Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.1% → 84.0%

Time: 1.1min

Alternatives: 26

Speedup: 0.5×

• 41.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 84.0% accurate, 0.5× speedup

Math

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

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 t) (* i y)))))
  (if (<= (+ (- t_1 (* b (- (* c z) (* i a)))) t_2) INFINITY)
    (+ (- t_1 (134-z0z1z2z3z4 b z c i a)) t_2)
    (+ (* a (* b i)) (134-z0z1z2z3z4 j t c y i)))))

Derivation

1. Split input into 2 regimes

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

   1. Initial program 73.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

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

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

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

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

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

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

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

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

      10. remove-double-neg N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. lower-134-z0z1z2z3z4 77.2%

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

   3. Applied rewrites 77.2%

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

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

   1. Initial program 73.1%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 49.1%

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

   4. Applied rewrites 49.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

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

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

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

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

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

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

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

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

      10. remove-double-neg N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-134-z0z1z2z3z4 51.2%

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

   6. Applied rewrites 51.2%

      \[\leadsto a \cdot \left(b \cdot i\right) + \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(j, t, c, y, i\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 83.6% accurate, 0.5× speedup

Math

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

FPCore

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 73.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

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

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

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

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

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

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

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

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

      10. remove-double-neg N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. *-commutative N/A

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

      16. lower-134-z0z1z2z3z4 77.4%

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

   3. Applied rewrites 77.4%

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

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

   1. Initial program 73.1%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 49.1%

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

   4. Applied rewrites 49.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

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

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

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

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

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

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

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

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

      10. remove-double-neg N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-134-z0z1z2z3z4 51.2%

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

   6. Applied rewrites 51.2%

      \[\leadsto a \cdot \left(b \cdot i\right) + \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(j, t, c, y, i\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 81.7% accurate, 0.5× speedup

Math

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

FPCore

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 73.1%

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

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

   1. Initial program 73.1%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 49.1%

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

   4. Applied rewrites 49.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

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

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

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

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

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

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

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

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

      10. remove-double-neg N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-134-z0z1z2z3z4 51.2%

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

   6. Applied rewrites 51.2%

      \[\leadsto a \cdot \left(b \cdot i\right) + \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(j, t, c, y, i\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 71.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;i \leq -7999999999999999506066406602255828322616218915776995826355329700310971934596797709094564220031266042413056:\\ \;\;\;\;a \cdot \left(b \cdot i\right) + \mathsf{134\_z0z1z2z3z4}\left(j, t, c, y, i\right)\\ \mathbf{elif}\;i \leq 6799999999999999771361204269095990591488:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)\right) + j \cdot \left(c \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(i, b, a, y, j\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (if (<=
     i
     -7999999999999999506066406602255828322616218915776995826355329700310971934596797709094564220031266042413056)
  (+ (* a (* b i)) (134-z0z1z2z3z4 j t c y i))
  (if (<= i 6799999999999999771361204269095990591488)
    (+
     (- (* x (- (* y z) (* t a))) (134-z0z1z2z3z4 b z c i a))
     (* j (* c t)))
    (134-z0z1z2z3z4 i b a y j))))

Derivation

1. Split input into 3 regimes

2. if i < -7.9999999999999995e105

   1. Initial program 73.1%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 49.1%

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

   4. Applied rewrites 49.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

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

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

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

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

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

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

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

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

      10. remove-double-neg N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-134-z0z1z2z3z4 51.2%

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

   6. Applied rewrites 51.2%

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

   if -7.9999999999999995e105 < i < 6.7999999999999998e39

   1. Initial program 73.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

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

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

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

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

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

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

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

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

      10. remove-double-neg N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. lower-134-z0z1z2z3z4 77.2%

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

   3. Applied rewrites 77.2%

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

   4. Taylor expanded in y around 0

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

      1. lower-*.f64 70.0%

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

   6. Applied rewrites 70.0%

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

   if 6.7999999999999998e39 < i

   1. Initial program 73.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

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

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

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

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

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

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

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

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

      10. remove-double-neg N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. lower-134-z0z1z2z3z4 77.2%

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

   3. Applied rewrites 77.2%

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

   4. Taylor expanded in i around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 39.2%

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

   6. Applied rewrites 39.2%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 39.2%

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 39.2%

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

   8. Applied rewrites 39.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-134-z0z1z2z3z4 38.9%

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

   10. Applied rewrites 38.9%

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

Alternative 5: 67.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{if}\;c \leq -47000000000000000882497468202382926760474282586130709860674048069879890039594240516162270598191842570956416285147869624605267034784581812224:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(c, t, j, z, b\right)\\ \mathbf{elif}\;c \leq \frac{-7713302612443153}{3213876088517980551083924184682325205044405987565585670602752}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + t\_1\\ \mathbf{elif}\;c \leq 4200000000000000159086051820587205661447942375116082460464186153870236755951616:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(a, i, b, x, t\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(c, t, j, z, b\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (let* ((t_1 (* j (- (* c t) (* i y)))))
  (if (<=
       c
       -47000000000000000882497468202382926760474282586130709860674048069879890039594240516162270598191842570956416285147869624605267034784581812224)
    (134-z0z1z2z3z4 c t j z b)
    (if (<=
         c
         -7713302612443153/3213876088517980551083924184682325205044405987565585670602752)
      (+ (* z (- (* x y) (* b c))) t_1)
      (if (<=
           c
           4200000000000000159086051820587205661447942375116082460464186153870236755951616)
        (+ (134-z0z1z2z3z4 a i b x t) t_1)
        (134-z0z1z2z3z4 c t j z b))))))

Derivation

1. Split input into 3 regimes

2. if c < -4.7000000000000001e139 or 4.2000000000000002e78 < c

   1. Initial program 73.1%

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

   2. Taylor expanded in c around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 38.8%

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

   4. Applied rewrites 38.8%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

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

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

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

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

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

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

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

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

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

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

      13. remove-double-neg N/A

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

      14. lower-134-z0z1z2z3z4 39.2%

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

   6. Applied rewrites 39.2%

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

   if -4.7000000000000001e139 < c < -2.3999999999999999e-45

   1. Initial program 73.1%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 58.5%

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

   4. Applied rewrites 58.5%

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

   if -2.3999999999999999e-45 < c < 4.2000000000000002e78

   1. Initial program 73.1%

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

   2. Taylor expanded in a around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 59.4%

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

   4. Applied rewrites 59.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift--.f64 N/A

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

      5. sub-negate-rev N/A

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

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

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

      7. mul-1-neg N/A

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

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

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

      9. remove-double-neg N/A

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

      10. sub-negate-rev N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. add-flip N/A

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

      14. sub-negate N/A

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

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

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

      16. lift-*.f64 N/A

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

      17. remove-double-neg N/A

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. lower-134-z0z1z2z3z4 62.4%

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

   6. Applied rewrites 62.4%

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(a, \color{blue}{i}, b, x, t\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 64.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := j \cdot \left(c \cdot t - i \cdot y\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + t\_1\\ \mathbf{if}\;t\_2 \leq \frac{6931674235302037}{173291855882550928723650886508942731464777317210988535948154973788413831737851601439998400381508723631086950685087723239310884864}:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(j, t, c, y, i\right) + x \cdot \left(y \cdot z - a \cdot t\right)\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;b \cdot \left(a \cdot i - c \cdot z\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) + \mathsf{134\_z0z1z2z3z4}\left(j, t, c, y, i\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (let* ((t_1 (* j (- (* c t) (* i y))))
       (t_2
        (+
         (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
         t_1)))
  (if (<=
       t_2
       6931674235302037/173291855882550928723650886508942731464777317210988535948154973788413831737851601439998400381508723631086950685087723239310884864)
    (+ (134-z0z1z2z3z4 j t c y i) (* x (- (* y z) (* a t))))
    (if (<= t_2 INFINITY)
      (+ (* b (- (* a i) (* c z))) t_1)
      (+ (* a (* b i)) (134-z0z1z2z3z4 j t c y i))))))

Derivation

1. Split input into 3 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < 3.9999999999999999e-113

   1. Initial program 73.1%

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

   2. Taylor expanded in b around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 59.6%

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

   4. Applied rewrites 59.6%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

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

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

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

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

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

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

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

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

      10. remove-double-neg N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. *-commutative N/A

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

      16. lower-134-z0z1z2z3z4 62.8%

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

   6. Applied rewrites 62.8%

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

   if 3.9999999999999999e-113 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 73.1%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 58.5%

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

   4. Applied rewrites 58.5%

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

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

   1. Initial program 73.1%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 49.1%

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

   4. Applied rewrites 49.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

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

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

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

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

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

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

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

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

      10. remove-double-neg N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-134-z0z1z2z3z4 51.2%

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

   6. Applied rewrites 51.2%

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

Alternative 7: 63.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{if}\;i \leq -9200000000000000494652599231133532570395869184:\\ \;\;\;\;a \cdot \left(b \cdot i\right) + \mathsf{134\_z0z1z2z3z4}\left(j, t, c, y, i\right)\\ \mathbf{elif}\;i \leq \frac{6137165078635627}{1427247692705959881058285969449495136382746624}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + t\_1\\ \mathbf{elif}\;i \leq 108000000000000002841598060393185870412347289647193203911040249628872955534546268587121803176431669988575907748942521916126535188801716815562484347968372693589481874810673628725641216:\\ \;\;\;\;b \cdot \left(a \cdot i - c \cdot z\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(i, b, a, y, j\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (let* ((t_1 (* j (- (* c t) (* i y)))))
  (if (<= i -9200000000000000494652599231133532570395869184)
    (+ (* a (* b i)) (134-z0z1z2z3z4 j t c y i))
    (if (<=
         i
         6137165078635627/1427247692705959881058285969449495136382746624)
      (+ (* z (- (* x y) (* b c))) t_1)
      (if (<=
           i
           108000000000000002841598060393185870412347289647193203911040249628872955534546268587121803176431669988575907748942521916126535188801716815562484347968372693589481874810673628725641216)
        (+ (* b (- (* a i) (* c z))) t_1)
        (134-z0z1z2z3z4 i b a y j))))))

Derivation

1. Split input into 4 regimes

2. if i < -9.2000000000000005e45

   1. Initial program 73.1%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 49.1%

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

   4. Applied rewrites 49.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

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

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

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

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

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

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

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

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

      10. remove-double-neg N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-134-z0z1z2z3z4 51.2%

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

   6. Applied rewrites 51.2%

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

   if -9.2000000000000005e45 < i < 4.2999999999999997e-30

   1. Initial program 73.1%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 58.5%

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

   4. Applied rewrites 58.5%

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

   if 4.2999999999999997e-30 < i < 1.08e182

   1. Initial program 73.1%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 58.5%

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

   4. Applied rewrites 58.5%

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

   if 1.08e182 < i

   1. Initial program 73.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

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

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

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

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

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

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

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

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

      10. remove-double-neg N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. lower-134-z0z1z2z3z4 77.2%

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

   3. Applied rewrites 77.2%

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

   4. Taylor expanded in i around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 39.2%

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

   6. Applied rewrites 39.2%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 39.2%

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 39.2%

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

   8. Applied rewrites 39.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-134-z0z1z2z3z4 38.9%

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

   10. Applied rewrites 38.9%

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

Alternative 8: 63.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := j \cdot \left(c \cdot t - i \cdot y\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + t\_1\\ \mathbf{if}\;t\_2 \leq \frac{6931674235302037}{173291855882550928723650886508942731464777317210988535948154973788413831737851601439998400381508723631086950685087723239310884864}:\\ \;\;\;\;t\_1 + x \cdot \left(y \cdot z - a \cdot t\right)\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;b \cdot \left(a \cdot i - c \cdot z\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) + \mathsf{134\_z0z1z2z3z4}\left(j, t, c, y, i\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (let* ((t_1 (* j (- (* c t) (* i y))))
       (t_2
        (+
         (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
         t_1)))
  (if (<=
       t_2
       6931674235302037/173291855882550928723650886508942731464777317210988535948154973788413831737851601439998400381508723631086950685087723239310884864)
    (+ t_1 (* x (- (* y z) (* a t))))
    (if (<= t_2 INFINITY)
      (+ (* b (- (* a i) (* c z))) t_1)
      (+ (* a (* b i)) (134-z0z1z2z3z4 j t c y i))))))

Derivation

1. Split input into 3 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < 3.9999999999999999e-113

   1. Initial program 73.1%

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

   2. Taylor expanded in b around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 59.6%

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

   4. Applied rewrites 59.6%

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

   if 3.9999999999999999e-113 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 73.1%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 58.5%

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

   4. Applied rewrites 58.5%

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

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

   1. Initial program 73.1%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 49.1%

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

   4. Applied rewrites 49.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

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

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

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

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

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

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

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

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

      10. remove-double-neg N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-134-z0z1z2z3z4 51.2%

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

   6. Applied rewrites 51.2%

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

Alternative 9: 62.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;i \leq -26499999999999998459331033260651466612499616802700899974089610585370856281920975974862367405259976867840:\\ \;\;\;\;a \cdot \left(b \cdot i\right) + \mathsf{134\_z0z1z2z3z4}\left(j, t, c, y, i\right)\\ \mathbf{elif}\;i \leq \frac{2803840303608807}{20769187434139310514121985316880384}:\\ \;\;\;\;j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(i, b, a, y, j\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (if (<=
     i
     -26499999999999998459331033260651466612499616802700899974089610585370856281920975974862367405259976867840)
  (+ (* a (* b i)) (134-z0z1z2z3z4 j t c y i))
  (if (<= i 2803840303608807/20769187434139310514121985316880384)
    (+ (* j (- (* c t) (* i y))) (* x (- (* y z) (* a t))))
    (134-z0z1z2z3z4 i b a y j))))

Derivation

1. Split input into 3 regimes

2. if i < -2.6499999999999998e103

   1. Initial program 73.1%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 49.1%

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

   4. Applied rewrites 49.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

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

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

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

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

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

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

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

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

      10. remove-double-neg N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-134-z0z1z2z3z4 51.2%

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

   6. Applied rewrites 51.2%

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

   if -2.6499999999999998e103 < i < 1.35e-19

   1. Initial program 73.1%

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

   2. Taylor expanded in b around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 59.6%

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

   4. Applied rewrites 59.6%

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

   if 1.35e-19 < i

   1. Initial program 73.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

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

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

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

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

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

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

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

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

      10. remove-double-neg N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. lower-134-z0z1z2z3z4 77.2%

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

   3. Applied rewrites 77.2%

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

   4. Taylor expanded in i around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 39.2%

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

   6. Applied rewrites 39.2%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 39.2%

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 39.2%

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

   8. Applied rewrites 39.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-134-z0z1z2z3z4 38.9%

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

   10. Applied rewrites 38.9%

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

Alternative 10: 59.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;i \leq -50000000000000000310004322520389159747584:\\ \;\;\;\;a \cdot \left(b \cdot i\right) + \mathsf{134\_z0z1z2z3z4}\left(j, t, c, y, i\right)\\ \mathbf{elif}\;i \leq \frac{2803840303608807}{20769187434139310514121985316880384}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(c \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(i, b, a, y, j\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (if (<= i -50000000000000000310004322520389159747584)
  (+ (* a (* b i)) (134-z0z1z2z3z4 j t c y i))
  (if (<= i 2803840303608807/20769187434139310514121985316880384)
    (+ (* z (- (* x y) (* b c))) (* j (* c t)))
    (134-z0z1z2z3z4 i b a y j))))

Derivation

1. Split input into 3 regimes

2. if i < -5e40

   1. Initial program 73.1%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 49.1%

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

   4. Applied rewrites 49.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

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

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

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

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

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

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

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

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

      10. remove-double-neg N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-134-z0z1z2z3z4 51.2%

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

   6. Applied rewrites 51.2%

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

   if -5e40 < i < 1.35e-19

   1. Initial program 73.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

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

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

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

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

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

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

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

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

      10. remove-double-neg N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. lower-134-z0z1z2z3z4 77.2%

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

   3. Applied rewrites 77.2%

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

   4. Taylor expanded in y around 0

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

      1. lower-*.f64 70.0%

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

   6. Applied rewrites 70.0%

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

   7. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 48.9%

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

   9. Applied rewrites 48.9%

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

   if 1.35e-19 < i

   1. Initial program 73.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

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

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

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

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

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

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

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

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

      10. remove-double-neg N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. lower-134-z0z1z2z3z4 77.2%

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

   3. Applied rewrites 77.2%

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

   4. Taylor expanded in i around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 39.2%

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

   6. Applied rewrites 39.2%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 39.2%

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 39.2%

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

   8. Applied rewrites 39.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-134-z0z1z2z3z4 38.9%

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

   10. Applied rewrites 38.9%

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

Alternative 11: 59.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;i \leq -59999999999999999817723503236360894134390639559794877150527488:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(i, b, a, y, j\right)\\ \mathbf{elif}\;i \leq \frac{2803840303608807}{20769187434139310514121985316880384}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(c \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(i, b, a, y, j\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (if (<=
     i
     -59999999999999999817723503236360894134390639559794877150527488)
  (134-z0z1z2z3z4 i b a y j)
  (if (<= i 2803840303608807/20769187434139310514121985316880384)
    (+ (* z (- (* x y) (* b c))) (* j (* c t)))
    (134-z0z1z2z3z4 i b a y j))))

Derivation

1. Split input into 2 regimes

2. if i < -6e61 or 1.35e-19 < i

   1. Initial program 73.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

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

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

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

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

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

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

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

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

      10. remove-double-neg N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. lower-134-z0z1z2z3z4 77.2%

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

   3. Applied rewrites 77.2%

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

   4. Taylor expanded in i around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 39.2%

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

   6. Applied rewrites 39.2%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 39.2%

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 39.2%

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

   8. Applied rewrites 39.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-134-z0z1z2z3z4 38.9%

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

   10. Applied rewrites 38.9%

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

   if -6e61 < i < 1.35e-19

   1. Initial program 73.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

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

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

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

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

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

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

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

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

      10. remove-double-neg N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. lower-134-z0z1z2z3z4 77.2%

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

   3. Applied rewrites 77.2%

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

   4. Taylor expanded in y around 0

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

      1. lower-*.f64 70.0%

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

   6. Applied rewrites 70.0%

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

   7. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 48.9%

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

   9. Applied rewrites 48.9%

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

Alternative 12: 58.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;i \leq -59999999999999999817723503236360894134390639559794877150527488:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(i, b, a, y, j\right)\\ \mathbf{elif}\;i \leq \frac{2803840303608807}{20769187434139310514121985316880384}:\\ \;\;\;\;j \cdot \left(c \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(i, b, a, y, j\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (if (<=
     i
     -59999999999999999817723503236360894134390639559794877150527488)
  (134-z0z1z2z3z4 i b a y j)
  (if (<= i 2803840303608807/20769187434139310514121985316880384)
    (+ (* j (* c t)) (* x (- (* y z) (* a t))))
    (134-z0z1z2z3z4 i b a y j))))

Derivation

1. Split input into 2 regimes

2. if i < -6e61 or 1.35e-19 < i

   1. Initial program 73.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

      4. distribute-rgt-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(i \cdot a - c \cdot z\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(b\right)\right) \cdot \left(i \cdot a - c \cdot z\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. sub-negate-rev N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. lift--.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z - i \cdot a\right)}\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      8. distribute-rgt-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      9. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      10. remove-double-neg N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      11. lift--.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{c \cdot z} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      13. *-commutative N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      15. lower-134-z0z1z2z3z4 77.2%

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   3. Applied rewrites 77.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(j \cdot y - a \cdot b\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - \color{blue}{a \cdot b}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - \color{blue}{a} \cdot b\right)\right) \]

      5. lower-*.f64 39.2%

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - a \cdot \color{blue}{b}\right)\right) \]

   6. Applied rewrites 39.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot y - a \cdot b\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot y - a \cdot b\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(j \cdot y - a \cdot b\right) \cdot i\right) \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(j \cdot y - a \cdot b\right)\right)\right) \cdot \color{blue}{i} \]

      6. lift--.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(j \cdot y - a \cdot b\right)\right)\right) \cdot i \]

      7. sub-negate-rev N/A

         \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot i \]

      8. lower-*.f64 N/A

         \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot \color{blue}{i} \]

      9. lower--.f64 39.2%

         \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot i \]

      10. lift-*.f64 N/A

          \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot i \]

      11. *-commutative N/A

          \[\leadsto \left(b \cdot a - j \cdot y\right) \cdot i \]

      12. lower-*.f64 39.2%

          \[\leadsto \left(b \cdot a - j \cdot y\right) \cdot i \]

   8. Applied rewrites 39.2%

      \[\leadsto \left(b \cdot a - j \cdot y\right) \cdot \color{blue}{i} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(b \cdot a - j \cdot y\right) \cdot \color{blue}{i} \]

      2. *-commutative N/A

         \[\leadsto i \cdot \color{blue}{\left(b \cdot a - j \cdot y\right)} \]

      3. lift--.f64 N/A

         \[\leadsto i \cdot \left(b \cdot a - \color{blue}{j \cdot y}\right) \]

      4. lift-*.f64 N/A

         \[\leadsto i \cdot \left(b \cdot a - j \cdot \color{blue}{y}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto i \cdot \left(b \cdot a - \color{blue}{j} \cdot y\right) \]

      6. *-commutative N/A

         \[\leadsto i \cdot \left(b \cdot a - y \cdot \color{blue}{j}\right) \]

      7. lower-134-z0z1z2z3z4 38.9%

         \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(i, \color{blue}{b}, a, y, j\right) \]

   10. Applied rewrites 38.9%

       \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(i, \color{blue}{b}, a, y, j\right) \]

   if -6e61 < i < 1.35e-19

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around 0

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{x} \cdot \left(y \cdot z - a \cdot t\right) \]

      3. lower--.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      4. lower-*.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      5. lower-*.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      6. lower-*.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      7. lower--.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - \color{blue}{a} \cdot t\right) \]

      9. lower-*.f64 59.6%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot \color{blue}{t}\right) \]

   4. Applied rewrites 59.6%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in y around 0

      \[\leadsto j \cdot \left(c \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 50.0%

         \[\leadsto j \cdot \left(c \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

   7. Applied rewrites 50.0%

      \[\leadsto j \cdot \left(c \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 53.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;c \leq -25000000000000001047038139105286448974785846666008457078585692795174912:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(c, t, j, z, b\right)\\ \mathbf{elif}\;c \leq 3700000000000:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(i, b, a, y, j\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(c, t, j, z, b\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (if (<=
     c
     -25000000000000001047038139105286448974785846666008457078585692795174912)
  (134-z0z1z2z3z4 c t j z b)
  (if (<= c 3700000000000)
    (134-z0z1z2z3z4 i b a y j)
    (134-z0z1z2z3z4 c t j z b))))

Derivation

1. Split input into 2 regimes

2. if c < -2.5000000000000001e70 or 3.7e12 < c

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(j \cdot t - b \cdot z\right)} \]

      2. lower--.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b} \cdot z\right) \]

      4. lower-*.f64 38.8%

         \[\leadsto c \cdot \left(j \cdot t - b \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 38.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(j \cdot t - b \cdot z\right)} \]

      2. lift--.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b \cdot z}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - b \cdot \color{blue}{z}\right) \]

      4. *-commutative N/A

         \[\leadsto c \cdot \left(j \cdot t - z \cdot \color{blue}{b}\right) \]

      5. fp-cancel-sub-sign-inv N/A

         \[\leadsto c \cdot \left(j \cdot t + \color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot b}\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto c \cdot \left(j \cdot t + \left(\mathsf{neg}\left(z \cdot b\right)\right)\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto c \cdot \left(j \cdot t + z \cdot \color{blue}{\left(\mathsf{neg}\left(b\right)\right)}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot \left(\mathsf{neg}\left(b\right)\right)}\right) \]

      9. lift-*.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot \left(\mathsf{neg}\left(b\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto c \cdot \left(t \cdot j - \color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot \left(\mathsf{neg}\left(b\right)\right)\right) \]

      11. distribute-lft-neg-in N/A

          \[\leadsto c \cdot \left(t \cdot j - \left(\mathsf{neg}\left(z \cdot \left(\mathsf{neg}\left(b\right)\right)\right)\right)\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto c \cdot \left(t \cdot j - z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right)}\right) \]

      13. remove-double-neg N/A

          \[\leadsto c \cdot \left(t \cdot j - z \cdot b\right) \]

      14. lower-134-z0z1z2z3z4 39.2%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(c, \color{blue}{t}, j, z, b\right) \]

   6. Applied rewrites 39.2%

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(c, \color{blue}{t}, j, z, b\right) \]

   if -2.5000000000000001e70 < c < 3.7e12

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. lift--.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. sub-negate-rev N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(i \cdot a - c \cdot z\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. distribute-rgt-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(i \cdot a - c \cdot z\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(b\right)\right) \cdot \left(i \cdot a - c \cdot z\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. sub-negate-rev N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. lift--.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z - i \cdot a\right)}\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      8. distribute-rgt-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      9. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      10. remove-double-neg N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      11. lift--.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{c \cdot z} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      13. *-commutative N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      15. lower-134-z0z1z2z3z4 77.2%

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   3. Applied rewrites 77.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(j \cdot y - a \cdot b\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - \color{blue}{a \cdot b}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - \color{blue}{a} \cdot b\right)\right) \]

      5. lower-*.f64 39.2%

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - a \cdot \color{blue}{b}\right)\right) \]

   6. Applied rewrites 39.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot y - a \cdot b\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot y - a \cdot b\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(j \cdot y - a \cdot b\right) \cdot i\right) \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(j \cdot y - a \cdot b\right)\right)\right) \cdot \color{blue}{i} \]

      6. lift--.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(j \cdot y - a \cdot b\right)\right)\right) \cdot i \]

      7. sub-negate-rev N/A

         \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot i \]

      8. lower-*.f64 N/A

         \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot \color{blue}{i} \]

      9. lower--.f64 39.2%

         \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot i \]

      10. lift-*.f64 N/A

          \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot i \]

      11. *-commutative N/A

          \[\leadsto \left(b \cdot a - j \cdot y\right) \cdot i \]

      12. lower-*.f64 39.2%

          \[\leadsto \left(b \cdot a - j \cdot y\right) \cdot i \]

   8. Applied rewrites 39.2%

      \[\leadsto \left(b \cdot a - j \cdot y\right) \cdot \color{blue}{i} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(b \cdot a - j \cdot y\right) \cdot \color{blue}{i} \]

      2. *-commutative N/A

         \[\leadsto i \cdot \color{blue}{\left(b \cdot a - j \cdot y\right)} \]

      3. lift--.f64 N/A

         \[\leadsto i \cdot \left(b \cdot a - \color{blue}{j \cdot y}\right) \]

      4. lift-*.f64 N/A

         \[\leadsto i \cdot \left(b \cdot a - j \cdot \color{blue}{y}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto i \cdot \left(b \cdot a - \color{blue}{j} \cdot y\right) \]

      6. *-commutative N/A

         \[\leadsto i \cdot \left(b \cdot a - y \cdot \color{blue}{j}\right) \]

      7. lower-134-z0z1z2z3z4 38.9%

         \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(i, \color{blue}{b}, a, y, j\right) \]

   10. Applied rewrites 38.9%

       \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(i, \color{blue}{b}, a, y, j\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 52.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;c \leq -25000000000000001047038139105286448974785846666008457078585692795174912:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(c, t, j, z, b\right)\\ \mathbf{elif}\;c \leq 4200000000000000159086051820587205661447942375116082460464186153870236755951616:\\ \;\;\;\;\left(b \cdot a - j \cdot y\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(c, t, j, z, b\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (if (<=
     c
     -25000000000000001047038139105286448974785846666008457078585692795174912)
  (134-z0z1z2z3z4 c t j z b)
  (if (<=
       c
       4200000000000000159086051820587205661447942375116082460464186153870236755951616)
    (* (- (* b a) (* j y)) i)
    (134-z0z1z2z3z4 c t j z b))))

Derivation

1. Split input into 2 regimes

2. if c < -2.5000000000000001e70 or 4.2000000000000002e78 < c

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(j \cdot t - b \cdot z\right)} \]

      2. lower--.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b} \cdot z\right) \]

      4. lower-*.f64 38.8%

         \[\leadsto c \cdot \left(j \cdot t - b \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 38.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(j \cdot t - b \cdot z\right)} \]

      2. lift--.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b \cdot z}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - b \cdot \color{blue}{z}\right) \]

      4. *-commutative N/A

         \[\leadsto c \cdot \left(j \cdot t - z \cdot \color{blue}{b}\right) \]

      5. fp-cancel-sub-sign-inv N/A

         \[\leadsto c \cdot \left(j \cdot t + \color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot b}\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto c \cdot \left(j \cdot t + \left(\mathsf{neg}\left(z \cdot b\right)\right)\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto c \cdot \left(j \cdot t + z \cdot \color{blue}{\left(\mathsf{neg}\left(b\right)\right)}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot \left(\mathsf{neg}\left(b\right)\right)}\right) \]

      9. lift-*.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot \left(\mathsf{neg}\left(b\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto c \cdot \left(t \cdot j - \color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot \left(\mathsf{neg}\left(b\right)\right)\right) \]

      11. distribute-lft-neg-in N/A

          \[\leadsto c \cdot \left(t \cdot j - \left(\mathsf{neg}\left(z \cdot \left(\mathsf{neg}\left(b\right)\right)\right)\right)\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto c \cdot \left(t \cdot j - z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right)}\right) \]

      13. remove-double-neg N/A

          \[\leadsto c \cdot \left(t \cdot j - z \cdot b\right) \]

      14. lower-134-z0z1z2z3z4 39.2%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(c, \color{blue}{t}, j, z, b\right) \]

   6. Applied rewrites 39.2%

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(c, \color{blue}{t}, j, z, b\right) \]

   if -2.5000000000000001e70 < c < 4.2000000000000002e78

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. lift--.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. sub-negate-rev N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(i \cdot a - c \cdot z\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. distribute-rgt-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(i \cdot a - c \cdot z\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(b\right)\right) \cdot \left(i \cdot a - c \cdot z\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. sub-negate-rev N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. lift--.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z - i \cdot a\right)}\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      8. distribute-rgt-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      9. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      10. remove-double-neg N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      11. lift--.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{c \cdot z} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      13. *-commutative N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      15. lower-134-z0z1z2z3z4 77.2%

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   3. Applied rewrites 77.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(j \cdot y - a \cdot b\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - \color{blue}{a \cdot b}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - \color{blue}{a} \cdot b\right)\right) \]

      5. lower-*.f64 39.2%

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - a \cdot \color{blue}{b}\right)\right) \]

   6. Applied rewrites 39.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot y - a \cdot b\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot y - a \cdot b\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(j \cdot y - a \cdot b\right) \cdot i\right) \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(j \cdot y - a \cdot b\right)\right)\right) \cdot \color{blue}{i} \]

      6. lift--.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(j \cdot y - a \cdot b\right)\right)\right) \cdot i \]

      7. sub-negate-rev N/A

         \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot i \]

      8. lower-*.f64 N/A

         \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot \color{blue}{i} \]

      9. lower--.f64 39.2%

         \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot i \]

      10. lift-*.f64 N/A

          \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot i \]

      11. *-commutative N/A

          \[\leadsto \left(b \cdot a - j \cdot y\right) \cdot i \]

      12. lower-*.f64 39.2%

          \[\leadsto \left(b \cdot a - j \cdot y\right) \cdot i \]

   8. Applied rewrites 39.2%

      \[\leadsto \left(b \cdot a - j \cdot y\right) \cdot \color{blue}{i} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 52.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} t_1 := c \cdot \left(j \cdot t - b \cdot z\right)\\ \mathbf{if}\;c \leq -25000000000000001047038139105286448974785846666008457078585692795174912:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 4200000000000000159086051820587205661447942375116082460464186153870236755951616:\\ \;\;\;\;\left(b \cdot a - j \cdot y\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (let* ((t_1 (* c (- (* j t) (* b z)))))
  (if (<=
       c
       -25000000000000001047038139105286448974785846666008457078585692795174912)
    t_1
    (if (<=
         c
         4200000000000000159086051820587205661447942375116082460464186153870236755951616)
      (* (- (* b a) (* j y)) i)
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((j * t) - (b * z));
	double tmp;
	if (c <= -2.5e+70) {
		tmp = t_1;
	} else if (c <= 4.2e+78) {
		tmp = ((b * a) - (j * y)) * i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((j * t) - (b * z))
    if (c <= (-2.5d+70)) then
        tmp = t_1
    else if (c <= 4.2d+78) then
        tmp = ((b * a) - (j * y)) * i
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((j * t) - (b * z));
	double tmp;
	if (c <= -2.5e+70) {
		tmp = t_1;
	} else if (c <= 4.2e+78) {
		tmp = ((b * a) - (j * y)) * i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((j * t) - (b * z))
	tmp = 0
	if c <= -2.5e+70:
		tmp = t_1
	elif c <= 4.2e+78:
		tmp = ((b * a) - (j * y)) * i
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(j * t) - Float64(b * z)))
	tmp = 0.0
	if (c <= -2.5e+70)
		tmp = t_1;
	elseif (c <= 4.2e+78)
		tmp = Float64(Float64(Float64(b * a) - Float64(j * y)) * i);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((j * t) - (b * z));
	tmp = 0.0;
	if (c <= -2.5e+70)
		tmp = t_1;
	elseif (c <= 4.2e+78)
		tmp = ((b * a) - (j * y)) * i;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(j * t), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -25000000000000001047038139105286448974785846666008457078585692795174912], t$95$1, If[LessEqual[c, 4200000000000000159086051820587205661447942375116082460464186153870236755951616], N[(N[(N[(b * a), $MachinePrecision] - N[(j * y), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if c < -2.5000000000000001e70 or 4.2000000000000002e78 < c

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(j \cdot t - b \cdot z\right)} \]

      2. lower--.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b} \cdot z\right) \]

      4. lower-*.f64 38.8%

         \[\leadsto c \cdot \left(j \cdot t - b \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 38.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   if -2.5000000000000001e70 < c < 4.2000000000000002e78

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. lift--.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. sub-negate-rev N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(i \cdot a - c \cdot z\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. distribute-rgt-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(i \cdot a - c \cdot z\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(b\right)\right) \cdot \left(i \cdot a - c \cdot z\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. sub-negate-rev N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. lift--.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z - i \cdot a\right)}\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      8. distribute-rgt-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      9. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      10. remove-double-neg N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      11. lift--.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{c \cdot z} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      13. *-commutative N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      15. lower-134-z0z1z2z3z4 77.2%

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   3. Applied rewrites 77.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(j \cdot y - a \cdot b\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - \color{blue}{a \cdot b}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - \color{blue}{a} \cdot b\right)\right) \]

      5. lower-*.f64 39.2%

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - a \cdot \color{blue}{b}\right)\right) \]

   6. Applied rewrites 39.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot y - a \cdot b\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot y - a \cdot b\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(j \cdot y - a \cdot b\right) \cdot i\right) \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(j \cdot y - a \cdot b\right)\right)\right) \cdot \color{blue}{i} \]

      6. lift--.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(j \cdot y - a \cdot b\right)\right)\right) \cdot i \]

      7. sub-negate-rev N/A

         \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot i \]

      8. lower-*.f64 N/A

         \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot \color{blue}{i} \]

      9. lower--.f64 39.2%

         \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot i \]

      10. lift-*.f64 N/A

          \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot i \]

      11. *-commutative N/A

          \[\leadsto \left(b \cdot a - j \cdot y\right) \cdot i \]

      12. lower-*.f64 39.2%

          \[\leadsto \left(b \cdot a - j \cdot y\right) \cdot i \]

   8. Applied rewrites 39.2%

      \[\leadsto \left(b \cdot a - j \cdot y\right) \cdot \color{blue}{i} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 52.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} t_1 := c \cdot \left(j \cdot t - b \cdot z\right)\\ \mathbf{if}\;c \leq -139999999999999992138831935449925184808511285378398708820252613393702318409515008:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 6500000000000000137014627496820924743680:\\ \;\;\;\;\left(z \cdot x - j \cdot i\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (let* ((t_1 (* c (- (* j t) (* b z)))))
  (if (<=
       c
       -139999999999999992138831935449925184808511285378398708820252613393702318409515008)
    t_1
    (if (<= c 6500000000000000137014627496820924743680)
      (* (- (* 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 * ((j * t) - (b * z));
	double tmp;
	if (c <= -1.4e+80) {
		tmp = t_1;
	} else if (c <= 6.5e+39) {
		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 * ((j * t) - (b * z))
    if (c <= (-1.4d+80)) then
        tmp = t_1
    else if (c <= 6.5d+39) 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 * ((j * t) - (b * z));
	double tmp;
	if (c <= -1.4e+80) {
		tmp = t_1;
	} else if (c <= 6.5e+39) {
		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 * ((j * t) - (b * z))
	tmp = 0
	if c <= -1.4e+80:
		tmp = t_1
	elif c <= 6.5e+39:
		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(j * t) - Float64(b * z)))
	tmp = 0.0
	if (c <= -1.4e+80)
		tmp = t_1;
	elseif (c <= 6.5e+39)
		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 * ((j * t) - (b * z));
	tmp = 0.0;
	if (c <= -1.4e+80)
		tmp = t_1;
	elseif (c <= 6.5e+39)
		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[(j * t), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -139999999999999992138831935449925184808511285378398708820252613393702318409515008], t$95$1, If[LessEqual[c, 6500000000000000137014627496820924743680], N[(N[(N[(z * x), $MachinePrecision] - N[(j * i), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if c < -1.3999999999999999e80 or 6.5000000000000001e39 < c

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(j \cdot t - b \cdot z\right)} \]

      2. lower--.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b} \cdot z\right) \]

      4. lower-*.f64 38.8%

         \[\leadsto c \cdot \left(j \cdot t - b \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 38.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   if -1.3999999999999999e80 < c < 6.5000000000000001e39

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. 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 39.3%

         \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 39.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   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 39.3%

         \[\leadsto \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right) \cdot \color{blue}{y} \]

      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 39.3%

          \[\leadsto \left(z \cdot x - i \cdot j\right) \cdot y \]

      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 39.3%

          \[\leadsto \left(z \cdot x - j \cdot i\right) \cdot y \]

   6. Applied rewrites 39.3%

      \[\leadsto \left(z \cdot x - j \cdot i\right) \cdot \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 41.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} t_1 := c \cdot \left(j \cdot t - b \cdot z\right)\\ \mathbf{if}\;c \leq -54999999999999995856782217794033543777047918854839284797535091765700111817594182285267951232722895270914328805700170328504758759671407312896:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq \frac{-5398307492432545}{12554203470773361527671578846415332832204710888928069025792}:\\ \;\;\;\;j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;c \leq 1350000000000000037384336378801607506132992:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (let* ((t_1 (* c (- (* j t) (* b z)))))
  (if (<=
       c
       -54999999999999995856782217794033543777047918854839284797535091765700111817594182285267951232722895270914328805700170328504758759671407312896)
    t_1
    (if (<=
         c
         -5398307492432545/12554203470773361527671578846415332832204710888928069025792)
      (* j (- (* c t) (* i y)))
      (if (<= c 1350000000000000037384336378801607506132992)
        (* a (* b i))
        t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((j * t) - (b * z));
	double tmp;
	if (c <= -5.5e+139) {
		tmp = t_1;
	} else if (c <= -4.3e-43) {
		tmp = j * ((c * t) - (i * y));
	} else if (c <= 1.35e+42) {
		tmp = a * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((j * t) - (b * z))
    if (c <= (-5.5d+139)) then
        tmp = t_1
    else if (c <= (-4.3d-43)) then
        tmp = j * ((c * t) - (i * y))
    else if (c <= 1.35d+42) then
        tmp = a * (b * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((j * t) - (b * z));
	double tmp;
	if (c <= -5.5e+139) {
		tmp = t_1;
	} else if (c <= -4.3e-43) {
		tmp = j * ((c * t) - (i * y));
	} else if (c <= 1.35e+42) {
		tmp = a * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((j * t) - (b * z))
	tmp = 0
	if c <= -5.5e+139:
		tmp = t_1
	elif c <= -4.3e-43:
		tmp = j * ((c * t) - (i * y))
	elif c <= 1.35e+42:
		tmp = a * (b * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(j * t) - Float64(b * z)))
	tmp = 0.0
	if (c <= -5.5e+139)
		tmp = t_1;
	elseif (c <= -4.3e-43)
		tmp = Float64(j * Float64(Float64(c * t) - Float64(i * y)));
	elseif (c <= 1.35e+42)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((j * t) - (b * z));
	tmp = 0.0;
	if (c <= -5.5e+139)
		tmp = t_1;
	elseif (c <= -4.3e-43)
		tmp = j * ((c * t) - (i * y));
	elseif (c <= 1.35e+42)
		tmp = a * (b * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(j * t), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -54999999999999995856782217794033543777047918854839284797535091765700111817594182285267951232722895270914328805700170328504758759671407312896], t$95$1, If[LessEqual[c, -5398307492432545/12554203470773361527671578846415332832204710888928069025792], N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1350000000000000037384336378801607506132992], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -5.4999999999999996e139 or 1.35e42 < c

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(j \cdot t - b \cdot z\right)} \]

      2. lower--.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b} \cdot z\right) \]

      4. lower-*.f64 38.8%

         \[\leadsto c \cdot \left(j \cdot t - b \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 38.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   if -5.4999999999999996e139 < c < -4.2999999999999996e-43

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around 0

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{x} \cdot \left(y \cdot z - a \cdot t\right) \]

      3. lower--.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      4. lower-*.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      5. lower-*.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      6. lower-*.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      7. lower--.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - \color{blue}{a} \cdot t\right) \]

      9. lower-*.f64 59.6%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot \color{blue}{t}\right) \]

   4. Applied rewrites 59.6%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in y around 0

      \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \color{blue}{c \cdot \left(j \cdot t\right)} \]
   6. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \color{blue}{\left(j \cdot t\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(\color{blue}{j} \cdot t\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right) \]

      5. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot \color{blue}{t}\right) \]

      6. lower-*.f64 35.2%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right) \]

   7. Applied rewrites 35.2%

      \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \color{blue}{c \cdot \left(j \cdot t\right)} \]

   8. Taylor expanded in x around 0

      \[\leadsto j \cdot \color{blue}{\left(c \cdot t - i \cdot y\right)} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - \color{blue}{i \cdot y}\right) \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot \color{blue}{y}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. lower-*.f64 38.8%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) \]

   10. Applied rewrites 38.8%

       \[\leadsto j \cdot \color{blue}{\left(c \cdot t - i \cdot y\right)} \]

   if -4.2999999999999996e-43 < c < 1.35e42

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. lift--.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. sub-negate-rev N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(i \cdot a - c \cdot z\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. distribute-rgt-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(i \cdot a - c \cdot z\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(b\right)\right) \cdot \left(i \cdot a - c \cdot z\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. sub-negate-rev N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. lift--.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z - i \cdot a\right)}\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      8. distribute-rgt-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      9. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      10. remove-double-neg N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      11. lift--.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{c \cdot z} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      13. *-commutative N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      15. lower-134-z0z1z2z3z4 77.2%

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   3. Applied rewrites 77.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(j \cdot y - a \cdot b\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - \color{blue}{a \cdot b}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - \color{blue}{a} \cdot b\right)\right) \]

      5. lower-*.f64 39.2%

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - a \cdot \color{blue}{b}\right)\right) \]

   6. Applied rewrites 39.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

   7. Taylor expanded in y around 0

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \color{blue}{i}\right) \]

      2. lower-*.f64 22.2%

         \[\leadsto a \cdot \left(b \cdot i\right) \]

   9. Applied rewrites 22.2%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 40.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;b \leq -180000000000000012012486656:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 24500000000000000923157099035783906969573975216719612870656:\\ \;\;\;\;j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot i\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (if (<= b -180000000000000012012486656)
  (* a (* b i))
  (if (<=
       b
       24500000000000000923157099035783906969573975216719612870656)
    (* j (- (* c t) (* i y)))
    (* (* a b) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -1.8e+26) {
		tmp = a * (b * i);
	} else if (b <= 2.45e+58) {
		tmp = j * ((c * t) - (i * y));
	} else {
		tmp = (a * b) * i;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-1.8d+26)) then
        tmp = a * (b * i)
    else if (b <= 2.45d+58) then
        tmp = j * ((c * t) - (i * y))
    else
        tmp = (a * b) * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -1.8e+26) {
		tmp = a * (b * i);
	} else if (b <= 2.45e+58) {
		tmp = j * ((c * t) - (i * y));
	} else {
		tmp = (a * b) * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -1.8e+26:
		tmp = a * (b * i)
	elif b <= 2.45e+58:
		tmp = j * ((c * t) - (i * y))
	else:
		tmp = (a * b) * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -1.8e+26)
		tmp = Float64(a * Float64(b * i));
	elseif (b <= 2.45e+58)
		tmp = Float64(j * Float64(Float64(c * t) - Float64(i * y)));
	else
		tmp = Float64(Float64(a * b) * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -1.8e+26)
		tmp = a * (b * i);
	elseif (b <= 2.45e+58)
		tmp = j * ((c * t) - (i * y));
	else
		tmp = (a * b) * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -180000000000000012012486656], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 24500000000000000923157099035783906969573975216719612870656], N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] * i), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.8000000000000001e26

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. lift--.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. sub-negate-rev N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(i \cdot a - c \cdot z\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. distribute-rgt-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(i \cdot a - c \cdot z\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(b\right)\right) \cdot \left(i \cdot a - c \cdot z\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. sub-negate-rev N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. lift--.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z - i \cdot a\right)}\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      8. distribute-rgt-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      9. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      10. remove-double-neg N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      11. lift--.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{c \cdot z} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      13. *-commutative N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      15. lower-134-z0z1z2z3z4 77.2%

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   3. Applied rewrites 77.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(j \cdot y - a \cdot b\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - \color{blue}{a \cdot b}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - \color{blue}{a} \cdot b\right)\right) \]

      5. lower-*.f64 39.2%

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - a \cdot \color{blue}{b}\right)\right) \]

   6. Applied rewrites 39.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

   7. Taylor expanded in y around 0

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \color{blue}{i}\right) \]

      2. lower-*.f64 22.2%

         \[\leadsto a \cdot \left(b \cdot i\right) \]

   9. Applied rewrites 22.2%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]

   if -1.8000000000000001e26 < b < 2.4500000000000001e58

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around 0

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{x} \cdot \left(y \cdot z - a \cdot t\right) \]

      3. lower--.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      4. lower-*.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      5. lower-*.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      6. lower-*.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      7. lower--.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - \color{blue}{a} \cdot t\right) \]

      9. lower-*.f64 59.6%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot \color{blue}{t}\right) \]

   4. Applied rewrites 59.6%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in y around 0

      \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \color{blue}{c \cdot \left(j \cdot t\right)} \]
   6. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \color{blue}{\left(j \cdot t\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(\color{blue}{j} \cdot t\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right) \]

      5. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot \color{blue}{t}\right) \]

      6. lower-*.f64 35.2%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right) \]

   7. Applied rewrites 35.2%

      \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \color{blue}{c \cdot \left(j \cdot t\right)} \]

   8. Taylor expanded in x around 0

      \[\leadsto j \cdot \color{blue}{\left(c \cdot t - i \cdot y\right)} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - \color{blue}{i \cdot y}\right) \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot \color{blue}{y}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. lower-*.f64 38.8%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) \]

   10. Applied rewrites 38.8%

       \[\leadsto j \cdot \color{blue}{\left(c \cdot t - i \cdot y\right)} \]

   if 2.4500000000000001e58 < b

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. lift--.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. sub-negate-rev N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(i \cdot a - c \cdot z\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. distribute-rgt-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(i \cdot a - c \cdot z\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(b\right)\right) \cdot \left(i \cdot a - c \cdot z\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. sub-negate-rev N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. lift--.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z - i \cdot a\right)}\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      8. distribute-rgt-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      9. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      10. remove-double-neg N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      11. lift--.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{c \cdot z} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      13. *-commutative N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      15. lower-134-z0z1z2z3z4 77.2%

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   3. Applied rewrites 77.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(j \cdot y - a \cdot b\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - \color{blue}{a \cdot b}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - \color{blue}{a} \cdot b\right)\right) \]

      5. lower-*.f64 39.2%

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - a \cdot \color{blue}{b}\right)\right) \]

   6. Applied rewrites 39.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot y - a \cdot b\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot y - a \cdot b\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(j \cdot y - a \cdot b\right) \cdot i\right) \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(j \cdot y - a \cdot b\right)\right)\right) \cdot \color{blue}{i} \]

      6. lift--.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(j \cdot y - a \cdot b\right)\right)\right) \cdot i \]

      7. sub-negate-rev N/A

         \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot i \]

      8. lower-*.f64 N/A

         \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot \color{blue}{i} \]

      9. lower--.f64 39.2%

         \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot i \]

      10. lift-*.f64 N/A

          \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot i \]

      11. *-commutative N/A

          \[\leadsto \left(b \cdot a - j \cdot y\right) \cdot i \]

      12. lower-*.f64 39.2%

          \[\leadsto \left(b \cdot a - j \cdot y\right) \cdot i \]

   8. Applied rewrites 39.2%

      \[\leadsto \left(b \cdot a - j \cdot y\right) \cdot \color{blue}{i} \]

   9. Taylor expanded in y around 0

      \[\leadsto \left(a \cdot b\right) \cdot i \]
   10. Step-by-step derivation

       1. lower-*.f64 22.4%

          \[\leadsto \left(a \cdot b\right) \cdot i \]

   11. Applied rewrites 22.4%

       \[\leadsto \left(a \cdot b\right) \cdot i \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 29.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;b \leq -14500000000000000:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq \frac{-1416953066986969}{833501804109981784259981473840157224643094790289488520049532226470504654727204008940179025108944286342866238824179155055736100206764920635045419506541353755761894697439251819807884785738976753091120627016985825247711343504684557661395484672}:\\ \;\;\;\;-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)\\ \mathbf{elif}\;b \leq 21000000000000001189505106290147333501344090768766123638784:\\ \;\;\;\;c \cdot \left(j \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot i\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (if (<= b -14500000000000000)
  (* a (* b i))
  (if (<=
       b
       -1416953066986969/833501804109981784259981473840157224643094790289488520049532226470504654727204008940179025108944286342866238824179155055736100206764920635045419506541353755761894697439251819807884785738976753091120627016985825247711343504684557661395484672)
    (* -1 (* i (* j y)))
    (if (<=
         b
         21000000000000001189505106290147333501344090768766123638784)
      (* c (* j t))
      (* (* a b) i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -1.45e+16) {
		tmp = a * (b * i);
	} else if (b <= -1.7e-225) {
		tmp = -1.0 * (i * (j * y));
	} else if (b <= 2.1e+58) {
		tmp = c * (j * t);
	} else {
		tmp = (a * b) * i;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-1.45d+16)) then
        tmp = a * (b * i)
    else if (b <= (-1.7d-225)) then
        tmp = (-1.0d0) * (i * (j * y))
    else if (b <= 2.1d+58) then
        tmp = c * (j * t)
    else
        tmp = (a * b) * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -1.45e+16) {
		tmp = a * (b * i);
	} else if (b <= -1.7e-225) {
		tmp = -1.0 * (i * (j * y));
	} else if (b <= 2.1e+58) {
		tmp = c * (j * t);
	} else {
		tmp = (a * b) * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -1.45e+16:
		tmp = a * (b * i)
	elif b <= -1.7e-225:
		tmp = -1.0 * (i * (j * y))
	elif b <= 2.1e+58:
		tmp = c * (j * t)
	else:
		tmp = (a * b) * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -1.45e+16)
		tmp = Float64(a * Float64(b * i));
	elseif (b <= -1.7e-225)
		tmp = Float64(-1.0 * Float64(i * Float64(j * y)));
	elseif (b <= 2.1e+58)
		tmp = Float64(c * Float64(j * t));
	else
		tmp = Float64(Float64(a * b) * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -1.45e+16)
		tmp = a * (b * i);
	elseif (b <= -1.7e-225)
		tmp = -1.0 * (i * (j * y));
	elseif (b <= 2.1e+58)
		tmp = c * (j * t);
	else
		tmp = (a * b) * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -14500000000000000], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1416953066986969/833501804109981784259981473840157224643094790289488520049532226470504654727204008940179025108944286342866238824179155055736100206764920635045419506541353755761894697439251819807884785738976753091120627016985825247711343504684557661395484672], N[(-1 * N[(i * N[(j * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 21000000000000001189505106290147333501344090768766123638784], N[(c * N[(j * t), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] * i), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.45e16

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. lift--.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. sub-negate-rev N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(i \cdot a - c \cdot z\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. distribute-rgt-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(i \cdot a - c \cdot z\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(b\right)\right) \cdot \left(i \cdot a - c \cdot z\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. sub-negate-rev N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. lift--.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z - i \cdot a\right)}\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      8. distribute-rgt-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      9. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      10. remove-double-neg N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      11. lift--.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{c \cdot z} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      13. *-commutative N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      15. lower-134-z0z1z2z3z4 77.2%

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   3. Applied rewrites 77.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(j \cdot y - a \cdot b\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - \color{blue}{a \cdot b}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - \color{blue}{a} \cdot b\right)\right) \]

      5. lower-*.f64 39.2%

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - a \cdot \color{blue}{b}\right)\right) \]

   6. Applied rewrites 39.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

   7. Taylor expanded in y around 0

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \color{blue}{i}\right) \]

      2. lower-*.f64 22.2%

         \[\leadsto a \cdot \left(b \cdot i\right) \]

   9. Applied rewrites 22.2%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]

   if -1.45e16 < b < -1.7e-225

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. 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 39.3%

         \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 39.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y\right)\right)} \]
   6. 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 22.3%

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y\right)\right) \]

   7. Applied rewrites 22.3%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y\right)\right)} \]

   if -1.7e-225 < b < 2.1000000000000001e58

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(j \cdot t - b \cdot z\right)} \]

      2. lower--.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b} \cdot z\right) \]

      4. lower-*.f64 38.8%

         \[\leadsto c \cdot \left(j \cdot t - b \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 38.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto c \cdot \left(j \cdot \color{blue}{t}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 22.5%

         \[\leadsto c \cdot \left(j \cdot t\right) \]

   7. Applied rewrites 22.5%

      \[\leadsto c \cdot \left(j \cdot \color{blue}{t}\right) \]

   if 2.1000000000000001e58 < b

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. lift--.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. sub-negate-rev N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(i \cdot a - c \cdot z\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. distribute-rgt-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(i \cdot a - c \cdot z\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(b\right)\right) \cdot \left(i \cdot a - c \cdot z\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. sub-negate-rev N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. lift--.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z - i \cdot a\right)}\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      8. distribute-rgt-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      9. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      10. remove-double-neg N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      11. lift--.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{c \cdot z} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      13. *-commutative N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      15. lower-134-z0z1z2z3z4 77.2%

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   3. Applied rewrites 77.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(j \cdot y - a \cdot b\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - \color{blue}{a \cdot b}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - \color{blue}{a} \cdot b\right)\right) \]

      5. lower-*.f64 39.2%

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - a \cdot \color{blue}{b}\right)\right) \]

   6. Applied rewrites 39.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot y - a \cdot b\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot y - a \cdot b\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(j \cdot y - a \cdot b\right) \cdot i\right) \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(j \cdot y - a \cdot b\right)\right)\right) \cdot \color{blue}{i} \]

      6. lift--.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(j \cdot y - a \cdot b\right)\right)\right) \cdot i \]

      7. sub-negate-rev N/A

         \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot i \]

      8. lower-*.f64 N/A

         \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot \color{blue}{i} \]

      9. lower--.f64 39.2%

         \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot i \]

      10. lift-*.f64 N/A

          \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot i \]

      11. *-commutative N/A

          \[\leadsto \left(b \cdot a - j \cdot y\right) \cdot i \]

      12. lower-*.f64 39.2%

          \[\leadsto \left(b \cdot a - j \cdot y\right) \cdot i \]

   8. Applied rewrites 39.2%

      \[\leadsto \left(b \cdot a - j \cdot y\right) \cdot \color{blue}{i} \]

   9. Taylor expanded in y around 0

      \[\leadsto \left(a \cdot b\right) \cdot i \]
   10. Step-by-step derivation

       1. lower-*.f64 22.4%

          \[\leadsto \left(a \cdot b\right) \cdot i \]

   11. Applied rewrites 22.4%

       \[\leadsto \left(a \cdot b\right) \cdot i \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 20: 29.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} t_1 := c \cdot \left(j \cdot t\right)\\ \mathbf{if}\;c \leq \frac{-4290987514424489}{12259964326927110866866776217202473468949912977468817408}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 52000000000000004190967118188018085197250560:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 469999999999999975576717977797941685112922973656463459718548369107617262217776701562974441173756323187809264862674962475780911815598089383150786409990048429331027285695435757190994122499435700208795648:\\ \;\;\;\;\left(\left(-c\right) \cdot b\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (let* ((t_1 (* c (* j t))))
  (if (<=
       c
       -4290987514424489/12259964326927110866866776217202473468949912977468817408)
    t_1
    (if (<= c 52000000000000004190967118188018085197250560)
      (* a (* b i))
      (if (<=
           c
           469999999999999975576717977797941685112922973656463459718548369107617262217776701562974441173756323187809264862674962475780911815598089383150786409990048429331027285695435757190994122499435700208795648)
        (* (* (- c) b) z)
        t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (j * t);
	double tmp;
	if (c <= -3.5e-40) {
		tmp = t_1;
	} else if (c <= 5.2e+43) {
		tmp = a * (b * i);
	} else if (c <= 4.7e+200) {
		tmp = (-c * b) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (j * t)
    if (c <= (-3.5d-40)) then
        tmp = t_1
    else if (c <= 5.2d+43) then
        tmp = a * (b * i)
    else if (c <= 4.7d+200) then
        tmp = (-c * b) * z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (j * t);
	double tmp;
	if (c <= -3.5e-40) {
		tmp = t_1;
	} else if (c <= 5.2e+43) {
		tmp = a * (b * i);
	} else if (c <= 4.7e+200) {
		tmp = (-c * b) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (j * t)
	tmp = 0
	if c <= -3.5e-40:
		tmp = t_1
	elif c <= 5.2e+43:
		tmp = a * (b * i)
	elif c <= 4.7e+200:
		tmp = (-c * b) * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(j * t))
	tmp = 0.0
	if (c <= -3.5e-40)
		tmp = t_1;
	elseif (c <= 5.2e+43)
		tmp = Float64(a * Float64(b * i));
	elseif (c <= 4.7e+200)
		tmp = Float64(Float64(Float64(-c) * b) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (j * t);
	tmp = 0.0;
	if (c <= -3.5e-40)
		tmp = t_1;
	elseif (c <= 5.2e+43)
		tmp = a * (b * i);
	elseif (c <= 4.7e+200)
		tmp = (-c * b) * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(j * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4290987514424489/12259964326927110866866776217202473468949912977468817408], t$95$1, If[LessEqual[c, 52000000000000004190967118188018085197250560], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 469999999999999975576717977797941685112922973656463459718548369107617262217776701562974441173756323187809264862674962475780911815598089383150786409990048429331027285695435757190994122499435700208795648], N[(N[((-c) * b), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.5000000000000002e-40 or 4.6999999999999998e200 < c

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(j \cdot t - b \cdot z\right)} \]

      2. lower--.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b} \cdot z\right) \]

      4. lower-*.f64 38.8%

         \[\leadsto c \cdot \left(j \cdot t - b \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 38.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto c \cdot \left(j \cdot \color{blue}{t}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 22.5%

         \[\leadsto c \cdot \left(j \cdot t\right) \]

   7. Applied rewrites 22.5%

      \[\leadsto c \cdot \left(j \cdot \color{blue}{t}\right) \]

   if -3.5000000000000002e-40 < c < 5.2000000000000004e43

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. lift--.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. sub-negate-rev N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(i \cdot a - c \cdot z\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. distribute-rgt-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(i \cdot a - c \cdot z\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(b\right)\right) \cdot \left(i \cdot a - c \cdot z\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. sub-negate-rev N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. lift--.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z - i \cdot a\right)}\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      8. distribute-rgt-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      9. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      10. remove-double-neg N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      11. lift--.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{c \cdot z} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      13. *-commutative N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      15. lower-134-z0z1z2z3z4 77.2%

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   3. Applied rewrites 77.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(j \cdot y - a \cdot b\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - \color{blue}{a \cdot b}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - \color{blue}{a} \cdot b\right)\right) \]

      5. lower-*.f64 39.2%

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - a \cdot \color{blue}{b}\right)\right) \]

   6. Applied rewrites 39.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

   7. Taylor expanded in y around 0

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \color{blue}{i}\right) \]

      2. lower-*.f64 22.2%

         \[\leadsto a \cdot \left(b \cdot i\right) \]

   9. Applied rewrites 22.2%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]

   if 5.2000000000000004e43 < c < 4.6999999999999998e200

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(j \cdot t - b \cdot z\right)} \]

      2. lower--.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b} \cdot z\right) \]

      4. lower-*.f64 38.8%

         \[\leadsto c \cdot \left(j \cdot t - b \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 38.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   5. Taylor expanded in z around inf

      \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(c \cdot z\right)\right)} \]
   6. 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 22.5%

         \[\leadsto -1 \cdot \left(b \cdot \left(c \cdot z\right)\right) \]

   7. Applied rewrites 22.5%

      \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(c \cdot z\right)\right)} \]
   8. 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 22.2%

          \[\leadsto \left(\left(-c\right) \cdot b\right) \cdot z \]

   9. Applied rewrites 22.2%

      \[\leadsto \left(\left(-c\right) \cdot b\right) \cdot z \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 21: 29.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} t_1 := c \cdot \left(j \cdot t\right)\\ \mathbf{if}\;c \leq \frac{-4290987514424489}{12259964326927110866866776217202473468949912977468817408}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 52000000000000004190967118188018085197250560:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 449999999999999969383489225493115588696703864275764557370108112011539275577780917490969607273906365752923733384545329432361067244769220689786693879825947789314966839269759655947717493145169070831697920:\\ \;\;\;\;\left(\left(-b\right) \cdot z\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (let* ((t_1 (* c (* j t))))
  (if (<=
       c
       -4290987514424489/12259964326927110866866776217202473468949912977468817408)
    t_1
    (if (<= c 52000000000000004190967118188018085197250560)
      (* a (* b i))
      (if (<=
           c
           449999999999999969383489225493115588696703864275764557370108112011539275577780917490969607273906365752923733384545329432361067244769220689786693879825947789314966839269759655947717493145169070831697920)
        (* (* (- b) z) c)
        t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (j * t);
	double tmp;
	if (c <= -3.5e-40) {
		tmp = t_1;
	} else if (c <= 5.2e+43) {
		tmp = a * (b * i);
	} else if (c <= 4.5e+200) {
		tmp = (-b * z) * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (j * t)
    if (c <= (-3.5d-40)) then
        tmp = t_1
    else if (c <= 5.2d+43) then
        tmp = a * (b * i)
    else if (c <= 4.5d+200) then
        tmp = (-b * z) * c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (j * t);
	double tmp;
	if (c <= -3.5e-40) {
		tmp = t_1;
	} else if (c <= 5.2e+43) {
		tmp = a * (b * i);
	} else if (c <= 4.5e+200) {
		tmp = (-b * z) * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (j * t)
	tmp = 0
	if c <= -3.5e-40:
		tmp = t_1
	elif c <= 5.2e+43:
		tmp = a * (b * i)
	elif c <= 4.5e+200:
		tmp = (-b * z) * c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(j * t))
	tmp = 0.0
	if (c <= -3.5e-40)
		tmp = t_1;
	elseif (c <= 5.2e+43)
		tmp = Float64(a * Float64(b * i));
	elseif (c <= 4.5e+200)
		tmp = Float64(Float64(Float64(-b) * z) * c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (j * t);
	tmp = 0.0;
	if (c <= -3.5e-40)
		tmp = t_1;
	elseif (c <= 5.2e+43)
		tmp = a * (b * i);
	elseif (c <= 4.5e+200)
		tmp = (-b * z) * c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(j * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4290987514424489/12259964326927110866866776217202473468949912977468817408], t$95$1, If[LessEqual[c, 52000000000000004190967118188018085197250560], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 449999999999999969383489225493115588696703864275764557370108112011539275577780917490969607273906365752923733384545329432361067244769220689786693879825947789314966839269759655947717493145169070831697920], N[(N[((-b) * z), $MachinePrecision] * c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.5000000000000002e-40 or 4.4999999999999997e200 < c

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(j \cdot t - b \cdot z\right)} \]

      2. lower--.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b} \cdot z\right) \]

      4. lower-*.f64 38.8%

         \[\leadsto c \cdot \left(j \cdot t - b \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 38.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto c \cdot \left(j \cdot \color{blue}{t}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 22.5%

         \[\leadsto c \cdot \left(j \cdot t\right) \]

   7. Applied rewrites 22.5%

      \[\leadsto c \cdot \left(j \cdot \color{blue}{t}\right) \]

   if -3.5000000000000002e-40 < c < 5.2000000000000004e43

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. lift--.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. sub-negate-rev N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(i \cdot a - c \cdot z\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. distribute-rgt-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(i \cdot a - c \cdot z\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(b\right)\right) \cdot \left(i \cdot a - c \cdot z\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. sub-negate-rev N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. lift--.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z - i \cdot a\right)}\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      8. distribute-rgt-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      9. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      10. remove-double-neg N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      11. lift--.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{c \cdot z} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      13. *-commutative N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      15. lower-134-z0z1z2z3z4 77.2%

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   3. Applied rewrites 77.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(j \cdot y - a \cdot b\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - \color{blue}{a \cdot b}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - \color{blue}{a} \cdot b\right)\right) \]

      5. lower-*.f64 39.2%

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - a \cdot \color{blue}{b}\right)\right) \]

   6. Applied rewrites 39.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

   7. Taylor expanded in y around 0

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \color{blue}{i}\right) \]

      2. lower-*.f64 22.2%

         \[\leadsto a \cdot \left(b \cdot i\right) \]

   9. Applied rewrites 22.2%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]

   if 5.2000000000000004e43 < c < 4.4999999999999997e200

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(j \cdot t - b \cdot z\right)} \]

      2. lower--.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b} \cdot z\right) \]

      4. lower-*.f64 38.8%

         \[\leadsto c \cdot \left(j \cdot t - b \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 38.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   5. Taylor expanded in z around inf

      \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(c \cdot z\right)\right)} \]
   6. 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 22.5%

         \[\leadsto -1 \cdot \left(b \cdot \left(c \cdot z\right)\right) \]

   7. Applied rewrites 22.5%

      \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(c \cdot z\right)\right)} \]
   8. 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. distribute-lft-neg-in N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot \color{blue}{z}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z\right) \]

      6. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(z \cdot c\right) \]

      7. associate-*r* N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(b\right)\right) \cdot z\right) \cdot c \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(b\right)\right) \cdot z\right) \cdot c \]

      9. lower-*.f64 N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(b\right)\right) \cdot z\right) \cdot c \]

      10. lower-neg.f64 22.2%

          \[\leadsto \left(\left(-b\right) \cdot z\right) \cdot c \]

   9. Applied rewrites 22.2%

      \[\leadsto \left(\left(-b\right) \cdot z\right) \cdot c \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 22: 29.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} t_1 := c \cdot \left(j \cdot t\right)\\ \mathbf{if}\;c \leq \frac{-2911741527645189}{3064991081731777716716694054300618367237478244367204352}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3900000000000000382794842022146125564911543999372148710821867947676628894613504:\\ \;\;\;\;\left(a \cdot b\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (let* ((t_1 (* c (* j t))))
  (if (<=
       c
       -2911741527645189/3064991081731777716716694054300618367237478244367204352)
    t_1
    (if (<=
         c
         3900000000000000382794842022146125564911543999372148710821867947676628894613504)
      (* (* a b) i)
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (j * t);
	double tmp;
	if (c <= -9.5e-40) {
		tmp = t_1;
	} else if (c <= 3.9e+78) {
		tmp = (a * b) * i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (j * t)
    if (c <= (-9.5d-40)) then
        tmp = t_1
    else if (c <= 3.9d+78) then
        tmp = (a * b) * i
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (j * t);
	double tmp;
	if (c <= -9.5e-40) {
		tmp = t_1;
	} else if (c <= 3.9e+78) {
		tmp = (a * b) * i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (j * t)
	tmp = 0
	if c <= -9.5e-40:
		tmp = t_1
	elif c <= 3.9e+78:
		tmp = (a * b) * i
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(j * t))
	tmp = 0.0
	if (c <= -9.5e-40)
		tmp = t_1;
	elseif (c <= 3.9e+78)
		tmp = Float64(Float64(a * b) * i);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (j * t);
	tmp = 0.0;
	if (c <= -9.5e-40)
		tmp = t_1;
	elseif (c <= 3.9e+78)
		tmp = (a * b) * i;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(j * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2911741527645189/3064991081731777716716694054300618367237478244367204352], t$95$1, If[LessEqual[c, 3900000000000000382794842022146125564911543999372148710821867947676628894613504], N[(N[(a * b), $MachinePrecision] * i), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if c < -9.5000000000000006e-40 or 3.9000000000000004e78 < c

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(j \cdot t - b \cdot z\right)} \]

      2. lower--.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b} \cdot z\right) \]

      4. lower-*.f64 38.8%

         \[\leadsto c \cdot \left(j \cdot t - b \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 38.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto c \cdot \left(j \cdot \color{blue}{t}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 22.5%

         \[\leadsto c \cdot \left(j \cdot t\right) \]

   7. Applied rewrites 22.5%

      \[\leadsto c \cdot \left(j \cdot \color{blue}{t}\right) \]

   if -9.5000000000000006e-40 < c < 3.9000000000000004e78

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. lift--.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. sub-negate-rev N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(i \cdot a - c \cdot z\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. distribute-rgt-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(i \cdot a - c \cdot z\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(b\right)\right) \cdot \left(i \cdot a - c \cdot z\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. sub-negate-rev N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. lift--.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z - i \cdot a\right)}\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      8. distribute-rgt-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      9. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      10. remove-double-neg N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      11. lift--.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{c \cdot z} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      13. *-commutative N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      15. lower-134-z0z1z2z3z4 77.2%

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   3. Applied rewrites 77.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(j \cdot y - a \cdot b\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - \color{blue}{a \cdot b}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - \color{blue}{a} \cdot b\right)\right) \]

      5. lower-*.f64 39.2%

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - a \cdot \color{blue}{b}\right)\right) \]

   6. Applied rewrites 39.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot y - a \cdot b\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot y - a \cdot b\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(j \cdot y - a \cdot b\right) \cdot i\right) \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(j \cdot y - a \cdot b\right)\right)\right) \cdot \color{blue}{i} \]

      6. lift--.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(j \cdot y - a \cdot b\right)\right)\right) \cdot i \]

      7. sub-negate-rev N/A

         \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot i \]

      8. lower-*.f64 N/A

         \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot \color{blue}{i} \]

      9. lower--.f64 39.2%

         \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot i \]

      10. lift-*.f64 N/A

          \[\leadsto \left(a \cdot b - j \cdot y\right) \cdot i \]

      11. *-commutative N/A

          \[\leadsto \left(b \cdot a - j \cdot y\right) \cdot i \]

      12. lower-*.f64 39.2%

          \[\leadsto \left(b \cdot a - j \cdot y\right) \cdot i \]

   8. Applied rewrites 39.2%

      \[\leadsto \left(b \cdot a - j \cdot y\right) \cdot \color{blue}{i} \]

   9. Taylor expanded in y around 0

      \[\leadsto \left(a \cdot b\right) \cdot i \]
   10. Step-by-step derivation

       1. lower-*.f64 22.4%

          \[\leadsto \left(a \cdot b\right) \cdot i \]

   11. Applied rewrites 22.4%

       \[\leadsto \left(a \cdot b\right) \cdot i \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 28.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} t_1 := c \cdot \left(j \cdot t\right)\\ \mathbf{if}\;c \leq \frac{-4290987514424489}{12259964326927110866866776217202473468949912977468817408}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3900000000000000382794842022146125564911543999372148710821867947676628894613504:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (let* ((t_1 (* c (* j t))))
  (if (<=
       c
       -4290987514424489/12259964326927110866866776217202473468949912977468817408)
    t_1
    (if (<=
         c
         3900000000000000382794842022146125564911543999372148710821867947676628894613504)
      (* a (* b i))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (j * t);
	double tmp;
	if (c <= -3.5e-40) {
		tmp = t_1;
	} else if (c <= 3.9e+78) {
		tmp = a * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (j * t)
    if (c <= (-3.5d-40)) then
        tmp = t_1
    else if (c <= 3.9d+78) then
        tmp = a * (b * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (j * t);
	double tmp;
	if (c <= -3.5e-40) {
		tmp = t_1;
	} else if (c <= 3.9e+78) {
		tmp = a * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (j * t)
	tmp = 0
	if c <= -3.5e-40:
		tmp = t_1
	elif c <= 3.9e+78:
		tmp = a * (b * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(j * t))
	tmp = 0.0
	if (c <= -3.5e-40)
		tmp = t_1;
	elseif (c <= 3.9e+78)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (j * t);
	tmp = 0.0;
	if (c <= -3.5e-40)
		tmp = t_1;
	elseif (c <= 3.9e+78)
		tmp = a * (b * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(j * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4290987514424489/12259964326927110866866776217202473468949912977468817408], t$95$1, If[LessEqual[c, 3900000000000000382794842022146125564911543999372148710821867947676628894613504], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if c < -3.5000000000000002e-40 or 3.9000000000000004e78 < c

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(j \cdot t - b \cdot z\right)} \]

      2. lower--.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b} \cdot z\right) \]

      4. lower-*.f64 38.8%

         \[\leadsto c \cdot \left(j \cdot t - b \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 38.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto c \cdot \left(j \cdot \color{blue}{t}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 22.5%

         \[\leadsto c \cdot \left(j \cdot t\right) \]

   7. Applied rewrites 22.5%

      \[\leadsto c \cdot \left(j \cdot \color{blue}{t}\right) \]

   if -3.5000000000000002e-40 < c < 3.9000000000000004e78

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. lift--.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. sub-negate-rev N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(i \cdot a - c \cdot z\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. distribute-rgt-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(i \cdot a - c \cdot z\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(b\right)\right) \cdot \left(i \cdot a - c \cdot z\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. sub-negate-rev N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. lift--.f64 N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z - i \cdot a\right)}\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      8. distribute-rgt-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      9. distribute-lft-neg-out N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      10. remove-double-neg N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      11. lift--.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{c \cdot z} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      13. *-commutative N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      15. lower-134-z0z1z2z3z4 77.2%

          \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   3. Applied rewrites 77.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(b, z, c, i, a\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(j \cdot y - a \cdot b\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - \color{blue}{a \cdot b}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - \color{blue}{a} \cdot b\right)\right) \]

      5. lower-*.f64 39.2%

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y - a \cdot \color{blue}{b}\right)\right) \]

   6. Applied rewrites 39.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

   7. Taylor expanded in y around 0

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \color{blue}{i}\right) \]

      2. lower-*.f64 22.2%

         \[\leadsto a \cdot \left(b \cdot i\right) \]

   9. Applied rewrites 22.2%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 24: 28.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} t_1 := c \cdot \left(j \cdot t\right)\\ \mathbf{if}\;t \leq \frac{-5609415803011879}{19342813113834066795298816}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1449999999999999980639788350416853003932704626439205672130083285472643144103231488:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
  :precision binary64
  (let* ((t_1 (* c (* j t))))
  (if (<= t -5609415803011879/19342813113834066795298816)
    t_1
    (if (<=
         t
         1449999999999999980639788350416853003932704626439205672130083285472643144103231488)
      (* (* y x) z)
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (j * t);
	double tmp;
	if (t <= -2.9e-10) {
		tmp = t_1;
	} else if (t <= 1.45e+81) {
		tmp = (y * x) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (j * t)
    if (t <= (-2.9d-10)) then
        tmp = t_1
    else if (t <= 1.45d+81) then
        tmp = (y * x) * z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (j * t);
	double tmp;
	if (t <= -2.9e-10) {
		tmp = t_1;
	} else if (t <= 1.45e+81) {
		tmp = (y * x) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (j * t)
	tmp = 0
	if t <= -2.9e-10:
		tmp = t_1
	elif t <= 1.45e+81:
		tmp = (y * x) * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(j * t))
	tmp = 0.0
	if (t <= -2.9e-10)
		tmp = t_1;
	elseif (t <= 1.45e+81)
		tmp = Float64(Float64(y * x) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (j * t);
	tmp = 0.0;
	if (t <= -2.9e-10)
		tmp = t_1;
	elseif (t <= 1.45e+81)
		tmp = (y * x) * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(j * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5609415803011879/19342813113834066795298816], t$95$1, If[LessEqual[t, 1449999999999999980639788350416853003932704626439205672130083285472643144103231488], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8999999999999998e-10 or 1.45e81 < t

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(j \cdot t - b \cdot z\right)} \]

      2. lower--.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b \cdot z}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{b} \cdot z\right) \]

      4. lower-*.f64 38.8%

         \[\leadsto c \cdot \left(j \cdot t - b \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 38.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto c \cdot \left(j \cdot \color{blue}{t}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 22.5%

         \[\leadsto c \cdot \left(j \cdot t\right) \]

   7. Applied rewrites 22.5%

      \[\leadsto c \cdot \left(j \cdot \color{blue}{t}\right) \]

   if -2.8999999999999998e-10 < t < 1.45e81

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. 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 39.3%

         \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot \color{blue}{z}\right) \]

   4. Applied rewrites 39.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

   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 22.4%

         \[\leadsto \left(y \cdot x\right) \cdot z \]

   9. Applied rewrites 22.4%

      \[\leadsto \left(y \cdot x\right) \cdot z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 25: 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 73.1%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

2. 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 39.3%

      \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot \color{blue}{z}\right) \]

4. Applied rewrites 39.3%

   \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

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 22.4%

      \[\leadsto \left(y \cdot x\right) \cdot z \]

9. Applied rewrites 22.4%

   \[\leadsto \left(y \cdot x\right) \cdot z \]
10. Add Preprocessing

Alternative 26: 22.4% 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 73.1%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

2. 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 39.3%

      \[\leadsto y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot \color{blue}{z}\right) \]

4. Applied rewrites 39.3%

   \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

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 "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64
  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))