Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 81.0% → 89.8%

Time: 5.2s

Alternatives: 23

Speedup: 0.4×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 81.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot t\_1\\ t_3 := \mathsf{fma}\left(t\_1, y - z, x\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;x + \mathsf{fma}\left(\frac{y - z}{a - z}, t, -\frac{\left(y - z\right) \cdot x}{a - z}\right)\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-296}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{-271}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}, -1, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z)))
        (t_2 (+ x (* (- y z) t_1)))
        (t_3 (fma t_1 (- y z) x)))
   (if (<= t_2 (- INFINITY))
     (+ x (fma (/ (- y z) (- a z)) t (- (/ (* (- y z) x) (- a z)))))
     (if (<= t_2 -2e-296)
       t_3
       (if (<= t_2 4e-271) (fma (/ (* (- t x) (- y a)) z) -1.0 t) t_3)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / (a - z);
	double t_2 = x + ((y - z) * t_1);
	double t_3 = fma(t_1, (y - z), x);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = x + fma(((y - z) / (a - z)), t, -(((y - z) * x) / (a - z)));
	} else if (t_2 <= -2e-296) {
		tmp = t_3;
	} else if (t_2 <= 4e-271) {
		tmp = fma((((t - x) * (y - a)) / z), -1.0, t);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(y - z) * t_1))
	t_3 = fma(t_1, Float64(y - z), x)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(x + fma(Float64(Float64(y - z) / Float64(a - z)), t, Float64(-Float64(Float64(Float64(y - z) * x) / Float64(a - z)))));
	elseif (t_2 <= -2e-296)
		tmp = t_3;
	elseif (t_2 <= 4e-271)
		tmp = fma(Float64(Float64(Float64(t - x) * Float64(y - a)) / z), -1.0, t);
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t + (-N[(N[(N[(y - z), $MachinePrecision] * x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e-296], t$95$3, If[LessEqual[t$95$2, 4e-271], N[(N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * -1.0 + t), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -inf.0

   1. Initial program 84.0%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. sub-div N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift--.f64 N/A

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

      16. lift--.f64 85.6

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

   4. Applied rewrites 85.6%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-296 or 3.99999999999999985e-271 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 91.9

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

   3. Applied rewrites 91.9%

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

   if -2e-296 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 3.99999999999999985e-271

   1. Initial program 6.7%

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

   2. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. sub-div N/A

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

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

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

      6. associate-*r/ N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   4. Applied rewrites 79.3%

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

Alternative 2: 47.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+306}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-68}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-296}:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{y - a}{z} \cdot x\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+300}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -5e+306)
     (/ (* t y) a)
     (if (<= t_1 -1e-68)
       (+ x t)
       (if (<= t_1 -2e-296)
         x
         (if (<= t_1 0.0)
           (* (/ (- y a) z) x)
           (if (<= t_1 2e+300) (+ x t) (/ (* t y) (- a z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -5e+306) {
		tmp = (t * y) / a;
	} else if (t_1 <= -1e-68) {
		tmp = x + t;
	} else if (t_1 <= -2e-296) {
		tmp = x;
	} else if (t_1 <= 0.0) {
		tmp = ((y - a) / z) * x;
	} else if (t_1 <= 2e+300) {
		tmp = x + t;
	} else {
		tmp = (t * y) / (a - z);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_1 <= (-5d+306)) then
        tmp = (t * y) / a
    else if (t_1 <= (-1d-68)) then
        tmp = x + t
    else if (t_1 <= (-2d-296)) then
        tmp = x
    else if (t_1 <= 0.0d0) then
        tmp = ((y - a) / z) * x
    else if (t_1 <= 2d+300) then
        tmp = x + t
    else
        tmp = (t * y) / (a - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -5e+306) {
		tmp = (t * y) / a;
	} else if (t_1 <= -1e-68) {
		tmp = x + t;
	} else if (t_1 <= -2e-296) {
		tmp = x;
	} else if (t_1 <= 0.0) {
		tmp = ((y - a) / z) * x;
	} else if (t_1 <= 2e+300) {
		tmp = x + t;
	} else {
		tmp = (t * y) / (a - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -5e+306:
		tmp = (t * y) / a
	elif t_1 <= -1e-68:
		tmp = x + t
	elif t_1 <= -2e-296:
		tmp = x
	elif t_1 <= 0.0:
		tmp = ((y - a) / z) * x
	elif t_1 <= 2e+300:
		tmp = x + t
	else:
		tmp = (t * y) / (a - z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -5e+306)
		tmp = Float64(Float64(t * y) / a);
	elseif (t_1 <= -1e-68)
		tmp = Float64(x + t);
	elseif (t_1 <= -2e-296)
		tmp = x;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(y - a) / z) * x);
	elseif (t_1 <= 2e+300)
		tmp = Float64(x + t);
	else
		tmp = Float64(Float64(t * y) / Float64(a - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -5e+306)
		tmp = (t * y) / a;
	elseif (t_1 <= -1e-68)
		tmp = x + t;
	elseif (t_1 <= -2e-296)
		tmp = x;
	elseif (t_1 <= 0.0)
		tmp = ((y - a) / z) * x;
	elseif (t_1 <= 2e+300)
		tmp = x + t;
	else
		tmp = (t * y) / (a - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+306], N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t$95$1, -1e-68], N[(x + t), $MachinePrecision], If[LessEqual[t$95$1, -2e-296], x, If[LessEqual[t$95$1, 0.0], N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 2e+300], N[(x + t), $MachinePrecision], N[(N[(t * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.99999999999999993e306

   1. Initial program 84.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 84.1

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

   3. Applied rewrites 84.1%

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

   4. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 58.7

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

   6. Applied rewrites 58.7%

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

   7. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 43.9

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

   9. Applied rewrites 43.9%

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

   if -4.99999999999999993e306 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000007e-68 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 2.0000000000000001e300

   1. Initial program 94.1%

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

   2. Taylor expanded in z around inf

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

      1. lift--.f64 25.8

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

   4. Applied rewrites 25.8%

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

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 46.1%

      \[\leadsto x + t \]

   if -1.00000000000000007e-68 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-296

   1. Initial program 74.2%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 44.5%

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

   if -2e-296 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 4.3%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. sub-div N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-div N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lift--.f64 4.2

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

   4. Applied rewrites 4.2%

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

   5. Taylor expanded in z around -inf

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

      1. lower-/.f64 N/A

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

      2. lift--.f64 60.5

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

   7. Applied rewrites 60.5%

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

   if 2.0000000000000001e300 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 86.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 86.9

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

   3. Applied rewrites 86.9%

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

   4. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 53.4

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

   6. Applied rewrites 53.4%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 49.3%

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

Alternative 3: 47.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot y}{a}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-68}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-296}:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{y - a}{z} \cdot x\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* t y) a)) (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -5e+306)
     t_1
     (if (<= t_2 -1e-68)
       (+ x t)
       (if (<= t_2 -2e-296)
         x
         (if (<= t_2 0.0)
           (* (/ (- y a) z) x)
           (if (<= t_2 5e+304) (+ x t) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * y) / a;
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -5e+306) {
		tmp = t_1;
	} else if (t_2 <= -1e-68) {
		tmp = x + t;
	} else if (t_2 <= -2e-296) {
		tmp = x;
	} else if (t_2 <= 0.0) {
		tmp = ((y - a) / z) * x;
	} else if (t_2 <= 5e+304) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t * y) / a
    t_2 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_2 <= (-5d+306)) then
        tmp = t_1
    else if (t_2 <= (-1d-68)) then
        tmp = x + t
    else if (t_2 <= (-2d-296)) then
        tmp = x
    else if (t_2 <= 0.0d0) then
        tmp = ((y - a) / z) * x
    else if (t_2 <= 5d+304) then
        tmp = x + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * y) / a;
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -5e+306) {
		tmp = t_1;
	} else if (t_2 <= -1e-68) {
		tmp = x + t;
	} else if (t_2 <= -2e-296) {
		tmp = x;
	} else if (t_2 <= 0.0) {
		tmp = ((y - a) / z) * x;
	} else if (t_2 <= 5e+304) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t * y) / a
	t_2 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_2 <= -5e+306:
		tmp = t_1
	elif t_2 <= -1e-68:
		tmp = x + t
	elif t_2 <= -2e-296:
		tmp = x
	elif t_2 <= 0.0:
		tmp = ((y - a) / z) * x
	elif t_2 <= 5e+304:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t * y) / a)
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -5e+306)
		tmp = t_1;
	elseif (t_2 <= -1e-68)
		tmp = Float64(x + t);
	elseif (t_2 <= -2e-296)
		tmp = x;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(Float64(y - a) / z) * x);
	elseif (t_2 <= 5e+304)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t * y) / a;
	t_2 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_2 <= -5e+306)
		tmp = t_1;
	elseif (t_2 <= -1e-68)
		tmp = x + t;
	elseif (t_2 <= -2e-296)
		tmp = x;
	elseif (t_2 <= 0.0)
		tmp = ((y - a) / z) * x;
	elseif (t_2 <= 5e+304)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+306], t$95$1, If[LessEqual[t$95$2, -1e-68], N[(x + t), $MachinePrecision], If[LessEqual[t$95$2, -2e-296], x, If[LessEqual[t$95$2, 0.0], N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$2, 5e+304], N[(x + t), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.99999999999999993e306 or 4.9999999999999997e304 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 85.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 85.3

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

   3. Applied rewrites 85.3%

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

   4. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 56.7

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

   6. Applied rewrites 56.7%

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

   7. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 42.7

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

   9. Applied rewrites 42.7%

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

   if -4.99999999999999993e306 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000007e-68 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.9999999999999997e304

   1. Initial program 94.1%

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

   2. Taylor expanded in z around inf

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

      1. lift--.f64 25.8

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

   4. Applied rewrites 25.8%

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

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 46.1%

      \[\leadsto x + t \]

   if -1.00000000000000007e-68 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-296

   1. Initial program 74.2%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 44.5%

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

   if -2e-296 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 4.3%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. sub-div N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-div N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lift--.f64 4.2

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

   4. Applied rewrites 4.2%

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

   5. Taylor expanded in z around -inf

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

      1. lower-/.f64 N/A

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

      2. lift--.f64 60.5

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

   7. Applied rewrites 60.5%

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

Alternative 4: 45.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot y}{a}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-68}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-296}:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* t y) a)) (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -5e+306)
     t_1
     (if (<= t_2 -1e-68)
       (+ x t)
       (if (<= t_2 -2e-296)
         x
         (if (<= t_2 0.0)
           (/ (* x (- y a)) z)
           (if (<= t_2 5e+304) (+ x t) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * y) / a;
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -5e+306) {
		tmp = t_1;
	} else if (t_2 <= -1e-68) {
		tmp = x + t;
	} else if (t_2 <= -2e-296) {
		tmp = x;
	} else if (t_2 <= 0.0) {
		tmp = (x * (y - a)) / z;
	} else if (t_2 <= 5e+304) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t * y) / a
    t_2 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_2 <= (-5d+306)) then
        tmp = t_1
    else if (t_2 <= (-1d-68)) then
        tmp = x + t
    else if (t_2 <= (-2d-296)) then
        tmp = x
    else if (t_2 <= 0.0d0) then
        tmp = (x * (y - a)) / z
    else if (t_2 <= 5d+304) then
        tmp = x + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * y) / a;
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -5e+306) {
		tmp = t_1;
	} else if (t_2 <= -1e-68) {
		tmp = x + t;
	} else if (t_2 <= -2e-296) {
		tmp = x;
	} else if (t_2 <= 0.0) {
		tmp = (x * (y - a)) / z;
	} else if (t_2 <= 5e+304) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t * y) / a
	t_2 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_2 <= -5e+306:
		tmp = t_1
	elif t_2 <= -1e-68:
		tmp = x + t
	elif t_2 <= -2e-296:
		tmp = x
	elif t_2 <= 0.0:
		tmp = (x * (y - a)) / z
	elif t_2 <= 5e+304:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t * y) / a)
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -5e+306)
		tmp = t_1;
	elseif (t_2 <= -1e-68)
		tmp = Float64(x + t);
	elseif (t_2 <= -2e-296)
		tmp = x;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (t_2 <= 5e+304)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t * y) / a;
	t_2 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_2 <= -5e+306)
		tmp = t_1;
	elseif (t_2 <= -1e-68)
		tmp = x + t;
	elseif (t_2 <= -2e-296)
		tmp = x;
	elseif (t_2 <= 0.0)
		tmp = (x * (y - a)) / z;
	elseif (t_2 <= 5e+304)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+306], t$95$1, If[LessEqual[t$95$2, -1e-68], N[(x + t), $MachinePrecision], If[LessEqual[t$95$2, -2e-296], x, If[LessEqual[t$95$2, 0.0], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$2, 5e+304], N[(x + t), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.99999999999999993e306 or 4.9999999999999997e304 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 85.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 85.3

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

   3. Applied rewrites 85.3%

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

   4. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 56.7

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

   6. Applied rewrites 56.7%

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

   7. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 42.7

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

   9. Applied rewrites 42.7%

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

   if -4.99999999999999993e306 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000007e-68 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.9999999999999997e304

   1. Initial program 94.1%

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

   2. Taylor expanded in z around inf

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

      1. lift--.f64 25.8

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

   4. Applied rewrites 25.8%

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

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 46.1%

      \[\leadsto x + t \]

   if -1.00000000000000007e-68 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-296

   1. Initial program 74.2%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 44.5%

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

   if -2e-296 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 4.3%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. sub-div N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-div N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lift--.f64 4.2

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

   4. Applied rewrites 4.2%

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

   5. Taylor expanded in z around -inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 48.5

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

   7. Applied rewrites 48.5%

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

Alternative 5: 43.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot y}{a}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-68}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-296}:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* t y) a)) (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -5e+306)
     t_1
     (if (<= t_2 -1e-68)
       (+ x t)
       (if (<= t_2 -2e-296)
         x
         (if (<= t_2 0.0) (* (/ y z) x) (if (<= t_2 5e+304) (+ x t) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * y) / a;
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -5e+306) {
		tmp = t_1;
	} else if (t_2 <= -1e-68) {
		tmp = x + t;
	} else if (t_2 <= -2e-296) {
		tmp = x;
	} else if (t_2 <= 0.0) {
		tmp = (y / z) * x;
	} else if (t_2 <= 5e+304) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t * y) / a
    t_2 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_2 <= (-5d+306)) then
        tmp = t_1
    else if (t_2 <= (-1d-68)) then
        tmp = x + t
    else if (t_2 <= (-2d-296)) then
        tmp = x
    else if (t_2 <= 0.0d0) then
        tmp = (y / z) * x
    else if (t_2 <= 5d+304) then
        tmp = x + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * y) / a;
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -5e+306) {
		tmp = t_1;
	} else if (t_2 <= -1e-68) {
		tmp = x + t;
	} else if (t_2 <= -2e-296) {
		tmp = x;
	} else if (t_2 <= 0.0) {
		tmp = (y / z) * x;
	} else if (t_2 <= 5e+304) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t * y) / a
	t_2 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_2 <= -5e+306:
		tmp = t_1
	elif t_2 <= -1e-68:
		tmp = x + t
	elif t_2 <= -2e-296:
		tmp = x
	elif t_2 <= 0.0:
		tmp = (y / z) * x
	elif t_2 <= 5e+304:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t * y) / a)
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -5e+306)
		tmp = t_1;
	elseif (t_2 <= -1e-68)
		tmp = Float64(x + t);
	elseif (t_2 <= -2e-296)
		tmp = x;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(y / z) * x);
	elseif (t_2 <= 5e+304)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t * y) / a;
	t_2 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_2 <= -5e+306)
		tmp = t_1;
	elseif (t_2 <= -1e-68)
		tmp = x + t;
	elseif (t_2 <= -2e-296)
		tmp = x;
	elseif (t_2 <= 0.0)
		tmp = (y / z) * x;
	elseif (t_2 <= 5e+304)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+306], t$95$1, If[LessEqual[t$95$2, -1e-68], N[(x + t), $MachinePrecision], If[LessEqual[t$95$2, -2e-296], x, If[LessEqual[t$95$2, 0.0], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$2, 5e+304], N[(x + t), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.99999999999999993e306 or 4.9999999999999997e304 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 85.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 85.3

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

   3. Applied rewrites 85.3%

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

   4. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 56.7

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

   6. Applied rewrites 56.7%

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

   7. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 42.7

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

   9. Applied rewrites 42.7%

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

   if -4.99999999999999993e306 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000007e-68 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.9999999999999997e304

   1. Initial program 94.1%

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

   2. Taylor expanded in z around inf

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

      1. lift--.f64 25.8

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

   4. Applied rewrites 25.8%

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

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 46.1%

      \[\leadsto x + t \]

   if -1.00000000000000007e-68 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-296

   1. Initial program 74.2%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 44.5%

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

   if -2e-296 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 4.3%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. sub-div N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-div N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lift--.f64 4.2

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

   4. Applied rewrites 4.2%

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

   5. Taylor expanded in a around 0

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

      1. lower-/.f64 31.6

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

   7. Applied rewrites 31.6%

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

Alternative 6: 76.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t}{a - z}, y - z, x\right)\\ t_2 := \frac{t - x}{a - z}\\ t_3 := x + \left(y - z\right) \cdot t\_2\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;\frac{\left(t - x\right) \cdot y}{a - z}\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{-296}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 4 \cdot 10^{-271}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y \cdot \left(t - x\right)}{z}, -1, t\right)\\ \mathbf{elif}\;t\_3 \leq 10^{+224}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ t (- a z)) (- y z) x))
        (t_2 (/ (- t x) (- a z)))
        (t_3 (+ x (* (- y z) t_2))))
   (if (<= t_3 (- INFINITY))
     (/ (* (- t x) y) (- a z))
     (if (<= t_3 -2e-296)
       t_1
       (if (<= t_3 4e-271)
         (fma (/ (* y (- t x)) z) -1.0 t)
         (if (<= t_3 1e+224) t_1 (+ x (* y t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t / (a - z)), (y - z), x);
	double t_2 = (t - x) / (a - z);
	double t_3 = x + ((y - z) * t_2);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = ((t - x) * y) / (a - z);
	} else if (t_3 <= -2e-296) {
		tmp = t_1;
	} else if (t_3 <= 4e-271) {
		tmp = fma(((y * (t - x)) / z), -1.0, t);
	} else if (t_3 <= 1e+224) {
		tmp = t_1;
	} else {
		tmp = x + (y * t_2);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t / Float64(a - z)), Float64(y - z), x)
	t_2 = Float64(Float64(t - x) / Float64(a - z))
	t_3 = Float64(x + Float64(Float64(y - z) * t_2))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(t - x) * y) / Float64(a - z));
	elseif (t_3 <= -2e-296)
		tmp = t_1;
	elseif (t_3 <= 4e-271)
		tmp = fma(Float64(Float64(y * Float64(t - x)) / z), -1.0, t);
	elseif (t_3 <= 1e+224)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * t_2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -2e-296], t$95$1, If[LessEqual[t$95$3, 4e-271], N[(N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * -1.0 + t), $MachinePrecision], If[LessEqual[t$95$3, 1e+224], t$95$1, N[(x + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -inf.0

   1. Initial program 84.0%

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

   2. Taylor expanded in y around inf

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

      1. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 91.9

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

   4. Applied rewrites 91.9%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-296 or 3.99999999999999985e-271 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 9.9999999999999997e223

   1. Initial program 91.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 91.9

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

   3. Applied rewrites 91.9%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 77.7%

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

   if -2e-296 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 3.99999999999999985e-271

   1. Initial program 6.7%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 78.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 57.2

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

   7. Applied rewrites 57.2%

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

   if 9.9999999999999997e223 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.7%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 78.5%

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

Alternative 7: 77.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(t - x\right) \cdot y}{a - z}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_3 := \mathsf{fma}\left(\frac{t}{a - z}, y - z, x\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-296}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{-271}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y \cdot \left(t - x\right)}{z}, -1, t\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- t x) y) (- a z)))
        (t_2 (+ x (* (- y z) (/ (- t x) (- a z)))))
        (t_3 (fma (/ t (- a z)) (- y z) x)))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-296)
       t_3
       (if (<= t_2 4e-271)
         (fma (/ (* y (- t x)) z) -1.0 t)
         (if (<= t_2 5e+304) t_3 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((t - x) * y) / (a - z);
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double t_3 = fma((t / (a - z)), (y - z), x);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-296) {
		tmp = t_3;
	} else if (t_2 <= 4e-271) {
		tmp = fma(((y * (t - x)) / z), -1.0, t);
	} else if (t_2 <= 5e+304) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(t - x) * y) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	t_3 = fma(Float64(t / Float64(a - z)), Float64(y - z), x)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-296)
		tmp = t_3;
	elseif (t_2 <= 4e-271)
		tmp = fma(Float64(Float64(y * Float64(t - x)) / z), -1.0, t);
	elseif (t_2 <= 5e+304)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-296], t$95$3, If[LessEqual[t$95$2, 4e-271], N[(N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * -1.0 + t), $MachinePrecision], If[LessEqual[t$95$2, 5e+304], t$95$3, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -inf.0 or 4.9999999999999997e304 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 85.2%

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

   2. Taylor expanded in y around inf

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

      1. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 91.3

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

   4. Applied rewrites 91.3%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-296 or 3.99999999999999985e-271 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.9999999999999997e304

   1. Initial program 92.5%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 92.5

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

   3. Applied rewrites 92.5%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 77.6%

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

   if -2e-296 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 3.99999999999999985e-271

   1. Initial program 6.7%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 78.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 57.2

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

   7. Applied rewrites 57.2%

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

Alternative 8: 77.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(t - x\right) \cdot y}{a - z}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_3 := \mathsf{fma}\left(\frac{t}{a - z}, y - z, x\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-296}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{-271}:\\ \;\;\;\;\frac{y - a}{z} \cdot x\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- t x) y) (- a z)))
        (t_2 (+ x (* (- y z) (/ (- t x) (- a z)))))
        (t_3 (fma (/ t (- a z)) (- y z) x)))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-296)
       t_3
       (if (<= t_2 4e-271)
         (* (/ (- y a) z) x)
         (if (<= t_2 5e+304) t_3 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((t - x) * y) / (a - z);
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double t_3 = fma((t / (a - z)), (y - z), x);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-296) {
		tmp = t_3;
	} else if (t_2 <= 4e-271) {
		tmp = ((y - a) / z) * x;
	} else if (t_2 <= 5e+304) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(t - x) * y) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	t_3 = fma(Float64(t / Float64(a - z)), Float64(y - z), x)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-296)
		tmp = t_3;
	elseif (t_2 <= 4e-271)
		tmp = Float64(Float64(Float64(y - a) / z) * x);
	elseif (t_2 <= 5e+304)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-296], t$95$3, If[LessEqual[t$95$2, 4e-271], N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$2, 5e+304], t$95$3, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -inf.0 or 4.9999999999999997e304 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 85.2%

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

   2. Taylor expanded in y around inf

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

      1. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 91.3

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

   4. Applied rewrites 91.3%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-296 or 3.99999999999999985e-271 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.9999999999999997e304

   1. Initial program 92.5%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 92.5

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

   3. Applied rewrites 92.5%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 77.6%

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

   if -2e-296 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 3.99999999999999985e-271

   1. Initial program 6.7%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. sub-div N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-div N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lift--.f64 6.4

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

   4. Applied rewrites 6.4%

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

   5. Taylor expanded in z around -inf

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

      1. lower-/.f64 N/A

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

      2. lift--.f64 57.7

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

   7. Applied rewrites 57.7%

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

Alternative 9: 89.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := \mathsf{fma}\left(t\_1, y - z, x\right)\\ t_3 := x + \left(y - z\right) \cdot t\_1\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{-296}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 4 \cdot 10^{-271}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}, -1, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z)))
        (t_2 (fma t_1 (- y z) x))
        (t_3 (+ x (* (- y z) t_1))))
   (if (<= t_3 -2e-296)
     t_2
     (if (<= t_3 4e-271) (fma (/ (* (- t x) (- y a)) z) -1.0 t) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / (a - z);
	double t_2 = fma(t_1, (y - z), x);
	double t_3 = x + ((y - z) * t_1);
	double tmp;
	if (t_3 <= -2e-296) {
		tmp = t_2;
	} else if (t_3 <= 4e-271) {
		tmp = fma((((t - x) * (y - a)) / z), -1.0, t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / Float64(a - z))
	t_2 = fma(t_1, Float64(y - z), x)
	t_3 = Float64(x + Float64(Float64(y - z) * t_1))
	tmp = 0.0
	if (t_3 <= -2e-296)
		tmp = t_2;
	elseif (t_3 <= 4e-271)
		tmp = fma(Float64(Float64(Float64(t - x) * Float64(y - a)) / z), -1.0, t);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -2e-296], t$95$2, If[LessEqual[t$95$3, 4e-271], N[(N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * -1.0 + t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-296 or 3.99999999999999985e-271 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 91.1

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

   3. Applied rewrites 91.1%

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

   if -2e-296 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 3.99999999999999985e-271

   1. Initial program 6.7%

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

   2. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. sub-div N/A

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

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

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

      6. associate-*r/ N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   4. Applied rewrites 79.3%

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

Alternative 10: 87.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := \mathsf{fma}\left(t\_1, y - z, x\right)\\ t_3 := x + \left(y - z\right) \cdot t\_1\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{-296}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 4 \cdot 10^{-271}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y \cdot \left(t - x\right)}{z}, -1, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z)))
        (t_2 (fma t_1 (- y z) x))
        (t_3 (+ x (* (- y z) t_1))))
   (if (<= t_3 -2e-296)
     t_2
     (if (<= t_3 4e-271) (fma (/ (* y (- t x)) z) -1.0 t) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / (a - z);
	double t_2 = fma(t_1, (y - z), x);
	double t_3 = x + ((y - z) * t_1);
	double tmp;
	if (t_3 <= -2e-296) {
		tmp = t_2;
	} else if (t_3 <= 4e-271) {
		tmp = fma(((y * (t - x)) / z), -1.0, t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / Float64(a - z))
	t_2 = fma(t_1, Float64(y - z), x)
	t_3 = Float64(x + Float64(Float64(y - z) * t_1))
	tmp = 0.0
	if (t_3 <= -2e-296)
		tmp = t_2;
	elseif (t_3 <= 4e-271)
		tmp = fma(Float64(Float64(y * Float64(t - x)) / z), -1.0, t);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -2e-296], t$95$2, If[LessEqual[t$95$3, 4e-271], N[(N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * -1.0 + t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-296 or 3.99999999999999985e-271 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 91.1

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

   3. Applied rewrites 91.1%

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

   if -2e-296 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 3.99999999999999985e-271

   1. Initial program 6.7%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 78.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 57.2

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

   7. Applied rewrites 57.2%

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

Alternative 11: 91.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(-1, x \cdot \left(\frac{y}{a - z} - \left(1 + \frac{z}{a - z}\right)\right), t \cdot \frac{y - z}{a - z}\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (fma
  -1.0
  (* x (- (/ y (- a z)) (+ 1.0 (/ z (- a z)))))
  (* t (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	return fma(-1.0, (x * ((y / (a - z)) - (1.0 + (z / (a - z))))), (t * ((y - z) / (a - z))));
}

Julia

function code(x, y, z, t, a)
	return fma(-1.0, Float64(x * Float64(Float64(y / Float64(a - z)) - Float64(1.0 + Float64(z / Float64(a - z))))), Float64(t * Float64(Float64(y - z) / Float64(a - z))))
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(-1.0 * N[(x * N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(1.0 + N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 81.0%

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

   1. lift-+.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. lift--.f64 N/A

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

   5. lift--.f64 N/A

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

   6. lift-/.f64 N/A

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

   7. +-commutative N/A

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

   8. *-commutative N/A

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

   9. lower-fma.f64 N/A

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

   10. lift-/.f64 N/A

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

   11. lift--.f64 N/A

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

   12. lift--.f64 N/A

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

   13. lift--.f64 81.1

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

3. Applied rewrites 81.1%

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

4. Taylor expanded in x around -inf

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

   1. lower-*.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 N/A

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

6. Applied rewrites 80.2%

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

7. Taylor expanded in t around 0

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

   1. lower-fma.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 N/A

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

   4. lift-/.f64 N/A

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

   5. lift--.f64 N/A

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

   6. lift-/.f64 N/A

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

   7. lift--.f64 N/A

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

   8. lift-+.f64 N/A

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

   9. sub-div N/A

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

   10. lower-*.f64 N/A

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

   11. lift-/.f64 N/A

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

9. Applied rewrites 91.1%

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

Alternative 12: 37.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -0.6:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-91}:\\ \;\;\;\;\frac{y - a}{z} \cdot x\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+26}:\\ \;\;\;\;\frac{t \cdot y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.8e+79)
   x
   (if (<= a -0.6)
     (/ (* t (- y z)) a)
     (if (<= a 1.3e-91)
       (* (/ (- y a) z) x)
       (if (<= a 1.7e+26) (/ (* t y) (- a z)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.8e+79) {
		tmp = x;
	} else if (a <= -0.6) {
		tmp = (t * (y - z)) / a;
	} else if (a <= 1.3e-91) {
		tmp = ((y - a) / z) * x;
	} else if (a <= 1.7e+26) {
		tmp = (t * y) / (a - z);
	} 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 <= (-5.8d+79)) then
        tmp = x
    else if (a <= (-0.6d0)) then
        tmp = (t * (y - z)) / a
    else if (a <= 1.3d-91) then
        tmp = ((y - a) / z) * x
    else if (a <= 1.7d+26) then
        tmp = (t * y) / (a - z)
    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 <= -5.8e+79) {
		tmp = x;
	} else if (a <= -0.6) {
		tmp = (t * (y - z)) / a;
	} else if (a <= 1.3e-91) {
		tmp = ((y - a) / z) * x;
	} else if (a <= 1.7e+26) {
		tmp = (t * y) / (a - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.8e+79:
		tmp = x
	elif a <= -0.6:
		tmp = (t * (y - z)) / a
	elif a <= 1.3e-91:
		tmp = ((y - a) / z) * x
	elif a <= 1.7e+26:
		tmp = (t * y) / (a - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.8e+79)
		tmp = x;
	elseif (a <= -0.6)
		tmp = Float64(Float64(t * Float64(y - z)) / a);
	elseif (a <= 1.3e-91)
		tmp = Float64(Float64(Float64(y - a) / z) * x);
	elseif (a <= 1.7e+26)
		tmp = Float64(Float64(t * y) / Float64(a - z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.8e+79)
		tmp = x;
	elseif (a <= -0.6)
		tmp = (t * (y - z)) / a;
	elseif (a <= 1.3e-91)
		tmp = ((y - a) / z) * x;
	elseif (a <= 1.7e+26)
		tmp = (t * y) / (a - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.8e+79], x, If[LessEqual[a, -0.6], N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, 1.3e-91], N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[a, 1.7e+26], N[(N[(t * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.79999999999999984e79 or 1.7000000000000001e26 < a

   1. Initial program 88.3%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 47.2%

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

   if -5.79999999999999984e79 < a < -0.599999999999999978

   1. Initial program 82.6%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 82.9

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

   3. Applied rewrites 82.9%

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

   4. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 41.6

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

   6. Applied rewrites 41.6%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 23.4%

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

   if -0.599999999999999978 < a < 1.30000000000000007e-91

   1. Initial program 74.1%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. sub-div N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-div N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lift--.f64 32.3

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

   4. Applied rewrites 32.3%

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

   5. Taylor expanded in z around -inf

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

      1. lower-/.f64 N/A

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

      2. lift--.f64 32.6

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

   7. Applied rewrites 32.6%

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

   if 1.30000000000000007e-91 < a < 1.7000000000000001e26

   1. Initial program 79.4%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 79.5

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

   3. Applied rewrites 79.5%

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

   4. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 48.3

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

   6. Applied rewrites 48.3%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 26.0%

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

Alternative 13: 63.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y - z}{a}\\ \mathbf{if}\;a \leq -1.1 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-215}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+31}:\\ \;\;\;\;\frac{\left(t - x\right) \cdot y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ (- y z) a)))))
   (if (<= a -1.1e+84)
     t_1
     (if (<= a 6.2e-215)
       (* t (/ (- y z) (- a z)))
       (if (<= a 1.15e+31) (/ (* (- t x) y) (- a z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * ((y - z) / a));
	double tmp;
	if (a <= -1.1e+84) {
		tmp = t_1;
	} else if (a <= 6.2e-215) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 1.15e+31) {
		tmp = ((t - x) * y) / (a - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t * ((y - z) / a))
    if (a <= (-1.1d+84)) then
        tmp = t_1
    else if (a <= 6.2d-215) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= 1.15d+31) then
        tmp = ((t - x) * y) / (a - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * ((y - z) / a));
	double tmp;
	if (a <= -1.1e+84) {
		tmp = t_1;
	} else if (a <= 6.2e-215) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 1.15e+31) {
		tmp = ((t - x) * y) / (a - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * ((y - z) / a))
	tmp = 0
	if a <= -1.1e+84:
		tmp = t_1
	elif a <= 6.2e-215:
		tmp = t * ((y - z) / (a - z))
	elif a <= 1.15e+31:
		tmp = ((t - x) * y) / (a - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(Float64(y - z) / a)))
	tmp = 0.0
	if (a <= -1.1e+84)
		tmp = t_1;
	elseif (a <= 6.2e-215)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= 1.15e+31)
		tmp = Float64(Float64(Float64(t - x) * y) / Float64(a - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * ((y - z) / a));
	tmp = 0.0;
	if (a <= -1.1e+84)
		tmp = t_1;
	elseif (a <= 6.2e-215)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= 1.15e+31)
		tmp = ((t - x) * y) / (a - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.1e+84], t$95$1, If[LessEqual[a, 6.2e-215], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e+31], N[(N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.0999999999999999e84 or 1.15e31 < a

   1. Initial program 88.2%

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

   2. Taylor expanded in a around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 79.2

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

   4. Applied rewrites 79.2%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 71.7%

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

   if -1.0999999999999999e84 < a < 6.19999999999999987e-215

   1. Initial program 75.8%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 75.9

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

   3. Applied rewrites 75.9%

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

   4. Taylor expanded in t around inf

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

      1. sub-div N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 61.4

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

   6. Applied rewrites 61.4%

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

   if 6.19999999999999987e-215 < a < 1.15e31

   1. Initial program 76.5%

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

   2. Taylor expanded in y around inf

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

      1. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 50.5

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

   4. Applied rewrites 50.5%

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

Alternative 14: 58.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-122}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-35}:\\ \;\;\;\;\frac{\left(t - x\right) \cdot y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (/ (- t x) a) x)))
   (if (<= a -3.4e+79)
     t_1
     (if (<= a -2.7e-122)
       (/ (* (- y z) t) (- a z))
       (if (<= a 3.8e-35) (/ (* (- t x) y) (- a z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, ((t - x) / a), x);
	double tmp;
	if (a <= -3.4e+79) {
		tmp = t_1;
	} else if (a <= -2.7e-122) {
		tmp = ((y - z) * t) / (a - z);
	} else if (a <= 3.8e-35) {
		tmp = ((t - x) * y) / (a - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(Float64(t - x) / a), x)
	tmp = 0.0
	if (a <= -3.4e+79)
		tmp = t_1;
	elseif (a <= -2.7e-122)
		tmp = Float64(Float64(Float64(y - z) * t) / Float64(a - z));
	elseif (a <= 3.8e-35)
		tmp = Float64(Float64(Float64(t - x) * y) / Float64(a - z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -3.4e+79], t$95$1, If[LessEqual[a, -2.7e-122], N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e-35], N[(N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.40000000000000032e79 or 3.8000000000000001e-35 < a

   1. Initial program 87.5%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 66.8

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

   4. Applied rewrites 66.8%

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

   if -3.40000000000000032e79 < a < -2.70000000000000009e-122

   1. Initial program 80.3%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 44.8

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

   4. Applied rewrites 44.8%

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

   if -2.70000000000000009e-122 < a < 3.8000000000000001e-35

   1. Initial program 73.3%

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

   2. Taylor expanded in y around inf

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

      1. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 54.7

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

   4. Applied rewrites 54.7%

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

Alternative 15: 68.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \mathbf{if}\;a \leq -1.1 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-35}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- t x) (/ (- y z) a) x)))
   (if (<= a -1.1e+84) t_1 (if (<= a 9e-35) (* t (/ (- y z) (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t - x), ((y - z) / a), x);
	double tmp;
	if (a <= -1.1e+84) {
		tmp = t_1;
	} else if (a <= 9e-35) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t - x), Float64(Float64(y - z) / a), x)
	tmp = 0.0
	if (a <= -1.1e+84)
		tmp = t_1;
	elseif (a <= 9e-35)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -1.1e+84], t$95$1, If[LessEqual[a, 9e-35], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.0999999999999999e84 or 9.0000000000000002e-35 < a

   1. Initial program 87.4%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 75.7

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

   4. Applied rewrites 75.7%

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

   if -1.0999999999999999e84 < a < 9.0000000000000002e-35

   1. Initial program 75.4%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 75.4

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

   3. Applied rewrites 75.4%

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

   4. Taylor expanded in t around inf

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

      1. sub-div N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 61.4

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

   6. Applied rewrites 61.4%

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

Alternative 16: 38.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-106}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-104}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+118}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.1e+84)
   x
   (if (<= a -8.2e-106)
     t
     (if (<= a 2.8e-104) (* (/ y z) x) (if (<= a 3.5e+118) (+ x t) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e+84) {
		tmp = x;
	} else if (a <= -8.2e-106) {
		tmp = t;
	} else if (a <= 2.8e-104) {
		tmp = (y / z) * x;
	} else if (a <= 3.5e+118) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.1d+84)) then
        tmp = x
    else if (a <= (-8.2d-106)) then
        tmp = t
    else if (a <= 2.8d-104) then
        tmp = (y / z) * x
    else if (a <= 3.5d+118) then
        tmp = x + t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e+84) {
		tmp = x;
	} else if (a <= -8.2e-106) {
		tmp = t;
	} else if (a <= 2.8e-104) {
		tmp = (y / z) * x;
	} else if (a <= 3.5e+118) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.1e+84:
		tmp = x
	elif a <= -8.2e-106:
		tmp = t
	elif a <= 2.8e-104:
		tmp = (y / z) * x
	elif a <= 3.5e+118:
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.1e+84)
		tmp = x;
	elseif (a <= -8.2e-106)
		tmp = t;
	elseif (a <= 2.8e-104)
		tmp = Float64(Float64(y / z) * x);
	elseif (a <= 3.5e+118)
		tmp = Float64(x + t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.1e+84)
		tmp = x;
	elseif (a <= -8.2e-106)
		tmp = t;
	elseif (a <= 2.8e-104)
		tmp = (y / z) * x;
	elseif (a <= 3.5e+118)
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.1e+84], x, If[LessEqual[a, -8.2e-106], t, If[LessEqual[a, 2.8e-104], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[a, 3.5e+118], N[(x + t), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.0999999999999999e84 or 3.50000000000000016e118 < a

   1. Initial program 89.4%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 51.5%

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

   if -1.0999999999999999e84 < a < -8.1999999999999998e-106

   1. Initial program 80.8%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 29.6%

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

   if -8.1999999999999998e-106 < a < 2.8e-104

   1. Initial program 73.1%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. sub-div N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-div N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lift--.f64 31.2

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

   4. Applied rewrites 31.2%

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

   5. Taylor expanded in a around 0

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

      1. lower-/.f64 32.0

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

   7. Applied rewrites 32.0%

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

   if 2.8e-104 < a < 3.50000000000000016e118

   1. Initial program 80.2%

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

   2. Taylor expanded in z around inf

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

      1. lift--.f64 20.2

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

   4. Applied rewrites 20.2%

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

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 32.5%

      \[\leadsto x + t \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 17: 39.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.4 \cdot 10^{-213}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{-176}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+118}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.1e+84)
   x
   (if (<= a 9.4e-213)
     t
     (if (<= a 2.85e-176) (/ (* x y) z) (if (<= a 3.5e+118) (+ x t) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e+84) {
		tmp = x;
	} else if (a <= 9.4e-213) {
		tmp = t;
	} else if (a <= 2.85e-176) {
		tmp = (x * y) / z;
	} else if (a <= 3.5e+118) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.1d+84)) then
        tmp = x
    else if (a <= 9.4d-213) then
        tmp = t
    else if (a <= 2.85d-176) then
        tmp = (x * y) / z
    else if (a <= 3.5d+118) then
        tmp = x + t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e+84) {
		tmp = x;
	} else if (a <= 9.4e-213) {
		tmp = t;
	} else if (a <= 2.85e-176) {
		tmp = (x * y) / z;
	} else if (a <= 3.5e+118) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.1e+84:
		tmp = x
	elif a <= 9.4e-213:
		tmp = t
	elif a <= 2.85e-176:
		tmp = (x * y) / z
	elif a <= 3.5e+118:
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.1e+84)
		tmp = x;
	elseif (a <= 9.4e-213)
		tmp = t;
	elseif (a <= 2.85e-176)
		tmp = Float64(Float64(x * y) / z);
	elseif (a <= 3.5e+118)
		tmp = Float64(x + t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.1e+84)
		tmp = x;
	elseif (a <= 9.4e-213)
		tmp = t;
	elseif (a <= 2.85e-176)
		tmp = (x * y) / z;
	elseif (a <= 3.5e+118)
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.1e+84], x, If[LessEqual[a, 9.4e-213], t, If[LessEqual[a, 2.85e-176], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 3.5e+118], N[(x + t), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.0999999999999999e84 or 3.50000000000000016e118 < a

   1. Initial program 89.4%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 51.5%

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

   if -1.0999999999999999e84 < a < 9.4e-213

   1. Initial program 75.8%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 34.3%

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

   if 9.4e-213 < a < 2.84999999999999992e-176

   1. Initial program 70.9%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. sub-div N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-div N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lift--.f64 28.6

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

   4. Applied rewrites 28.6%

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

   5. Taylor expanded in a around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 27.0

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

   7. Applied rewrites 27.0%

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

   if 2.84999999999999992e-176 < a < 3.50000000000000016e118

   1. Initial program 78.9%

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

   2. Taylor expanded in z around inf

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

      1. lift--.f64 21.5

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

   4. Applied rewrites 21.5%

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

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 31.8%

      \[\leadsto x + t \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 18: 60.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+165}:\\ \;\;\;\;\left(1 + \frac{z}{a - z}\right) \cdot x\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-35}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.1e+165)
   (* (+ 1.0 (/ z (- a z))) x)
   (if (<= a 9.2e-35) (* t (/ (- y z) (- a z))) (fma y (/ (- t x) a) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.1e+165) {
		tmp = (1.0 + (z / (a - z))) * x;
	} else if (a <= 9.2e-35) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = fma(y, ((t - x) / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.1e+165)
		tmp = Float64(Float64(1.0 + Float64(z / Float64(a - z))) * x);
	elseif (a <= 9.2e-35)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = fma(y, Float64(Float64(t - x) / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.1e+165], N[(N[(1.0 + N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[a, 9.2e-35], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.1000000000000001e165

   1. Initial program 92.1%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. sub-div N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-div N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lift--.f64 63.2

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

   4. Applied rewrites 63.2%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift--.f64 57.7

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

   7. Applied rewrites 57.7%

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

   if -2.1000000000000001e165 < a < 9.1999999999999996e-35

   1. Initial program 76.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 76.4

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

   3. Applied rewrites 76.4%

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

   4. Taylor expanded in t around inf

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

      1. sub-div N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 59.1

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

   6. Applied rewrites 59.1%

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

   if 9.1999999999999996e-35 < a

   1. Initial program 86.4%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 64.7

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

   4. Applied rewrites 64.7%

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

Alternative 19: 59.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \mathbf{if}\;a \leq -1.85 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-35}:\\ \;\;\;\;\frac{\left(t - x\right) \cdot y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (/ (- t x) a) x)))
   (if (<= a -1.85e+59)
     t_1
     (if (<= a 3.8e-35) (/ (* (- t x) y) (- a z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, ((t - x) / a), x);
	double tmp;
	if (a <= -1.85e+59) {
		tmp = t_1;
	} else if (a <= 3.8e-35) {
		tmp = ((t - x) * y) / (a - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(Float64(t - x) / a), x)
	tmp = 0.0
	if (a <= -1.85e+59)
		tmp = t_1;
	elseif (a <= 3.8e-35)
		tmp = Float64(Float64(Float64(t - x) * y) / Float64(a - z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -1.85e+59], t$95$1, If[LessEqual[a, 3.8e-35], N[(N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.84999999999999999e59 or 3.8000000000000001e-35 < a

   1. Initial program 87.3%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 66.6

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

   4. Applied rewrites 66.6%

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

   if -1.84999999999999999e59 < a < 3.8000000000000001e-35

   1. Initial program 75.1%

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

   2. Taylor expanded in y around inf

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

      1. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 52.6

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

   4. Applied rewrites 52.6%

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

Alternative 20: 51.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \mathbf{if}\;a \leq -5.5 \cdot 10^{-136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-78}:\\ \;\;\;\;\frac{y - a}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (/ (- t x) a) x)))
   (if (<= a -5.5e-136) t_1 (if (<= a 4.2e-78) (* (/ (- y a) z) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, ((t - x) / a), x);
	double tmp;
	if (a <= -5.5e-136) {
		tmp = t_1;
	} else if (a <= 4.2e-78) {
		tmp = ((y - a) / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(Float64(t - x) / a), x)
	tmp = 0.0
	if (a <= -5.5e-136)
		tmp = t_1;
	elseif (a <= 4.2e-78)
		tmp = Float64(Float64(Float64(y - a) / z) * x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -5.5e-136], t$95$1, If[LessEqual[a, 4.2e-78], N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.4999999999999999e-136 or 4.2000000000000001e-78 < a

   1. Initial program 84.8%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 59.9

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

   4. Applied rewrites 59.9%

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

   if -5.4999999999999999e-136 < a < 4.2000000000000001e-78

   1. Initial program 73.4%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. sub-div N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-div N/A

         \[\leadsto \mathsf{fma}\left(\frac{y - z}{a - z}, -1, 1\right) \cdot x \]

      8. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{y - z}{a - z}, -1, 1\right) \cdot x \]

      9. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{y - z}{a - z}, -1, 1\right) \cdot x \]

      10. lift--.f64 31.5

          \[\leadsto \mathsf{fma}\left(\frac{y - z}{a - z}, -1, 1\right) \cdot x \]

   4. Applied rewrites 31.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, -1, 1\right) \cdot x} \]

   5. Taylor expanded in z around -inf

      \[\leadsto \frac{y - a}{z} \cdot x \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y - a}{z} \cdot x \]

      2. lift--.f64 33.8

         \[\leadsto \frac{y - a}{z} \cdot x \]

   7. Applied rewrites 33.8%

      \[\leadsto \frac{y - a}{z} \cdot x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 50.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+140}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+90}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8e+140) t (if (<= z 9.8e+90) (+ x (/ (* t y) a)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e+140) {
		tmp = t;
	} else if (z <= 9.8e+90) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8d+140)) then
        tmp = t
    else if (z <= 9.8d+90) then
        tmp = x + ((t * y) / a)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e+140) {
		tmp = t;
	} else if (z <= 9.8e+90) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8e+140:
		tmp = t
	elif z <= 9.8e+90:
		tmp = x + ((t * y) / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8e+140)
		tmp = t;
	elseif (z <= 9.8e+90)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8e+140)
		tmp = t;
	elseif (z <= 9.8e+90)
		tmp = x + ((t * y) / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8e+140], t, If[LessEqual[z, 9.8e+90], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -8.00000000000000047e140 or 9.8000000000000006e90 < z

   1. Initial program 62.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t} \]
   3. Step-by-step derivation

   4. Applied rewrites 51.3%

      \[\leadsto \color{blue}{t} \]

   if -8.00000000000000047e140 < z < 9.8000000000000006e90

   1. Initial program 89.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in z around 0

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(t - x\right)}{a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto x + \frac{y \cdot \left(t - x\right)}{\color{blue}{a}} \]

      2. *-commutative N/A

         \[\leadsto x + \frac{\left(t - x\right) \cdot y}{a} \]

      3. lower-*.f64 N/A

         \[\leadsto x + \frac{\left(t - x\right) \cdot y}{a} \]

      4. lift--.f64 59.5

         \[\leadsto x + \frac{\left(t - x\right) \cdot y}{a} \]

   4. Applied rewrites 59.5%

      \[\leadsto x + \color{blue}{\frac{\left(t - x\right) \cdot y}{a}} \]

   5. Taylor expanded in x around 0

      \[\leadsto x + \frac{t \cdot y}{a} \]
   6. Step-by-step derivation

   7. Applied rewrites 49.8%

      \[\leadsto x + \frac{t \cdot y}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 22: 38.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-9}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.1e+84) x (if (<= a 1.7e-9) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e+84) {
		tmp = x;
	} else if (a <= 1.7e-9) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.1d+84)) then
        tmp = x
    else if (a <= 1.7d-9) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e+84) {
		tmp = x;
	} else if (a <= 1.7e-9) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.1e+84:
		tmp = x
	elif a <= 1.7e-9:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.1e+84)
		tmp = x;
	elseif (a <= 1.7e-9)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.1e+84)
		tmp = x;
	elseif (a <= 1.7e-9)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.1e+84], x, If[LessEqual[a, 1.7e-9], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.0999999999999999e84 or 1.6999999999999999e-9 < a

   1. Initial program 87.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 45.2%

      \[\leadsto \color{blue}{x} \]

   if -1.0999999999999999e84 < a < 1.6999999999999999e-9

   1. Initial program 75.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t} \]
   3. Step-by-step derivation

   4. Applied rewrites 33.6%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 24.8% accurate, 29.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 t)

C

double code(double x, double y, double z, double t, double a) {
	return 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 = t
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return t;
}

Python

def code(x, y, z, t, a):
	return t

Julia

function code(x, y, z, t, a)
	return t
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 81.0%

   \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

2. Taylor expanded in z around inf

   \[\leadsto \color{blue}{t} \]
3. Step-by-step derivation

4. Applied rewrites 24.8%

   \[\leadsto \color{blue}{t} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025105 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))