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

Percentage Accurate: 68.2% → 90.8%

Time: 11.1s

Alternatives: 21

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-264} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z - a, \mathsf{fma}\left(-1, y, x\right), t \cdot y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -1e-264) (not (<= t_1 0.0)))
     (fma (/ (- z t) (- a t)) (- y x) x)
     (/ (fma (- z a) (fma -1.0 y x) (* t y)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -1e-264) || !(t_1 <= 0.0)) {
		tmp = fma(((z - t) / (a - t)), (y - x), x);
	} else {
		tmp = fma((z - a), fma(-1.0, y, x), (t * y)) / t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -1e-264) || !(t_1 <= 0.0))
		tmp = fma(Float64(Float64(z - t) / Float64(a - t)), Float64(y - x), x);
	else
		tmp = Float64(fma(Float64(z - a), fma(-1.0, y, x), Float64(t * y)) / t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-264], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(z - a), $MachinePrecision] * N[(-1.0 * y + x), $MachinePrecision] + N[(t * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1e-264 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 71.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 91.8

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

   4. Applied rewrites 91.8%

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

   if -1e-264 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.9%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

      9. distribute-rgt-out-- N/A

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 94.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 99.9%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-264} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z - a, \mathsf{fma}\left(-1, y, x\right), t \cdot y\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-264} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot \left(z - a\right)}{-t} + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -1e-264) (not (<= t_1 0.0)))
     (fma (/ (- z t) (- a t)) (- y x) x)
     (+ (/ (* (- y x) (- z a)) (- t)) y))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -1e-264) || !(t_1 <= 0.0)) {
		tmp = fma(((z - t) / (a - t)), (y - x), x);
	} else {
		tmp = (((y - x) * (z - a)) / -t) + y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -1e-264) || !(t_1 <= 0.0))
		tmp = fma(Float64(Float64(z - t) / Float64(a - t)), Float64(y - x), x);
	else
		tmp = Float64(Float64(Float64(Float64(y - x) * Float64(z - a)) / Float64(-t)) + y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-264], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(N[(y - x), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision] / (-t)), $MachinePrecision] + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1e-264 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 71.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 91.8

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

   4. Applied rewrites 91.8%

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

   if -1e-264 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 3.9

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

   4. Applied rewrites 3.9%

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

   5. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. associate-*r* N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. mul-1-neg N/A

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

      8. associate-*r* N/A

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

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

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

      10. associate-*r/ N/A

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

      11. +-commutative N/A

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

      12. lower-+.f64 N/A

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

   7. Applied rewrites 99.8%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-264} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot \left(z - a\right)}{-t} + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-264} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -1e-264) (not (<= t_1 0.0)))
     (fma (/ (- z t) (- a t)) (- y x) x)
     (fma (/ x t) (- z a) y))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -1e-264) || !(t_1 <= 0.0)) {
		tmp = fma(((z - t) / (a - t)), (y - x), x);
	} else {
		tmp = fma((x / t), (z - a), y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -1e-264) || !(t_1 <= 0.0))
		tmp = fma(Float64(Float64(z - t) / Float64(a - t)), Float64(y - x), x);
	else
		tmp = fma(Float64(x / t), Float64(z - a), y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-264], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision], N[(N[(x / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1e-264 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 71.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 91.8

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

   4. Applied rewrites 91.8%

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

   if -1e-264 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.9%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

      9. distribute-rgt-out-- N/A

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 94.2%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 94.2%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-264} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.45 \cdot 10^{-112}:\\ \;\;\;\;x + \frac{z - t}{a} \cdot \left(y - x\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+160}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ x t) (- z a) y)))
   (if (<= t -1.3e-17)
     t_1
     (if (<= t 3.45e-112)
       (+ x (* (/ (- z t) a) (- y x)))
       (if (<= t 9.2e+21)
         (+ x (/ (* (- y x) z) (- a t)))
         (if (<= t 4.8e+160) (* (- z t) (/ y (- a t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x / t), (z - a), y);
	double tmp;
	if (t <= -1.3e-17) {
		tmp = t_1;
	} else if (t <= 3.45e-112) {
		tmp = x + (((z - t) / a) * (y - x));
	} else if (t <= 9.2e+21) {
		tmp = x + (((y - x) * z) / (a - t));
	} else if (t <= 4.8e+160) {
		tmp = (z - t) * (y / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x / t), Float64(z - a), y)
	tmp = 0.0
	if (t <= -1.3e-17)
		tmp = t_1;
	elseif (t <= 3.45e-112)
		tmp = Float64(x + Float64(Float64(Float64(z - t) / a) * Float64(y - x)));
	elseif (t <= 9.2e+21)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / Float64(a - t)));
	elseif (t <= 4.8e+160)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[t, -1.3e-17], t$95$1, If[LessEqual[t, 3.45e-112], N[(x + N[(N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e+21], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e+160], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.30000000000000002e-17 or 4.8000000000000003e160 < t

   1. Initial program 33.3%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

      9. distribute-rgt-out-- N/A

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 83.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 81.8%

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

   if -1.30000000000000002e-17 < t < 3.45000000000000009e-112

   1. Initial program 89.2%

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

   3. Taylor expanded in a around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 88.6

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

   5. Applied rewrites 88.6%

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

   if 3.45000000000000009e-112 < t < 9.2e21

   1. Initial program 91.2%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 84.3

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

   5. Applied rewrites 84.3%

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

   if 9.2e21 < t < 4.8000000000000003e160

   1. Initial program 55.3%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 72.9

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

   5. Applied rewrites 72.9%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \mathbf{elif}\;t \leq 3.45 \cdot 10^{-112}:\\ \;\;\;\;x + \frac{z - t}{a} \cdot \left(y - x\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+160}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-106}:\\ \;\;\;\;x + \frac{z - t}{a} \cdot \left(y - x\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(-\left(z - t\right), \frac{x}{a - t}, x\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+160}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ x t) (- z a) y)))
   (if (<= t -1.3e-17)
     t_1
     (if (<= t 1.7e-106)
       (+ x (* (/ (- z t) a) (- y x)))
       (if (<= t 1.35e+24)
         (fma (- (- z t)) (/ x (- a t)) x)
         (if (<= t 4.8e+160) (* (- z t) (/ y (- a t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x / t), (z - a), y);
	double tmp;
	if (t <= -1.3e-17) {
		tmp = t_1;
	} else if (t <= 1.7e-106) {
		tmp = x + (((z - t) / a) * (y - x));
	} else if (t <= 1.35e+24) {
		tmp = fma(-(z - t), (x / (a - t)), x);
	} else if (t <= 4.8e+160) {
		tmp = (z - t) * (y / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x / t), Float64(z - a), y)
	tmp = 0.0
	if (t <= -1.3e-17)
		tmp = t_1;
	elseif (t <= 1.7e-106)
		tmp = Float64(x + Float64(Float64(Float64(z - t) / a) * Float64(y - x)));
	elseif (t <= 1.35e+24)
		tmp = fma(Float64(-Float64(z - t)), Float64(x / Float64(a - t)), x);
	elseif (t <= 4.8e+160)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[t, -1.3e-17], t$95$1, If[LessEqual[t, 1.7e-106], N[(x + N[(N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e+24], N[((-N[(z - t), $MachinePrecision]) * N[(x / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 4.8e+160], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.30000000000000002e-17 or 4.8000000000000003e160 < t

   1. Initial program 33.3%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

      9. distribute-rgt-out-- N/A

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 83.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 81.8%

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

   if -1.30000000000000002e-17 < t < 1.69999999999999991e-106

   1. Initial program 89.4%

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

   3. Taylor expanded in a around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 88.8

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

   5. Applied rewrites 88.8%

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

   if 1.69999999999999991e-106 < t < 1.35e24

   1. Initial program 87.5%

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

   3. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. distribute-rgt-in N/A

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

      3. mul-1-neg N/A

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

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

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

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

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

      10. mul-1-neg N/A

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

      11. *-lft-identity N/A

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

      12. lower-fma.f64 N/A

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

      13. mul-1-neg N/A

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

      14. lower-neg.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 78.2

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

   5. Applied rewrites 78.2%

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

   if 1.35e24 < t < 4.8000000000000003e160

   1. Initial program 56.9%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 75.0

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

   5. Applied rewrites 75.0%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-106}:\\ \;\;\;\;x + \frac{z - t}{a} \cdot \left(y - x\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(-\left(z - t\right), \frac{x}{a - t}, x\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+160}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-56}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{a}, z, x\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+160}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ x t) (- z a) y)))
   (if (<= t -9.5e+62)
     t_1
     (if (<= t -8e-56)
       (/ (* (- z t) y) (- a t))
       (if (<= t 1.4e+24)
         (fma (/ (- y x) a) z x)
         (if (<= t 4.8e+160) (* (- z t) (/ y (- a t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x / t), (z - a), y);
	double tmp;
	if (t <= -9.5e+62) {
		tmp = t_1;
	} else if (t <= -8e-56) {
		tmp = ((z - t) * y) / (a - t);
	} else if (t <= 1.4e+24) {
		tmp = fma(((y - x) / a), z, x);
	} else if (t <= 4.8e+160) {
		tmp = (z - t) * (y / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x / t), Float64(z - a), y)
	tmp = 0.0
	if (t <= -9.5e+62)
		tmp = t_1;
	elseif (t <= -8e-56)
		tmp = Float64(Float64(Float64(z - t) * y) / Float64(a - t));
	elseif (t <= 1.4e+24)
		tmp = fma(Float64(Float64(y - x) / a), z, x);
	elseif (t <= 4.8e+160)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[t, -9.5e+62], t$95$1, If[LessEqual[t, -8e-56], N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+24], N[(N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[t, 4.8e+160], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.5000000000000003e62 or 4.8000000000000003e160 < t

   1. Initial program 29.8%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

      9. distribute-rgt-out-- N/A

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 87.3%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 87.3%

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

   if -9.5000000000000003e62 < t < -8.0000000000000003e-56

   1. Initial program 69.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 77.7

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

   4. Applied rewrites 77.7%

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

   5. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 69.3

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

   7. Applied rewrites 69.3%

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

   if -8.0000000000000003e-56 < t < 1.4000000000000001e24

   1. Initial program 89.6%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 81.0

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

   5. Applied rewrites 81.0%

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

   if 1.4000000000000001e24 < t < 4.8000000000000003e160

   1. Initial program 56.9%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 75.0

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

   5. Applied rewrites 75.0%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+62}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-56}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{a}, z, x\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+160}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{y}{a - t}\\ t_2 := \mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{+63}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{a}, z, x\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z t) (/ y (- a t)))) (t_2 (fma (/ x t) (- z a) y)))
   (if (<= t -2.2e+63)
     t_2
     (if (<= t -7.6e-56)
       t_1
       (if (<= t 1.4e+24)
         (fma (/ (- y x) a) z x)
         (if (<= t 4.8e+160) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * (y / (a - t));
	double t_2 = fma((x / t), (z - a), y);
	double tmp;
	if (t <= -2.2e+63) {
		tmp = t_2;
	} else if (t <= -7.6e-56) {
		tmp = t_1;
	} else if (t <= 1.4e+24) {
		tmp = fma(((y - x) / a), z, x);
	} else if (t <= 4.8e+160) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) * Float64(y / Float64(a - t)))
	t_2 = fma(Float64(x / t), Float64(z - a), y)
	tmp = 0.0
	if (t <= -2.2e+63)
		tmp = t_2;
	elseif (t <= -7.6e-56)
		tmp = t_1;
	elseif (t <= 1.4e+24)
		tmp = fma(Float64(Float64(y - x) / a), z, x);
	elseif (t <= 4.8e+160)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[t, -2.2e+63], t$95$2, If[LessEqual[t, -7.6e-56], t$95$1, If[LessEqual[t, 1.4e+24], N[(N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[t, 4.8e+160], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1999999999999999e63 or 4.8000000000000003e160 < t

   1. Initial program 29.8%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

      9. distribute-rgt-out-- N/A

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 87.3%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 87.3%

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

   if -2.1999999999999999e63 < t < -7.6000000000000004e-56 or 1.4000000000000001e24 < t < 4.8000000000000003e160

   1. Initial program 61.7%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 71.2

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

   5. Applied rewrites 71.2%

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

   if -7.6000000000000004e-56 < t < 1.4000000000000001e24

   1. Initial program 89.6%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 81.0

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

   5. Applied rewrites 81.0%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-56}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{a}, z, x\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+160}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{\mathsf{fma}\left(-1, y, x\right)}{t}, z - a, y\right)\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.45 \cdot 10^{-112}:\\ \;\;\;\;x + \frac{z - t}{a} \cdot \left(y - x\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (fma -1.0 y x) t) (- z a) y)))
   (if (<= t -1.2e-17)
     t_1
     (if (<= t 3.45e-112)
       (+ x (* (/ (- z t) a) (- y x)))
       (if (<= t 7e+21) (+ x (/ (* (- y x) z) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((fma(-1.0, y, x) / t), (z - a), y);
	double tmp;
	if (t <= -1.2e-17) {
		tmp = t_1;
	} else if (t <= 3.45e-112) {
		tmp = x + (((z - t) / a) * (y - x));
	} else if (t <= 7e+21) {
		tmp = x + (((y - x) * z) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(fma(-1.0, y, x) / t), Float64(z - a), y)
	tmp = 0.0
	if (t <= -1.2e-17)
		tmp = t_1;
	elseif (t <= 3.45e-112)
		tmp = Float64(x + Float64(Float64(Float64(z - t) / a) * Float64(y - x)));
	elseif (t <= 7e+21)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(-1.0 * y + x), $MachinePrecision] / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[t, -1.2e-17], t$95$1, If[LessEqual[t, 3.45e-112], N[(x + N[(N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+21], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.19999999999999993e-17 or 7e21 < t

   1. Initial program 39.9%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

      9. distribute-rgt-out-- N/A

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 78.5%

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

   if -1.19999999999999993e-17 < t < 3.45000000000000009e-112

   1. Initial program 89.2%

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

   3. Taylor expanded in a around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 88.6

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

   5. Applied rewrites 88.6%

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

   if 3.45000000000000009e-112 < t < 7e21

   1. Initial program 91.2%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 84.3

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

   5. Applied rewrites 84.3%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(-1, y, x\right)}{t}, z - a, y\right)\\ \mathbf{elif}\;t \leq 3.45 \cdot 10^{-112}:\\ \;\;\;\;x + \frac{z - t}{a} \cdot \left(y - x\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(-1, y, x\right)}{t}, z - a, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 44.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1, y - x, x\right)\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.56 \cdot 10^{-55}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-239}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-x}{a}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma 1.0 (- y x) x)))
   (if (<= t -2.6e+67)
     t_1
     (if (<= t -1.56e-55)
       (/ (* (- z t) y) a)
       (if (<= t 7.8e-239)
         (fma (/ y a) z x)
         (if (<= t 5e+24) (fma (/ (- x) a) z x) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(1.0, (y - x), x);
	double tmp;
	if (t <= -2.6e+67) {
		tmp = t_1;
	} else if (t <= -1.56e-55) {
		tmp = ((z - t) * y) / a;
	} else if (t <= 7.8e-239) {
		tmp = fma((y / a), z, x);
	} else if (t <= 5e+24) {
		tmp = fma((-x / a), z, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(1.0, Float64(y - x), x)
	tmp = 0.0
	if (t <= -2.6e+67)
		tmp = t_1;
	elseif (t <= -1.56e-55)
		tmp = Float64(Float64(Float64(z - t) * y) / a);
	elseif (t <= 7.8e-239)
		tmp = fma(Float64(y / a), z, x);
	elseif (t <= 5e+24)
		tmp = fma(Float64(Float64(-x) / a), z, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(1.0 * N[(y - x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -2.6e+67], t$95$1, If[LessEqual[t, -1.56e-55], N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 7.8e-239], N[(N[(y / a), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[t, 5e+24], N[(N[((-x) / a), $MachinePrecision] * z + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.6e67 or 5.00000000000000045e24 < t

   1. Initial program 38.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 77.0

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

   4. Applied rewrites 77.0%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{1}, y - x, x\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 50.1%

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

   if -2.6e67 < t < -1.56e-55

   1. Initial program 67.7%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 52.4

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

   5. Applied rewrites 52.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 39.5%

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

   if -1.56e-55 < t < 7.8e-239

   1. Initial program 89.7%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 85.8

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

   5. Applied rewrites 85.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 74.3%

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

   if 7.8e-239 < t < 5.00000000000000045e24

   1. Initial program 89.5%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 76.0

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

   5. Applied rewrites 76.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 70.9%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+67}:\\ \;\;\;\;\mathsf{fma}\left(1, y - x, x\right)\\ \mathbf{elif}\;t \leq -1.56 \cdot 10^{-55}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-239}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-x}{a}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1, y - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 44.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1, y - x, x\right)\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.56 \cdot 10^{-55}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-239}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(-x, \frac{z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma 1.0 (- y x) x)))
   (if (<= t -2.6e+67)
     t_1
     (if (<= t -1.56e-55)
       (/ (* (- z t) y) a)
       (if (<= t 7.2e-239)
         (fma (/ y a) z x)
         (if (<= t 5e+24) (fma (- x) (/ z a) x) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(1.0, (y - x), x);
	double tmp;
	if (t <= -2.6e+67) {
		tmp = t_1;
	} else if (t <= -1.56e-55) {
		tmp = ((z - t) * y) / a;
	} else if (t <= 7.2e-239) {
		tmp = fma((y / a), z, x);
	} else if (t <= 5e+24) {
		tmp = fma(-x, (z / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(1.0, Float64(y - x), x)
	tmp = 0.0
	if (t <= -2.6e+67)
		tmp = t_1;
	elseif (t <= -1.56e-55)
		tmp = Float64(Float64(Float64(z - t) * y) / a);
	elseif (t <= 7.2e-239)
		tmp = fma(Float64(y / a), z, x);
	elseif (t <= 5e+24)
		tmp = fma(Float64(-x), Float64(z / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(1.0 * N[(y - x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -2.6e+67], t$95$1, If[LessEqual[t, -1.56e-55], N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 7.2e-239], N[(N[(y / a), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[t, 5e+24], N[((-x) * N[(z / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.6e67 or 5.00000000000000045e24 < t

   1. Initial program 38.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 77.0

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

   4. Applied rewrites 77.0%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{1}, y - x, x\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 50.1%

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

   if -2.6e67 < t < -1.56e-55

   1. Initial program 67.7%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 52.4

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

   5. Applied rewrites 52.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 39.5%

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

   if -1.56e-55 < t < 7.2000000000000002e-239

   1. Initial program 89.7%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 85.8

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

   5. Applied rewrites 85.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 74.3%

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

   if 7.2000000000000002e-239 < t < 5.00000000000000045e24

   1. Initial program 89.5%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 76.0

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

   5. Applied rewrites 76.0%

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

   6. Taylor expanded in y around 0

      \[\leadsto x + \color{blue}{-1 \cdot \frac{x \cdot z}{a}} \]
   7. Step-by-step derivation

   8. Applied rewrites 68.8%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+67}:\\ \;\;\;\;\mathsf{fma}\left(1, y - x, x\right)\\ \mathbf{elif}\;t \leq -1.56 \cdot 10^{-55}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-239}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(-x, \frac{z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1, y - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 70.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y - x}{a}, x\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+160}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ x t) (- z a) y)))
   (if (<= t -1.3e-17)
     t_1
     (if (<= t 1.4e+24)
       (fma (- z t) (/ (- y x) a) x)
       (if (<= t 4.8e+160) (* (- z t) (/ y (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x / t), (z - a), y);
	double tmp;
	if (t <= -1.3e-17) {
		tmp = t_1;
	} else if (t <= 1.4e+24) {
		tmp = fma((z - t), ((y - x) / a), x);
	} else if (t <= 4.8e+160) {
		tmp = (z - t) * (y / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x / t), Float64(z - a), y)
	tmp = 0.0
	if (t <= -1.3e-17)
		tmp = t_1;
	elseif (t <= 1.4e+24)
		tmp = fma(Float64(z - t), Float64(Float64(y - x) / a), x);
	elseif (t <= 4.8e+160)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[t, -1.3e-17], t$95$1, If[LessEqual[t, 1.4e+24], N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 4.8e+160], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.30000000000000002e-17 or 4.8000000000000003e160 < t

   1. Initial program 33.3%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

      9. distribute-rgt-out-- N/A

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 83.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 81.8%

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

   if -1.30000000000000002e-17 < t < 1.4000000000000001e24

   1. Initial program 89.0%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 82.5

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

   5. Applied rewrites 82.5%

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

   if 1.4000000000000001e24 < t < 4.8000000000000003e160

   1. Initial program 56.9%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 75.0

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

   5. Applied rewrites 75.0%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y - x}{a}, x\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+160}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-239}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{a}, x\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+23}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-x}{a}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ x t) (- z a) y)))
   (if (<= t -1.2e-17)
     t_1
     (if (<= t 7.8e-239)
       (fma (- z t) (/ y a) x)
       (if (<= t 1.5e+23) (fma (/ (- x) a) z 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);
	double tmp;
	if (t <= -1.2e-17) {
		tmp = t_1;
	} else if (t <= 7.8e-239) {
		tmp = fma((z - t), (y / a), x);
	} else if (t <= 1.5e+23) {
		tmp = fma((-x / a), z, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x / t), Float64(z - a), y)
	tmp = 0.0
	if (t <= -1.2e-17)
		tmp = t_1;
	elseif (t <= 7.8e-239)
		tmp = fma(Float64(z - t), Float64(y / a), x);
	elseif (t <= 1.5e+23)
		tmp = fma(Float64(Float64(-x) / a), z, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[t, -1.2e-17], t$95$1, If[LessEqual[t, 7.8e-239], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 1.5e+23], N[(N[((-x) / a), $MachinePrecision] * z + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.19999999999999993e-17 or 1.5e23 < t

   1. Initial program 40.3%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

      9. distribute-rgt-out-- N/A

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 79.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 71.6%

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

   if -1.19999999999999993e-17 < t < 7.8e-239

   1. Initial program 88.6%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 85.7

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

   5. Applied rewrites 85.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 74.1%

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

   if 7.8e-239 < t < 1.5e23

   1. Initial program 89.5%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 76.0

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

   5. Applied rewrites 76.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 70.9%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-239}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{a}, x\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+23}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-x}{a}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \mathbf{if}\;t \leq -1.56 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-239}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+23}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-x}{a}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ x t) (- z a) y)))
   (if (<= t -1.56e-55)
     t_1
     (if (<= t 7.8e-239)
       (fma (/ y a) z x)
       (if (<= t 1.5e+23) (fma (/ (- x) a) z 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);
	double tmp;
	if (t <= -1.56e-55) {
		tmp = t_1;
	} else if (t <= 7.8e-239) {
		tmp = fma((y / a), z, x);
	} else if (t <= 1.5e+23) {
		tmp = fma((-x / a), z, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x / t), Float64(z - a), y)
	tmp = 0.0
	if (t <= -1.56e-55)
		tmp = t_1;
	elseif (t <= 7.8e-239)
		tmp = fma(Float64(y / a), z, x);
	elseif (t <= 1.5e+23)
		tmp = fma(Float64(Float64(-x) / a), z, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[t, -1.56e-55], t$95$1, If[LessEqual[t, 7.8e-239], N[(N[(y / a), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[t, 1.5e+23], N[(N[((-x) / a), $MachinePrecision] * z + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.56e-55 or 1.5e23 < t

   1. Initial program 43.9%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

      9. distribute-rgt-out-- N/A

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 74.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 68.1%

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

   if -1.56e-55 < t < 7.8e-239

   1. Initial program 89.7%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 85.8

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

   5. Applied rewrites 85.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 74.3%

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

   if 7.8e-239 < t < 1.5e23

   1. Initial program 89.5%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 76.0

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

   5. Applied rewrites 76.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 70.9%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.56 \cdot 10^{-55}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-239}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+23}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-x}{a}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 46.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1, y - x, x\right)\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.56 \cdot 10^{-55}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+93}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma 1.0 (- y x) x)))
   (if (<= t -2.6e+67)
     t_1
     (if (<= t -1.56e-55)
       (/ (* (- z t) y) a)
       (if (<= t 2.4e+93) (fma (/ y a) z x) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(1.0, (y - x), x);
	double tmp;
	if (t <= -2.6e+67) {
		tmp = t_1;
	} else if (t <= -1.56e-55) {
		tmp = ((z - t) * y) / a;
	} else if (t <= 2.4e+93) {
		tmp = fma((y / a), z, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(1.0, Float64(y - x), x)
	tmp = 0.0
	if (t <= -2.6e+67)
		tmp = t_1;
	elseif (t <= -1.56e-55)
		tmp = Float64(Float64(Float64(z - t) * y) / a);
	elseif (t <= 2.4e+93)
		tmp = fma(Float64(y / a), z, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(1.0 * N[(y - x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -2.6e+67], t$95$1, If[LessEqual[t, -1.56e-55], N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 2.4e+93], N[(N[(y / a), $MachinePrecision] * z + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.6e67 or 2.4000000000000001e93 < t

   1. Initial program 31.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 76.7

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

   4. Applied rewrites 76.7%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{1}, y - x, x\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 57.7%

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

   if -2.6e67 < t < -1.56e-55

   1. Initial program 67.7%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 52.4

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

   5. Applied rewrites 52.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 39.5%

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

   if -1.56e-55 < t < 2.4000000000000001e93

   1. Initial program 86.1%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 73.5

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

   5. Applied rewrites 73.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 55.4%

      \[\leadsto \mathsf{fma}\left(\frac{y}{a}, z, x\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+67}:\\ \;\;\;\;\mathsf{fma}\left(1, y - x, x\right)\\ \mathbf{elif}\;t \leq -1.56 \cdot 10^{-55}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+93}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1, y - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 70.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-13} \lor \neg \left(t \leq 2 \cdot 10^{+25}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5e-13) (not (<= t 2e+25)))
   (fma (/ x t) (- z a) y)
   (fma (/ z a) (- y x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5e-13) || !(t <= 2e+25)) {
		tmp = fma((x / t), (z - a), y);
	} else {
		tmp = fma((z / a), (y - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5e-13) || !(t <= 2e+25))
		tmp = fma(Float64(x / t), Float64(z - a), y);
	else
		tmp = fma(Float64(z / a), Float64(y - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5e-13], N[Not[LessEqual[t, 2e+25]], $MachinePrecision]], N[(N[(x / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + y), $MachinePrecision], N[(N[(z / a), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.9999999999999999e-13 or 2.00000000000000018e25 < t

   1. Initial program 39.8%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

      9. distribute-rgt-out-- N/A

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 78.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 72.2%

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

   if -4.9999999999999999e-13 < t < 2.00000000000000018e25

   1. Initial program 89.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 94.9

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

   4. Applied rewrites 94.9%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 78.1

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

   7. Applied rewrites 78.1%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-13} \lor \neg \left(t \leq 2 \cdot 10^{+25}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 69.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-17} \lor \neg \left(t \leq 2 \cdot 10^{+25}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{a}, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.3e-17) (not (<= t 2e+25)))
   (fma (/ x t) (- z a) y)
   (fma (/ (- y x) a) z x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.3e-17) || !(t <= 2e+25)) {
		tmp = fma((x / t), (z - a), y);
	} else {
		tmp = fma(((y - x) / a), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.3e-17) || !(t <= 2e+25))
		tmp = fma(Float64(x / t), Float64(z - a), y);
	else
		tmp = fma(Float64(Float64(y - x) / a), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.3e-17], N[Not[LessEqual[t, 2e+25]], $MachinePrecision]], N[(N[(x / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + y), $MachinePrecision], N[(N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.30000000000000002e-17 or 2.00000000000000018e25 < t

   1. Initial program 39.8%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

      9. distribute-rgt-out-- N/A

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 78.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 72.2%

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

   if -1.30000000000000002e-17 < t < 2.00000000000000018e25

   1. Initial program 89.1%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 77.8

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

   5. Applied rewrites 77.8%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-17} \lor \neg \left(t \leq 2 \cdot 10^{+25}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z - a, y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{a}, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 48.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+67} \lor \neg \left(t \leq 2.4 \cdot 10^{+93}\right):\\ \;\;\;\;\mathsf{fma}\left(1, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -9e+67) (not (<= t 2.4e+93)))
   (fma 1.0 (- y x) x)
   (fma (/ y a) z x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9e+67) || !(t <= 2.4e+93)) {
		tmp = fma(1.0, (y - x), x);
	} else {
		tmp = fma((y / a), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -9e+67) || !(t <= 2.4e+93))
		tmp = fma(1.0, Float64(y - x), x);
	else
		tmp = fma(Float64(y / a), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -9e+67], N[Not[LessEqual[t, 2.4e+93]], $MachinePrecision]], N[(1.0 * N[(y - x), $MachinePrecision] + x), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.9999999999999997e67 or 2.4000000000000001e93 < t

   1. Initial program 31.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 76.7

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

   4. Applied rewrites 76.7%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{1}, y - x, x\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 57.7%

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

   if -8.9999999999999997e67 < t < 2.4000000000000001e93

   1. Initial program 83.5%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 67.3

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

   5. Applied rewrites 67.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 50.7%

      \[\leadsto \mathsf{fma}\left(\frac{y}{a}, z, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+67} \lor \neg \left(t \leq 2.4 \cdot 10^{+93}\right):\\ \;\;\;\;\mathsf{fma}\left(1, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 34.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.56 \cdot 10^{-55} \lor \neg \left(t \leq 5 \cdot 10^{+24}\right):\\ \;\;\;\;\mathsf{fma}\left(1, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{x}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.56e-55) (not (<= t 5e+24)))
   (fma 1.0 (- y x) x)
   (fma t (/ x a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.56e-55) || !(t <= 5e+24)) {
		tmp = fma(1.0, (y - x), x);
	} else {
		tmp = fma(t, (x / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.56e-55) || !(t <= 5e+24))
		tmp = fma(1.0, Float64(y - x), x);
	else
		tmp = fma(t, Float64(x / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.56e-55], N[Not[LessEqual[t, 5e+24]], $MachinePrecision]], N[(1.0 * N[(y - x), $MachinePrecision] + x), $MachinePrecision], N[(t * N[(x / a), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.56e-55 or 5.00000000000000045e24 < t

   1. Initial program 43.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 76.7

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

   4. Applied rewrites 76.7%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{1}, y - x, x\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 43.5%

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

   if -1.56e-55 < t < 5.00000000000000045e24

   1. Initial program 89.6%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 84.0

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

   5. Applied rewrites 84.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 65.5%

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

   9. Taylor expanded in z around 0

      \[\leadsto x + \frac{t \cdot x}{\color{blue}{a}} \]
   10. Step-by-step derivation

   11. Applied rewrites 44.5%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.56 \cdot 10^{-55} \lor \neg \left(t \leq 5 \cdot 10^{+24}\right):\\ \;\;\;\;\mathsf{fma}\left(1, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{x}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-43} \lor \neg \left(t \leq 3.2 \cdot 10^{-91}\right):\\ \;\;\;\;\mathsf{fma}\left(1, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.1e-43) (not (<= t 3.2e-91)))
   (fma 1.0 (- y x) x)
   (/ (* y z) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.1e-43) || !(t <= 3.2e-91)) {
		tmp = fma(1.0, (y - x), x);
	} else {
		tmp = (y * z) / a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.1e-43) || !(t <= 3.2e-91))
		tmp = fma(1.0, Float64(y - x), x);
	else
		tmp = Float64(Float64(y * z) / a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.1e-43], N[Not[LessEqual[t, 3.2e-91]], $MachinePrecision]], N[(1.0 * N[(y - x), $MachinePrecision] + x), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.0999999999999999e-43 or 3.19999999999999996e-91 < t

   1. Initial program 50.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 79.5

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

   4. Applied rewrites 79.5%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{1}, y - x, x\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 38.9%

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

   if -3.0999999999999999e-43 < t < 3.19999999999999996e-91

   1. Initial program 89.9%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 83.8

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

   5. Applied rewrites 83.8%

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

   6. Taylor expanded in x around 0

      \[\leadsto \frac{y \cdot z}{\color{blue}{a}} \]
   7. Step-by-step derivation

   8. Applied rewrites 27.2%

      \[\leadsto \frac{y \cdot z}{\color{blue}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-43} \lor \neg \left(t \leq 3.2 \cdot 10^{-91}\right):\\ \;\;\;\;\mathsf{fma}\left(1, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 19.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(1, y - x, x\right) \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (fma 1.0 (- y x) x))

C

double code(double x, double y, double z, double t, double a) {
	return fma(1.0, (y - x), x);
}

Julia

function code(x, y, z, t, a)
	return fma(1.0, Float64(y - x), x)
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(1.0 * N[(y - x), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 66.6%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-/l* N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-/.f64 85.9

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

4. Applied rewrites 85.9%

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

5. Taylor expanded in t around inf

   \[\leadsto \mathsf{fma}\left(\color{blue}{1}, y - x, x\right) \]
6. Step-by-step derivation

7. Applied rewrites 24.5%

   \[\leadsto \mathsf{fma}\left(\color{blue}{1}, y - x, x\right) \]
8. Add Preprocessing

Alternative 21: 2.8% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(1, -x, x\right) \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (fma 1.0 (- x) x))

C

double code(double x, double y, double z, double t, double a) {
	return fma(1.0, -x, x);
}

Julia

function code(x, y, z, t, a)
	return fma(1.0, Float64(-x), x)
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(1.0 * (-x) + x), $MachinePrecision]

Derivation

1. Initial program 66.6%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-/l* N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-/.f64 85.9

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

4. Applied rewrites 85.9%

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

5. Taylor expanded in t around inf

   \[\leadsto \mathsf{fma}\left(\color{blue}{1}, y - x, x\right) \]
6. Step-by-step derivation

7. Applied rewrites 24.5%

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

8. Taylor expanded in x around inf

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

   1. mul-1-neg N/A

      \[\leadsto \mathsf{fma}\left(1, \color{blue}{\mathsf{neg}\left(x\right)}, x\right) \]

   2. lower-neg.f64 2.7

      \[\leadsto \mathsf{fma}\left(1, \color{blue}{-x}, x\right) \]

10. Applied rewrites 2.7%

    \[\leadsto \mathsf{fma}\left(1, \color{blue}{-x}, x\right) \]
11. Add Preprocessing

Developer Target 1: 86.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} 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 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - x))
    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 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024352 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< a -646122513817703/4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t)))) (if (< a 1887201585041587/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t)))))))

  (+ x (/ (* (- y x) (- z t)) (- a t))))