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

Percentage Accurate: 67.0% → 88.9%

Time: 5.2s

Alternatives: 18

Speedup: 0.7×

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: 67.0% 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: 88.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - z}{t - a}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-154}:\\ \;\;\;\;\mathsf{fma}\left(y - x, t\_1, x\right)\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{t \cdot y - \left(y - x\right) \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t z) (- t a))) (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 -5e-154)
     (fma (- y x) t_1 x)
     (if (<= t_2 0.0)
       (/ (- (* t y) (* (- y x) (- z a))) t)
       (+ x (* (- y x) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) / (t - a);
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -5e-154) {
		tmp = fma((y - x), t_1, x);
	} else if (t_2 <= 0.0) {
		tmp = ((t * y) - ((y - x) * (z - a))) / t;
	} else {
		tmp = x + ((y - x) * t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - z) / Float64(t - a))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -5e-154)
		tmp = fma(Float64(y - x), t_1, x);
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(Float64(t * y) - Float64(Float64(y - x) * Float64(z - a))) / t);
	else
		tmp = Float64(x + Float64(Float64(y - x) * t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] / N[(t - a), $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-154], N[(N[(y - x), $MachinePrecision] * t$95$1 + x), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(N[(N[(t * y), $MachinePrecision] - N[(N[(y - x), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * t$95$1), $MachinePrecision]), $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-154

   1. Initial program 70.8%

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

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

      6. lift--.f64 N/A

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

      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. sub-negate N/A

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

      14. sub-negate N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 N/A

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

      18. lower--.f64 89.8

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

   3. Applied rewrites 89.8%

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

   if -5.0000000000000002e-154 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 27.4%

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

   2. Taylor expanded in t around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 79.7

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

   4. Applied rewrites 79.7%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 79.3

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

   7. Applied rewrites 79.3%

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

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

   1. Initial program 71.8%

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

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

      5. lift--.f64 N/A

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

      6. 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. sub-negate N/A

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

      12. sub-negate N/A

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

      13. frac-2neg-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lower--.f64 90.0

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

   3. Applied rewrites 90.0%

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

Alternative 2: 88.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - z}{t - a}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-154}:\\ \;\;\;\;\mathsf{fma}\left(y - x, t\_1, x\right)\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t} + y\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t z) (- t a))) (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 -5e-154)
     (fma (- y x) t_1 x)
     (if (<= t_2 0.0) (+ (/ (* x (- z a)) t) y) (+ x (* (- y x) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) / (t - a);
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -5e-154) {
		tmp = fma((y - x), t_1, x);
	} else if (t_2 <= 0.0) {
		tmp = ((x * (z - a)) / t) + y;
	} else {
		tmp = x + ((y - x) * t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - z) / Float64(t - a))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -5e-154)
		tmp = fma(Float64(y - x), t_1, x);
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(Float64(x * Float64(z - a)) / t) + y);
	else
		tmp = Float64(x + Float64(Float64(y - x) * t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] / N[(t - a), $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-154], N[(N[(y - x), $MachinePrecision] * t$95$1 + x), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + y), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * t$95$1), $MachinePrecision]), $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-154

   1. Initial program 70.8%

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

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

      6. lift--.f64 N/A

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

      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. sub-negate N/A

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

      14. sub-negate N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 N/A

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

      18. lower--.f64 89.8

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

   3. Applied rewrites 89.8%

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

   if -5.0000000000000002e-154 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 27.4%

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

   2. Taylor expanded in t around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 79.7

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

   4. Applied rewrites 79.7%

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

   5. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 79.3

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

   7. Applied rewrites 79.3%

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

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

   1. Initial program 71.8%

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

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

      5. lift--.f64 N/A

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

      6. 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. sub-negate N/A

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

      12. sub-negate N/A

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

      13. frac-2neg-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lower--.f64 90.0

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

   3. Applied rewrites 90.0%

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

Alternative 3: 88.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - x, \frac{t - z}{t - a}, x\right)\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t} + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y x) (/ (- t z) (- t a)) x))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 -5e-154) t_1 (if (<= t_2 0.0) (+ (/ (* x (- z a)) t) y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - x), ((t - z) / (t - a)), x);
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -5e-154) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = ((x * (z - a)) / t) + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - x), Float64(Float64(t - z) / Float64(t - a)), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -5e-154)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(Float64(x * Float64(z - a)) / t) + y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] + x), $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-154], t$95$1, If[LessEqual[t$95$2, 0.0], N[(N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -5.0000000000000002e-154 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 71.3%

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

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

      6. lift--.f64 N/A

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

      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. sub-negate N/A

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

      14. sub-negate N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 N/A

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

      18. lower--.f64 89.9

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

   3. Applied rewrites 89.9%

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

   if -5.0000000000000002e-154 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 27.4%

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

   2. Taylor expanded in t around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 79.7

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

   4. Applied rewrites 79.7%

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

   5. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 79.3

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

   7. Applied rewrites 79.3%

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

Alternative 4: 69.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - x, \frac{z - t}{a}, x\right)\\ \mathbf{if}\;a \leq -1.12 \cdot 10^{-129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-217}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+34}:\\ \;\;\;\;\left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right) + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y x) (/ (- z t) a) x)))
   (if (<= a -1.12e-129)
     t_1
     (if (<= a -1.7e-217)
       (/ (* (- y x) z) (- a t))
       (if (<= a 3.4e+34) (+ (- (/ (* (- y x) (- z a)) t)) y) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - x), ((z - t) / a), x);
	double tmp;
	if (a <= -1.12e-129) {
		tmp = t_1;
	} else if (a <= -1.7e-217) {
		tmp = ((y - x) * z) / (a - t);
	} else if (a <= 3.4e+34) {
		tmp = -(((y - x) * (z - a)) / t) + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - x), Float64(Float64(z - t) / a), x)
	tmp = 0.0
	if (a <= -1.12e-129)
		tmp = t_1;
	elseif (a <= -1.7e-217)
		tmp = Float64(Float64(Float64(y - x) * z) / Float64(a - t));
	elseif (a <= 3.4e+34)
		tmp = Float64(Float64(-Float64(Float64(Float64(y - x) * Float64(z - a)) / t)) + y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -1.12e-129], t$95$1, If[LessEqual[a, -1.7e-217], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e+34], N[((-N[(N[(N[(y - x), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]) + y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.12000000000000006e-129 or 3.3999999999999999e34 < a

   1. Initial program 67.9%

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

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a}} \]
   3. 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 70.1

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

   4. Applied rewrites 70.1%

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

   if -1.12000000000000006e-129 < a < -1.70000000000000008e-217

   1. Initial program 63.1%

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

   2. Taylor expanded in z around inf

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

      1. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 53.9

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

   4. Applied rewrites 53.9%

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

   if -1.70000000000000008e-217 < a < 3.3999999999999999e34

   1. Initial program 66.3%

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

   2. Taylor expanded in t around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 73.3

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

   4. Applied rewrites 73.3%

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

Alternative 5: 68.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - x, \frac{z - t}{a}, x\right)\\ \mathbf{if}\;a \leq -1.12 \cdot 10^{-129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-217}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+34}:\\ \;\;\;\;y - \frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y x) (/ (- z t) a) x)))
   (if (<= a -1.12e-129)
     t_1
     (if (<= a -1.7e-217)
       (/ (* (- y x) z) (- a t))
       (if (<= a 3.4e+34) (- y (/ (* z (- y x)) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - x), ((z - t) / a), x);
	double tmp;
	if (a <= -1.12e-129) {
		tmp = t_1;
	} else if (a <= -1.7e-217) {
		tmp = ((y - x) * z) / (a - t);
	} else if (a <= 3.4e+34) {
		tmp = y - ((z * (y - x)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - x), Float64(Float64(z - t) / a), x)
	tmp = 0.0
	if (a <= -1.12e-129)
		tmp = t_1;
	elseif (a <= -1.7e-217)
		tmp = Float64(Float64(Float64(y - x) * z) / Float64(a - t));
	elseif (a <= 3.4e+34)
		tmp = Float64(y - Float64(Float64(z * Float64(y - x)) / t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -1.12e-129], t$95$1, If[LessEqual[a, -1.7e-217], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e+34], N[(y - N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.12000000000000006e-129 or 3.3999999999999999e34 < a

   1. Initial program 67.9%

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

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a}} \]
   3. 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 70.1

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

   4. Applied rewrites 70.1%

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

   if -1.12000000000000006e-129 < a < -1.70000000000000008e-217

   1. Initial program 63.1%

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

   2. Taylor expanded in z around inf

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

      1. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 53.9

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

   4. Applied rewrites 53.9%

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

   if -1.70000000000000008e-217 < a < 3.3999999999999999e34

   1. Initial program 66.3%

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

   2. Taylor expanded in t around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 73.3

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

   4. Applied rewrites 73.3%

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

   5. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 69.7

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

   7. Applied rewrites 69.7%

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

Alternative 6: 66.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-40}:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t} + y\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-109}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.35e-40)
   (+ (/ (* x (- z a)) t) y)
   (if (<= t 5.2e-109) (+ x (* (- y x) (/ z a))) (* y (/ (- z t) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.35e-40) {
		tmp = ((x * (z - a)) / t) + y;
	} else if (t <= 5.2e-109) {
		tmp = x + ((y - x) * (z / a));
	} else {
		tmp = y * ((z - t) / (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 (t <= (-1.35d-40)) then
        tmp = ((x * (z - a)) / t) + y
    else if (t <= 5.2d-109) then
        tmp = x + ((y - x) * (z / a))
    else
        tmp = y * ((z - t) / (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 (t <= -1.35e-40) {
		tmp = ((x * (z - a)) / t) + y;
	} else if (t <= 5.2e-109) {
		tmp = x + ((y - x) * (z / a));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.35e-40:
		tmp = ((x * (z - a)) / t) + y
	elif t <= 5.2e-109:
		tmp = x + ((y - x) * (z / a))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.35e-40)
		tmp = Float64(Float64(Float64(x * Float64(z - a)) / t) + y);
	elseif (t <= 5.2e-109)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / a)));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.35e-40)
		tmp = ((x * (z - a)) / t) + y;
	elseif (t <= 5.2e-109)
		tmp = x + ((y - x) * (z / a));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.35e-40], N[(N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + y), $MachinePrecision], If[LessEqual[t, 5.2e-109], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.35e-40

   1. Initial program 48.9%

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

   2. Taylor expanded in t around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 59.2

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

   4. Applied rewrites 59.2%

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

   5. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 56.1

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

   7. Applied rewrites 56.1%

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

   if -1.35e-40 < t < 5.1999999999999997e-109

   1. Initial program 89.9%

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

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

      5. lift--.f64 N/A

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

      6. 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. sub-negate N/A

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

      12. sub-negate N/A

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

      13. frac-2neg-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lower--.f64 95.9

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

   3. Applied rewrites 95.9%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 81.1

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

   6. Applied rewrites 81.1%

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

   if 5.1999999999999997e-109 < t

   1. Initial program 56.4%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 19.2%

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

   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. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.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 56.6

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

   7. Applied rewrites 56.6%

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

Alternative 7: 65.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-40}:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t} + y\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-109}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.35e-40)
   (+ (/ (* x (- z a)) t) y)
   (if (<= t 5.2e-109) (fma z (/ (- y x) a) x) (* y (/ (- z t) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.35e-40) {
		tmp = ((x * (z - a)) / t) + y;
	} else if (t <= 5.2e-109) {
		tmp = fma(z, ((y - x) / a), x);
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.35e-40)
		tmp = Float64(Float64(Float64(x * Float64(z - a)) / t) + y);
	elseif (t <= 5.2e-109)
		tmp = fma(z, Float64(Float64(y - x) / 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[LessEqual[t, -1.35e-40], N[(N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + y), $MachinePrecision], If[LessEqual[t, 5.2e-109], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.35e-40

   1. Initial program 48.9%

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

   2. Taylor expanded in t around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 59.2

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

   4. Applied rewrites 59.2%

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

   5. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 56.1

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

   7. Applied rewrites 56.1%

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

   if -1.35e-40 < t < 5.1999999999999997e-109

   1. Initial program 89.9%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]
   3. 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 78.5

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

   4. Applied rewrites 78.5%

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

   if 5.1999999999999997e-109 < t

   1. Initial program 56.4%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 19.2%

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

   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. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.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 56.6

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

   7. Applied rewrites 56.6%

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

Alternative 8: 64.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.4 \cdot 10^{-41}:\\ \;\;\;\;y - \frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-109}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8.4e-41)
   (- y (/ (* z (- y x)) t))
   (if (<= t 5.2e-109) (fma z (/ (- y x) a) x) (* y (/ (- z t) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8.4e-41) {
		tmp = y - ((z * (y - x)) / t);
	} else if (t <= 5.2e-109) {
		tmp = fma(z, ((y - x) / a), x);
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8.4e-41)
		tmp = Float64(y - Float64(Float64(z * Float64(y - x)) / t));
	elseif (t <= 5.2e-109)
		tmp = fma(z, Float64(Float64(y - x) / 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[LessEqual[t, -8.4e-41], N[(y - N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e-109], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.40000000000000051e-41

   1. Initial program 48.9%

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

   2. Taylor expanded in t around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 59.2

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

   4. Applied rewrites 59.2%

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

   5. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 55.9

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

   7. Applied rewrites 55.9%

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

   if -8.40000000000000051e-41 < t < 5.1999999999999997e-109

   1. Initial program 89.9%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]
   3. 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 78.5

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

   4. Applied rewrites 78.5%

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

   if 5.1999999999999997e-109 < t

   1. Initial program 56.4%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 19.2%

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

   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. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.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 56.6

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

   7. Applied rewrites 56.6%

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

Alternative 9: 64.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{if}\;a \leq -1.28 \cdot 10^{-123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-16}:\\ \;\;\;\;y - \frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma z (/ (- y x) a) x)))
   (if (<= a -1.28e-123) t_1 (if (<= a 6e-16) (- y (/ (* z (- y x)) t)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(z, ((y - x) / a), x);
	double tmp;
	if (a <= -1.28e-123) {
		tmp = t_1;
	} else if (a <= 6e-16) {
		tmp = y - ((z * (y - x)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(z, Float64(Float64(y - x) / a), x)
	tmp = 0.0
	if (a <= -1.28e-123)
		tmp = t_1;
	elseif (a <= 6e-16)
		tmp = Float64(y - Float64(Float64(z * Float64(y - x)) / t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -1.28e-123], t$95$1, If[LessEqual[a, 6e-16], N[(y - N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.28000000000000002e-123 or 5.99999999999999987e-16 < a

   1. Initial program 68.1%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]
   3. 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 61.9

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

   4. Applied rewrites 61.9%

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

   if -1.28000000000000002e-123 < a < 5.99999999999999987e-16

   1. Initial program 65.2%

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

   2. Taylor expanded in t around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 76.0

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

   4. Applied rewrites 76.0%

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

   5. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 72.7

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

   7. Applied rewrites 72.7%

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

Alternative 10: 59.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+139}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+132}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.5e+139) y (if (<= t 8.6e+132) (fma z (/ (- y x) a) x) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.5e+139) {
		tmp = y;
	} else if (t <= 8.6e+132) {
		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 <= -2.5e+139)
		tmp = y;
	elseif (t <= 8.6e+132)
		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, -2.5e+139], y, If[LessEqual[t, 8.6e+132], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -2.50000000000000015e139 or 8.59999999999999964e132 < t

   1. Initial program 29.6%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 54.8%

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

   if -2.50000000000000015e139 < t < 8.59999999999999964e132

   1. Initial program 81.2%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]
   3. 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 61.4

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

   4. Applied rewrites 61.4%

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

Alternative 11: 40.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+224}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+155}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-148}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-215}:\\ \;\;\;\;-t \cdot \frac{y}{a - t}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y x) z) a)))
   (if (<= z -2.8e+224)
     (* y (/ (- z t) a))
     (if (<= z -3.5e+155)
       (* z (/ (- x y) t))
       (if (<= z -2.1e+93)
         t_1
         (if (<= z -1.15e-148)
           x
           (if (<= z 6e-215)
             (- (* t (/ y (- a t))))
             (if (<= z 1.7e-17) x t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - x) * z) / a;
	double tmp;
	if (z <= -2.8e+224) {
		tmp = y * ((z - t) / a);
	} else if (z <= -3.5e+155) {
		tmp = z * ((x - y) / t);
	} else if (z <= -2.1e+93) {
		tmp = t_1;
	} else if (z <= -1.15e-148) {
		tmp = x;
	} else if (z <= 6e-215) {
		tmp = -(t * (y / (a - t)));
	} else if (z <= 1.7e-17) {
		tmp = 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 = ((y - x) * z) / a
    if (z <= (-2.8d+224)) then
        tmp = y * ((z - t) / a)
    else if (z <= (-3.5d+155)) then
        tmp = z * ((x - y) / t)
    else if (z <= (-2.1d+93)) then
        tmp = t_1
    else if (z <= (-1.15d-148)) then
        tmp = x
    else if (z <= 6d-215) then
        tmp = -(t * (y / (a - t)))
    else if (z <= 1.7d-17) then
        tmp = 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 = ((y - x) * z) / a;
	double tmp;
	if (z <= -2.8e+224) {
		tmp = y * ((z - t) / a);
	} else if (z <= -3.5e+155) {
		tmp = z * ((x - y) / t);
	} else if (z <= -2.1e+93) {
		tmp = t_1;
	} else if (z <= -1.15e-148) {
		tmp = x;
	} else if (z <= 6e-215) {
		tmp = -(t * (y / (a - t)));
	} else if (z <= 1.7e-17) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - x) * z) / a
	tmp = 0
	if z <= -2.8e+224:
		tmp = y * ((z - t) / a)
	elif z <= -3.5e+155:
		tmp = z * ((x - y) / t)
	elif z <= -2.1e+93:
		tmp = t_1
	elif z <= -1.15e-148:
		tmp = x
	elif z <= 6e-215:
		tmp = -(t * (y / (a - t)))
	elif z <= 1.7e-17:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - x) * z) / a)
	tmp = 0.0
	if (z <= -2.8e+224)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (z <= -3.5e+155)
		tmp = Float64(z * Float64(Float64(x - y) / t));
	elseif (z <= -2.1e+93)
		tmp = t_1;
	elseif (z <= -1.15e-148)
		tmp = x;
	elseif (z <= 6e-215)
		tmp = Float64(-Float64(t * Float64(y / Float64(a - t))));
	elseif (z <= 1.7e-17)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - x) * z) / a;
	tmp = 0.0;
	if (z <= -2.8e+224)
		tmp = y * ((z - t) / a);
	elseif (z <= -3.5e+155)
		tmp = z * ((x - y) / t);
	elseif (z <= -2.1e+93)
		tmp = t_1;
	elseif (z <= -1.15e-148)
		tmp = x;
	elseif (z <= 6e-215)
		tmp = -(t * (y / (a - t)));
	elseif (z <= 1.7e-17)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -2.8e+224], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.5e+155], N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.1e+93], t$95$1, If[LessEqual[z, -1.15e-148], x, If[LessEqual[z, 6e-215], (-N[(t * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), If[LessEqual[z, 1.7e-17], x, t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.80000000000000008e224

   1. Initial program 70.1%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 5.8%

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

   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. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.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 54.9

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

   7. Applied rewrites 54.9%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 40.1%

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

   if -2.80000000000000008e224 < z < -3.49999999999999985e155

   1. Initial program 65.8%

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

   2. Taylor expanded in t around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 42.5

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

   4. Applied rewrites 42.5%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 47.2

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

   7. Applied rewrites 47.2%

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

   if -3.49999999999999985e155 < z < -2.0999999999999998e93 or 1.6999999999999999e-17 < z

   1. Initial program 67.4%

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

   2. Taylor expanded in z around inf

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

      1. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 56.0

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

   4. Applied rewrites 56.0%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 34.4%

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

   if -2.0999999999999998e93 < z < -1.14999999999999999e-148 or 6.00000000000000051e-215 < z < 1.6999999999999999e-17

   1. Initial program 67.7%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 30.5%

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

   if -1.14999999999999999e-148 < z < 6.00000000000000051e-215

   1. Initial program 64.6%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   3. 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 40.2

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

   4. Applied rewrites 40.2%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 6.4%

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

   8. Taylor expanded in z around 0

      \[\leadsto -1 \cdot \color{blue}{\frac{t \cdot y}{a - t}} \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 41.0

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

   10. Applied rewrites 41.0%

       \[\leadsto -t \cdot \frac{y}{a - t} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 12: 38.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-217}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-16}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1400000:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+168}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y x) z) a)))
   (if (<= a -4.5e+38)
     x
     (if (<= a -1.7e-217)
       t_1
       (if (<= a 1.9e-16)
         y
         (if (<= a 1400000.0)
           (/ (* x (- z a)) t)
           (if (<= a 6.2e+168) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - x) * z) / a;
	double tmp;
	if (a <= -4.5e+38) {
		tmp = x;
	} else if (a <= -1.7e-217) {
		tmp = t_1;
	} else if (a <= 1.9e-16) {
		tmp = y;
	} else if (a <= 1400000.0) {
		tmp = (x * (z - a)) / t;
	} else if (a <= 6.2e+168) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = ((y - x) * z) / a
    if (a <= (-4.5d+38)) then
        tmp = x
    else if (a <= (-1.7d-217)) then
        tmp = t_1
    else if (a <= 1.9d-16) then
        tmp = y
    else if (a <= 1400000.0d0) then
        tmp = (x * (z - a)) / t
    else if (a <= 6.2d+168) then
        tmp = t_1
    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 t_1 = ((y - x) * z) / a;
	double tmp;
	if (a <= -4.5e+38) {
		tmp = x;
	} else if (a <= -1.7e-217) {
		tmp = t_1;
	} else if (a <= 1.9e-16) {
		tmp = y;
	} else if (a <= 1400000.0) {
		tmp = (x * (z - a)) / t;
	} else if (a <= 6.2e+168) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - x) * z) / a
	tmp = 0
	if a <= -4.5e+38:
		tmp = x
	elif a <= -1.7e-217:
		tmp = t_1
	elif a <= 1.9e-16:
		tmp = y
	elif a <= 1400000.0:
		tmp = (x * (z - a)) / t
	elif a <= 6.2e+168:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - x) * z) / a)
	tmp = 0.0
	if (a <= -4.5e+38)
		tmp = x;
	elseif (a <= -1.7e-217)
		tmp = t_1;
	elseif (a <= 1.9e-16)
		tmp = y;
	elseif (a <= 1400000.0)
		tmp = Float64(Float64(x * Float64(z - a)) / t);
	elseif (a <= 6.2e+168)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - x) * z) / a;
	tmp = 0.0;
	if (a <= -4.5e+38)
		tmp = x;
	elseif (a <= -1.7e-217)
		tmp = t_1;
	elseif (a <= 1.9e-16)
		tmp = y;
	elseif (a <= 1400000.0)
		tmp = (x * (z - a)) / t;
	elseif (a <= 6.2e+168)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -4.5e+38], x, If[LessEqual[a, -1.7e-217], t$95$1, If[LessEqual[a, 1.9e-16], y, If[LessEqual[a, 1400000.0], N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 6.2e+168], t$95$1, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.4999999999999998e38 or 6.19999999999999993e168 < a

   1. Initial program 67.3%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 49.4%

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

   if -4.4999999999999998e38 < a < -1.70000000000000008e-217 or 1.4e6 < a < 6.19999999999999993e168

   1. Initial program 67.6%

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

   2. Taylor expanded in z around inf

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

      1. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 41.9

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

   4. Applied rewrites 41.9%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 27.7%

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

   if -1.70000000000000008e-217 < a < 1.90000000000000006e-16

   1. Initial program 65.7%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 36.3%

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

   if 1.90000000000000006e-16 < a < 1.4e6

   1. Initial program 71.9%

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

   2. Taylor expanded in t around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 53.5

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

   4. Applied rewrites 53.5%

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

   5. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 24.2

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

   7. Applied rewrites 24.2%

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

Alternative 13: 37.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{a - t}\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-222}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-82}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.92 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y (- a t)))))
   (if (<= z -1.3e+93)
     t_1
     (if (<= z -8e-222) x (if (<= z 1.25e-82) y (if (<= z 1.92e+28) x t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / (a - t));
	double tmp;
	if (z <= -1.3e+93) {
		tmp = t_1;
	} else if (z <= -8e-222) {
		tmp = x;
	} else if (z <= 1.25e-82) {
		tmp = y;
	} else if (z <= 1.92e+28) {
		tmp = 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 = z * (y / (a - t))
    if (z <= (-1.3d+93)) then
        tmp = t_1
    else if (z <= (-8d-222)) then
        tmp = x
    else if (z <= 1.25d-82) then
        tmp = y
    else if (z <= 1.92d+28) then
        tmp = 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 = z * (y / (a - t));
	double tmp;
	if (z <= -1.3e+93) {
		tmp = t_1;
	} else if (z <= -8e-222) {
		tmp = x;
	} else if (z <= 1.25e-82) {
		tmp = y;
	} else if (z <= 1.92e+28) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / (a - t))
	tmp = 0
	if z <= -1.3e+93:
		tmp = t_1
	elif z <= -8e-222:
		tmp = x
	elif z <= 1.25e-82:
		tmp = y
	elif z <= 1.92e+28:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / Float64(a - t)))
	tmp = 0.0
	if (z <= -1.3e+93)
		tmp = t_1;
	elseif (z <= -8e-222)
		tmp = x;
	elseif (z <= 1.25e-82)
		tmp = y;
	elseif (z <= 1.92e+28)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / (a - t));
	tmp = 0.0;
	if (z <= -1.3e+93)
		tmp = t_1;
	elseif (z <= -8e-222)
		tmp = x;
	elseif (z <= 1.25e-82)
		tmp = y;
	elseif (z <= 1.92e+28)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+93], t$95$1, If[LessEqual[z, -8e-222], x, If[LessEqual[z, 1.25e-82], y, If[LessEqual[z, 1.92e+28], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3e93 or 1.91999999999999998e28 < z

   1. Initial program 67.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   3. 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 39.0

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

   4. Applied rewrites 39.0%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 34.1%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 41.3

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

   9. Applied rewrites 41.3%

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

   if -1.3e93 < z < -8.00000000000000038e-222 or 1.25e-82 < z < 1.91999999999999998e28

   1. Initial program 68.5%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 29.5%

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

   if -8.00000000000000038e-222 < z < 1.25e-82

   1. Initial program 64.3%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 37.9%

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

Alternative 14: 36.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-151}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+105}:\\ \;\;\;\;\frac{y}{x} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.3e+28)
   x
   (if (<= a 6.2e-151)
     (* z (/ (- x y) t))
     (if (<= a 2.7e+105) (* (/ y x) x) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.3e+28) {
		tmp = x;
	} else if (a <= 6.2e-151) {
		tmp = z * ((x - y) / t);
	} else if (a <= 2.7e+105) {
		tmp = (y / x) * x;
	} 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 <= (-2.3d+28)) then
        tmp = x
    else if (a <= 6.2d-151) then
        tmp = z * ((x - y) / t)
    else if (a <= 2.7d+105) then
        tmp = (y / x) * x
    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 <= -2.3e+28) {
		tmp = x;
	} else if (a <= 6.2e-151) {
		tmp = z * ((x - y) / t);
	} else if (a <= 2.7e+105) {
		tmp = (y / x) * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.3e+28:
		tmp = x
	elif a <= 6.2e-151:
		tmp = z * ((x - y) / t)
	elif a <= 2.7e+105:
		tmp = (y / x) * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.3e+28)
		tmp = x;
	elseif (a <= 6.2e-151)
		tmp = Float64(z * Float64(Float64(x - y) / t));
	elseif (a <= 2.7e+105)
		tmp = Float64(Float64(y / x) * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.3e+28)
		tmp = x;
	elseif (a <= 6.2e-151)
		tmp = z * ((x - y) / t);
	elseif (a <= 2.7e+105)
		tmp = (y / x) * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.3e+28], x, If[LessEqual[a, 6.2e-151], N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e+105], N[(N[(y / x), $MachinePrecision] * x), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.29999999999999984e28 or 2.70000000000000016e105 < a

   1. Initial program 68.0%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 47.7%

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

   if -2.29999999999999984e28 < a < 6.19999999999999969e-151

   1. Initial program 64.9%

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

   2. Taylor expanded in t around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 73.9

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

   4. Applied rewrites 73.9%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 42.1

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

   7. Applied rewrites 42.1%

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

   if 6.19999999999999969e-151 < a < 2.70000000000000016e105

   1. Initial program 69.4%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 65.4%

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

   5. Taylor expanded in t around inf

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

      1. lower-/.f64 23.9

         \[\leadsto \frac{y}{x} \cdot x \]

   7. Applied rewrites 23.9%

      \[\leadsto \frac{y}{x} \cdot x \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 35.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a}\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-222}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-82}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+134}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z a))))
   (if (<= z -2.7e+93)
     t_1
     (if (<= z -8e-222) x (if (<= z 1.25e-82) y (if (<= z 7e+134) x t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double tmp;
	if (z <= -2.7e+93) {
		tmp = t_1;
	} else if (z <= -8e-222) {
		tmp = x;
	} else if (z <= 1.25e-82) {
		tmp = y;
	} else if (z <= 7e+134) {
		tmp = 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 = y * (z / a)
    if (z <= (-2.7d+93)) then
        tmp = t_1
    else if (z <= (-8d-222)) then
        tmp = x
    else if (z <= 1.25d-82) then
        tmp = y
    else if (z <= 7d+134) then
        tmp = 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 = y * (z / a);
	double tmp;
	if (z <= -2.7e+93) {
		tmp = t_1;
	} else if (z <= -8e-222) {
		tmp = x;
	} else if (z <= 1.25e-82) {
		tmp = y;
	} else if (z <= 7e+134) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / a)
	tmp = 0
	if z <= -2.7e+93:
		tmp = t_1
	elif z <= -8e-222:
		tmp = x
	elif z <= 1.25e-82:
		tmp = y
	elif z <= 7e+134:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / a))
	tmp = 0.0
	if (z <= -2.7e+93)
		tmp = t_1;
	elseif (z <= -8e-222)
		tmp = x;
	elseif (z <= 1.25e-82)
		tmp = y;
	elseif (z <= 7e+134)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / a);
	tmp = 0.0;
	if (z <= -2.7e+93)
		tmp = t_1;
	elseif (z <= -8e-222)
		tmp = x;
	elseif (z <= 1.25e-82)
		tmp = y;
	elseif (z <= 7e+134)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.7e+93], t$95$1, If[LessEqual[z, -8e-222], x, If[LessEqual[z, 1.25e-82], y, If[LessEqual[z, 7e+134], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6999999999999999e93 or 7.00000000000000006e134 < z

   1. Initial program 67.6%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   3. 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 38.7

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

   4. Applied rewrites 38.7%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 35.2%

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

   8. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 33.7

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

   10. Applied rewrites 33.7%

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

   if -2.6999999999999999e93 < z < -8.00000000000000038e-222 or 1.25e-82 < z < 7.00000000000000006e134

   1. Initial program 68.2%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 28.1%

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

   if -8.00000000000000038e-222 < z < 1.25e-82

   1. Initial program 64.3%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 37.9%

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

Alternative 16: 34.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-192}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+105}:\\ \;\;\;\;\frac{y}{x} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.5e+38)
   x
   (if (<= a -2e-192) (* y (/ z a)) (if (<= a 2.7e+105) (* (/ y x) x) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.5e+38) {
		tmp = x;
	} else if (a <= -2e-192) {
		tmp = y * (z / a);
	} else if (a <= 2.7e+105) {
		tmp = (y / x) * x;
	} 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 <= (-4.5d+38)) then
        tmp = x
    else if (a <= (-2d-192)) then
        tmp = y * (z / a)
    else if (a <= 2.7d+105) then
        tmp = (y / x) * x
    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 <= -4.5e+38) {
		tmp = x;
	} else if (a <= -2e-192) {
		tmp = y * (z / a);
	} else if (a <= 2.7e+105) {
		tmp = (y / x) * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.5e+38:
		tmp = x
	elif a <= -2e-192:
		tmp = y * (z / a)
	elif a <= 2.7e+105:
		tmp = (y / x) * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.5e+38)
		tmp = x;
	elseif (a <= -2e-192)
		tmp = Float64(y * Float64(z / a));
	elseif (a <= 2.7e+105)
		tmp = Float64(Float64(y / x) * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.5e+38)
		tmp = x;
	elseif (a <= -2e-192)
		tmp = y * (z / a);
	elseif (a <= 2.7e+105)
		tmp = (y / x) * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.5e+38], x, If[LessEqual[a, -2e-192], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e+105], N[(N[(y / x), $MachinePrecision] * x), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.4999999999999998e38 or 2.70000000000000016e105 < a

   1. Initial program 67.7%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 48.1%

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

   if -4.4999999999999998e38 < a < -2.0000000000000002e-192

   1. Initial program 66.3%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   3. 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 46.5

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

   4. Applied rewrites 46.5%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 24.8%

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

   8. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 19.6

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

   10. Applied rewrites 19.6%

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

   if -2.0000000000000002e-192 < a < 2.70000000000000016e105

   1. Initial program 66.7%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 60.3%

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

   5. Taylor expanded in t around inf

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

      1. lower-/.f64 30.2

         \[\leadsto \frac{y}{x} \cdot x \]

   7. Applied rewrites 30.2%

      \[\leadsto \frac{y}{x} \cdot x \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 17: 32.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -50000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+105}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -50000000.0) x (if (<= a 2.7e+105) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -50000000.0) {
		tmp = x;
	} else if (a <= 2.7e+105) {
		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 <= (-50000000.0d0)) then
        tmp = x
    else if (a <= 2.7d+105) 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 <= -50000000.0) {
		tmp = x;
	} else if (a <= 2.7e+105) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -50000000.0:
		tmp = x
	elif a <= 2.7e+105:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -50000000.0)
		tmp = x;
	elseif (a <= 2.7e+105)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -50000000.0)
		tmp = x;
	elseif (a <= 2.7e+105)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -50000000.0], x, If[LessEqual[a, 2.7e+105], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -5e7 or 2.70000000000000016e105 < a

   1. Initial program 68.1%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 46.7%

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

   if -5e7 < a < 2.70000000000000016e105

   1. Initial program 66.3%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 33.0%

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

Alternative 18: 24.9% accurate, 17.9× 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 67.0%

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

2. Taylor expanded in a around inf

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

4. Applied rewrites 24.9%

   \[\leadsto \color{blue}{x} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025127 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64
  (+ x (/ (* (- y x) (- z t)) (- a t))))