \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 39.7%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto c \cdot \left(a \cdot \color{blue}{j}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 23.0%

         \[\leadsto c \cdot \left(a \cdot j\right) \]

   7. Applied rewrites 23.0%

      \[\leadsto c \cdot \left(a \cdot \color{blue}{j}\right) \]

   if -1.0200000000000001e-52 < j < 3.8000000000000001e34

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(a \cdot j - b \cdot z\right)} \]

      2. lower--.f64 N/A

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{b \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{b} \cdot z\right) \]

      4. lower-*.f64 39.7%

         \[\leadsto c \cdot \left(a \cdot j - b \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 39.7%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   5. Taylor expanded in z around inf

      \[\leadsto c \cdot \left(-1 \cdot \color{blue}{\left(b \cdot z\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \left(-1 \cdot \left(b \cdot \color{blue}{z}\right)\right) \]

      2. lower-*.f64 22.6%

         \[\leadsto c \cdot \left(-1 \cdot \left(b \cdot z\right)\right) \]

   7. Applied rewrites 22.6%

      \[\leadsto c \cdot \left(-1 \cdot \color{blue}{\left(b \cdot z\right)}\right) \]

   8. Taylor expanded in z around inf

      \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(c \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(c \cdot z\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(c \cdot \color{blue}{z}\right)\right) \]

      3. lower-*.f64 22.9%

         \[\leadsto -1 \cdot \left(b \cdot \left(c \cdot z\right)\right) \]

   10. Applied rewrites 22.9%

       \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(c \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(c \cdot z\right)}\right) \]

       2. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right) \]

       3. lift-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right) \]

       4. lift-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right) \]

       5. associate-*r* N/A

          \[\leadsto \mathsf{neg}\left(\left(b \cdot c\right) \cdot z\right) \]

       6. distribute-lft-neg-in N/A

          \[\leadsto \left(\mathsf{neg}\left(b \cdot c\right)\right) \cdot z \]

       7. lower-*.f64 N/A

          \[\leadsto \left(\mathsf{neg}\left(b \cdot c\right)\right) \cdot z \]

       8. *-commutative N/A

          \[\leadsto \left(\mathsf{neg}\left(c \cdot b\right)\right) \cdot z \]

       9. distribute-lft-neg-in N/A

          \[\leadsto \left(\left(\mathsf{neg}\left(c\right)\right) \cdot b\right) \cdot z \]

       10. lower-*.f64 N/A

           \[\leadsto \left(\left(\mathsf{neg}\left(c\right)\right) \cdot b\right) \cdot z \]

       11. lower-neg.f64 22.3%

           \[\leadsto \left(\left(-c\right) \cdot b\right) \cdot z \]

   12. Applied rewrites 22.3%

       \[\leadsto \left(\left(-c\right) \cdot b\right) \cdot z \]

   if 3.8000000000000001e34 < j

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around 0

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{x} \cdot \left(y \cdot z - a \cdot t\right) \]

      3. lower--.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      4. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      5. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      6. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      7. lower--.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - \color{blue}{a} \cdot t\right) \]

      9. lower-*.f64 59.8%

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot \color{blue}{t}\right) \]

   4. Applied rewrites 59.8%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in i around 0

      \[\leadsto a \cdot \left(c \cdot j\right) + \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   6. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(\color{blue}{y \cdot z} - a \cdot t\right) \]

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot \color{blue}{z} - a \cdot t\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) \]

      5. lower--.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot \color{blue}{t}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      7. lower-*.f64 51.3%

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

   7. Applied rewrites 51.3%

      \[\leadsto a \cdot \left(c \cdot j\right) + \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

   8. Taylor expanded in x around 0

      \[\leadsto a \cdot \left(c \cdot \color{blue}{j}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) \]

      2. lower-*.f64 23.0%

         \[\leadsto a \cdot \left(c \cdot j\right) \]

   10. Applied rewrites 23.0%

       \[\leadsto a \cdot \left(c \cdot \color{blue}{j}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 22: 27.6% accurate, 3.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq 6400000000000000277614700637562790869057877279692411595467352251751147602493959110024472035328:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (if (<=
     y
     6400000000000000277614700637562790869057877279692411595467352251751147602493959110024472035328)
  (* c (* a j))
  (* (* 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 tmp;
	if (y <= 6.4e+93) {
		tmp = c * (a * j);
	} else {
		tmp = (y * x) * z;
	}
	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 (y <= 6.4d+93) then
        tmp = c * (a * j)
    else
        tmp = (y * x) * z
    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 (y <= 6.4e+93) {
		tmp = c * (a * j);
	} else {
		tmp = (y * x) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= 6.4e+93:
		tmp = c * (a * j)
	else:
		tmp = (y * x) * z
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= 6.4e+93)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(Float64(y * x) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= 6.4e+93)
		tmp = c * (a * j);
	else
		tmp = (y * x) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, 6400000000000000277614700637562790869057877279692411595467352251751147602493959110024472035328], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.4000000000000003e93

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(a \cdot j - b \cdot z\right)} \]

      2. lower--.f64 N/A

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{b \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{b} \cdot z\right) \]

      4. lower-*.f64 39.7%

         \[\leadsto c \cdot \left(a \cdot j - b \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 39.7%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto c \cdot \left(a \cdot \color{blue}{j}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 23.0%

         \[\leadsto c \cdot \left(a \cdot j\right) \]

   7. Applied rewrites 23.0%

      \[\leadsto c \cdot \left(a \cdot \color{blue}{j}\right) \]

   if 6.4000000000000003e93 < y

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + \color{blue}{x \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + \color{blue}{x} \cdot z\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right) \]

      5. lower-*.f64 39.6%

         \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 39.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \color{blue}{z}\right) \]

      2. lower-*.f64 22.9%

         \[\leadsto x \cdot \left(y \cdot z\right) \]

   7. Applied rewrites 22.9%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \color{blue}{z}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto x \cdot \left(y \cdot z\right) \]

      3. associate-*r* N/A

         \[\leadsto \left(x \cdot y\right) \cdot z \]

      4. lower-*.f64 N/A

         \[\leadsto \left(x \cdot y\right) \cdot z \]

      5. *-commutative N/A

         \[\leadsto \left(y \cdot x\right) \cdot z \]

      6. lower-*.f64 22.6%

         \[\leadsto \left(y \cdot x\right) \cdot z \]

   9. Applied rewrites 22.6%

      \[\leadsto \left(y \cdot x\right) \cdot z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 27.5% accurate, 3.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq 23999999999999999026001386952408705555807906151562834552073736235360894150822906212384768:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (if (<=
     y
     23999999999999999026001386952408705555807906151562834552073736235360894150822906212384768)
  (* a (* c j))
  (* (* 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 tmp;
	if (y <= 2.4e+88) {
		tmp = a * (c * j);
	} else {
		tmp = (y * x) * z;
	}
	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 (y <= 2.4d+88) then
        tmp = a * (c * j)
    else
        tmp = (y * x) * z
    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 (y <= 2.4e+88) {
		tmp = a * (c * j);
	} else {
		tmp = (y * x) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= 2.4e+88:
		tmp = a * (c * j)
	else:
		tmp = (y * x) * z
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= 2.4e+88)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(Float64(y * x) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= 2.4e+88)
		tmp = a * (c * j);
	else
		tmp = (y * x) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, 23999999999999999026001386952408705555807906151562834552073736235360894150822906212384768], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.3999999999999999e88

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around 0

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{x} \cdot \left(y \cdot z - a \cdot t\right) \]

      3. lower--.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      4. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      5. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      6. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      7. lower--.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - \color{blue}{a} \cdot t\right) \]

      9. lower-*.f64 59.8%

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot \color{blue}{t}\right) \]

   4. Applied rewrites 59.8%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in i around 0

      \[\leadsto a \cdot \left(c \cdot j\right) + \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   6. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(\color{blue}{y \cdot z} - a \cdot t\right) \]

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot \color{blue}{z} - a \cdot t\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) \]

      5. lower--.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot \color{blue}{t}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      7. lower-*.f64 51.3%

         \[\leadsto a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

   7. Applied rewrites 51.3%

      \[\leadsto a \cdot \left(c \cdot j\right) + \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

   8. Taylor expanded in x around 0

      \[\leadsto a \cdot \left(c \cdot \color{blue}{j}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(c \cdot j\right) \]

      2. lower-*.f64 23.0%

         \[\leadsto a \cdot \left(c \cdot j\right) \]

   10. Applied rewrites 23.0%

       \[\leadsto a \cdot \left(c \cdot \color{blue}{j}\right) \]

   if 2.3999999999999999e88 < y

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + \color{blue}{x \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + \color{blue}{x} \cdot z\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right) \]

      5. lower-*.f64 39.6%

         \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 39.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \color{blue}{z}\right) \]

      2. lower-*.f64 22.9%

         \[\leadsto x \cdot \left(y \cdot z\right) \]

   7. Applied rewrites 22.9%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \color{blue}{z}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto x \cdot \left(y \cdot z\right) \]

      3. associate-*r* N/A

         \[\leadsto \left(x \cdot y\right) \cdot z \]

      4. lower-*.f64 N/A

         \[\leadsto \left(x \cdot y\right) \cdot z \]

      5. *-commutative N/A

         \[\leadsto \left(y \cdot x\right) \cdot z \]

      6. lower-*.f64 22.6%

         \[\leadsto \left(y \cdot x\right) \cdot z \]

   9. Applied rewrites 22.6%

      \[\leadsto \left(y \cdot x\right) \cdot z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 24: 22.9% accurate, 5.5× speedup

Math

\[\left(y \cdot x\right) \cdot z \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (* (* y x) z))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return (y * x) * z;
}

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 = (y * x) * z
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 (y * x) * z;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return (y * x) * z

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(y * x) * z)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = (y * x) * z;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision]

Derivation

1. Initial program 73.9%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

2. Taylor expanded in y around inf

   \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

   2. lower-+.f64 N/A

      \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + \color{blue}{x \cdot z}\right) \]

   3. lower-*.f64 N/A

      \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + \color{blue}{x} \cdot z\right) \]

   4. lower-*.f64 N/A

      \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right) \]

   5. lower-*.f64 39.6%

      \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot \color{blue}{z}\right) \]

4. Applied rewrites 39.6%

   \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

5. Taylor expanded in x around inf

   \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
6. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto x \cdot \left(y \cdot \color{blue}{z}\right) \]

   2. lower-*.f64 22.9%

      \[\leadsto x \cdot \left(y \cdot z\right) \]

7. Applied rewrites 22.9%

   \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
8. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto x \cdot \left(y \cdot \color{blue}{z}\right) \]

   2. lift-*.f64 N/A

      \[\leadsto x \cdot \left(y \cdot z\right) \]

   3. associate-*r* N/A

      \[\leadsto \left(x \cdot y\right) \cdot z \]

   4. lower-*.f64 N/A

      \[\leadsto \left(x \cdot y\right) \cdot z \]

   5. *-commutative N/A

      \[\leadsto \left(y \cdot x\right) \cdot z \]

   6. lower-*.f64 22.6%

      \[\leadsto \left(y \cdot x\right) \cdot z \]

9. Applied rewrites 22.6%

   \[\leadsto \left(y \cdot x\right) \cdot z \]
10. Add Preprocessing

Alternative 25: 22.6% accurate, 5.5× speedup

Math

\[x \cdot \left(y \cdot z\right) \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (* x (* y z)))

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);
}

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)
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);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return x * (y * z)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(x * Float64(y * z))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = x * (y * z);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 73.9%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

2. Taylor expanded in y around inf

   \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

   2. lower-+.f64 N/A

      \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + \color{blue}{x \cdot z}\right) \]

   3. lower-*.f64 N/A

      \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + \color{blue}{x} \cdot z\right) \]

   4. lower-*.f64 N/A

      \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right) \]

   5. lower-*.f64 39.6%

      \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot \color{blue}{z}\right) \]

4. Applied rewrites 39.6%

   \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

5. Taylor expanded in x around inf

   \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
6. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto x \cdot \left(y \cdot \color{blue}{z}\right) \]

   2. lower-*.f64 22.9%

      \[\leadsto x \cdot \left(y \cdot z\right) \]

7. Applied rewrites 22.9%

   \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64
  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))