Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3

Percentage Accurate: 69.5% → 96.3%

Time: 6.4s

Alternatives: 17

Speedup: 0.7×

Specification

Math

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

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (/ (* (- y z) (- t x)) (- a z))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (((y - z) * (t - x)) / (a - 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)
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
    code = x + (((y - z) * (t - x)) / (a - z))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (((y - z) * (t - x)) / (a - z));
}

Python

def code(x, y, z, t, a):
	return x + (((y - z) * (t - x)) / (a - z))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (((y - z) * (t - x)) / (a - z));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 69.5% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (/ (* (- y z) (- t x)) (- a z))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (((y - z) * (t - x)) / (a - 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)
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
    code = x + (((y - z) * (t - x)) / (a - z))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (((y - z) * (t - x)) / (a - z));
}

Python

def code(x, y, z, t, a):
	return x + (((y - z) * (t - x)) / (a - z))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (((y - z) * (t - x)) / (a - z));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{z - y}{z - a}, t, \frac{a - y}{a - z} \cdot x\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (fma (/ (- z y) (- z a)) t (* (/ (- a y) (- a z)) x)))

C

double code(double x, double y, double z, double t, double a) {
	return fma(((z - y) / (z - a)), t, (((a - y) / (a - z)) * x));
}

Julia

function code(x, y, z, t, a)
	return fma(Float64(Float64(z - y) / Float64(z - a)), t, Float64(Float64(Float64(a - y) / Float64(a - z)) * x))
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * t + N[(N[(N[(a - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.5%

   \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
2. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. add-flip N/A

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

   3. lift-/.f64 N/A

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

   4. distribute-neg-frac N/A

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

   5. sub-to-fraction-rev N/A

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

   6. add-flip N/A

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

   7. +-commutative N/A

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

   8. lift-*.f64 N/A

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

   9. lift--.f64 N/A

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

   10. sub-flip N/A

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

   11. distribute-rgt-in N/A

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

   12. associate-+l+ N/A

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

   13. div-add N/A

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

3. Applied rewrites 76.5%

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

   1. lift--.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. associate-/l* N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 N/A

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

   8. lift-neg.f64 N/A

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

   9. sub-negate-rev N/A

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

   10. lift--.f64 N/A

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

   11. frac-2neg-rev N/A

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

   12. lower-/.f64 82.9

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

   13. lift-+.f64 N/A

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

   14. lift--.f64 N/A

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

   15. associate-+r- N/A

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

   16. lower--.f64 N/A

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

   17. lift--.f64 N/A

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

   18. associate-+l- N/A

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

   19. lower--.f64 N/A

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

   20. +-inverses 91.1

       \[\leadsto \mathsf{fma}\left(\frac{z - y}{z - a}, t, \frac{x}{z - a} \cdot \left(\left(y - \color{blue}{0}\right) - a\right)\right) \]

5. Applied rewrites 91.1%

   \[\leadsto \mathsf{fma}\left(\frac{z - y}{z - a}, t, \color{blue}{\frac{x}{z - a} \cdot \left(\left(y - 0\right) - a\right)}\right) \]
6. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(\frac{z - y}{z - a}, t, \color{blue}{\frac{x}{z - a} \cdot \left(\left(y - 0\right) - a\right)}\right) \]

   2. lift-/.f64 N/A

      \[\leadsto \mathsf{fma}\left(\frac{z - y}{z - a}, t, \color{blue}{\frac{x}{z - a}} \cdot \left(\left(y - 0\right) - a\right)\right) \]

   3. frac-2neg N/A

      \[\leadsto \mathsf{fma}\left(\frac{z - y}{z - a}, t, \color{blue}{\frac{\mathsf{neg}\left(x\right)}{\mathsf{neg}\left(\left(z - a\right)\right)}} \cdot \left(\left(y - 0\right) - a\right)\right) \]

   4. lift--.f64 N/A

      \[\leadsto \mathsf{fma}\left(\frac{z - y}{z - a}, t, \frac{\mathsf{neg}\left(x\right)}{\mathsf{neg}\left(\color{blue}{\left(z - a\right)}\right)} \cdot \left(\left(y - 0\right) - a\right)\right) \]

   5. sub-negate-rev N/A

      \[\leadsto \mathsf{fma}\left(\frac{z - y}{z - a}, t, \frac{\mathsf{neg}\left(x\right)}{\color{blue}{a - z}} \cdot \left(\left(y - 0\right) - a\right)\right) \]

   6. lift--.f64 N/A

      \[\leadsto \mathsf{fma}\left(\frac{z - y}{z - a}, t, \frac{\mathsf{neg}\left(x\right)}{\color{blue}{a - z}} \cdot \left(\left(y - 0\right) - a\right)\right) \]

   7. associate-*l/ N/A

      \[\leadsto \mathsf{fma}\left(\frac{z - y}{z - a}, t, \color{blue}{\frac{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\left(y - 0\right) - a\right)}{a - z}}\right) \]

   8. associate-*r/ N/A

      \[\leadsto \mathsf{fma}\left(\frac{z - y}{z - a}, t, \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \frac{\left(y - 0\right) - a}{a - z}}\right) \]

   9. lift--.f64 N/A

      \[\leadsto \mathsf{fma}\left(\frac{z - y}{z - a}, t, \left(\mathsf{neg}\left(x\right)\right) \cdot \frac{\color{blue}{\left(y - 0\right) - a}}{a - z}\right) \]

   10. lift--.f64 N/A

       \[\leadsto \mathsf{fma}\left(\frac{z - y}{z - a}, t, \left(\mathsf{neg}\left(x\right)\right) \cdot \frac{\color{blue}{\left(y - 0\right)} - a}{a - z}\right) \]

   11. --rgt-identity N/A

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

   12. sub-div N/A

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

   13. lift-/.f64 N/A

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

   14. lift-/.f64 N/A

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

   15. lift--.f64 N/A

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

   16. *-commutative N/A

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

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

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

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

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

   19. lift--.f64 N/A

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

   20. sub-negate-rev N/A

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

7. Applied rewrites 96.3%

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

Alternative 2: 90.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+113}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{z - a}, t - x, x\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(\left(y - 0\right) - a, x, t \cdot \left(z - y\right)\right) \cdot \frac{1}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z - a}, y - z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_1 -1e+113)
     (fma (/ (- z y) (- z a)) (- t x) x)
     (if (<= t_1 5e+43)
       (* (fma (- (- y 0.0) a) x (* t (- z y))) (/ 1.0 (- z a)))
       (fma (/ (- x t) (- z a)) (- y z) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_1 <= -1e+113) {
		tmp = fma(((z - y) / (z - a)), (t - x), x);
	} else if (t_1 <= 5e+43) {
		tmp = fma(((y - 0.0) - a), x, (t * (z - y))) * (1.0 / (z - a));
	} else {
		tmp = fma(((x - t) / (z - a)), (y - z), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_1 <= -1e+113)
		tmp = fma(Float64(Float64(z - y) / Float64(z - a)), Float64(t - x), x);
	elseif (t_1 <= 5e+43)
		tmp = Float64(fma(Float64(Float64(y - 0.0) - a), x, Float64(t * Float64(z - y))) * Float64(1.0 / Float64(z - a)));
	else
		tmp = fma(Float64(Float64(x - t) / Float64(z - a)), Float64(y - z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+113], N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 5e+43], N[(N[(N[(N[(y - 0.0), $MachinePrecision] - a), $MachinePrecision] * x + N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1e113

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. frac-2neg N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lower--.f64 85.1

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

   3. Applied rewrites 85.1%

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

   if -1e113 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 5.0000000000000004e43

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. frac-2neg N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lower--.f64 85.1

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

   3. Applied rewrites 85.1%

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

   5. Applied rewrites 74.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - 0\right) - a, x, t \cdot \left(z - y\right)\right) \cdot \frac{1}{z - a}} \]

   if 5.0000000000000004e43 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

      4. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. remove-double-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. frac-2neg N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lower--.f64 80.9

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

   3. Applied rewrites 80.9%

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

Alternative 3: 89.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1, t, \frac{a - y}{a - z} \cdot x\right)\\ \mathbf{if}\;z \leq -7 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+110}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{z - a}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma 1.0 t (* (/ (- a y) (- a z)) x))))
   (if (<= z -7e+100)
     t_1
     (if (<= z 3.8e+110) (fma (/ (- z y) (- z a)) (- t x) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(1.0, t, (((a - y) / (a - z)) * x));
	double tmp;
	if (z <= -7e+100) {
		tmp = t_1;
	} else if (z <= 3.8e+110) {
		tmp = fma(((z - y) / (z - a)), (t - x), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(1.0, t, Float64(Float64(Float64(a - y) / Float64(a - z)) * x))
	tmp = 0.0
	if (z <= -7e+100)
		tmp = t_1;
	elseif (z <= 3.8e+110)
		tmp = fma(Float64(Float64(z - y) / Float64(z - a)), Float64(t - x), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(1.0 * t + N[(N[(N[(a - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e+100], t$95$1, If[LessEqual[z, 3.8e+110], N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.99999999999999953e100 or 3.79999999999999989e110 < z

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift-/.f64 N/A

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

      4. distribute-neg-frac N/A

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

      5. sub-to-fraction-rev N/A

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

      6. add-flip N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-flip N/A

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

      11. distribute-rgt-in N/A

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

      12. associate-+l+ N/A

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

      13. div-add N/A

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

   3. Applied rewrites 76.5%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lift-neg.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lift--.f64 N/A

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

      11. frac-2neg-rev N/A

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

      12. lower-/.f64 82.9

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

      13. lift-+.f64 N/A

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

      14. lift--.f64 N/A

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

      15. associate-+r- N/A

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

      16. lower--.f64 N/A

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

      17. lift--.f64 N/A

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

      18. associate-+l- N/A

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

      19. lower--.f64 N/A

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

      20. +-inverses 91.1

          \[\leadsto \mathsf{fma}\left(\frac{z - y}{z - a}, t, \frac{x}{z - a} \cdot \left(\left(y - \color{blue}{0}\right) - a\right)\right) \]

   5. Applied rewrites 91.1%

      \[\leadsto \mathsf{fma}\left(\frac{z - y}{z - a}, t, \color{blue}{\frac{x}{z - a} \cdot \left(\left(y - 0\right) - a\right)}\right) \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{z - y}{z - a}, t, \color{blue}{\frac{x}{z - a} \cdot \left(\left(y - 0\right) - a\right)}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{z - y}{z - a}, t, \color{blue}{\frac{x}{z - a}} \cdot \left(\left(y - 0\right) - a\right)\right) \]

      3. frac-2neg N/A

         \[\leadsto \mathsf{fma}\left(\frac{z - y}{z - a}, t, \color{blue}{\frac{\mathsf{neg}\left(x\right)}{\mathsf{neg}\left(\left(z - a\right)\right)}} \cdot \left(\left(y - 0\right) - a\right)\right) \]

      4. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{z - y}{z - a}, t, \frac{\mathsf{neg}\left(x\right)}{\mathsf{neg}\left(\color{blue}{\left(z - a\right)}\right)} \cdot \left(\left(y - 0\right) - a\right)\right) \]

      5. sub-negate-rev N/A

         \[\leadsto \mathsf{fma}\left(\frac{z - y}{z - a}, t, \frac{\mathsf{neg}\left(x\right)}{\color{blue}{a - z}} \cdot \left(\left(y - 0\right) - a\right)\right) \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{z - y}{z - a}, t, \frac{\mathsf{neg}\left(x\right)}{\color{blue}{a - z}} \cdot \left(\left(y - 0\right) - a\right)\right) \]

      7. associate-*l/ N/A

         \[\leadsto \mathsf{fma}\left(\frac{z - y}{z - a}, t, \color{blue}{\frac{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\left(y - 0\right) - a\right)}{a - z}}\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{fma}\left(\frac{z - y}{z - a}, t, \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \frac{\left(y - 0\right) - a}{a - z}}\right) \]

      9. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{z - y}{z - a}, t, \left(\mathsf{neg}\left(x\right)\right) \cdot \frac{\color{blue}{\left(y - 0\right) - a}}{a - z}\right) \]

      10. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{z - y}{z - a}, t, \left(\mathsf{neg}\left(x\right)\right) \cdot \frac{\color{blue}{\left(y - 0\right)} - a}{a - z}\right) \]

      11. --rgt-identity N/A

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

      12. sub-div N/A

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

      13. lift-/.f64 N/A

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

      14. lift-/.f64 N/A

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

      15. lift--.f64 N/A

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

      16. *-commutative N/A

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

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

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

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

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

   7. Applied rewrites 96.3%

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

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{1}, t, \frac{a - y}{a - z} \cdot x\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 67.0%

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

   if -6.99999999999999953e100 < z < 3.79999999999999989e110

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. frac-2neg N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lower--.f64 85.1

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

   3. Applied rewrites 85.1%

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

Alternative 4: 86.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z - y}{z - a}, t - x, x\right)\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{-171}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-134}:\\ \;\;\;\;-1 \cdot \left(\frac{a - y}{z - a} \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- z y) (- z a)) (- t x) x)))
   (if (<= t -2.1e-171)
     t_1
     (if (<= t 3.2e-134) (* -1.0 (* (/ (- a y) (- z a)) x)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((z - y) / (z - a)), (t - x), x);
	double tmp;
	if (t <= -2.1e-171) {
		tmp = t_1;
	} else if (t <= 3.2e-134) {
		tmp = -1.0 * (((a - y) / (z - a)) * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(z - y) / Float64(z - a)), Float64(t - x), x)
	tmp = 0.0
	if (t <= -2.1e-171)
		tmp = t_1;
	elseif (t <= 3.2e-134)
		tmp = Float64(-1.0 * Float64(Float64(Float64(a - y) / Float64(z - a)) * x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -2.1e-171], t$95$1, If[LessEqual[t, 3.2e-134], N[(-1.0 * N[(N[(N[(a - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.1e-171 or 3.2000000000000001e-134 < t

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. frac-2neg N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lower--.f64 85.1

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

   3. Applied rewrites 85.1%

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

   if -2.1e-171 < t < 3.2000000000000001e-134

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift-/.f64 N/A

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

      4. distribute-neg-frac N/A

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

      5. sub-to-fraction-rev N/A

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

      6. add-flip N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-flip N/A

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

      11. distribute-rgt-in N/A

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

      12. associate-+l+ N/A

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

      13. div-add N/A

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

   3. Applied rewrites 76.5%

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

   4. Taylor expanded in x around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(\frac{y}{a - z} - \frac{a}{a - z}\right)\right) \]

      6. lower-/.f64 N/A

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

      7. lower--.f64 52.5

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

   6. Applied rewrites 52.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 52.5

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

      4. lift--.f64 N/A

         \[\leadsto -1 \cdot \left(\left(\frac{y}{a - z} - \frac{a}{a - z}\right) \cdot x\right) \]

      5. lift-/.f64 N/A

         \[\leadsto -1 \cdot \left(\left(\frac{y}{a - z} - \frac{a}{a - z}\right) \cdot x\right) \]

      6. lift-/.f64 N/A

         \[\leadsto -1 \cdot \left(\left(\frac{y}{a - z} - \frac{a}{a - z}\right) \cdot x\right) \]

      7. sub-div N/A

         \[\leadsto -1 \cdot \left(\frac{y - a}{a - z} \cdot x\right) \]

      8. --rgt-identity N/A

         \[\leadsto -1 \cdot \left(\frac{\left(y - 0\right) - a}{a - z} \cdot x\right) \]

      9. lift--.f64 N/A

         \[\leadsto -1 \cdot \left(\frac{\left(y - 0\right) - a}{a - z} \cdot x\right) \]

      10. sub-negate-rev N/A

          \[\leadsto -1 \cdot \left(\frac{\mathsf{neg}\left(\left(a - \left(y - 0\right)\right)\right)}{a - z} \cdot x\right) \]

      11. lift--.f64 N/A

          \[\leadsto -1 \cdot \left(\frac{\mathsf{neg}\left(\left(a - \left(y - 0\right)\right)\right)}{a - z} \cdot x\right) \]

      12. sub-negate-rev N/A

          \[\leadsto -1 \cdot \left(\frac{\mathsf{neg}\left(\left(a - \left(y - 0\right)\right)\right)}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot x\right) \]

      13. lift--.f64 N/A

          \[\leadsto -1 \cdot \left(\frac{\mathsf{neg}\left(\left(a - \left(y - 0\right)\right)\right)}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot x\right) \]

      14. frac-2neg-rev N/A

          \[\leadsto -1 \cdot \left(\frac{a - \left(y - 0\right)}{z - a} \cdot x\right) \]

      15. lower-/.f64 N/A

          \[\leadsto -1 \cdot \left(\frac{a - \left(y - 0\right)}{z - a} \cdot x\right) \]

      16. lift--.f64 N/A

          \[\leadsto -1 \cdot \left(\frac{a - \left(y - 0\right)}{z - a} \cdot x\right) \]

      17. --rgt-identity N/A

          \[\leadsto -1 \cdot \left(\frac{a - y}{z - a} \cdot x\right) \]

      18. lower--.f64 52.5

          \[\leadsto -1 \cdot \left(\frac{a - y}{z - a} \cdot x\right) \]

   8. Applied rewrites 52.5%

      \[\leadsto -1 \cdot \left(\frac{a - y}{z - a} \cdot \color{blue}{x}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 83.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x - t}{z - a}, y - z, x\right)\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{-157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-55}:\\ \;\;\;\;-1 \cdot \left(\frac{a - y}{z - a} \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- x t) (- z a)) (- y z) x)))
   (if (<= t -2.9e-157)
     t_1
     (if (<= t 2.9e-55) (* -1.0 (* (/ (- a y) (- z a)) x)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((x - t) / (z - a)), (y - z), x);
	double tmp;
	if (t <= -2.9e-157) {
		tmp = t_1;
	} else if (t <= 2.9e-55) {
		tmp = -1.0 * (((a - y) / (z - a)) * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(x - t) / Float64(z - a)), Float64(y - z), x)
	tmp = 0.0
	if (t <= -2.9e-157)
		tmp = t_1;
	elseif (t <= 2.9e-55)
		tmp = Float64(-1.0 * Float64(Float64(Float64(a - y) / Float64(z - a)) * x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -2.9e-157], t$95$1, If[LessEqual[t, 2.9e-55], N[(-1.0 * N[(N[(N[(a - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.89999999999999988e-157 or 2.9e-55 < t

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

      4. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. remove-double-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. frac-2neg N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lower--.f64 80.9

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

   3. Applied rewrites 80.9%

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

   if -2.89999999999999988e-157 < t < 2.9e-55

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift-/.f64 N/A

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

      4. distribute-neg-frac N/A

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

      5. sub-to-fraction-rev N/A

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

      6. add-flip N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-flip N/A

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

      11. distribute-rgt-in N/A

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

      12. associate-+l+ N/A

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

      13. div-add N/A

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

   3. Applied rewrites 76.5%

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

   4. Taylor expanded in x around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(\frac{y}{a - z} - \frac{a}{a - z}\right)\right) \]

      6. lower-/.f64 N/A

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

      7. lower--.f64 52.5

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

   6. Applied rewrites 52.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 52.5

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

      4. lift--.f64 N/A

         \[\leadsto -1 \cdot \left(\left(\frac{y}{a - z} - \frac{a}{a - z}\right) \cdot x\right) \]

      5. lift-/.f64 N/A

         \[\leadsto -1 \cdot \left(\left(\frac{y}{a - z} - \frac{a}{a - z}\right) \cdot x\right) \]

      6. lift-/.f64 N/A

         \[\leadsto -1 \cdot \left(\left(\frac{y}{a - z} - \frac{a}{a - z}\right) \cdot x\right) \]

      7. sub-div N/A

         \[\leadsto -1 \cdot \left(\frac{y - a}{a - z} \cdot x\right) \]

      8. --rgt-identity N/A

         \[\leadsto -1 \cdot \left(\frac{\left(y - 0\right) - a}{a - z} \cdot x\right) \]

      9. lift--.f64 N/A

         \[\leadsto -1 \cdot \left(\frac{\left(y - 0\right) - a}{a - z} \cdot x\right) \]

      10. sub-negate-rev N/A

          \[\leadsto -1 \cdot \left(\frac{\mathsf{neg}\left(\left(a - \left(y - 0\right)\right)\right)}{a - z} \cdot x\right) \]

      11. lift--.f64 N/A

          \[\leadsto -1 \cdot \left(\frac{\mathsf{neg}\left(\left(a - \left(y - 0\right)\right)\right)}{a - z} \cdot x\right) \]

      12. sub-negate-rev N/A

          \[\leadsto -1 \cdot \left(\frac{\mathsf{neg}\left(\left(a - \left(y - 0\right)\right)\right)}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot x\right) \]

      13. lift--.f64 N/A

          \[\leadsto -1 \cdot \left(\frac{\mathsf{neg}\left(\left(a - \left(y - 0\right)\right)\right)}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot x\right) \]

      14. frac-2neg-rev N/A

          \[\leadsto -1 \cdot \left(\frac{a - \left(y - 0\right)}{z - a} \cdot x\right) \]

      15. lower-/.f64 N/A

          \[\leadsto -1 \cdot \left(\frac{a - \left(y - 0\right)}{z - a} \cdot x\right) \]

      16. lift--.f64 N/A

          \[\leadsto -1 \cdot \left(\frac{a - \left(y - 0\right)}{z - a} \cdot x\right) \]

      17. --rgt-identity N/A

          \[\leadsto -1 \cdot \left(\frac{a - y}{z - a} \cdot x\right) \]

      18. lower--.f64 52.5

          \[\leadsto -1 \cdot \left(\frac{a - y}{z - a} \cdot x\right) \]

   8. Applied rewrites 52.5%

      \[\leadsto -1 \cdot \left(\frac{a - y}{z - a} \cdot \color{blue}{x}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 67.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, t - x, x\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+114}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{z}, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.4e+35)
   (fma (/ z (- z a)) (- t x) x)
   (if (<= z 8.2e+114)
     (+ x (/ (* y (- t x)) (- a z)))
     (fma (/ (- z y) z) (- t x) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.4e+35) {
		tmp = fma((z / (z - a)), (t - x), x);
	} else if (z <= 8.2e+114) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else {
		tmp = fma(((z - y) / z), (t - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.4e+35)
		tmp = fma(Float64(z / Float64(z - a)), Float64(t - x), x);
	elseif (z <= 8.2e+114)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / Float64(a - z)));
	else
		tmp = fma(Float64(Float64(z - y) / z), Float64(t - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.4e+35], N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 8.2e+114], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4000000000000001e35

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. frac-2neg N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lower--.f64 85.1

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

   3. Applied rewrites 85.1%

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

   4. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{z}}{z - a}, t - x, x\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 47.5%

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

   if -3.4000000000000001e35 < z < 8.2000000000000001e114

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 56.6

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

   4. Applied rewrites 56.6%

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

   if 8.2000000000000001e114 < z

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. frac-2neg N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lower--.f64 85.1

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

   3. Applied rewrites 85.1%

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

   4. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{z - y}{z}}, t - x, x\right) \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower--.f64 38.4

         \[\leadsto \mathsf{fma}\left(\frac{z - y}{z}, t - x, x\right) \]

   6. Applied rewrites 38.4%

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

Alternative 7: 67.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z - y}{z}, t - x, x\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-162}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z - a}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-95}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+115}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{x - t}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- z y) z) (- t x) x)))
   (if (<= z -9e+39)
     t_1
     (if (<= z -1.3e-162)
       (* (- y a) (/ x (- z a)))
       (if (<= z 2.7e-95)
         (fma (/ y a) (- t x) x)
         (if (<= z 2.1e+115) (fma z (/ (- x t) (- a z)) x) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((z - y) / z), (t - x), x);
	double tmp;
	if (z <= -9e+39) {
		tmp = t_1;
	} else if (z <= -1.3e-162) {
		tmp = (y - a) * (x / (z - a));
	} else if (z <= 2.7e-95) {
		tmp = fma((y / a), (t - x), x);
	} else if (z <= 2.1e+115) {
		tmp = fma(z, ((x - t) / (a - z)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(z - y) / z), Float64(t - x), x)
	tmp = 0.0
	if (z <= -9e+39)
		tmp = t_1;
	elseif (z <= -1.3e-162)
		tmp = Float64(Float64(y - a) * Float64(x / Float64(z - a)));
	elseif (z <= 2.7e-95)
		tmp = fma(Float64(y / a), Float64(t - x), x);
	elseif (z <= 2.1e+115)
		tmp = fma(z, Float64(Float64(x - t) / Float64(a - z)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -9e+39], t$95$1, If[LessEqual[z, -1.3e-162], N[(N[(y - a), $MachinePrecision] * N[(x / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e-95], N[(N[(y / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 2.1e+115], N[(z * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.99999999999999991e39 or 2.10000000000000003e115 < z

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. frac-2neg N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lower--.f64 85.1

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

   3. Applied rewrites 85.1%

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

   4. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{z - y}{z}}, t - x, x\right) \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower--.f64 38.4

         \[\leadsto \mathsf{fma}\left(\frac{z - y}{z}, t - x, x\right) \]

   6. Applied rewrites 38.4%

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

   if -8.99999999999999991e39 < z < -1.3e-162

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift-/.f64 N/A

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

      4. distribute-neg-frac N/A

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

      5. sub-to-fraction-rev N/A

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

      6. add-flip N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-flip N/A

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

      11. distribute-rgt-in N/A

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

      12. associate-+l+ N/A

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

      13. div-add N/A

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

   3. Applied rewrites 76.5%

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

   4. Taylor expanded in x around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(\frac{y}{a - z} - \frac{a}{a - z}\right)\right) \]

      6. lower-/.f64 N/A

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

      7. lower--.f64 52.5

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

   6. Applied rewrites 52.5%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. sub-div N/A

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

      9. --rgt-identity N/A

         \[\leadsto \left(\mathsf{neg}\left(x\right)\right) \cdot \frac{\left(y - 0\right) - a}{a - z} \]

      10. lift--.f64 N/A

          \[\leadsto \left(\mathsf{neg}\left(x\right)\right) \cdot \frac{\left(y - 0\right) - a}{a - z} \]

      11. lift--.f64 N/A

          \[\leadsto \left(\mathsf{neg}\left(x\right)\right) \cdot \frac{\left(y - 0\right) - a}{\color{blue}{a} - z} \]

      12. associate-*r/ N/A

          \[\leadsto \frac{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\left(y - 0\right) - a\right)}{\color{blue}{a - z}} \]

      13. associate-*l/ N/A

          \[\leadsto \frac{\mathsf{neg}\left(x\right)}{a - z} \cdot \color{blue}{\left(\left(y - 0\right) - a\right)} \]

      14. lift--.f64 N/A

          \[\leadsto \frac{\mathsf{neg}\left(x\right)}{a - z} \cdot \left(\left(y - \color{blue}{0}\right) - a\right) \]

      15. sub-negate-rev N/A

          \[\leadsto \frac{\mathsf{neg}\left(x\right)}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot \left(\left(y - \color{blue}{0}\right) - a\right) \]

      16. lift--.f64 N/A

          \[\leadsto \frac{\mathsf{neg}\left(x\right)}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot \left(\left(y - 0\right) - a\right) \]

      17. frac-2neg N/A

          \[\leadsto \frac{x}{z - a} \cdot \left(\color{blue}{\left(y - 0\right)} - a\right) \]

      18. lift-/.f64 N/A

          \[\leadsto \frac{x}{z - a} \cdot \left(\color{blue}{\left(y - 0\right)} - a\right) \]

   8. Applied rewrites 47.1%

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

   if -1.3e-162 < z < 2.7e-95

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. frac-2neg N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lower--.f64 85.1

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

   3. Applied rewrites 85.1%

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

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{a}}, t - x, x\right) \]
   5. Step-by-step derivation

      1. lower-/.f64 50.5

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

   6. Applied rewrites 50.5%

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

   if 2.7e-95 < z < 2.10000000000000003e115

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. frac-2neg N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lower--.f64 85.1

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

   3. Applied rewrites 85.1%

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

   4. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{z}}{z - a}, t - x, x\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 47.5%

      \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{z}}{z - a}, t - x, x\right) \]
   7. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. associate-/l* N/A

         \[\leadsto \color{blue}{z \cdot \frac{t - x}{z - a}} + x \]

      6. lower-fma.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lift--.f64 N/A

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

      12. frac-2neg-rev N/A

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

      13. lower-/.f64 47.1

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

   8. Applied rewrites 47.1%

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

Alternative 8: 66.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+93}:\\ \;\;\;\;\left(x - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+54}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x - t}{z - a} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5.8e+93)
   (* (- x t) (/ y (- z a)))
   (if (<= y 4.5e+54)
     (fma (/ z (- z a)) (- t x) x)
     (* (/ (- x t) (- z a)) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.8e+93) {
		tmp = (x - t) * (y / (z - a));
	} else if (y <= 4.5e+54) {
		tmp = fma((z / (z - a)), (t - x), x);
	} else {
		tmp = ((x - t) / (z - a)) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5.8e+93)
		tmp = Float64(Float64(x - t) * Float64(y / Float64(z - a)));
	elseif (y <= 4.5e+54)
		tmp = fma(Float64(z / Float64(z - a)), Float64(t - x), x);
	else
		tmp = Float64(Float64(Float64(x - t) / Float64(z - a)) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5.8e+93], N[(N[(x - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e+54], N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.7999999999999997e93

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

      4. lift-/.f64 N/A

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

      5. mult-flip N/A

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

      6. *-commutative N/A

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

      7. remove-double-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. frac-2neg N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 69.4

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

      15. lift-*.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

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

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

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

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

      20. lift--.f64 N/A

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

      21. sub-negate-rev N/A

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

      22. lower-*.f64 N/A

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

      23. lower--.f64 N/A

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

      24. lower--.f64 69.4

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

   3. Applied rewrites 69.4%

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

   4. Taylor expanded in y around -inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 37.9

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

   6. Applied rewrites 37.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 43.2

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

   8. Applied rewrites 43.2%

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

   if -5.7999999999999997e93 < y < 4.49999999999999984e54

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. frac-2neg N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lower--.f64 85.1

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

   3. Applied rewrites 85.1%

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

   4. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{z}}{z - a}, t - x, x\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 47.5%

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

   if 4.49999999999999984e54 < y

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

      4. lift-/.f64 N/A

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

      5. mult-flip N/A

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

      6. *-commutative N/A

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

      7. remove-double-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. frac-2neg N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 69.4

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

      15. lift-*.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

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

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

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

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

      20. lift--.f64 N/A

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

      21. sub-negate-rev N/A

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

      22. lower-*.f64 N/A

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

      23. lower--.f64 N/A

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

      24. lower--.f64 69.4

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

   3. Applied rewrites 69.4%

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

   4. Taylor expanded in y around -inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 37.9

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

   6. Applied rewrites 37.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

         \[\leadsto y \cdot \color{blue}{\frac{x - t}{z - a}} \]

      4. frac-2neg-rev N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

         \[\leadsto y \cdot \frac{t - x}{a - \color{blue}{z}} \]

      9. lift--.f64 N/A

         \[\leadsto y \cdot \frac{t - x}{a - \color{blue}{z}} \]

      10. *-commutative N/A

          \[\leadsto \frac{t - x}{a - z} \cdot \color{blue}{y} \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{t - x}{a - z} \cdot \color{blue}{y} \]

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lift--.f64 N/A

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

      17. frac-2neg-rev N/A

          \[\leadsto \frac{x - t}{z - a} \cdot y \]

      18. lower-/.f64 41.9

          \[\leadsto \frac{x - t}{z - a} \cdot y \]

   8. Applied rewrites 41.9%

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

Alternative 9: 64.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - a\right) \cdot \frac{x}{z - a}\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-166}:\\ \;\;\;\;\left(x - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-31}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y a) (/ x (- z a)))))
   (if (<= x -5.2e-23)
     t_1
     (if (<= x -2.7e-166)
       (* (- x t) (/ y (- z a)))
       (if (<= x 1.2e-31) (/ (* t (- y z)) (- a z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - a) * (x / (z - a));
	double tmp;
	if (x <= -5.2e-23) {
		tmp = t_1;
	} else if (x <= -2.7e-166) {
		tmp = (x - t) * (y / (z - a));
	} else if (x <= 1.2e-31) {
		tmp = (t * (y - z)) / (a - 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)
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) :: t_1
    real(8) :: tmp
    t_1 = (y - a) * (x / (z - a))
    if (x <= (-5.2d-23)) then
        tmp = t_1
    else if (x <= (-2.7d-166)) then
        tmp = (x - t) * (y / (z - a))
    else if (x <= 1.2d-31) then
        tmp = (t * (y - z)) / (a - 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 t_1 = (y - a) * (x / (z - a));
	double tmp;
	if (x <= -5.2e-23) {
		tmp = t_1;
	} else if (x <= -2.7e-166) {
		tmp = (x - t) * (y / (z - a));
	} else if (x <= 1.2e-31) {
		tmp = (t * (y - z)) / (a - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - a) * (x / (z - a))
	tmp = 0
	if x <= -5.2e-23:
		tmp = t_1
	elif x <= -2.7e-166:
		tmp = (x - t) * (y / (z - a))
	elif x <= 1.2e-31:
		tmp = (t * (y - z)) / (a - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - a) * Float64(x / Float64(z - a)))
	tmp = 0.0
	if (x <= -5.2e-23)
		tmp = t_1;
	elseif (x <= -2.7e-166)
		tmp = Float64(Float64(x - t) * Float64(y / Float64(z - a)));
	elseif (x <= 1.2e-31)
		tmp = Float64(Float64(t * Float64(y - z)) / Float64(a - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - a) * (x / (z - a));
	tmp = 0.0;
	if (x <= -5.2e-23)
		tmp = t_1;
	elseif (x <= -2.7e-166)
		tmp = (x - t) * (y / (z - a));
	elseif (x <= 1.2e-31)
		tmp = (t * (y - z)) / (a - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - a), $MachinePrecision] * N[(x / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.2e-23], t$95$1, If[LessEqual[x, -2.7e-166], N[(N[(x - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.2e-31], N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.2e-23 or 1.2e-31 < x

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift-/.f64 N/A

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

      4. distribute-neg-frac N/A

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

      5. sub-to-fraction-rev N/A

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

      6. add-flip N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-flip N/A

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

      11. distribute-rgt-in N/A

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

      12. associate-+l+ N/A

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

      13. div-add N/A

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

   3. Applied rewrites 76.5%

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

   4. Taylor expanded in x around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(\frac{y}{a - z} - \frac{a}{a - z}\right)\right) \]

      6. lower-/.f64 N/A

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

      7. lower--.f64 52.5

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

   6. Applied rewrites 52.5%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. sub-div N/A

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

      9. --rgt-identity N/A

         \[\leadsto \left(\mathsf{neg}\left(x\right)\right) \cdot \frac{\left(y - 0\right) - a}{a - z} \]

      10. lift--.f64 N/A

          \[\leadsto \left(\mathsf{neg}\left(x\right)\right) \cdot \frac{\left(y - 0\right) - a}{a - z} \]

      11. lift--.f64 N/A

          \[\leadsto \left(\mathsf{neg}\left(x\right)\right) \cdot \frac{\left(y - 0\right) - a}{\color{blue}{a} - z} \]

      12. associate-*r/ N/A

          \[\leadsto \frac{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\left(y - 0\right) - a\right)}{\color{blue}{a - z}} \]

      13. associate-*l/ N/A

          \[\leadsto \frac{\mathsf{neg}\left(x\right)}{a - z} \cdot \color{blue}{\left(\left(y - 0\right) - a\right)} \]

      14. lift--.f64 N/A

          \[\leadsto \frac{\mathsf{neg}\left(x\right)}{a - z} \cdot \left(\left(y - \color{blue}{0}\right) - a\right) \]

      15. sub-negate-rev N/A

          \[\leadsto \frac{\mathsf{neg}\left(x\right)}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot \left(\left(y - \color{blue}{0}\right) - a\right) \]

      16. lift--.f64 N/A

          \[\leadsto \frac{\mathsf{neg}\left(x\right)}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot \left(\left(y - 0\right) - a\right) \]

      17. frac-2neg N/A

          \[\leadsto \frac{x}{z - a} \cdot \left(\color{blue}{\left(y - 0\right)} - a\right) \]

      18. lift-/.f64 N/A

          \[\leadsto \frac{x}{z - a} \cdot \left(\color{blue}{\left(y - 0\right)} - a\right) \]

   8. Applied rewrites 47.1%

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

   if -5.2e-23 < x < -2.70000000000000006e-166

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

      4. lift-/.f64 N/A

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

      5. mult-flip N/A

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

      6. *-commutative N/A

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

      7. remove-double-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. frac-2neg N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 69.4

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

      15. lift-*.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

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

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

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

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

      20. lift--.f64 N/A

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

      21. sub-negate-rev N/A

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

      22. lower-*.f64 N/A

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

      23. lower--.f64 N/A

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

      24. lower--.f64 69.4

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

   3. Applied rewrites 69.4%

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

   4. Taylor expanded in y around -inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 37.9

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

   6. Applied rewrites 37.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 43.2

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

   8. Applied rewrites 43.2%

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

   if -2.70000000000000006e-166 < x < 1.2e-31

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.1

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

   4. Applied rewrites 39.1%

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

Alternative 10: 60.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+93}:\\ \;\;\;\;\left(x - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+52}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{x - t}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x - t}{z - a} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5.8e+93)
   (* (- x t) (/ y (- z a)))
   (if (<= y 2.05e+52)
     (fma z (/ (- x t) (- a z)) x)
     (* (/ (- x t) (- z a)) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.8e+93) {
		tmp = (x - t) * (y / (z - a));
	} else if (y <= 2.05e+52) {
		tmp = fma(z, ((x - t) / (a - z)), x);
	} else {
		tmp = ((x - t) / (z - a)) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5.8e+93)
		tmp = Float64(Float64(x - t) * Float64(y / Float64(z - a)));
	elseif (y <= 2.05e+52)
		tmp = fma(z, Float64(Float64(x - t) / Float64(a - z)), x);
	else
		tmp = Float64(Float64(Float64(x - t) / Float64(z - a)) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5.8e+93], N[(N[(x - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e+52], N[(z * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.7999999999999997e93

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

      4. lift-/.f64 N/A

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

      5. mult-flip N/A

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

      6. *-commutative N/A

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

      7. remove-double-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. frac-2neg N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 69.4

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

      15. lift-*.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

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

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

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

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

      20. lift--.f64 N/A

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

      21. sub-negate-rev N/A

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

      22. lower-*.f64 N/A

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

      23. lower--.f64 N/A

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

      24. lower--.f64 69.4

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

   3. Applied rewrites 69.4%

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

   4. Taylor expanded in y around -inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 37.9

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

   6. Applied rewrites 37.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 43.2

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

   8. Applied rewrites 43.2%

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

   if -5.7999999999999997e93 < y < 2.05e52

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. frac-2neg N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lower--.f64 85.1

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

   3. Applied rewrites 85.1%

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

   4. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{z}}{z - a}, t - x, x\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 47.5%

      \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{z}}{z - a}, t - x, x\right) \]
   7. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. associate-/l* N/A

         \[\leadsto \color{blue}{z \cdot \frac{t - x}{z - a}} + x \]

      6. lower-fma.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lift--.f64 N/A

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

      12. frac-2neg-rev N/A

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

      13. lower-/.f64 47.1

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

   8. Applied rewrites 47.1%

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

   if 2.05e52 < y

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

      4. lift-/.f64 N/A

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

      5. mult-flip N/A

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

      6. *-commutative N/A

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

      7. remove-double-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. frac-2neg N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 69.4

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

      15. lift-*.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

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

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

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

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

      20. lift--.f64 N/A

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

      21. sub-negate-rev N/A

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

      22. lower-*.f64 N/A

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

      23. lower--.f64 N/A

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

      24. lower--.f64 69.4

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

   3. Applied rewrites 69.4%

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

   4. Taylor expanded in y around -inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 37.9

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

   6. Applied rewrites 37.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

         \[\leadsto y \cdot \color{blue}{\frac{x - t}{z - a}} \]

      4. frac-2neg-rev N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

         \[\leadsto y \cdot \frac{t - x}{a - \color{blue}{z}} \]

      9. lift--.f64 N/A

         \[\leadsto y \cdot \frac{t - x}{a - \color{blue}{z}} \]

      10. *-commutative N/A

          \[\leadsto \frac{t - x}{a - z} \cdot \color{blue}{y} \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{t - x}{a - z} \cdot \color{blue}{y} \]

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lift--.f64 N/A

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

      17. frac-2neg-rev N/A

          \[\leadsto \frac{x - t}{z - a} \cdot y \]

      18. lower-/.f64 41.9

          \[\leadsto \frac{x - t}{z - a} \cdot y \]

   8. Applied rewrites 41.9%

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

Alternative 11: 58.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+33}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+114}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.4e+33)
   (+ x t)
   (if (<= z 8e+114) (fma (/ y a) (- t x) x) (/ (* t (- y z)) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.4e+33) {
		tmp = x + t;
	} else if (z <= 8e+114) {
		tmp = fma((y / a), (t - x), x);
	} else {
		tmp = (t * (y - z)) / (a - z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.4e+33)
		tmp = Float64(x + t);
	elseif (z <= 8e+114)
		tmp = fma(Float64(y / a), Float64(t - x), x);
	else
		tmp = Float64(Float64(t * Float64(y - z)) / Float64(a - z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.4e+33], N[(x + t), $MachinePrecision], If[LessEqual[z, 8e+114], N[(N[(y / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.39999999999999988e33

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in z around inf

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

      1. lower--.f64 18.9

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

   4. Applied rewrites 18.9%

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

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 34.8%

      \[\leadsto x + t \]

   if -4.39999999999999988e33 < z < 8e114

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. frac-2neg N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lower--.f64 85.1

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

   3. Applied rewrites 85.1%

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

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{a}}, t - x, x\right) \]
   5. Step-by-step derivation

      1. lower-/.f64 50.5

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

   6. Applied rewrites 50.5%

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

   if 8e114 < z

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.1

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

   4. Applied rewrites 39.1%

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

Alternative 12: 58.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+33}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+115}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.4e+33)
   (+ x t)
   (if (<= z 2.2e+115) (fma (/ y a) (- t x) x) (+ x (- t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.4e+33) {
		tmp = x + t;
	} else if (z <= 2.2e+115) {
		tmp = fma((y / a), (t - x), x);
	} else {
		tmp = x + (t - x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.4e+33)
		tmp = Float64(x + t);
	elseif (z <= 2.2e+115)
		tmp = fma(Float64(y / a), Float64(t - x), x);
	else
		tmp = Float64(x + Float64(t - x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.4e+33], N[(x + t), $MachinePrecision], If[LessEqual[z, 2.2e+115], N[(N[(y / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.39999999999999988e33

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in z around inf

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

      1. lower--.f64 18.9

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

   4. Applied rewrites 18.9%

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

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 34.8%

      \[\leadsto x + t \]

   if -4.39999999999999988e33 < z < 2.2e115

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. frac-2neg N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lower--.f64 85.1

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

   3. Applied rewrites 85.1%

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

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{a}}, t - x, x\right) \]
   5. Step-by-step derivation

      1. lower-/.f64 50.5

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

   6. Applied rewrites 50.5%

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

   if 2.2e115 < z

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in z around inf

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

      1. lower--.f64 18.9

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

   4. Applied rewrites 18.9%

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

Alternative 13: 44.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, \frac{x - t}{a}, x\right)\\ \mathbf{if}\;a \leq -1.95 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-258}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-185}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{+163}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma z (/ (- x t) a) x)))
   (if (<= a -1.95e+73)
     t_1
     (if (<= a -7e-258)
       (+ x t)
       (if (<= a 9.2e-185)
         (/ (* y (- x t)) z)
         (if (<= a 1.06e+163) (+ x t) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(z, ((x - t) / a), x);
	double tmp;
	if (a <= -1.95e+73) {
		tmp = t_1;
	} else if (a <= -7e-258) {
		tmp = x + t;
	} else if (a <= 9.2e-185) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 1.06e+163) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(z, Float64(Float64(x - t) / a), x)
	tmp = 0.0
	if (a <= -1.95e+73)
		tmp = t_1;
	elseif (a <= -7e-258)
		tmp = Float64(x + t);
	elseif (a <= 9.2e-185)
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	elseif (a <= 1.06e+163)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -1.95e+73], t$95$1, If[LessEqual[a, -7e-258], N[(x + t), $MachinePrecision], If[LessEqual[a, 9.2e-185], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 1.06e+163], N[(x + t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.95e73 or 1.06e163 < a

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. frac-2neg N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lower--.f64 85.1

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

   3. Applied rewrites 85.1%

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

   4. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{z}}{z - a}, t - x, x\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 47.5%

      \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{z}}{z - a}, t - x, x\right) \]
   7. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. associate-/l* N/A

         \[\leadsto \color{blue}{z \cdot \frac{t - x}{z - a}} + x \]

      6. lower-fma.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lift--.f64 N/A

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

      12. frac-2neg-rev N/A

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

      13. lower-/.f64 47.1

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

   8. Applied rewrites 47.1%

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

   9. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(z, \color{blue}{\frac{x - t}{a}}, x\right) \]
   10. Step-by-step derivation

       1. lower-/.f64 N/A

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

       2. lower--.f64 33.8

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

   11. Applied rewrites 33.8%

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

   if -1.95e73 < a < -7.00000000000000003e-258 or 9.2000000000000003e-185 < a < 1.06e163

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 18.9

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 18.9%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 34.8%

      \[\leadsto x + t \]

   if -7.00000000000000003e-258 < a < 9.2000000000000003e-185

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      3. remove-double-neg N/A

         \[\leadsto \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) \]

      5. mult-flip N/A

         \[\leadsto \color{blue}{\left(\left(y - z\right) \cdot \left(t - x\right)\right) \cdot \frac{1}{a - z}} + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)} + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) \]

      7. remove-double-neg N/A

         \[\leadsto \frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) + \color{blue}{x} \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{a - z}, \left(y - z\right) \cdot \left(t - x\right), x\right)} \]

      9. frac-2neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - z\right)\right)}}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - z\right)\right)}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      11. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{-1}{\mathsf{neg}\left(\left(a - z\right)\right)}}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      12. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      13. sub-negate-rev N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{\color{blue}{z - a}}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      14. lower--.f64 69.4

          \[\leadsto \mathsf{fma}\left(\frac{-1}{\color{blue}{z - a}}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\left(y - z\right) \cdot \left(t - x\right)}, x\right) \]

      16. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \left(y - z\right) \cdot \color{blue}{\left(t - x\right)}, x\right) \]

      17. sub-negate-rev N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \left(y - z\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(x - t\right)\right)\right)}, x\right) \]

      18. distribute-rgt-neg-out N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\mathsf{neg}\left(\left(y - z\right) \cdot \left(x - t\right)\right)}, x\right) \]

      19. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\left(\mathsf{neg}\left(\left(y - z\right)\right)\right) \cdot \left(x - t\right)}, x\right) \]

      20. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \left(\mathsf{neg}\left(\color{blue}{\left(y - z\right)}\right)\right) \cdot \left(x - t\right), x\right) \]

      21. sub-negate-rev N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\left(z - y\right)} \cdot \left(x - t\right), x\right) \]

      22. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\left(z - y\right) \cdot \left(x - t\right)}, x\right) \]

      23. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\left(z - y\right)} \cdot \left(x - t\right), x\right) \]

      24. lower--.f64 69.4

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \left(z - y\right) \cdot \color{blue}{\left(x - t\right)}, x\right) \]

   3. Applied rewrites 69.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{z - a}, \left(z - y\right) \cdot \left(x - t\right), x\right)} \]

   4. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{\frac{y \cdot \left(x - t\right)}{z - a}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot \left(x - t\right)}{\color{blue}{z - a}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{y \cdot \left(x - t\right)}{\color{blue}{z} - a} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{y \cdot \left(x - t\right)}{z - a} \]

      4. lower--.f64 37.9

         \[\leadsto \frac{y \cdot \left(x - t\right)}{z - \color{blue}{a}} \]

   6. Applied rewrites 37.9%

      \[\leadsto \color{blue}{\frac{y \cdot \left(x - t\right)}{z - a}} \]

   7. Taylor expanded in z around inf

      \[\leadsto \frac{y \cdot \left(x - t\right)}{\color{blue}{z}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot \left(x - t\right)}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{y \cdot \left(x - t\right)}{z} \]

      3. lower--.f64 23.6

         \[\leadsto \frac{y \cdot \left(x - t\right)}{z} \]

   9. Applied rewrites 23.6%

      \[\leadsto \frac{y \cdot \left(x - t\right)}{\color{blue}{z}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 41.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -1 \cdot \left(x \cdot -1\right)\\ \mathbf{if}\;a \leq -5.8 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-258}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-185}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+147}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -1.0 (* x -1.0))))
   (if (<= a -5.8e+156)
     t_1
     (if (<= a -7e-258)
       (+ x t)
       (if (<= a 9.2e-185)
         (/ (* y (- x t)) z)
         (if (<= a 2.35e+147) (+ x t) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -1.0 * (x * -1.0);
	double tmp;
	if (a <= -5.8e+156) {
		tmp = t_1;
	} else if (a <= -7e-258) {
		tmp = x + t;
	} else if (a <= 9.2e-185) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 2.35e+147) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
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) :: t_1
    real(8) :: tmp
    t_1 = (-1.0d0) * (x * (-1.0d0))
    if (a <= (-5.8d+156)) then
        tmp = t_1
    else if (a <= (-7d-258)) then
        tmp = x + t
    else if (a <= 9.2d-185) then
        tmp = (y * (x - t)) / z
    else if (a <= 2.35d+147) then
        tmp = x + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -1.0 * (x * -1.0);
	double tmp;
	if (a <= -5.8e+156) {
		tmp = t_1;
	} else if (a <= -7e-258) {
		tmp = x + t;
	} else if (a <= 9.2e-185) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 2.35e+147) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -1.0 * (x * -1.0)
	tmp = 0
	if a <= -5.8e+156:
		tmp = t_1
	elif a <= -7e-258:
		tmp = x + t
	elif a <= 9.2e-185:
		tmp = (y * (x - t)) / z
	elif a <= 2.35e+147:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-1.0 * Float64(x * -1.0))
	tmp = 0.0
	if (a <= -5.8e+156)
		tmp = t_1;
	elseif (a <= -7e-258)
		tmp = Float64(x + t);
	elseif (a <= 9.2e-185)
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	elseif (a <= 2.35e+147)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -1.0 * (x * -1.0);
	tmp = 0.0;
	if (a <= -5.8e+156)
		tmp = t_1;
	elseif (a <= -7e-258)
		tmp = x + t;
	elseif (a <= 9.2e-185)
		tmp = (y * (x - t)) / z;
	elseif (a <= 2.35e+147)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-1.0 * N[(x * -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.8e+156], t$95$1, If[LessEqual[a, -7e-258], N[(x + t), $MachinePrecision], If[LessEqual[a, 9.2e-185], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 2.35e+147], N[(x + t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.80000000000000021e156 or 2.3500000000000001e147 < a

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} \]

      2. add-flip N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\right)\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}}\right)\right) \]

      4. distribute-neg-frac N/A

         \[\leadsto x - \color{blue}{\frac{\mathsf{neg}\left(\left(y - z\right) \cdot \left(t - x\right)\right)}{a - z}} \]

      5. sub-to-fraction-rev N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - z\right) - \left(\mathsf{neg}\left(\left(y - z\right) \cdot \left(t - x\right)\right)\right)}{a - z}} \]

      6. add-flip N/A

         \[\leadsto \frac{\color{blue}{x \cdot \left(a - z\right) + \left(y - z\right) \cdot \left(t - x\right)}}{a - z} \]

      7. +-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot \left(t - x\right) + x \cdot \left(a - z\right)}}{a - z} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot \left(t - x\right)} + x \cdot \left(a - z\right)}{a - z} \]

      9. lift--.f64 N/A

         \[\leadsto \frac{\left(y - z\right) \cdot \color{blue}{\left(t - x\right)} + x \cdot \left(a - z\right)}{a - z} \]

      10. sub-flip N/A

          \[\leadsto \frac{\left(y - z\right) \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(x\right)\right)\right)} + x \cdot \left(a - z\right)}{a - z} \]

      11. distribute-rgt-in N/A

          \[\leadsto \frac{\color{blue}{\left(t \cdot \left(y - z\right) + \left(\mathsf{neg}\left(x\right)\right) \cdot \left(y - z\right)\right)} + x \cdot \left(a - z\right)}{a - z} \]

      12. associate-+l+ N/A

          \[\leadsto \frac{\color{blue}{t \cdot \left(y - z\right) + \left(\left(\mathsf{neg}\left(x\right)\right) \cdot \left(y - z\right) + x \cdot \left(a - z\right)\right)}}{a - z} \]

      13. div-add N/A

          \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z} + \frac{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(y - z\right) + x \cdot \left(a - z\right)}{a - z}} \]

   3. Applied rewrites 76.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - y}{z - a}, t, \frac{\left(-x\right) \cdot \left(\left(y - z\right) + \left(z - a\right)\right)}{a - z}\right)} \]

   4. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(\frac{y}{a - z} - \frac{a}{a - z}\right)\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(x \cdot \left(\frac{y}{a - z} - \frac{a}{a - z}\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \color{blue}{\left(\frac{y}{a - z} - \frac{a}{a - z}\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(\frac{y}{a - z} - \color{blue}{\frac{a}{a - z}}\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(\frac{y}{a - z} - \frac{\color{blue}{a}}{a - z}\right)\right) \]

      5. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(\frac{y}{a - z} - \frac{a}{a - z}\right)\right) \]

      6. lower-/.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(\frac{y}{a - z} - \frac{a}{\color{blue}{a - z}}\right)\right) \]

      7. lower--.f64 52.5

         \[\leadsto -1 \cdot \left(x \cdot \left(\frac{y}{a - z} - \frac{a}{a - \color{blue}{z}}\right)\right) \]

   6. Applied rewrites 52.5%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(\frac{y}{a - z} - \frac{a}{a - z}\right)\right)} \]

   7. Taylor expanded in a around inf

      \[\leadsto -1 \cdot \left(x \cdot -1\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 26.7%

      \[\leadsto -1 \cdot \left(x \cdot -1\right) \]

   if -5.80000000000000021e156 < a < -7.00000000000000003e-258 or 9.2000000000000003e-185 < a < 2.3500000000000001e147

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 18.9

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 18.9%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 34.8%

      \[\leadsto x + t \]

   if -7.00000000000000003e-258 < a < 9.2000000000000003e-185

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      3. remove-double-neg N/A

         \[\leadsto \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) \]

      5. mult-flip N/A

         \[\leadsto \color{blue}{\left(\left(y - z\right) \cdot \left(t - x\right)\right) \cdot \frac{1}{a - z}} + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)} + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) \]

      7. remove-double-neg N/A

         \[\leadsto \frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) + \color{blue}{x} \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{a - z}, \left(y - z\right) \cdot \left(t - x\right), x\right)} \]

      9. frac-2neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - z\right)\right)}}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - z\right)\right)}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      11. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{-1}{\mathsf{neg}\left(\left(a - z\right)\right)}}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      12. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      13. sub-negate-rev N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{\color{blue}{z - a}}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      14. lower--.f64 69.4

          \[\leadsto \mathsf{fma}\left(\frac{-1}{\color{blue}{z - a}}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\left(y - z\right) \cdot \left(t - x\right)}, x\right) \]

      16. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \left(y - z\right) \cdot \color{blue}{\left(t - x\right)}, x\right) \]

      17. sub-negate-rev N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \left(y - z\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(x - t\right)\right)\right)}, x\right) \]

      18. distribute-rgt-neg-out N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\mathsf{neg}\left(\left(y - z\right) \cdot \left(x - t\right)\right)}, x\right) \]

      19. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\left(\mathsf{neg}\left(\left(y - z\right)\right)\right) \cdot \left(x - t\right)}, x\right) \]

      20. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \left(\mathsf{neg}\left(\color{blue}{\left(y - z\right)}\right)\right) \cdot \left(x - t\right), x\right) \]

      21. sub-negate-rev N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\left(z - y\right)} \cdot \left(x - t\right), x\right) \]

      22. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\left(z - y\right) \cdot \left(x - t\right)}, x\right) \]

      23. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\left(z - y\right)} \cdot \left(x - t\right), x\right) \]

      24. lower--.f64 69.4

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \left(z - y\right) \cdot \color{blue}{\left(x - t\right)}, x\right) \]

   3. Applied rewrites 69.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{z - a}, \left(z - y\right) \cdot \left(x - t\right), x\right)} \]

   4. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{\frac{y \cdot \left(x - t\right)}{z - a}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot \left(x - t\right)}{\color{blue}{z - a}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{y \cdot \left(x - t\right)}{\color{blue}{z} - a} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{y \cdot \left(x - t\right)}{z - a} \]

      4. lower--.f64 37.9

         \[\leadsto \frac{y \cdot \left(x - t\right)}{z - \color{blue}{a}} \]

   6. Applied rewrites 37.9%

      \[\leadsto \color{blue}{\frac{y \cdot \left(x - t\right)}{z - a}} \]

   7. Taylor expanded in z around inf

      \[\leadsto \frac{y \cdot \left(x - t\right)}{\color{blue}{z}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot \left(x - t\right)}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{y \cdot \left(x - t\right)}{z} \]

      3. lower--.f64 23.6

         \[\leadsto \frac{y \cdot \left(x - t\right)}{z} \]

   9. Applied rewrites 23.6%

      \[\leadsto \frac{y \cdot \left(x - t\right)}{\color{blue}{z}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 38.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{+93}:\\ \;\;\;\;\frac{x \cdot y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -6.9e+93) (/ (* x y) (- z a)) (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6.9e+93) {
		tmp = (x * y) / (z - a);
	} else {
		tmp = x + t;
	}
	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)
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) :: tmp
    if (y <= (-6.9d+93)) then
        tmp = (x * y) / (z - a)
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6.9e+93) {
		tmp = (x * y) / (z - a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -6.9e+93:
		tmp = (x * y) / (z - a)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -6.9e+93)
		tmp = Float64(Float64(x * y) / Float64(z - a));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -6.9e+93)
		tmp = (x * y) / (z - a);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -6.9e+93], N[(N[(x * y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.8999999999999995e93

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      3. remove-double-neg N/A

         \[\leadsto \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) \]

      5. mult-flip N/A

         \[\leadsto \color{blue}{\left(\left(y - z\right) \cdot \left(t - x\right)\right) \cdot \frac{1}{a - z}} + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)} + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) \]

      7. remove-double-neg N/A

         \[\leadsto \frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) + \color{blue}{x} \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{a - z}, \left(y - z\right) \cdot \left(t - x\right), x\right)} \]

      9. frac-2neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - z\right)\right)}}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - z\right)\right)}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      11. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{-1}{\mathsf{neg}\left(\left(a - z\right)\right)}}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      12. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      13. sub-negate-rev N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{\color{blue}{z - a}}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      14. lower--.f64 69.4

          \[\leadsto \mathsf{fma}\left(\frac{-1}{\color{blue}{z - a}}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\left(y - z\right) \cdot \left(t - x\right)}, x\right) \]

      16. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \left(y - z\right) \cdot \color{blue}{\left(t - x\right)}, x\right) \]

      17. sub-negate-rev N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \left(y - z\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(x - t\right)\right)\right)}, x\right) \]

      18. distribute-rgt-neg-out N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\mathsf{neg}\left(\left(y - z\right) \cdot \left(x - t\right)\right)}, x\right) \]

      19. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\left(\mathsf{neg}\left(\left(y - z\right)\right)\right) \cdot \left(x - t\right)}, x\right) \]

      20. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \left(\mathsf{neg}\left(\color{blue}{\left(y - z\right)}\right)\right) \cdot \left(x - t\right), x\right) \]

      21. sub-negate-rev N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\left(z - y\right)} \cdot \left(x - t\right), x\right) \]

      22. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\left(z - y\right) \cdot \left(x - t\right)}, x\right) \]

      23. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\left(z - y\right)} \cdot \left(x - t\right), x\right) \]

      24. lower--.f64 69.4

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \left(z - y\right) \cdot \color{blue}{\left(x - t\right)}, x\right) \]

   3. Applied rewrites 69.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{z - a}, \left(z - y\right) \cdot \left(x - t\right), x\right)} \]

   4. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{\frac{y \cdot \left(x - t\right)}{z - a}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot \left(x - t\right)}{\color{blue}{z - a}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{y \cdot \left(x - t\right)}{\color{blue}{z} - a} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{y \cdot \left(x - t\right)}{z - a} \]

      4. lower--.f64 37.9

         \[\leadsto \frac{y \cdot \left(x - t\right)}{z - \color{blue}{a}} \]

   6. Applied rewrites 37.9%

      \[\leadsto \color{blue}{\frac{y \cdot \left(x - t\right)}{z - a}} \]

   7. Taylor expanded in x around inf

      \[\leadsto \frac{x \cdot y}{\color{blue}{z} - a} \]
   8. Step-by-step derivation

      1. lower-*.f64 20.9

         \[\leadsto \frac{x \cdot y}{z - a} \]

   9. Applied rewrites 20.9%

      \[\leadsto \frac{x \cdot y}{\color{blue}{z} - a} \]

   if -6.8999999999999995e93 < y

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 18.9

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 18.9%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 34.8%

      \[\leadsto x + t \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 37.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2200000000:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-111}:\\ \;\;\;\;-1 \cdot \left(x \cdot -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2200000000.0)
   (+ x t)
   (if (<= z 3.2e-111) (* -1.0 (* x -1.0)) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2200000000.0) {
		tmp = x + t;
	} else if (z <= 3.2e-111) {
		tmp = -1.0 * (x * -1.0);
	} else {
		tmp = x + t;
	}
	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)
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) :: tmp
    if (z <= (-2200000000.0d0)) then
        tmp = x + t
    else if (z <= 3.2d-111) then
        tmp = (-1.0d0) * (x * (-1.0d0))
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2200000000.0) {
		tmp = x + t;
	} else if (z <= 3.2e-111) {
		tmp = -1.0 * (x * -1.0);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2200000000.0:
		tmp = x + t
	elif z <= 3.2e-111:
		tmp = -1.0 * (x * -1.0)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2200000000.0)
		tmp = Float64(x + t);
	elseif (z <= 3.2e-111)
		tmp = Float64(-1.0 * Float64(x * -1.0));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2200000000.0)
		tmp = x + t;
	elseif (z <= 3.2e-111)
		tmp = -1.0 * (x * -1.0);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2200000000.0], N[(x + t), $MachinePrecision], If[LessEqual[z, 3.2e-111], N[(-1.0 * N[(x * -1.0), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2e9 or 3.1999999999999998e-111 < z

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 18.9

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 18.9%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 34.8%

      \[\leadsto x + t \]

   if -2.2e9 < z < 3.1999999999999998e-111

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} \]

      2. add-flip N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\right)\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}}\right)\right) \]

      4. distribute-neg-frac N/A

         \[\leadsto x - \color{blue}{\frac{\mathsf{neg}\left(\left(y - z\right) \cdot \left(t - x\right)\right)}{a - z}} \]

      5. sub-to-fraction-rev N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - z\right) - \left(\mathsf{neg}\left(\left(y - z\right) \cdot \left(t - x\right)\right)\right)}{a - z}} \]

      6. add-flip N/A

         \[\leadsto \frac{\color{blue}{x \cdot \left(a - z\right) + \left(y - z\right) \cdot \left(t - x\right)}}{a - z} \]

      7. +-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot \left(t - x\right) + x \cdot \left(a - z\right)}}{a - z} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot \left(t - x\right)} + x \cdot \left(a - z\right)}{a - z} \]

      9. lift--.f64 N/A

         \[\leadsto \frac{\left(y - z\right) \cdot \color{blue}{\left(t - x\right)} + x \cdot \left(a - z\right)}{a - z} \]

      10. sub-flip N/A

          \[\leadsto \frac{\left(y - z\right) \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(x\right)\right)\right)} + x \cdot \left(a - z\right)}{a - z} \]

      11. distribute-rgt-in N/A

          \[\leadsto \frac{\color{blue}{\left(t \cdot \left(y - z\right) + \left(\mathsf{neg}\left(x\right)\right) \cdot \left(y - z\right)\right)} + x \cdot \left(a - z\right)}{a - z} \]

      12. associate-+l+ N/A

          \[\leadsto \frac{\color{blue}{t \cdot \left(y - z\right) + \left(\left(\mathsf{neg}\left(x\right)\right) \cdot \left(y - z\right) + x \cdot \left(a - z\right)\right)}}{a - z} \]

      13. div-add N/A

          \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z} + \frac{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(y - z\right) + x \cdot \left(a - z\right)}{a - z}} \]

   3. Applied rewrites 76.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - y}{z - a}, t, \frac{\left(-x\right) \cdot \left(\left(y - z\right) + \left(z - a\right)\right)}{a - z}\right)} \]

   4. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(\frac{y}{a - z} - \frac{a}{a - z}\right)\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(x \cdot \left(\frac{y}{a - z} - \frac{a}{a - z}\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \color{blue}{\left(\frac{y}{a - z} - \frac{a}{a - z}\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(\frac{y}{a - z} - \color{blue}{\frac{a}{a - z}}\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(\frac{y}{a - z} - \frac{\color{blue}{a}}{a - z}\right)\right) \]

      5. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(\frac{y}{a - z} - \frac{a}{a - z}\right)\right) \]

      6. lower-/.f64 N/A

         \[\leadsto -1 \cdot \left(x \cdot \left(\frac{y}{a - z} - \frac{a}{\color{blue}{a - z}}\right)\right) \]

      7. lower--.f64 52.5

         \[\leadsto -1 \cdot \left(x \cdot \left(\frac{y}{a - z} - \frac{a}{a - \color{blue}{z}}\right)\right) \]

   6. Applied rewrites 52.5%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(\frac{y}{a - z} - \frac{a}{a - z}\right)\right)} \]

   7. Taylor expanded in a around inf

      \[\leadsto -1 \cdot \left(x \cdot -1\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 26.7%

      \[\leadsto -1 \cdot \left(x \cdot -1\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 34.8% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ x + t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x t))

C

double code(double x, double y, double z, double t, double a) {
	return x + t;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
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
    code = x + t
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + t;
}

Python

def code(x, y, z, t, a):
	return x + t

Julia

function code(x, y, z, t, a)
	return Float64(x + t)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + t;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + t), $MachinePrecision]

Derivation

1. Initial program 69.5%

   \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

2. Taylor expanded in z around inf

   \[\leadsto x + \color{blue}{\left(t - x\right)} \]
3. Step-by-step derivation

   1. lower--.f64 18.9

      \[\leadsto x + \left(t - \color{blue}{x}\right) \]

4. Applied rewrites 18.9%

   \[\leadsto x + \color{blue}{\left(t - x\right)} \]

5. Taylor expanded in x around 0

   \[\leadsto x + t \]
6. Step-by-step derivation

7. Applied rewrites 34.8%

   \[\leadsto x + t \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025143 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64
  (+ x (/ (* (- y z) (- t x)) (- a z))))