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

Percentage Accurate: 67.6% → 89.5%

Time: 10.2s

Alternatives: 18

Speedup: 0.3×

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: 67.6% 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: 89.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-197}:\\ \;\;\;\;x + \left(y - x\right) \cdot t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\mathsf{fma}\left(\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}, -1, y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, t\_1, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))) (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 -5e-197)
     (+ x (* (- y x) t_1))
     (if (<= t_2 0.0)
       (fma (/ (* (- y x) (- z a)) t) -1.0 y)
       (fma (- y x) t_1 x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -5e-197) {
		tmp = x + ((y - x) * t_1);
	} else if (t_2 <= 0.0) {
		tmp = fma((((y - x) * (z - a)) / t), -1.0, y);
	} else {
		tmp = fma((y - x), t_1, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -5e-197)
		tmp = Float64(x + Float64(Float64(y - x) * t_1));
	elseif (t_2 <= 0.0)
		tmp = fma(Float64(Float64(Float64(y - x) * Float64(z - a)) / t), -1.0, y);
	else
		tmp = fma(Float64(y - x), t_1, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-197], N[(x + N[(N[(y - x), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(N[(N[(N[(y - x), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] * -1.0 + y), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * t$95$1 + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -5.0000000000000002e-197

   1. Initial program 75.4%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

      7. sub-div N/A

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

      8. lower-*.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-div N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 92.6

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

   4. Applied rewrites 92.6%

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

   if -5.0000000000000002e-197 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.4%

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

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. sub-div N/A

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

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

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

      6. associate-*r/ N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   5. Applied rewrites 100.0%

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

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

   1. Initial program 70.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 86.5

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

   4. Applied rewrites 86.5%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-197}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;\mathsf{fma}\left(\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}, -1, y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-197} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}, -1, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -5e-197) (not (<= t_1 0.0)))
     (fma (- y x) (/ (- z t) (- a t)) x)
     (fma (/ (* (- y x) (- z a)) t) -1.0 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 <= -5e-197) || !(t_1 <= 0.0)) {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	} else {
		tmp = fma((((y - x) * (z - a)) / t), -1.0, 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 <= -5e-197) || !(t_1 <= 0.0))
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	else
		tmp = fma(Float64(Float64(Float64(y - x) * Float64(z - a)) / t), -1.0, 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, -5e-197], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(N[(y - x), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] * -1.0 + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -5.0000000000000002e-197 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 72.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 89.7

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

   4. Applied rewrites 89.7%

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

   if -5.0000000000000002e-197 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.4%

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

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. sub-div N/A

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

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

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

      6. associate-*r/ N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   5. Applied rewrites 100.0%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-197} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}, -1, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-197} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a \cdot \left(y - x\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -5e-197) (not (<= t_1 0.0)))
     (fma (- y x) (/ (- z t) (- a t)) x)
     (+ y (/ (* a (- y x)) 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 <= -5e-197) || !(t_1 <= 0.0)) {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	} else {
		tmp = y + ((a * (y - x)) / 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 <= -5e-197) || !(t_1 <= 0.0))
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	else
		tmp = Float64(y + Float64(Float64(a * Float64(y - x)) / 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, -5e-197], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y + N[(N[(a * N[(y - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -5.0000000000000002e-197 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 72.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 89.7

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

   4. Applied rewrites 89.7%

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

   if -5.0000000000000002e-197 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.4%

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

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. sub-div N/A

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

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

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

      6. associate-*r/ N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 83.1

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

   8. Applied rewrites 83.1%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-197} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a \cdot \left(y - x\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{a \cdot \left(y - x\right)}{t}\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-228}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a - t}, x\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+98}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ (* a (- y x)) t))))
   (if (<= t -4.4e+89)
     t_1
     (if (<= t -2.8e-228)
       (fma y (/ z (- a t)) x)
       (if (<= t 1.1e+98) (fma (- y x) (/ z a) x) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((a * (y - x)) / t);
	double tmp;
	if (t <= -4.4e+89) {
		tmp = t_1;
	} else if (t <= -2.8e-228) {
		tmp = fma(y, (z / (a - t)), x);
	} else if (t <= 1.1e+98) {
		tmp = fma((y - x), (z / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(a * Float64(y - x)) / t))
	tmp = 0.0
	if (t <= -4.4e+89)
		tmp = t_1;
	elseif (t <= -2.8e-228)
		tmp = fma(y, Float64(z / Float64(a - t)), x);
	elseif (t <= 1.1e+98)
		tmp = fma(Float64(y - 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[(y + N[(N[(a * N[(y - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.4e+89], t$95$1, If[LessEqual[t, -2.8e-228], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 1.1e+98], N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.4e89 or 1.10000000000000004e98 < t

   1. Initial program 36.7%

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

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. sub-div N/A

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

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

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

      6. associate-*r/ N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   5. Applied rewrites 65.1%

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

   6. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 56.7

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

   8. Applied rewrites 56.7%

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

   if -4.4e89 < t < -2.8000000000000003e-228

   1. Initial program 86.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 89.9

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

   4. Applied rewrites 89.9%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 82.6

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

   7. Applied rewrites 82.6%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 64.7%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 60.7%

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

   if -2.8000000000000003e-228 < t < 1.10000000000000004e98

   1. Initial program 82.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 95.9

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

   4. Applied rewrites 95.9%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 69.9

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

   7. Applied rewrites 69.9%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+89}:\\ \;\;\;\;y + \frac{a \cdot \left(y - x\right)}{t}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-228}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a - t}, x\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+98}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a \cdot \left(y - x\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+116}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-228}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a - t}, x\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.25e+116)
   y
   (if (<= t -2.8e-228)
     (fma y (/ z (- a t)) x)
     (if (<= t 1.4e+88) (fma (- y x) (/ z a) x) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.25e+116) {
		tmp = y;
	} else if (t <= -2.8e-228) {
		tmp = fma(y, (z / (a - t)), x);
	} else if (t <= 1.4e+88) {
		tmp = fma((y - x), (z / a), x);
	} else {
		tmp = y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.25e+116)
		tmp = y;
	elseif (t <= -2.8e-228)
		tmp = fma(y, Float64(z / Float64(a - t)), x);
	elseif (t <= 1.4e+88)
		tmp = fma(Float64(y - x), Float64(z / a), x);
	else
		tmp = y;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.25e+116], y, If[LessEqual[t, -2.8e-228], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 1.4e+88], N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision] + x), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.25000000000000006e116 or 1.39999999999999994e88 < t

   1. Initial program 37.9%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{y} \]
   4. Step-by-step derivation

   5. Applied rewrites 48.8%

      \[\leadsto \color{blue}{y} \]

   if -1.25000000000000006e116 < t < -2.8000000000000003e-228

   1. Initial program 84.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 89.2

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

   4. Applied rewrites 89.2%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 82.2

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

   7. Applied rewrites 82.2%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 64.0%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 60.2%

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

   if -2.8000000000000003e-228 < t < 1.39999999999999994e88

   1. Initial program 83.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 95.7

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

   4. Applied rewrites 95.7%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 70.6

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

   7. Applied rewrites 70.6%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+116}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-228}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a - t}, x\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+116}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-236}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a - t}, x\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.25e+116)
   y
   (if (<= t -9e-236)
     (fma y (/ z (- a t)) x)
     (if (<= t 1.4e+88) (fma z (/ (- y x) a) x) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.25e+116) {
		tmp = y;
	} else if (t <= -9e-236) {
		tmp = fma(y, (z / (a - t)), x);
	} else if (t <= 1.4e+88) {
		tmp = fma(z, ((y - x) / a), x);
	} else {
		tmp = y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.25e+116)
		tmp = y;
	elseif (t <= -9e-236)
		tmp = fma(y, Float64(z / Float64(a - t)), x);
	elseif (t <= 1.4e+88)
		tmp = fma(z, Float64(Float64(y - x) / a), x);
	else
		tmp = y;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.25e+116], y, If[LessEqual[t, -9e-236], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 1.4e+88], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.25000000000000006e116 or 1.39999999999999994e88 < t

   1. Initial program 37.9%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{y} \]
   4. Step-by-step derivation

   5. Applied rewrites 48.8%

      \[\leadsto \color{blue}{y} \]

   if -1.25000000000000006e116 < t < -8.99999999999999997e-236

   1. Initial program 85.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 89.7

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

   4. Applied rewrites 89.7%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 80.7

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

   7. Applied rewrites 80.7%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 63.4%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 61.1%

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

   if -8.99999999999999997e-236 < t < 1.39999999999999994e88

   1. Initial program 82.4%

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

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 67.4

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

   5. Applied rewrites 67.4%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+116}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-236}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a - t}, x\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 39.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+161}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-155}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{-240}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.6e+161)
   x
   (if (<= a -3.3e-155)
     (+ x y)
     (if (<= a 7.4e-240) (* x (/ (- z a) t)) (if (<= a 4.5e+75) y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.6e+161) {
		tmp = x;
	} else if (a <= -3.3e-155) {
		tmp = x + y;
	} else if (a <= 7.4e-240) {
		tmp = x * ((z - a) / t);
	} else if (a <= 4.5e+75) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.6d+161)) then
        tmp = x
    else if (a <= (-3.3d-155)) then
        tmp = x + y
    else if (a <= 7.4d-240) then
        tmp = x * ((z - a) / t)
    else if (a <= 4.5d+75) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.6e+161) {
		tmp = x;
	} else if (a <= -3.3e-155) {
		tmp = x + y;
	} else if (a <= 7.4e-240) {
		tmp = x * ((z - a) / t);
	} else if (a <= 4.5e+75) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.6e+161:
		tmp = x
	elif a <= -3.3e-155:
		tmp = x + y
	elif a <= 7.4e-240:
		tmp = x * ((z - a) / t)
	elif a <= 4.5e+75:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.6e+161)
		tmp = x;
	elseif (a <= -3.3e-155)
		tmp = Float64(x + y);
	elseif (a <= 7.4e-240)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (a <= 4.5e+75)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.6e+161)
		tmp = x;
	elseif (a <= -3.3e-155)
		tmp = x + y;
	elseif (a <= 7.4e-240)
		tmp = x * ((z - a) / t);
	elseif (a <= 4.5e+75)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.6e+161], x, If[LessEqual[a, -3.3e-155], N[(x + y), $MachinePrecision], If[LessEqual[a, 7.4e-240], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e+75], y, x]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.59999999999999984e161 or 4.5000000000000004e75 < a

   1. Initial program 65.8%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Applied rewrites 55.9%

      \[\leadsto \color{blue}{x} \]

   if -3.59999999999999984e161 < a < -3.29999999999999986e-155

   1. Initial program 72.0%

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

   3. Taylor expanded in t around inf

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

      1. lift--.f64 28.9

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

   5. Applied rewrites 28.9%

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

   6. Taylor expanded in x around 0

      \[\leadsto x + y \]
   7. Step-by-step derivation

   8. Applied rewrites 35.7%

      \[\leadsto x + y \]

   if -3.29999999999999986e-155 < a < 7.4000000000000003e-240

   1. Initial program 69.1%

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

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. sub-div N/A

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

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

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

      6. associate-*r/ N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   5. Applied rewrites 86.0%

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

   6. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 43.9

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

   8. Applied rewrites 43.9%

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

   if 7.4000000000000003e-240 < a < 4.5000000000000004e75

   1. Initial program 64.8%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{y} \]
   4. Step-by-step derivation

   5. Applied rewrites 43.6%

      \[\leadsto \color{blue}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+161}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-155}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{-240}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+93} \lor \neg \left(x \leq 6.4 \cdot 10^{-149}\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -4.7e+93) (not (<= x 6.4e-149)))
   (fma (- y x) (/ z (- a t)) x)
   (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.7e+93) || !(x <= 6.4e-149)) {
		tmp = fma((y - x), (z / (a - t)), x);
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -4.7e+93) || !(x <= 6.4e-149))
		tmp = fma(Float64(y - x), Float64(z / Float64(a - t)), x);
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -4.7e+93], N[Not[LessEqual[x, 6.4e-149]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.6999999999999998e93 or 6.40000000000000004e-149 < x

   1. Initial program 64.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 79.9

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

   4. Applied rewrites 79.9%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 68.7%

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

   if -4.6999999999999998e93 < x < 6.40000000000000004e-149

   1. Initial program 71.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 88.2

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

   4. Applied rewrites 88.2%

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

   5. Taylor expanded in y around inf

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

      1. sub-div N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 80.5

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

   7. Applied rewrites 80.5%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+93} \lor \neg \left(x \leq 6.4 \cdot 10^{-149}\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+73} \lor \neg \left(a \leq 9.8 \cdot 10^{-57}\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.15e+73) (not (<= a 9.8e-57)))
   (fma (- y x) (/ (- z t) a) x)
   (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.15e+73) || !(a <= 9.8e-57)) {
		tmp = fma((y - x), ((z - t) / a), x);
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.15e+73) || !(a <= 9.8e-57))
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / a), x);
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.15e+73], N[Not[LessEqual[a, 9.8e-57]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.15e73 or 9.79999999999999976e-57 < a

   1. Initial program 68.8%

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

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 74.0

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

   5. Applied rewrites 74.0%

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

   if -1.15e73 < a < 9.79999999999999976e-57

   1. Initial program 67.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 80.0

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

   4. Applied rewrites 80.0%

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

   5. Taylor expanded in y around inf

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

      1. sub-div N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 71.6

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

   7. Applied rewrites 71.6%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+73} \lor \neg \left(a \leq 9.8 \cdot 10^{-57}\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+74} \lor \neg \left(a \leq 9.8 \cdot 10^{-57}\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.45e+74) (not (<= a 9.8e-57)))
   (fma (- y x) (/ z a) x)
   (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.45e+74) || !(a <= 9.8e-57)) {
		tmp = fma((y - x), (z / a), x);
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.45e+74) || !(a <= 9.8e-57))
		tmp = fma(Float64(y - x), Float64(z / a), x);
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.45e+74], N[Not[LessEqual[a, 9.8e-57]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.4500000000000001e74 or 9.79999999999999976e-57 < a

   1. Initial program 68.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 87.1

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

   4. Applied rewrites 87.1%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 66.9

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

   7. Applied rewrites 66.9%

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

   if -1.4500000000000001e74 < a < 9.79999999999999976e-57

   1. Initial program 67.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 80.0

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

   4. Applied rewrites 80.0%

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

   5. Taylor expanded in y around inf

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

      1. sub-div N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 71.6

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

   7. Applied rewrites 71.6%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+74} \lor \neg \left(a \leq 9.8 \cdot 10^{-57}\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+54} \lor \neg \left(a \leq 9.8 \cdot 10^{-57}\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.4e+54) (not (<= a 9.8e-57)))
   (fma (- y x) (/ z a) x)
   (/ (* (- z t) y) (- a t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.4e+54) || !(a <= 9.8e-57)) {
		tmp = fma((y - x), (z / a), x);
	} else {
		tmp = ((z - t) * y) / (a - t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.4e+54) || !(a <= 9.8e-57))
		tmp = fma(Float64(y - x), Float64(z / a), x);
	else
		tmp = Float64(Float64(Float64(z - t) * y) / Float64(a - t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.4e+54], N[Not[LessEqual[a, 9.8e-57]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.4000000000000001e54 or 9.79999999999999976e-57 < a

   1. Initial program 67.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 86.8

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

   4. Applied rewrites 86.8%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 66.4

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

   7. Applied rewrites 66.4%

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

   if -3.4000000000000001e54 < a < 9.79999999999999976e-57

   1. Initial program 68.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 59.2

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

   5. Applied rewrites 59.2%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+54} \lor \neg \left(a \leq 9.8 \cdot 10^{-57}\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+115}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.5e+115) y (if (<= t 1.4e+88) (fma z (/ (- y x) a) x) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.5e+115) {
		tmp = y;
	} else if (t <= 1.4e+88) {
		tmp = fma(z, ((y - x) / a), x);
	} else {
		tmp = y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.5e+115)
		tmp = y;
	elseif (t <= 1.4e+88)
		tmp = fma(z, Float64(Float64(y - x) / a), x);
	else
		tmp = y;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.5e+115], y, If[LessEqual[t, 1.4e+88], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -9.4999999999999997e115 or 1.39999999999999994e88 < t

   1. Initial program 37.9%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{y} \]
   4. Step-by-step derivation

   5. Applied rewrites 48.8%

      \[\leadsto \color{blue}{y} \]

   if -9.4999999999999997e115 < t < 1.39999999999999994e88

   1. Initial program 83.7%

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

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 60.9

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

   5. Applied rewrites 60.9%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+115}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+117}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+194}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.2e+117)
   y
   (if (<= t 4.9e+30) (+ x (/ (* y z) a)) (if (<= t 1.12e+194) (+ x y) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.2e+117) {
		tmp = y;
	} else if (t <= 4.9e+30) {
		tmp = x + ((y * z) / a);
	} else if (t <= 1.12e+194) {
		tmp = x + y;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.2d+117)) then
        tmp = y
    else if (t <= 4.9d+30) then
        tmp = x + ((y * z) / a)
    else if (t <= 1.12d+194) then
        tmp = x + y
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.2e+117) {
		tmp = y;
	} else if (t <= 4.9e+30) {
		tmp = x + ((y * z) / a);
	} else if (t <= 1.12e+194) {
		tmp = x + y;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.2e+117:
		tmp = y
	elif t <= 4.9e+30:
		tmp = x + ((y * z) / a)
	elif t <= 1.12e+194:
		tmp = x + y
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.2e+117)
		tmp = y;
	elseif (t <= 4.9e+30)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (t <= 1.12e+194)
		tmp = Float64(x + y);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.2e+117)
		tmp = y;
	elseif (t <= 4.9e+30)
		tmp = x + ((y * z) / a);
	elseif (t <= 1.12e+194)
		tmp = x + y;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.2e+117], y, If[LessEqual[t, 4.9e+30], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.12e+194], N[(x + y), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.20000000000000005e117 or 1.11999999999999994e194 < t

   1. Initial program 30.2%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{y} \]
   4. Step-by-step derivation

   5. Applied rewrites 56.0%

      \[\leadsto \color{blue}{y} \]

   if -3.20000000000000005e117 < t < 4.89999999999999984e30

   1. Initial program 83.3%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 57.0

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

   5. Applied rewrites 57.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 49.8%

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

   if 4.89999999999999984e30 < t < 1.11999999999999994e194

   1. Initial program 63.9%

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

   3. Taylor expanded in t around inf

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

      1. lift--.f64 29.0

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

   5. Applied rewrites 29.0%

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

   6. Taylor expanded in x around 0

      \[\leadsto x + y \]
   7. Step-by-step derivation

   8. Applied rewrites 45.0%

      \[\leadsto x + y \]
3. Recombined 3 regimes into one program.

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+117}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+194}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 42.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+34}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+39}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.2e+34)
   (* z (/ (- y x) a))
   (if (<= z 1.9e+39) (+ x y) (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e+34) {
		tmp = z * ((y - x) / a);
	} else if (z <= 1.9e+39) {
		tmp = x + y;
	} else {
		tmp = z * (y / (a - t));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7.2d+34)) then
        tmp = z * ((y - x) / a)
    else if (z <= 1.9d+39) then
        tmp = x + y
    else
        tmp = z * (y / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e+34) {
		tmp = z * ((y - x) / a);
	} else if (z <= 1.9e+39) {
		tmp = x + y;
	} else {
		tmp = z * (y / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.2e+34:
		tmp = z * ((y - x) / a)
	elif z <= 1.9e+39:
		tmp = x + y
	else:
		tmp = z * (y / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.2e+34)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (z <= 1.9e+39)
		tmp = Float64(x + y);
	else
		tmp = Float64(z * Float64(y / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.2e+34)
		tmp = z * ((y - x) / a);
	elseif (z <= 1.9e+39)
		tmp = x + y;
	else
		tmp = z * (y / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.2e+34], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+39], N[(x + y), $MachinePrecision], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.2000000000000001e34

   1. Initial program 69.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 95.2

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

   4. Applied rewrites 95.2%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 81.6

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

   7. Applied rewrites 81.6%

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

   8. Taylor expanded in t around 0

      \[\leadsto z \cdot \frac{y - x}{a} \]
   9. Step-by-step derivation

   10. Applied rewrites 56.4%

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

   if -7.2000000000000001e34 < z < 1.8999999999999999e39

   1. Initial program 68.9%

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

   3. Taylor expanded in t around inf

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

      1. lift--.f64 25.8

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

   5. Applied rewrites 25.8%

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

   6. Taylor expanded in x around 0

      \[\leadsto x + y \]
   7. Step-by-step derivation

   8. Applied rewrites 45.0%

      \[\leadsto x + y \]

   if 1.8999999999999999e39 < z

   1. Initial program 63.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 89.1

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

   4. Applied rewrites 89.1%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 75.0

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

   7. Applied rewrites 75.0%

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

   8. Taylor expanded in x around 0

      \[\leadsto z \cdot \frac{y}{\color{blue}{a - t}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lift--.f64 41.6

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

   10. Applied rewrites 41.6%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+34}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+39}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 41.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+34}:\\ \;\;\;\;\frac{z \cdot \left(y - x\right)}{a}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+39}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.2e+34)
   (/ (* z (- y x)) a)
   (if (<= z 1.9e+39) (+ x y) (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e+34) {
		tmp = (z * (y - x)) / a;
	} else if (z <= 1.9e+39) {
		tmp = x + y;
	} else {
		tmp = z * (y / (a - t));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7.2d+34)) then
        tmp = (z * (y - x)) / a
    else if (z <= 1.9d+39) then
        tmp = x + y
    else
        tmp = z * (y / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e+34) {
		tmp = (z * (y - x)) / a;
	} else if (z <= 1.9e+39) {
		tmp = x + y;
	} else {
		tmp = z * (y / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.2e+34:
		tmp = (z * (y - x)) / a
	elif z <= 1.9e+39:
		tmp = x + y
	else:
		tmp = z * (y / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.2e+34)
		tmp = Float64(Float64(z * Float64(y - x)) / a);
	elseif (z <= 1.9e+39)
		tmp = Float64(x + y);
	else
		tmp = Float64(z * Float64(y / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.2e+34)
		tmp = (z * (y - x)) / a;
	elseif (z <= 1.9e+39)
		tmp = x + y;
	else
		tmp = z * (y / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.2e+34], N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 1.9e+39], N[(x + y), $MachinePrecision], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.2000000000000001e34

   1. Initial program 69.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 95.2

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

   4. Applied rewrites 95.2%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 81.6

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

   7. Applied rewrites 81.6%

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

   8. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 48.9

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

   10. Applied rewrites 48.9%

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

   if -7.2000000000000001e34 < z < 1.8999999999999999e39

   1. Initial program 68.9%

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

   3. Taylor expanded in t around inf

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

      1. lift--.f64 25.8

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

   5. Applied rewrites 25.8%

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

   6. Taylor expanded in x around 0

      \[\leadsto x + y \]
   7. Step-by-step derivation

   8. Applied rewrites 45.0%

      \[\leadsto x + y \]

   if 1.8999999999999999e39 < z

   1. Initial program 63.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 89.1

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

   4. Applied rewrites 89.1%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 75.0

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

   7. Applied rewrites 75.0%

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

   8. Taylor expanded in x around 0

      \[\leadsto z \cdot \frac{y}{\color{blue}{a - t}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lift--.f64 41.6

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

   10. Applied rewrites 41.6%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+34}:\\ \;\;\;\;\frac{z \cdot \left(y - x\right)}{a}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+39}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 40.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+34}:\\ \;\;\;\;\frac{z \cdot \left(y - x\right)}{a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+54}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.2e+34)
   (/ (* z (- y x)) a)
   (if (<= z 6e+54) (+ x y) (/ (* y z) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e+34) {
		tmp = (z * (y - x)) / a;
	} else if (z <= 6e+54) {
		tmp = x + y;
	} else {
		tmp = (y * z) / (a - t);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7.2d+34)) then
        tmp = (z * (y - x)) / a
    else if (z <= 6d+54) then
        tmp = x + y
    else
        tmp = (y * z) / (a - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e+34) {
		tmp = (z * (y - x)) / a;
	} else if (z <= 6e+54) {
		tmp = x + y;
	} else {
		tmp = (y * z) / (a - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.2e+34:
		tmp = (z * (y - x)) / a
	elif z <= 6e+54:
		tmp = x + y
	else:
		tmp = (y * z) / (a - t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.2e+34)
		tmp = Float64(Float64(z * Float64(y - x)) / a);
	elseif (z <= 6e+54)
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(y * z) / Float64(a - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.2e+34)
		tmp = (z * (y - x)) / a;
	elseif (z <= 6e+54)
		tmp = x + y;
	else
		tmp = (y * z) / (a - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.2e+34], N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 6e+54], N[(x + y), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.2000000000000001e34

   1. Initial program 69.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 95.2

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

   4. Applied rewrites 95.2%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 81.6

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

   7. Applied rewrites 81.6%

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

   8. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 48.9

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

   10. Applied rewrites 48.9%

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

   if -7.2000000000000001e34 < z < 5.9999999999999998e54

   1. Initial program 68.7%

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

   3. Taylor expanded in t around inf

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

      1. lift--.f64 26.1

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

   5. Applied rewrites 26.1%

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

   6. Taylor expanded in x around 0

      \[\leadsto x + y \]
   7. Step-by-step derivation

   8. Applied rewrites 45.1%

      \[\leadsto x + y \]

   if 5.9999999999999998e54 < z

   1. Initial program 64.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 88.7

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

   4. Applied rewrites 88.7%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 75.9

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

   7. Applied rewrites 75.9%

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

   8. Taylor expanded in x around 0

      \[\leadsto \frac{y \cdot z}{\color{blue}{a - t}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 36.1

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

   10. Applied rewrites 36.1%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+34}:\\ \;\;\;\;\frac{z \cdot \left(y - x\right)}{a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+54}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 39.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.3e+73) x (if (<= a 4.5e+75) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.3e+73) {
		tmp = x;
	} else if (a <= 4.5e+75) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.3d+73)) then
        tmp = x
    else if (a <= 4.5d+75) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.3e+73) {
		tmp = x;
	} else if (a <= 4.5e+75) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.3e+73:
		tmp = x
	elif a <= 4.5e+75:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.3e+73)
		tmp = x;
	elseif (a <= 4.5e+75)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.3e+73)
		tmp = x;
	elseif (a <= 4.5e+75)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.3e+73], x, If[LessEqual[a, 4.5e+75], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.3e73 or 4.5000000000000004e75 < a

   1. Initial program 67.1%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Applied rewrites 46.4%

      \[\leadsto \color{blue}{x} \]

   if -1.3e73 < a < 4.5000000000000004e75

   1. Initial program 68.5%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{y} \]
   4. Step-by-step derivation

   5. Applied rewrites 37.4%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 24.8% accurate, 29.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

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
end function

Java

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

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 67.9%

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

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Applied rewrites 23.5%

   \[\leadsto \color{blue}{x} \]

6. Final simplification 23.5%

   \[\leadsto x \]
7. Add Preprocessing

Developer Target 1: 86.4% 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 2025037 
(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))))